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1D engine simulation of a turbocharged SI engine with CFD computation on components
Ulrica Renberg
TRITA-MMK 2008:09
ISSN 1400-1179
ISRN KTH/MMK/R-08/09-SE
Licentiate Thesis
Department of Machine Design
Royal Institute of Technology
S-100 44 Stockholm
TRITA-MMK 2008:09 ISSN 1400-1179 ISRN/KTH/MMK/R-08/09-SE 1D engine simulation of a turbocharged SI engine with CFD computation on components Ulrica Renberg Licentiate thesis Academic thesis, which with the approval of Kungliga Tekniska Högskolan, will be printed for public review in fulfillment of the requirements for a Licentiate of Engineering in Machine Design. The public review is held at Kungliga Tekniska Högskolan, Brinellvägen 64 in room M3 at 10:00 AM on the 5th
of September 2008.
Abstract
Techniques that can increase the SI- engine efficiency while keeping the emissions very low is to
reduce the engine displacement volume combined with a charging system. Advanced systems are
needed for an effective boosting of the engine and today 1D engine simulation tools are often used
for their optimization.
This thesis concerns 1D engine simulation of a turbocharged SI engine and the introduction of
CFD computations on components as a way to assess inaccuracies in the 1D model.
1D engine simulations have been performed on a turbocharged SI engine and the results have been
validated by on-engine measurements in test cell. The operating points considered have been in the
engine’s low speed and load region, with the turbocharger’s waste-gate closed.
The instantaneous on-engine turbine efficiency was calculated for two different turbochargers
based on high frequency measurements in test cell. Unfortunately the instantaneous mass flow
rates and temperatures directly upstream and downstream of the turbine could not be measured
and simulated values from the calibrated engine model were used. The on-engine turbine efficiency
was compared with the efficiency computed by the 1D code using steady flow data to describe the
turbine performance.
The results show that the on-engine turbine efficiency shows a hysteretic effect over the exhaust
pulse so that the discrepancy between measured and quasi-steady values increases for decreasing
mass flow rate after a pulse peak.
Flow modeling in pipe geometries that can be representative to those of an exhaust manifold,
single bent pipes and double bent pipes and also the outer runners of an exhaust manifold, have
been computed in both 1D and 3D under steady and pulsating flow conditions. The results have
been compared in terms of pressure losses.
The results show that calculated pressure gradient for a straight pipe under steady flow is similar
using either 1D or 3D computations. The calculated pressure drop over a bend is clearly higher
using 1D computations compared to 3D computations, both for steady and pulsating flow. Also,
the slow decay of the secondary flow structure that develops over a bend, gives a higher pressure
gradient in the 3D calculations compared to the 1D calculation in the straight pipe parts
downstream of a bend.
Keywords: 1D modeling, CFD modeling, turbine efficiency, pipe flow, turbocharged engine
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Contents
1. INTRODUCTION ............................................................................................................................5
1.1. OBJECTIVES.....................................................................................................................................7
2. SOME ASPECTS OF TURBOCHARGED ENGINES .................................................................9
2.1. BACKGROUND TO CURRENT ENGINE SIMULATION TOOLS ...........................................................9 2.2. TURBOCHARGER STEADY FLOW PERFORMANCE ........................................................................10 2.3. TURBOCHARGER QUASI-STEADY PERFORMANCE MODELING....................................................13 2.3.1 ADEQUATENESS OF QUASI-STEADY APPROACH .............................................................................14 2.3.2 PERFORMANCE DATA ....................................................................................................................14 2.4. TURBINE BEHAVIOR UNDER STEADY AND UNSTEADY FLOW ......................................................15 2.5. ASSESSMENT OF FLOW UNSTEADINESS ........................................................................................18
3. THEORETICAL BACKGROUND ...............................................................................................21
3.1. GOVERNING EQUATIONS...............................................................................................................21 3.2. 1D MODELING................................................................................................................................22 3.3. ENGINE SIMULATION.....................................................................................................................24 3.3.1 MODEL STRUCTURE .......................................................................................................................24 3.3.2 MODELING OF FLUID FLOW...........................................................................................................24 3.3.2.1 Discretization method.................................................................................................................25 3.3.2.2 Pipe flow ....................................................................................................................................26 3.3.2.2.1 Straight pipe..............................................................................................................................26 3.3.2.2.2 Bent pipe ..................................................................................................................................27 3.3.2.3 Flow split ....................................................................................................................................27 3.3.3 ENGINE CYLINDER ........................................................................................................................28 3.3.3.1 Combustion model .....................................................................................................................28 3.3.3.2 Engine cylinder valves.................................................................................................................28 3.3.4 TURBOCHARGER ............................................................................................................................29 3.3.4.1 Performance maps ......................................................................................................................29 3.4. NUMERICAL COMPUTATION OF TURBULENT FLOWS ..................................................................30 3.4.1 BASIC CONSERVATION EQUATIONS ...............................................................................................30 3.4.2 TURBULENT FLOWS AND THEIR MODELING ..................................................................................31 3.4.2.1 Eddy Viscosity Models................................................................................................................33 3.4.3 BOUNDARY CONDITIONS...............................................................................................................34 3.4.3.1 Turbulent flow boundary conditions ...........................................................................................35 3.4.3.2 Wall boundary conditions ...........................................................................................................35 3.4.4 INLET CONDITIONS .......................................................................................................................36 3.4.5 DISCRETIZATION ...........................................................................................................................36 3.4.5.1 Spatial discretization of the convective term................................................................................36 3.4.5.2 Temporal discretization ..............................................................................................................37 3.4.5.3 Discretization error estimation ....................................................................................................37 3.4.6 SOLUTION ALGORITHM..................................................................................................................38 3.5. COUPLED 1D & 3D SIMULATION TOOL........................................................................................38
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3.5.1 BOUNDARY INTERFACES................................................................................................................39 3.5.2 TIME STEPPING ..............................................................................................................................40 3.6. EXPERIMENTAL METHOD .............................................................................................................40 3.6.1 ENGINE IN TEST CELL ...................................................................................................................40 3.6.2 MEASUREMENT METHODS .............................................................................................................40 3.6.2.1 Pressure ......................................................................................................................................41 3.6.2.2 Temperature ...............................................................................................................................41 3.6.2.3 Mass flow rate.............................................................................................................................41 3.6.2.4 Turbocharger speed ....................................................................................................................41
4. RESULTS .........................................................................................................................................43
4.1. ENGINE MODELING .......................................................................................................................43 4.1.1 CALIBRATION ................................................................................................................................43 4.1.2 INSTANTANEOUS TURBINE EFFICIENCY ........................................................................................44 4.1.3 ACCURACY OF THE CALCULATED TURBINE EFFICIENCY................................................................48 4.2. CFD MODELING OF PIPE FLOWS ..................................................................................................50 4.2.1 METHODS ......................................................................................................................................51 4.2.2 BENT PIPE GEOMETRIES ................................................................................................................51 4.2.2.1 Steady flow .................................................................................................................................53 4.2.2.1.1 Three-dimensional CFD results compared to 1D ......................................................................59 4.2.2.2 Pulsating flow .............................................................................................................................69 4.2.2.2.1 Full CFD results compared to 1D .............................................................................................72 4.2.3 EXHAUST MANIFOLD .....................................................................................................................72 4.2.3.1 Steady flow .................................................................................................................................72 4.2.3.1.1 CFD results compared with 1D results .....................................................................................75 4.2.3.2 Pulsating flow .............................................................................................................................76 4.2.3.2.1 Flow in manifold versus 1D ......................................................................................................79 4.3. INTEGRATED 1D/3D SIMULATIONS ..............................................................................................80 4.4. EXPERIMENTAL RESULTS .............................................................................................................81 4.4.1 OPERATING CONDITIONS ..............................................................................................................81 4.4.2 MEASUREMENT ACCURACY............................................................................................................82
5. SUMMARY AND CONCLUSIONS ..............................................................................................85
5.1. 1D COMPUTATIONS .......................................................................................................................85 5.2. CFD COMPUTATIONS ....................................................................................................................86 5.3. COMPARISON OF 1D AND 3D COMPUTATIONS.............................................................................88
6. FUTURE WORK .............................................................................................................................91
7. ACKNOWLEDGEMENT ..............................................................................................................93
8. NOMENCLATURE........................................................................................................................95
9. REFERENCES..............................................................................................................................101
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10. APPENDIX ..................................................................................................................................105
3
4
1. Introduction A future demand for the SI engine is to increase its efficiency to meet the requirements of lower
fuel consumption and CO2-emissions. It is especially important in the low load region where the SI
engine has large pumping losses due to throttling. Main stream developments are downsizing and
stratified combustion.
Downsizing is equivalent to reducing the displacement volume of the engine and has the effect of
decreasing the engine’s pumping and frictional losses. Having the engine run at low speed allows
these losses to be reduced even further. In addition, the operating point of a smaller engine is
shifted towards higher load, resulting in higher efficiency due to the increased break mean effective
pressure (BMEP). For acceptable drivability the downsized engine must be combined with an
effective boosting system. The advanced charging system must maintain a high specific power,
show good low end torque performance and also have fast transient response. For the SI engine
the most promising solution to reduce fuel economy while keeping emissions very low is to
combine a small displacement volume with technologies as turbocharging, direct injection and
variable valve actuation. A potential increase in efficiency between 10-30 % can be attained
[17,19]. Some examples of advanced turbocharging technologies under development for downsized
SI engine applications are electrically driven waste-gate valves, twin-entry turbine housings, variable
geometry turbines (VGT), and VGT mechanisms.
To manage a theoretical optimization of an advanced turbocharging system today's engine
simulation techniques need further improvement. Since CFD modeling of the whole engine is not
feasible 1D codes are frequently used to optimize complex boosting systems for improved engine
performance. Still, a 1D flow assumption through these components may not be sufficiently
accurate for component optimization. On-engine measurements are required for model calibration
as their predictive performance is limited. The flow through the turbine is heavily pulsating and yet
is it modeled with the use of steady flow performance maps and the assumption of quasi-steady
behavior. The performance data used are also very sparse, especially for low mass flow rates and
turbine pressure ratios and often does not cover the entire operating range of the heavily pulsating
flow the on-engine turbine is exposed to. The inappropriateness of the quasi-steady modeling has
been emphasized by several researchers. Continuing research work is needed in the field of on-
engine turbocharger performance to get a deeper knowledge of the unsteady flow behavior and
how it differs from that of the steady flow case as is assumed in the 1D model. Better knowledge in
5
this area will allow improved accuracy of the 1D engine simulations which are very beneficial not
the least for their flexibility and their low computing cost.
In the pursuit of improving today’s engine simulation techniques, sub-models for different
components, such as the turbine, the inlet or exhaust manifold must be revised.
Secondary flow effects in the exhaust manifold affect the instantaneous turbine performance as the
turbine is mounted directly downstream of it. Large Eddy simulations (LES) on a radial turbine
showed that both small and large scale perturbations at turbine inlet were shown to deteriorate the
turbine shaft power [28].
This project has been focused on two issues:
o Instantaneous turbine efficiency calculations using 1D engine simulation techniques.
o Flow modeling in pipe geometries representative to those of an engine exhaust manifold.
The first part included work that is an attempt to assess the discrepancies between the
instantaneous turbine efficiency calculated from on-engine measurements and that from using the
quasi-steady approach with steady-flow performance maps. Two different turbochargers were
considered and the operating points were in the closed waste gate region.
The second part concerned modeling of gas flow through single and double bent pipe geometries
using one dimensional engine calculations and CFD, both under steady and pulsatile flow
conditions. The reason for studying bent pipe geometries is that the exhaust manifold easily can be
represented as a set of bends and junctions. The modeling of the latter component will be a part of
the continuing project. A better understanding of how the 1D simulation tool treats the flow
through complex geometries as the manifold and how that differs from the 3D flow calculation is
important in trying to improve the predictive quality of the engine calculations. In this case,
improvement by means of providing better inlet conditions to the turbine sub model.
The first part of the work shows upon the restricted predictive property of the 1D engine
simulation tools, in essence due to the limitations of the turbine performance modeling. To draw
any bigger conclusions from the results, comparing the calculated instantaneous turbine efficiency
6
from measurements and from 1D engine simulation, high frequency measurements of mass flow
rate and temperature must be performed; simulated values were used in this case.
The second part of the work is aimed at contributing to an insight of the affects of the 1D
assumption through engine components. This is done studying the secondary flow structures as
these are obtained from 3D CFD calculations of the same problem set-ups. It is not trivial to
convert a complex 3D geometry into a corresponding 1D model. The 3D computations on an
exhaust manifold indicated the presence of a time-dependent and strong secondary flow.
Additionally, an intermittent backflow was observed. Both these effects could cause deterioration
of the turbine power output as compared to ideal inflow conditions to the turbine.
Hand in hand with the development of improved engine simulation techniques comes the need for
advanced measurement techniques for on-engine applications as well. The very harsh environment
in the engine exhaust system puts severe demands on the measuring devices to be used there.
1.1. Objectives The objectives are:
o To assess the accuracy of the simulated quasi-steady turbine performance by on-engine
experiments
The method used for this objective is to compare the calculated instantaneous turbine efficiency
based on high frequency measurements of pressure and turbine shaft speed with simulated values
using performance maps. Measurements and simulations were performed on two different
turbochargers in the closed waste gate region
o To assess and identify inaccuracies in the 1D engine simulation model when applied to
engine manifolds and in particular to bent pipes.
1D engine simulations were performed on single and double bent pipe geometries as well as on the
two outer runners of an exhaust manifold under steady and pulsatile flow. The results are assessed
by comparing, in terms of losses, to full 3D CFD results for the same geometrical configuration
and flow conditions.
7
o To assess the feasibility of carrying out a coupled 1D engine simulation and CFD
calculations of the exhaust manifold and thereby retain 3D accuracy but with lower
computational costs.
The basic idea is that the coupling may enable the advantages of both approaches and eliminating
the corresponding drawbacks. Since the 3D calculations are heavy and require long turn-over time,
there is a basic interest in reducing that time while maintaining the accuracy. So far this aspect is
not yet completed and only initial data is available in this thesis.
8
2. Some aspects of turbocharged engines
2.1. Background to current engine simulation tools One drawback with today’s commonly used 1D engine simulation tools of turbocharged engines is
their restricted predictive qualities. This is in particular true for the calculated turbine power which
often must be adjusted with special efficiency and mass multipliers to get simulated results close to
measured values. There is a strive for an improved turbine sub-model that can describe the turbine
behavior under on-engine like conditions, characterized by very hot and pulsating flow, yet with
low computing effort. There are a number of issues connected to the present turbine modeling
procedure and even doubts about its adequateness, from the fundamental concept of treating the
turbocharger as a quasi-steady flow device, using measured steady flow performance data to
describe the turbocharger behavior, to the sparsity of the measured data provided by the
turbocharger manufacturer. Measured data usually do not cover the entire operating range of the
turbo for on-engine applications. The erroneously predicted turbine power will depend on the
accuracy of the provided inlet conditions, i.e. simulated conditions at the outlet of the exhaust
manifold. Depending on the sensitivity of the turbine model to inlet disturbances these
inaccuracies may be important for the overall engine output results.
A justifiable area to investigate is therefore how well the gas flow through complex geometries as
the exhaust manifold is modeled. This type of geometry consists of bent pipes and flow splits
where multidimensional effects as propagating pressure waves are reflected and transmitted at
junctions, pipe ends etc. and secondary flow structures are developed. The accumulation on the
blade outlet shroud (on the suction side) of low energy fluid, which comes from the internal
secondary flows, gives rise to the increased losses at the rotating turbine blades. This was the
conclusion from comparing Laser Doppler Velocimetry measurements of the internal flow through
a radial turbine together with CFD analysis. Measurements and simulations showed good
agreement [33].
Despite the multidimensional nature of the flow processes taking place in manifold geometries, 1D
engine calculations are commonly used to optimize the influence of these systems on the engine
performance. The simulation accuracy is restricted by the 1D flow assumption together with the
use of semi-empirical correlations for the pressure loss and flow discharge coefficients. This way of
modeling the exhaust manifold may not be sufficiently accurate for component optimization or
9
applicable for predictive engine simulations. Although correction factors are used in the 1D code
to account for multidimensional flow effects, CFD calculations modeling the fluid turbulence
through these types of geometries would be more accurate [22, 23, 27]. CFD modeling of the
whole engine is not feasible due to the huge need for computational resources. Unfortunately, this
situation will not be changed in the foreseeable future. Therefore, one has to restrict full CFD
calculations to individual components or at most a couple of components. A way to improve
engine calculations, within the limitations of computational resources, is to limit the CFD
calculations to certain components and either integrate these with a 1D model of the rest of the
engine or to improve the correction factors used in nowadays 1D engine codes. In a coupled
1D/3D calculation the discharge and pressure loss coefficients were determined and applied to an
intake plenum of a turbocharged DI Diesel engine and used in a stand alone 1D model of the same
engine at full load conditions. The coupled procedure gave a slight improvement of the accuracy of
the simulated results. It is presumed that constant coefficients used in 1D engine simulation codes
cannot be used to capture complex transient phenomena [23].
2.2. Turbocharger steady flow performance A common way of presenting the radial turbine performance characteristics is to plot the efficiency
versus a normalized velocity parameter called blade speed ratio (BR). The blade speed ratio, Ur/Cs
is defined as:
21
1
03
403 12
2602
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅⋅⋅
⋅⋅=
−κ
κ
π
pp
Tc
DN
CU
p
tc
s
r (1)
This relation can be derived under the assumption of ideal gas and isotropic flow. The efficiency
versus blade speed ratio characteristic is important when designing turbochargers. For given
turbine inlet operating conditions the rotor diameter D should be chosen so that the turbine
operating point lies in the high efficiency region during most of the time of an engine cycle. The
relation between the turbine efficiency and BR for steady flow is described by a parabola with peak
efficiency at a BR of about 0.7 [2], Figure 1.
10
Figure 1 An example of a radial inflow turbine characteristic, total-to-static efficiency versus blade
speed ratio for steady flow conditions, [36].
It can be understood that the left part of the efficiency parabola relates to high gas velocities and
the right to lower gas velocities. The total-to-static isentropic efficiency is the one often used when
describing the on-engine turbine efficiency. The efficiency is originally defined as the quotient of
the actual enthalpy drop over the turbine and the enthalpy change of the gas if it is expanded
isentropically through the turbine:
shh
hh=TS
,0403
0403
−
−η (2)
By reasons of inaccuracies of the efficiency calculated in this way due to thermal radiation losses
and also because of difficulties with fast temperature measurements, the efficiency can instead be
calculated as the ratio between utilized power and the largest possible power the turbine can
extract:
isentr
extr
P
P=TSη (3)
Dale and Watson [3] calculated the extracted power for a twin entry radial turbine from
instantaneous torque measurements. They used a dynamometer to measure the mean torque and
the fluctuating torque was calculated from differentiating the turbocharger speed measurement
signal. The resulting expression for the instantaneous turbine efficiency:
11
⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜
⎝
⎛ −
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−⋅⋅+
⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜
⎝
⎛ −
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
−⋅⋅
⋅⋅+ ⎟⎠⎞
⎜⎝⎛
κ
1κ
b03,P4P
1b03,Tpcbexh,mκ
1κ
a03,P4P
1a03,Tpcaexh,m
π2tcNdt
tcdNJ
cellloadTQ
=TSη
&&
(4)
Using a compressor to absorb the turbine load, the extracted power is calculated as the sum of the
compressor power and the power to accelerate the turbine shaft [1]:
⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜
⎝
⎛ −
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−
∫
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
κ
κ
P
PTpcm
mechη
pcm
+NJ
=P
mechη
P+P
=TS1
03
4103exh
T02
T01dT
air
dt
tcdN
tcrotor
2
60
2π
isentr
compracc
&
&
η
(5)
To give a value for the instantaneous efficiency calculated by either of the two latter expressions,
care must be taken to compensate for the different measurement locations of the different
parameters. The instantaneously measured torque is a result of the state of the fluid in the rotor
which was at the measuring location upstream of the turbine at an earlier point in time. Calculating
the instantaneous isentropic power a phase lag should be applied to the inlet conditions to account
for the different pulse transmission phenomena in the volute casing. A mean volute path length
can be used to calculate an estimation of this lag. From CFD analysis of the flow through a turbine
under steady and unsteady flow, it is possible to calculate the time for an acoustic and convective
wave to pass along the turbine volute. From turbine volute entry to the throat the mass flow pulse
was concluded to be an acoustic phenomenon and the temperature pulse a convective
phenomenon [30]. This confirms the results by [21]. Downstream of the volute throat the
propagation of pulses is more complex, a mix of acoustic and convective transmission. Winterbone
et al. [32] compared the travel time for the pressure pulse at turbine volute entry to half the way
around the circumference of the casing, with the time for the energy contained in the pressure
12
pulse to be delivered at the rotor (through the phase lag between the pressure and torque signals).
Since the transmission time for the half way distance is much shorter than the time to reach the
rotor they deduced that the lag must be caused by the energy transfer from the casing to the rotor.
This since no substantial change in wave pattern was seen along the casing. There is no absolute
correct way of shifting the upstream measured quantities. Dale and Watson [5] used the
propagation time for a sonic wave whereas Baines et al. [35] and Winterbone et al. [32] used the
propagation time for the bulk flow. The results seems to be contradictory, Baines et al. on one
hand claim that the bulk flow transmission is more important than the pressure wave transmission
in determining the pulse flow performance whereas on the other hand, Karamanis et al. and
Arcoumanis et al. [37, 38] state that the opposite is valid.
Ehrlich et al. performed measurements in an engine test cell on a turbocharged (twin entry) 6-
cylinder medium speed diesel engine with focus on understanding the process of energy transport
from the cylinder to turbine inlet [21]. They measured the instantaneous total and static pressure
using in house constructed probes connected to a high frequency dynamic pressure transducer.
The velocity field in the horizontal central plane was measured, using Particle Image Velocimetry
(PIV), at chosen crank angles during the engine cycle to characterize the turbine inlet velocity
profile during an exhaust valve event. The results indicated that the transport mechanism in the
exhaust manifold must be modeled as both a convective and an acoustic propagation.
2.3. Turbocharger quasi-steady performance modeling The 1D model assumes a quasi-steady behavior of the turbine which means that the turbine is
expected to behave at any instant in the same way as it would under steady flow at the given
instantaneous conditions. Turbocharger performance data is normally measured by the
turbocharger manufacturer under steady flow conditions. This data is used by the 1D engine
simulation tool to calculate the compressor and turbine power under both steady and unsteady
flow conditions. The calculation of compressor power and efficiency is more reliable than on the
turbine side, the on-engine conditions for the compressor are more or less the same as for the
steady state conditions [20]. The calculated turbine power is not well predicted and must for almost
every operating point be adjusted with efficiency and mass flow parameters (so called “multipliers”)
to match simulated results to measured values. The level of error of the predicted turbine power is
especially pronounced in the low speed and load region, where the waste gate is closed. At these
operating points the model cannot control the waste gate opening to let a proper amount of flow
13
pass through the valve to meet target boost pressure. The efficiency of the turbine may have to be
adjusted by as much as 30 % [1, 29].
2.3.1 Adequateness of quasi-steady approach
Several researchers have presented results from turbocharger flow measurements. Among them are
studies from measurements on turbochargers under steady and pulsating flow, for single and twin
entry radial turbines with and without guide vanes, [1, 3, 29, 35]. These authors have shown that
the turbine power and mass flow rate show large deviations from their steady state characteristics
and there are indications that the quasi-steady approach is inadequate. CFD analysis of a radial
turbine [30] shows that the instantaneous performance of the rotor at unsteady flow conditions
does not vary significantly from that at steady flow conditions. The results indicate that the rotor
could be seen as a quasi-steady flow device for power extraction while the volute passage
significantly alters the shape of the unsteady mass flow characteristics. This conclusion is also
supported by the results of [35]. Capobianco and Marelli [17, 18,19] performed measurements on a
single entry radial turbine in steady and unsteady flow conditions. The instantaneous mass flow rate
was measured with a hot wire probe but it was also calculated from the instantaneously measured
pressure together with turbine steady mass flow characteristics using the quasi-steady assumption.
The amplitude of the experimental mass flow rate oscillations showed to increase substantially with
higher average turbine expansion ratio (higher oscillation frequency). This was not seen for the
mass flow rate calculated with the quasi-steady assumption where the oscillation amplitude
remained almost constant. They suggested that for lower pulse frequencies, if the mass flow rate
cannot be measured instantaneously, using that from 1D quasi-steady calculation is quite accurate
for turbine efficiency calculations even though other authors as Szymko et al. [41] have highlighted
large discrepancies between instantaneous unsteady mass flow rate from quasi-steady calculations
and measured values at higher pulse frequencies.
2.3.2 Performance data
A common opinion is that turbine performance data provided by the turbocharger manufacturers
is not well suited for research purposes [3]. Baines et al. [4] address the inaccuracies in turbine
efficiency calculations to the use of steady-flow turbine data to predict the performance of
turbocharged engines, which is also consistent with general experience. Performance data from
turbocharger manufacturers, used as input in the engine model to describe the steady flow
14
characteristics of the particular turbine, are quite sparse for the open waste gate region, if at all
included. Capobianco et al. [17] extended their study to include measurements for a range of waste-
gate valve opening angles for a single entry nozzle-less waste-gated turbocharger. A compressor
was used as a dynamometer and the turbine load range was considerably extended compared to
performance data from the turbocharger manufacturer since the tests included the open waste gate
region. The gas temperature was about 400 K. The study showed that for a small automotive
turbocharger where the flow through the by-pass valve is substantial, maybe even greater compared
to the flow that passes the rotor, the flow interactions in the turbine volute casing significantly
affected the mass flow rate and efficiency. The overall turbine efficiency calculated from isentropic
expansion of the entire mass flow (rotor plus by-pass flow) was much smaller when the waste gate
valve was opened while keeping the overall turbine expansion ratio and inlet temperature constant.
For small valve openings there was a significant reduction of specific turbine work, probably
caused by flow perturbations due to fluid interactions in the dividing section of the turbine
housing.
2.4. Turbine behavior under steady and unsteady flow Dale and Watson [3] built a turbocharger test facility in the middle of 1980 to study the turbine's
behavior under more engine-like conditions. A dynamometer was used to absorb the turbine load
instead of using a matching turbo compressor, or less likely several compressors, which gave a
broader load range of the turbine compared to that provided by the manufacturer. The tests were
performed on a twin-entry vaneless radial flow turbine in steady and pulsating flow, by the use of
counter-rotating chopper valves. To analyze the performance of a turbine under unsteady flow
conditions it is most common to use a pulse generator upstream of the turbine. The shape and
amplitude using a pulse generator is often different from the situation on a SI engine, [1]. In
addition, the heavily fluctuating temperature typical for the on-engine turbocharger is not taken
into account. Dale and Watson’s work was focused on the aerodynamic efficiency of the turbine so
the gas temperature was kept rather low, about 400 K, to minimize heat transfer losses. Prior to
their work, studies on radial flow turbines had only included instantaneous measurements of
pressure. Dale and Watson also measured the instantaneous mass flow rate and turbine torque. The
instantaneous mass flow rate which showed to deviate from the steady flow curve, for a specific
speed and turbine expansion ratio, was used in the calculations of the instantaneous turbine
efficiency. The results indicated that the turbine did not obey the quasi-steady assumption; the
15
unsteady turbine efficiency did not follow the parabolic shaped steady flow curve when plotted
against BR, Figure 2.
Figure 2 Instantaneous unsteady turbine efficiency versus blade speed ratio for a twin entry scroll turbine (identical inlet
conditions) together with the turbine efficiency calculated from the quasi-steady assumption [3].
Instantaneous deviations from the steady flow turbine performance were as high as 10 %. The
peak efficiency and mass flow parameter values were higher for the unsteady flow. The cycle
averaged turbine efficiency however was lower for the unsteady flow.
Baines et al. [4] came to the same conclusion that the instantaneous unsteady flow turbine
efficiency was lower than the steady flow value for most of the time during an engine cycle. They
considered the deviations from the steady flow behavior to be a cause of flow processes occurring
upstream of the rotor. They commented on the instantaneously much higher unsteady flow turbine
efficiency, compared to steady-state values, as being misleading since the turbine only spent a short
time of the pulse cycle at the high efficiency conditions. The same test rig and performance data
acquisition system was used as in [3].
Iwasaki et al. [20] performed steady and unsteady flow measurements on a twin entry turbocharger
of a 6-cylinder medium duty diesel engine. They showed that for a fixed turbocharger speed and
expansion ratio the unsteady mass flow parameter was lower than corresponding steady flow value
16
over the entire operating range tested. The discrepancy was higher for lower expansion ratios,
almost 20 %.
Karamanis et al. [37] did measurements on a single entry nozzleless radial turbine under steady and
unsteady flow. A compressor was used as load absorber. Two counter rotating chopper plates were
used to produce the pulsating flow. Their results confirmed the instantaneous deviations between
the steady and unsteady performance characteristics. The unsteady cycle averaged efficiency was
shown to be lower compared to the steady flow value.
Palfreyman et al. [39] compared results from CFD analysis of a mixed flow turbine with
experimental data from steady and pulsating flow measurements. The experimental setup and data
acquisition system used was the same as [37].
Capobianco and Marelli [19] presented results from measurements on a single entry nozzleless
waste-gated turbocharger for a downsized engine, both in steady and unsteady flow with closed
waste gate. Instantaneous turbine inlet and outlet pressure was measured with high frequency strain
gauge transducers and only averaged values of mass flow rate and temperature were measured. The
instantaneous mass flow rate was in the first studies taken from 1D engine simulations whereas
later work included measured values from using hot wire probes. Instantaneous temperature was
approximated from measured instantaneous pressure and average values of temperature and
pressure assuming an adiabatic process of an ideal gas:
κκ
pp
T=Tm
im,i
1
3,
3,33
−
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅ (6)
This approach has been used by many researchers for the instantaneous turbine inlet temperature
when only average temperature is measured. Another approach is to assume that the turbine inlet
total temperature is constant during a pulse. Then the average temperature can be used to calculate
the instantaneous temperature. Using the first approximation, (6), to calculate the instantaneous
exhaust gas energy yields good agreement with measurements [37]. Capobianco and Marelli [19]
used different approaches to assess the unsteady overall cycle averaged turbine efficiency.
Comparing the results from the different approaches they concluded that the most reliable way to
determine it was to use instantaneous values for the measured parameters at the turbine inlet and
17
outlet. In accordance with the results presented by Dales and Watson [3] and Baines et al. [4]
Capobianco and Marelli [19] showed that the steady flow turbine efficiencies (averaged values)
were always higher than corresponding unsteady flow values at the same expansion ratio, about 12-
13%. No significant differences for the average efficiency levels were found using measured or
calculated values.
Several studies have shown the presence of clear discrepancies between the steady and unsteady
flow performance of the turbocharger. However, to draw the correct conclusions about the turbine
behavior from calculated performance parameters it is important to have a good estimate of the
accuracy of the data. Baines et al. [4] pointed out that the accuracy in the speed measurement was
crucial for correct determination of the instantaneous turbine torque. Dale and Watson [3, 5] also
showed that amended measurement of especially instantaneous turbine torque could improve the
accuracy of the estimated efficiency significantly.
Not only studies on the efficiency are of importance, but also the flow unsteadiness effects on the
turbine inlet energy. Results regarding the energy content of a pulse, being higher for pulsating flow
than for steady flow, were presented already in the seventies. For a given mean mass flow the
turbine produces higher torque under unsteady flow [31]. Capobianco and Marelli [19] presented
results from a study on the relation between flow unsteadiness and available energy at turbine inlet.
They came to the conclusion that the available turbine inlet energy is a result of both pressure
amplitude and mean pressure. Only a little effect was seen for the oscillating temperature amplitude
on the turbine inlet energy (for moderate mean inlet temperature). This indicates that the
instantaneous temperature approximation from measured instantaneous pressure and average
temperature, when instantaneous temperatures have not been measured, can be used in
performance calculations without bigger inaccuracies [18, 19].
2.5. Assessment of flow unsteadiness To get a rough estimation of the deviations for the actual turbine performance from its measured
steady flow behavior, one has to determine flow unsteadiness effects. One has to define a measure
that characterizes flow unsteadiness in a relevant manner. Work has been done trying to find
correlation criteria between steady and unsteady flow. Pulsating flow characteristics are often
associated with the ratio between pressure amplitude and its mean value. Iwasaki et al [20]
performed steady and unsteady flow measurements in test rig on a twin entry turbocharger for
18
medium duty diesel engine application. They showed that a pulsation factor Kp for several
turbocharger specifications, showed the same trend with turbine expansion ratio. Kp is defined as
the ratio between the difference in maximum and minimum instantaneous pressure of the pulse
and the mean relative pressure at turbine inlet:
atmm
ip PP
p=K
−
Δ
,3
,3 (7)
The pulsation factor was high at low turbine expansion ratios (a value of about 2) and decreased
with higher expansion ratios as the flow condition approached that of steady flow. The expansion
ratio was calculated with the mean values for turbine inlet and outlet pressure over the pulse.
Iwasaki et al. [20] also showed results from measuring the static pressure along the turbine scroll
and calculations of the instantaneous flow angle relative to the turbine rotor, the incidence angle β,
in steady and unsteady flow. The static pressure variation along the scroll was smaller for low
engine speeds. The results indicated that these pressure variations had a greater impact on β which
showed larger variations compared to higher engine speed operating points. The variation of β was
higher for unsteady flow compared to steady flow at the same turbine speed and BR. Other
experiments on a twin entry turbocharger under unsteady flow showed large variations in incidence
angle and unfavorable gas angles to the rotor during the pulse, even close to the design point
operation of the turbocharger [34]. The relative flow angle effects the incidence losses and thereby
the turbine efficiency [20, 32]. In addition Iwasaki et al. [20] showed that the degree of reaction
fluctuated along the scroll and differed more from corresponding steady state value at low engine
speed. The higher flow unsteadiness was considered to be the cause of it although they could not
give any clear explanation. To investigate the deviations of the measured unsteady efficiency from
measured steady state values, two correction factors were introduced and used to multiply the
steady flow mass and efficiency performance in an iteratively manner until the calculated turbine
power was close to the on-engine measured unsteady results. This was made for 4- and 6-cylinder
diesel and gasoline engines with single and twin entry turbines at full load conditions. Changing
the engine speed and thereby the turbine expansion ratio revealed the same tendency for the two
correction coefficients for all tested engines. At higher expansion ratios their values were
approximately unity corresponding to steady flow [20].
19
20
3. Theoretical background In this chapter the governing equations of fluid dynamics are described. In the first section in a
more general sense and in the proceeding sections 1D modeling and in particular engine modeling
will be described in more detail, continuing with CFD modeling and then integrated engine/CFD
calculations.. The computer softwares used are a commercial 1D engine simulation software, GT-
Power, and a CFD software STAR-CD. The same conditions are used to handle the heat transfer
modeling in the two codes. However, as heat transfer issues have not been a part of this work, the
heat transfer modeling in the two codes is not described further. The last section contains a
description of the experimental method.
3.1. Governing equations The governing equations for fluid motion are derived from the principles of conservation of mass,
momentum and energy. In general terms for 3D unsteady compressible flow:
Continuity equation:
( ) 0=uρx
+tρ
jj∂
∂∂∂ (8)
Momentum equation:
( ) ( ) ij
ijji
ji fρ+
xΠ
=uuρx
+uρt ∂
∂
∂∂
∂∂ (9)
ijijij τ+pδ=Π − (10)
ijk
kijij δ
xu
sμ=τ∂∂⋅−⋅ μ
322 (11)
⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂
∂∂
⋅=i
j
j
iij x
u+
xu
21s (12)
⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂∂
−⎟⎟⎠
⎞⎜⎜⎝
⎛
∂
∂
∂∂
⋅ ijk
k
i
j
j
iij δ
xu
xu
+xu
μ=τ32 (13)
Energy conservation:
21
[ ] [ ] ( ) ( ) extijjjj
jj
jj
j
W+Qτux
+xq
puxt
p=huρx
+hρt
&&+∂∂
∂
∂−
∂∂
+∂∂
∂∂
∂∂ (14)
jt xTk=q
∂∂⋅− (15)
In the equations above Einstein summation convention is used. The physical properties of the
fluid are assumed to be represented by linear constitutive relations and the coefficient of viscosity
(υ) and heat conductivity (kt). To close the system of equations a relation between the
thermodynamic variables ( eT,ρ,p, ) is needed. For a perfect gas:
ρRT=p (16)
The coefficients of viscosity and thermal conductivity can be related to the thermodynamic
quantities using kinetic theory, for example the Sutherland’s formulas:
21
23
C+TTC=μ ⋅ (17)
43
23
C+TTC=k ⋅ (18)
where C1, C2 , C3 and C4 are constants for a specific gas.
3.2. 1D modeling The one-dimensional flow model involves the simultaneous of the flow in a pipe-like configuration
(Figure 3). The axial velocity component is assumed to be much larger than the velocity
components in the cross-.sectional plane. The governing equations are the same for this case as for
the general 3-D case. However, by assuming that the flow varies only in the axial (stream wise)
direction, the three conservation relations (of mass, momentum and energy) can be simplified.
( ) 0=uρx
+tρ
x∂∂
∂∂ (19)
22
( ) ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂
⋅∂
−⋅∂∂
⋅∂∂
2
2
232
xu
μ+xdp=uρ
xu+uρ
tx
xxx (20)
[ ] [ ] extxx
xxxx W+Qxq
xu
τxpu
tp=huρ
x+hρ
t&&+
∂∂
−∂∂⋅+
∂∂⋅+
∂∂
⋅⋅∂∂
⋅∂∂
(21)
ρp+e=h (22)
Consider a straight pipe with radius R, Figure 3.
Figure 3 A straight pipe with constant cross-sectional area with a small fluid element representing a control volume, after
[40].
One may derive these equations by consider directly the flow in the pipe, looking on the
conservation of mass, momentum and energy in a small segment of the pipe (i.e. a control volume)
For steady flow of a compressible fluid flowing through a circular constant cross sectional area
pipe, Equations (19-21) applied to a control volume of a small element after integration yields:
2211 uρ=uρ ⋅⋅ (23)
dxfρuD
+ρu+pρu+p ⋅⋅= 2222
211
2
(24)
qu+h=u+h −22
22
2
21
1 (25)
The sub scripts 1 and 2 represent the upstream and downstream conditions of the control volume,
respectively, and u is the mean axial velocity, D the pipe diameter and f is the friction factor.
23
The friction factor f is used to account for the geometry of the pipe, surface roughness, and Re
effects. It may be evaluated for given conditions by the use of various empirical or to less extent
through theoretical assumptions and considerations
3.3. Engine simulation The flow and combustion in an internal combustion engine is quite intricate and complicated.
Despite this complexity it is conceivable to look upon the engine as a piping system through which
the fluid flows, from upstream the inlet air filter to the exhaust pipe, joining engine components as
the compressor, the intercooler, the cylinders, and the turbine. Such a simplified approach has the
advantage of enabling one to assess different designs in a short time. The main disadvantage of the
approach is its limited accuracy and the results are more of qualitative character. However, the
applicability of the approach and the errors associated with it are not uniform to all engine
components. As shown here, rather good results may be obtained for certain parts of the engine
manifolds and less good results for other components such as the turbo-charger or the flow and
combustion in the cylinder (not studied here).
3.3.1 Model structure
To simulate the entire engine the system is broken up into different components as pipes, pipe
bends, flow splits and other components as the engine cylinders, the cylinder valves, the
compressor and turbine. The flow through the pipe components is modeled with the assumption
of one dimensional flow while the flow properties through the more complex parts of the engine
as the intake and exhaust valves, the flow through the compressor and turbine, and the combustion
process in the cylinder, are modeled without spatial resolution and rely on empirical relations and
measured input data. Input data can be measured pressure loss coefficients for the valve flow,
crank angle resolved pressure for the in-cylinder process and turbocharger performance maps for
the turbine/compressor sub models. More details on the modeling of various engine components
are given in the subsequent sections.
3.3.2 Modeling of fluid flow
The equations used to simulate the flow in the different components are the somewhat modified
1D equations (19-22). In the corresponding momentum equation an additional pressure loss
coefficient term pC is added to account for bent pipes or pipes with irregular cross sections. The
24
pure 1D flow assumption would not capture the effects on the flow that these geometrical
properties may cause. The fundamental equations using the explicit time solver and for constant
cross sectional area pipes are given by:
Continuity:
( ) (∑ ⋅⋅⋅boundaries
Au=Vdtd ρρ ) (26)
Momentum:
( ) ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛⋅−
⋅⋅⋅−⎟
⎠
⎞⎜⎝
⎛⋅⋅+⋅ ∑ 2
ρudxdC
2uρ
DC
4uuρdxd
dxdp=uρ
dtd 2
p
2f
boundaries (27)
Energy:
( )[ ] ( ) ( walltotgboundaries
TTAhhAu+dtdVp=u+e
dtd
−⋅⋅−⋅⋅⋅⋅⋅ ∑ ρρ 2 ) (28)
3.3.2.1 Discretization method
The pipe volumes to be modeled are further discretized by the 1D code into smaller sub-segments
(control volumes) with a recommended length of typically 30-40 mm, whereas the flow splits are
not further discretized. The method used to discretize the pipe volumes in space is the staggered grid,
the scalar variables are solved at locations offset to where the vector variables are solved. Scalar
variables as density, internal energy, pressure and temperature are assumed to be uniform over each
sub-volume and are calculated at the centre. Vector variables as the gas velocity and mass flux are
calculated at the boundaries which connect the sub-volumes.
For integration in time can be either implicit or explicit. The explicit time solver is recommended
and it is a non-iterative method, for which the time-step size is limited by the Courant condition,
| |( ) C≤c+udxdt (29)
25
where C is a parameter, less than or equal to 1 and it is set by the user. Using the explicit time step
scheme the variables at a new time step is calculated from the variables of the previous time step in
the sub volume in question and its closest neighbors. The implicit method uses a set of algebraic
equations to solve simultaneously for the values of all sub volumes and boundaries at the new time
step in an iteratively manner until convergence is reached. The explicit method will more accurately
predict pressure pulsations that are important in engine systems.
3.3.2.2 Pipe flow
Pipe objects are used to model the flow through tubes with constant or tapered diameter and the
code assumes uniformity of the flow field in the perpendicular planes. The code assumes circular
cross-sectional area but the user can adjust heat transfer multipliers, friction multipliers, and /or
pressure loss coefficients to account for affects of other geometries.
3.3.2.2.1 Straight pipe
Flow losses due to wall friction is calculated using expressions for the skin friction coefficient Cf as
a function of Re and wall roughness. For turbulent flow, Re>4000 and for a smooth pipe:
0.25Re
0.08=Cf (30)
For a rough pipe this parameter has a larger value than given by equations (30) and hence equation
(31) is used:
2
10 1.74212log
0.25
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅ +hD
=C
r
roughf, (31)
Re is based on the pipe diameter. If necessary a friction multiplier can be used to scale the
calculated friction in a single pipe or flow split and it is also possible to use a global steady friction
multiplier comprising all pipes. For increased frictional losses due to unsteady flow, like the
pulsating flow of an engine, a global unsteady friction multiplier is used. It scales the calculated
friction losses in all pipes and flow splits and is adapted to the amplitude and frequency of the
pulsatile flow.
26
( )unstunstconstsf,f FM+MC=C ⋅⋅ 1 (32)
Cf is the instantaneous friction factor, Cf,s the instantaneous friction factor using correlation for
steady flow, Mconst is the constant global friction multiplier (set to 1 for unsteady flow), Munst a global
unsteady friction multiplier, and Funst is the instantaneous unsteady friction factor. The latter is
calculated by the code at every time step but is a hidden function for the user. It depends on the
fluid viscosity and acceleration among other quantities. Gamma Technologies comment on the
unsteady friction modeling to be experimental and only to be validated for a limited set of
measurements from data for liquid systems.
3.3.2.2.2 Bent pipe
Pressure loss coefficients are used in the code to account for pressure losses in pipes due to the
effect of irregular cross-sections, decreasing pipe diameter or bends. The pressure loss coefficient
pC can either be calculated by the code or be set by the user. It is defined as the dimensionless
pressure loss:
( )211
tot,2tot,1
21 uρ
pp=Cp
⋅⋅
− (33)
where subscripts 1 and 2 denote the upstream and downstream conditions of the bend,
respectively. The exact calculations of the forward and reverse pressure loss coefficient are
unknown for the user, but they do not include the wall friction.
3.3.2.3 Flow split
When a sub volume has several openings it is defined as a “flow split”. The methods used for the
flow through a flow split are very much as that of a pipe. The scalar quantities as mass and energy
are solved at the centre of the volume but the flow split is designed to conserve the momentum in
three dimensions and the momentum equations are solved separately for each of the volume
openings. A characteristic velocity vector is calculated from all of the ports of the flow split and the
outlet momentum flux is calculated by using the component of the characteristic velocity in the
direction of the outlet port [42].
27
3.3.3 Engine cylinder
The intake and exhaust ports of an engine cylinder are modeled as pipes even though special
considerations must be made to model the friction and heat transfer losses correctly. The modeling
of cylinder valves requires measured discharge coefficients to properly describe the flow area and
the in-cylinder combustion process needs input from measured cylinder pressure to determine the
energy released at every crank angle.
3.3.3.1 Combustion model
The role of a combustion model is to simulate the amount of energy generated during combustion.
The first law of thermodynamics states that energy released by combustion of the fuel (δQ) equals
the heat transfer to cylinder walls (δQHT), energy lost into the crevices (δQCrev), the change in
internal energy (δU) and the amount of work done by the system (δW):
WUQQQ CrevHT ∂+∂+∂+∂=∂ (34)
The rate of heat release can then be expressed as:
θθθθθ ∂∂
+∂∂
+⎟⎠⎞
⎜⎝⎛
∂∂
∂∂
=∂∂ CrevHT QQVpVpfQ ,,, (35)
The measured cylinder pressure, if measured, can be used as input to calculate the overall heat
release rate over an engine cycle
3.3.3.2 Engine cylinder valves
Different types of cylinder valves can be modeled with the use of object templates for the
characteristic valve in question, a cam driven valve for instance. The valve is seen as a special type
of connection. Connections are planes joining physical components together, locations at which
the momentum equation is solved to compute the mass flow rate and velocity. Valve connection
objects require input of a discharge coefficient describing the flow area. This is to correct for
frictional losses and errors in the assumption of the velocity profile. It is needed for both directions
of the flow through the valve and it is given for varying valve lifts. The discharge coefficient DC is
defined as the effective flow area divided by the reference flow area (on which the measurements
are based on) and it is usually calculated from flow measurements on the cylinder head. For gases:
28
isisRDisiseff UρAC=UρA=m ⋅⋅⋅⋅⋅& (36)
( ) γ/10 Ris Pρ=ρ (37)
21
1
11
2
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡ −
−⋅−
κκ
R0is Pγ
RT=U (38)
3.3.4 Turbocharger
The 1D engine model comprises a turbine sub-model which is simulated by a zero-dimensional
object in space. The turbocharger is replaced by parameters that are based on turbocharger
performance data under steady flow conditions in a gas stand using air at moderate temperature.
3.3.4.1 Performance maps
The turbocharger performance maps contain series of data points describing the different
operating conditions of the compressor/turbine by turbo shaft speed, mass flow rate, pressure
ratio and efficiency. The maps are preprocessed by the software since the original available data
points are often sparse and do not cover the entire operating range of the heavily pulsating mass
flow rate and pressure ratio for on-engine turbocharger application. To create suitable maps that
define the turbine performance, the raw data is not only interpolated but also extrapolated to give
data at the high and low extreme values of engine speed, pressure ratio, efficiency, and mass flow
rate. A typical turbocharger efficiency performance map for a gasoline passenger car is shown in
Figure 4:
29
Figure 4 A turbine map for turbocharger 1, generated by GT-Power. White circles are the measured raw data from the
turbocharger manufacturer and the color field the extra- and interpolated map points needed in the simulation. The
simulation entry points during an engine cycle at 1300 rpm and wide open throttle are also shown, after [29].
It is quite clear that the actually measured data points are quite few, especially in the low mass flow
rate and pressure ratio region.
3.4. Numerical computation of turbulent flows In the following sections we consider the model (conservation) equations and the additional
equations needed for accounting for turbulence. Thereafter we consider the needed boundary
conditions to solve the system of equations. The following sub-sections deal with numerical issues;
namely discretization of space and the differential equation and possible solution algorithms for the
resulting system of non-linear algebraic equations. Computational fluid dynamic (CFD) has
different meaning depending on the context. In the strict sense it deals with numerically solving a
system of partial differential equations related to fluid flow, with appropriate boundary conditions.
In a more general sense CFD means solving a scientific or engineering flow problem using
computational methods as a tool for obtaining the sought results. In the following we use CFD the
latter sense.
3.4.1 Basic conservation equations
The governing equations of fluid motion (equations (8)-(15)) are well established since over 150
years back. These equations have analytical solution only for a small number of cases (geometry
30
and parameter values). These partial differential equations are derived from the conservation of
mass, momentum and energy. The governing equations in Section 3.1 are written in a general form
(Cartesian coordinate’s notation) and apply to incompressible and compressible flow whether it is
laminar or turbulent. For turbulent flow the dependent variables solved for are the ensemble
averaged values, the mean quantities, and an extra term adds to the momentum equation to
account for the additional stresses due to the velocity fluctuations about the mean value. This
additional stress is linked to the mean velocity field through turbulence models and will be further
explained in the following.
3.4.2 Turbulent flows and their modeling
Fluid flow can be characterized as being either laminar or turbulent. A dimensionless parameter,
the Reynolds number (Re), is used to characterize flows to the importance of inertia relative the
importance of viscousity. Re is defined as:
υLU ⋅
=Re (39)
Thus, Re is a combination of the property of the flow (i.e. characteristic velocity U), the geometry
(characteristic length L) and the property of the fluid (the kinematic viscosity υ) Turbulent flows a
characterized by large values of Re. How large Re should be in order to have a transition from
laminar to turbulent flow is problem dependent.
Turbulent flow through a pipe can be described as being composed of a mean flow in the direction
of the pipe axis together with random irregular velocity fluctuations in all three directions. This
irregular motion, if visualized resembles (random) motion of “eddies” of different sizes. The term
“eddies” is often used in turbulence without giving an exact definition to it. However, loosely
speaking the eddies have a size and thereby they are related to the length scales that are found in a
turbulent flow field. All eddies are in random motion relative to each other and the largest have
the size of the flow itself. Due to the randomness of the motion a statistical approach must be used
to characterize the flow and to be able to analyze and compare different flows (in the same or look-
alike geometries). Large scale motions are limited by the geometry of the vessel. The large scales
are responsible to the fast long-distance transport and mixing. Smaller scales determine the local
mixing. The smallest scales of the flow are determined by the rate at which viscosity can eliminate
energy from the smallest eddies. The smaller the eddy (scale) is, the faster it decays (for a given
31
kinematic viscosity of the fluid). The smallest scales are thus independent of the flow geometry and
the largest scales of the flow. The big separation between the small and large scales of turbulence is
the basis of the classical turbulence theory of Kolmogorov. Energy is transferred in average from
the larger scales to the smaller ones.
Eddies are like stirrers, transporting fast moving fluid from the center towards the wall with low
momentum flow. Large-scale stirring by these turbulent eddies together with momentum diffusion
down the local velocity gradients give a very effective transport of momentum. For turbulent flow
the momentum transfer is estimated to be thousands to million times more effective than for the
laminar case in which molecular diffusivity is responsible for the mixing. Better transport of
momentum gives higher shear stresses at the wall and greater resistance to the flow. Greater sheer
stress at the wall means more drag on vehicles and larger pressure drop in pipes. But higher wall
shear stress also comes with positive effects as better mixing and enhanced heat and mass transfer,
essential for combustion in the engine cylinder for example.
The Navier Stokes equations describe the flow whether it is laminar or turbulent. For high Re flows
however, the scale ratio of largest to smallest, is too large to be able to handle on currently available
computers. Therefore Direct Numerical Simulation (DNS) can be used to study only relatively low
Re turbulent flows. For higher Re, statistical methods describing the turbulent flow in terms of the
mean velocity field and higher moments has to be used. The averaging processes of the dependent
variables and the governing equations lead to the formation of higher order correlation terms.
Describing/modeling these terms in terms of low order statistics is referred to as the “closure
problem”. These additional terms (such as the Reynolds stresses) must be linked (in the simplest
cases) to the mean velocity field through turbulence models. In this way the set of equations
needed to solve for the properties of the turbulent flow becomes closed in the sense that the
number of equations equals to the number of unknowns.
For high Re flow the instantaneous velocity varies randomly in both space and time. To solve for
the instantaneous velocity would not be feasible. The approach is to perform statistical analysis and
use the governing equations to solve for the mean flow properties. One way to do this is called the
Reynolds decomposition. The dependent variables are separated into a mean component and a
fluctuating component. For the velocity vector this yields:
32
( ) ( ) ( )tX,utX,UtX,U ′+= (40)
The instantaneous velocity vector U is the mean value U plus a fluctuating component u’.
Substituting for all the dependent variables, written as a mean and a fluctuating component, into
the Navier Stokes equations, results in the Reynolds Averaged Navier Stokes equations (RANS).
This procedure leads to the presence of additional terms in the RANS equations, such as the
Reynolds stress tensor in the momentum equations. Most often one uses two additional variables
to characterize the local turbulence. The turbulent velocity scale can be easily related to the specific
turbulent kinetic energy, k, at least for isotropic turbulence. As a second variable one may use the
rate of dissipation of turbulent kinetic energy, k, or some other variable. Most often, these two
variables are computed through their own partial differential equation. These equations can be
derived from the basic conservation laws with the addition of some assumptions (and models) so
the system of equations can be closed (i.e. being solvable).
The relation between the stress tensor components ijτ and the velocity gradients in the Navier
Stokes equations for the laminar case is given by (13) (for a so called Newtonian fluid). For the
turbulent case using RANS the fluctuations about the ensemble averaged velocity gives an
additional term, ji uu ′⋅′⋅ρ− , called the Reynolds stress. The expression for the stress tensor
becomes:
jiijk
k
i
j
j
iij uuδ
xU
xU
+xU
μ=τ ′⋅′⋅−⎥⎥⎦
⎤
⎢⎢⎣
⎡⋅
∂∂⋅−⎟
⎟⎠
⎞⎜⎜⎝
⎛
∂
∂
∂∂
ρ32
(41)
The Reynolds stresses represents the additional stresses due to the fluctuating components of the
turbulent flow and they must be related to the mean velocity field. This is done through the use of
turbulence models.
3.4.2.1 Eddy Viscosity Models
There are several turbulence models available and they are subdivided into different categories. In
the classical Eddy Viscosity (k-ε) model the Reynolds stresses are directly related to the local
gradients of the mean velocity field through:
33
ijk
kTijTji k
xUSuu δρυυρ ⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅+
∂∂⋅−⋅=′⋅′⋅−
32 (42)
⎟⎟⎠
⎞⎜⎜⎝
⎛
∂∂
+∂∂
=i
j
j
iij x
UxUS (43)
2ii uu
k′⋅′
= (44)
To close the set of equations the turbulent viscosity Tν must be expressed with known quantities.
The turbulent viscosity is linked to and k ε by:
ερυ μ
2kCT⋅
⋅= (45)
μC is an empirical coefficient, often set as constant.
There are different ´variant of ε−k models which may differ in the form of the equations, the
treatment of the near wall region and/or in the relation between the Reynolds stresses and the rates
of strain (there are both linear and non-linear relations).
3.4.3 Boundary conditions
Boundary conditions determine the particular flow field, since the basic governing equations are
not problem dependent. One may use different types of boundary conditions, but not all
possibilities lead to a solution or a single solution. Thus, only certain combinations of boundary
conditions lead to a well posed problem (i.e. a problem which has a unique solution that depends
continuously on the boundary data). An example that leads to a not well posed problem is if the
total mass to and from the domain is not in balance. Examples to possible boundary conditions are
such that defines the inlet mass flux and fluid properties, whereas at the outlet boundaries, the
gradients of the variables across the boundary surface are assumed to vanish. It is common that
commercial codes require less number of conditions than those required theoretically. This may
happen since the code itself includes assumptions not specified by or to the user. Such effects may
sometimes lead to difficulties in interpreting the numerical results.
34
3.4.3.1 Turbulent flow boundary conditions
Most popular turbulence models are based on partial differential equations. These equations also
require appropriate (for well posedness and physically reasonable) boundary conditions on the
boundaries of the domain and on solid objects.
3.4.3.2 Wall boundary conditions
At solid walls no-slip condition (zero velocity) are natural and correct from physical and
mathematical point of view. However, in the boundary layer close to the wall there are very large
velocity gradient in the wall normal direction. To resolve numerically such large gradients one must
have an appropriate resolution. The mean behavior of turbulent flows near solid (straight) walls at
very high Reynolds numbers can be described by a model that is physically sound. This description
is termed as the law of the wall. The law of the wall describes the velocity profile in the wall
boundary layer which is made up of a viscous sub-layer, a buffer zone and a logarithmic layer. This
approach eliminates the need to study the details of the flow very close to the wall. Instead the near
wall region is replaced by the wall model. It should be pointed out that this model is valid only for
fully developed (high Re) turbulent flow past a straight (in the streamwise direction) wall. In a real
engine geometry, these requirements are hardly met. However, it is even more difficult to define
better models for transitional flows with large scale penetrating and altering the classical form of
the boundary layer.
In the framework of standard turbulence models (such as the k-ε system) one uses one or another
version of the law of the wall or alternatively turbulence models that are acting at different
distances from the wall. For the standard wall function the boundary layer is just one grid cell thick
with its central node assumed to be at a certain distance from the wall. For example STAR-CD
offers two-layer wall models also in addition to the simpler wall functions to represent the
distribution of velocity, the turbulence energy, temperature etc. across the boundary layer.
With the two-layer models the near wall region is treated more or less like the interior flow with the
no-slip condition applied directly to the boundary cell faces. At some distance from the wall
though, where the viscous effects are small, the ε−k turbulence model is switched to a low Re
form of the governing equations. A finer mesh is needed for the near wall layer.
35
3.4.4 Inlet conditions
Using the RANS equations together with a turbulence model both the inlet mean velocity and
certain turbulence quantities are needed. The turbulent kinetic energy is sometimes available
from experiments but otherwise it can be assumed as a portion of the mean flow kinetic energy. It
is often much smaller than unity and for fully developed turbulent pipe flow it is of the order 10%
or less. The dissipation rate of turbulent kinetic energy
k
ε is difficult to measure and can be
estimated by assuming or knowing k and the turbulent integral length scale l . The latter is
bounded by the characteristic dimensions of the vessel or the device.
3.4.5 Discretization
The continuous differential equations are valid for all points in the space of interest and for all
times. The first step in formulating a tractable problem is to restrict the problem into a finite
number of (discrete) points in space and time. This process leads to a set of distinct points in the
domain of interest. The functions that we are interested in are defined only on this finite set of
points. If the set of points can be organized so that the points become vertices for polyhedral
volumes we can talk about local control volumes. The conservation of mass, momentum energy
(and turbulence quantities) can be satisfied for each control volume. This approach leads to the so
called “Finite Volume” (FV) approach. If one uses polynomial approximations to the dependent
variables one may derive finite difference or finite volume approximations to differential equations.
The order of approximation is defined as the exponent of the typical grid (volume) size in the
expression of the discretization error. The integration in time is also done through a finite different
type of expression; explicit or implicit. In the latter case an iterative approach has to be used so as
to ensure the convergence of the iterative process to a prescribed level of error. The integration in
time allows one to study both steady-state and transient cases. In the following some details of the
methods we have used are given.
3.4.5.1 Spatial discretization of the convective term
There are different classes of convective flux approximation and the choice of it is especially
important at high Re. STAR-CD offers several schemes. One lower first order scheme is the
Upwind Differencing scheme (UP), generating discretized equation forms that are easy to solve but
has the effect of smearing out gradients (numerical diffusion) and should in general be avoided.
Higher order schemes include among others second order Linear Upwind Differencing scheme
36
(LUP), Central Differencing scheme (CD) and a Monotone Advection and Reconstruction scheme
(MARS). Higher order schemes may better preserve steep gradients but may result in equations
that are more difficult to converge and even lead to numerical instabilities and/or introducing non-
physical spatial oscillations.
3.4.5.2 Temporal discretization
There are two options for the temporal discretization in the used code; either a first order fully
implicit scheme or a second order Crank-Nicholson scheme. Using the former scheme the fluxes
over the time interval are calculated from the new time-level values of the variables. The latter is
second order accurate in time but may generate non-physical oscillations if the time step size is too
large. Even though an implicit scheme avoids stability restriction on the time step size compared to
explicit schemes, the time step is in practice still limited by other factors, such as the needed
temporal resolution to follow transients of the flow. This means that the Courant condition (29)
must be satisfied. In particular this may mean that there is a need for small time steps for grids with
small mesh spacing or for flow with local high velocity.
3.4.5.3 Discretization error estimation
In the used code the error estimation gives an approximated magnitude and distribution of the
convergence error. In contrast to the convergence error it is much more difficult to assess the
discretization error. This error includes the errors caused by the finite mesh spacing, its
irregularities and discretization errors of the derivatives in the differential equations. Further error
may be due to the time-step taken in the temporal integration of the discrete governing equations.
The most difficult error to estimate is the modeling error itself (i.e. the error due to the differential
equations themselves). Of course comparison with experiments is a way to assess the global
accuracy; however, this approach is very crude since it includes also experimental errors and
uncertainties as well as uncertainties in the boundary conditions that are imposed in the numerical
calculations.
The implemented Residual Error Estimate (REE) method is based on a cell residual from the local
imbalance between the face interpolation and the control volume integration. The cell residual of a
specific variable is then normalized in a proper way to give an estimation of the absolute magnitude
of the convergence error with the same physical dimension as the variable in question. This error
37
estimator has limited value as explained in the paragraph above, though it is important to know it
as an indicator.
3.4.6 Solution algorithm
STAR-CD use implicit methods to solve the algebraic FV-equations that results from the
discretized governing equations. There are three implemented algorithms that can be used:
SIMPLE, PISO, and SIMPISO. SIMPLE and SIMPISO are solely for steady state calculations and
PISO can be used for both steady state and transient applications. Common for all three
algorithms is:
A predictor-correction strategy by temporarily decoupling the flow equations from each other so
that they can be solved sequentially (operator splitting). The vector set of unknowns are split into a
sequence of scalar sets.
A combination of the FV mass and momentum conservation equations gives an equation set for
the pressure enforcing the continuity.
o The solution sequence is a predictor step that produces a tentative velocity field and the
preliminary fields are then refined in one or several corrector stages so that the mass and
momentum equations are both satisfactory balanced.
As the dependent variables are decoupled and also linearized they result in large sets of algebraic
equations. The equations resulting in the above mentioned correction steps are often a Poisson
equation. That equation can be solved efficiently by either Conjugate-Gradient method or by a
Multi-Grid method.
3.5. Coupled 1D & 3D simulation tool The coupled simulation tool that has been used in this work is integrated calculations using the 1D
engine simulation software GT-Power and the CFD software STAR-CD. By integrated calculations
is meant that through special connections in the 1D model, the 1D code exchanges boundary
values to the 3D computational domain at each CFD time step. This allows for a detailed modeling
of geometries where the 1D flow assumption is less appropriate, for components with significant
3D flow, and the remainder of the engine system can be modeled in 1D. The computer cost can be
38
kept very low as the CFD domain is restricted to parts of the engine where it is mostly needed and
not the entire system of components.
3.5.1 Boundary interfaces
The coupling between the two softwares occurs at the boundary interfaces (cell faces) of the
“connection objects” in the 1D code. A sketch of the1D-3D interfacing boundary geometry is
shown in Figure 5.
Figure 5 A sketch of the 1D-3D interfacing boundary geometry.
The figure shows three boundary interfaces which are the locations for the exchange of
information between the CFD domain being modeled in STAR-CD and the rest of the 1D
geometry being modeled in GT-Power. It is very critical that these boundary interfaces are placed
in areas where the flow is almost one-dimensional. The flow entering/leaving the 1D/3D
boundary regions must not have too large secondary flow components as this may lead to
incompatibility between the two solvers. Additionally, the mismatch may also leas to stability
problems with oscillations or even divergence of the coupled system. In fact the coupled system
may not have a solution at all as long as the level of incompatibility is significant. Since GT-Power
is one-dimensional the three-dimensional CFD results must be averaged over a plane before being
passed back into the 1D code interfacing parts. This region is the 2D cross sectional area of the
39
individual1D/3D interfaces times a certain length into the CFD domain, marked as the shaded
areas extended a length DX into the CFD domain in Figure 5. In this way the interfacing CFD
regions can be thought of as sub-volumes adjacent to the GT-Power sub-volumes where DX is set
to the discretization length in the 1D code.
The CFD code controls the starting and ending of the 1D calculations. The latter is first run for a
number of cycles (time steps) alone to give better boundary conditions sent into the CFD model
when the coupled calculations start, i.e. without start up transients. There is also a way to prepare
the 1D model in order to produce not only good boundary conditions but also good initial
conditions. GT-Power then has to be run in its original state and data as temperature, pressure and
velocity for the pipe object next to the CFD domain is stored and later used in the coupled
simulation to initialize the flow field in the CFD model.
3.5.2 Time stepping
The time steps used by the codes are typically not equal as the CFD code is often run with an
implicit discretization scheme and GT-Power an explicit scheme with adaptive time stepping based
on the Courant condition. Usually the time step size used by GT-Power is smaller than the CFD
code time step. This means that GT-Power will step a number of times until completing a full CFD
time step so that the two codes at the end of the CFD time step are at the same point in time.
3.6. Experimental method
3.6.1 Engine in test cell
The experimental tests are performed on a 4 cylinder 2-liter standard production turbocharged SI
engine from 2004. For measurement and control, a PC based in house system is used.
3.6.2 Measurement methods
The measurement system takes both analogue and digital input. Analogue input is measured by
using either a fast system for crank angle resolved data or by using a slower time averaged system.
The fast system consists of a 12-bit PowerDAQ card [6] with a sampling frequency of 1.2 MHz
divided over a maximum of 16 channels. The resolution used in this work is 0.4 CAD
corresponding to a total sampling frequency of approximately 0.23 MHz at 1300 rpm. The slow
40
measurement system has a sampling frequency of 1 Hz and it is built up of different Nudam
modules [7] for analogue voltage input or thermocouples output signals.
3.6.2.1 Pressure
The cylinder pressure is measured on all cylinders with GM12D cylinder pressure transducers [8].
The pressure is measured at several locations on the engine: before and after the compressor, in the
inlet and exhaust port of cylinder 4, in the inlet plenum, and just upstream and downstream of the
turbine. The fast analogue system is used for the pressure measurements, on the intake side with
strain gauge transducers and on the exhaust side with piezo-resistive transducers.
3.6.2.2 Temperature
Measurement of the mass averaged temperature at different locations on the engine uses the slow
analogue system. Thermocouples are mounted before and after the compressor, after the
intercooler, in the inlet plenum, before and after the turbine and in the catalyst.
3.6.2.3 Mass flow rate
The exhaust gas flow is measured indirectly by measuring the fuel flow and the air to fuel ratio
(AFR). It was compared with results from the control system measurement of the inlet air mass
flow rate and lambda measurements.
3.6.2.4 Turbocharger speed
When modeling a turbocharged engine it is most important to get the turbocharger speed correct.
A Micro-Epsilon eddy current probe [9] is positioned on the compressor shroud. The transducer
senses the blade passages of the impeller and a signal processing unit converts this output signal, in
this case, to one digital signal per revolution. At a turbo speed of 94000 rpm and an engine speed
of 1300 rpm, the turbine speed is determined every 5 crank angle (from the time between two
consecutive pulses). The turbo speed is then linearly interpolated to instantaneous values at the
crank angles for the analogue measuring points. The digital system used for the turbine speed
measurement consists of a Microchip PIC18F452 microcontroller recording the pulse time with a
time resolution of 10-7 s. The time data are continuously transferred to the PC and synchronized
with the analogue system. This is done by measuring the one per engine revolution pulse with the
same 10-7 s time base for each revolution during the measurements.
41
42
4. Results
The first part of this chapter shows the results from calibration of a 1D engine model to measured
data. Results are then presented for a study where the calculated instantaneous turbine efficiency
from 1D engine simulation using steady flow turbine performance maps is compared with the
turbine efficiency calculated from on-engine measurements. Two different turbochargers are
considered. Results are also presented for a comparative study between 1D and CFD calculations
on single and double bent pipe geometries under steady and pulsatile flow. Results related to the
comparison between the 1D and CFD calculations on the exhaust manifold are shown. Initial
results of the integrated 1D and CFD calculations are summarized.
4.1. Engine modeling Modeling the engine as a system of zero and one dimensional components implies that data is
needed as input to the models to give accurate results. Trends for various engine output
performance parameters can easily be seen when varying different parameters in the engine model.
However, the 1D engine calculation tools suffer from limited predictivity of turbocharged engine
models. Measurements as turbocharger speed, air mass flow rate, and cylinder pressure are needed
for thorough model calibration [1, 29, 36]. One source of error is the treatment of the turbine as a
quasi-steady flow device and probably also the simulated inlet conditions used for interpolation in
the performance maps since the geometry upstream of the turbine contains secondary flow
structures.
4.1.1 Calibration
The model is calibrated by controlling the cycle averaged turbo speed to measured values. The
calculated turbine power is not well predicted and must often be adjusted with efficiency and mass
multipliers to give simulated results close to measured values. Problem with erroneous predicted
turbine power is especially pronounced in the region where the waste gate is closed since the model
cannot control the waste gate to meet target boost pressure. For this purpose, and with closed
waste gate, a PI controller controlling the turbine efficiency multiplier is used in the model.
Adjustments are then made to other parts of the model to get important variables close to
measured, volumetric efficiency among others. The compressor model needed no correction. A
comparison between measured and simulated pressure traces before and after the turbine as well as
turbo shaft speed and shaft acceleration are shown in Figure 6.
43
Figure 6 Measured and simulated pressure traces before and after the turbine (P1T, P2T), turbo shaft speed (Ntc) and
shaft acceleration (dNtc/dt) for TB1at 1300 rpm and wide open throttle.
After calibration measured and simulated results show good agreement. The relative error is 1.5%
and 3%, respectively for the cycle averaged pressure before and after the turbine for TB1 and TB2
it is 1.6% and 0.4%, respectively. The relative error for the cycle averaged inlet temperature and
mass flow rate are 0.2% and 0.9% for TB1 and 0.2% and 2.6% for TB2 at 1300 rpm.
4.1.2 Instantaneous turbine efficiency
A comparison is made between the calculated instantaneous turbine efficiency from 1D engine
simulation using the quasi-steady flow assumption and that from on-engine measurements. High
frequency measurements are required to calculate the instantaneous turbine efficiency over an
engine cycle according to equation (5). However, since high resolution mass flow rate and
44
temperature measurements are difficult to perform in on-engine applications, only cycle averaged
quantities are measured. The instantaneous values for mass flow rate and temperature used in the
efficiency calculations are therefore taken from engine simulations and require well calibrated
models. Crank angle resolved measurements as pressure and turbocharger speed are averaged over
300 consecutive cycles.
The on-engine turbine efficiency is derived for two different turbochargers, TB1 and TB2, in the
closed waste gate region with the engine running at 1000 and 1300 rpm and wide open throttle.
Figure 4 shows that the operating point during an engine cycle for TB1 at 1300 rpm is in the
extrapolated region of the generated turbine map during large periods.
In Figure 7 the TB1 turbine efficiency is shown versus blade speed ratio (BR) as is common when
presenting turbine efficiency characteristics. For simplicity the results are presented for only one of
the four exhaust pulses, as they all show the same behavior.
Figure 7 Comparison between instantaneous turbine efficiency based on measurements and results from using tabulated
steady-flow efficiencies versus U/Cs, for TB1 at 1300 rpm and wide open throttle. The additional markers show the
points of the pulse exceeding 2 kW.
45
The arrows in Figure 7 show how the efficiency is changing as one exhaust pulse is traversed
through the turbine. The highly fluctuating mass flow, pressure, and isentropic power at turbine
inlet all peak near the region of the lowest blade speed ratio point, the left most point in Figure 7.
The same efficiency characteristic as for TB1 at 1300 rpm is seen for TB2 and also for the 1000
rpm cases, as shown in Figure 8.
Figure 8 A comparison between the instantaneous turbine efficiency, based on measurements and results from using
tabulated steady-flow efficiencies, versus U/Cs. The upper diagram shows TB2 at 1300 rpm, the lower left diagram TB1 at
1000 rpm and the lower right diagram TB2 at 1000 rpm, all at wide open throttle. The markers show the points exceeding
2 kW.
The measured efficiency shows somewhat similar results for the two turbochargers. At 1300 rpm,
the instantaneous efficiency for TB1 and TB2 increases on the upslope of the pressure pulse to a
maximum value of about 0.65 before the mass flow and pressure pulse peak. The efficiency
decreases to approximately 0.5 at pulse peak (lowest BSR point) and then again it increases, on the
down slope of the pulse, to about 0.9 (higher for TB2 though). Similar results for the measured
efficiency of TB1 and TB2 also holds for the 1000 rpm cases.
46
Ignoring the lowest energy points of the pulse, the results show that measured instantaneous
turbine efficiency compared to tabulated steady-flow efficiency values agree better on the upslope
part of each pressure pulse from close to the maximum efficiency region and up to the peak of the
pulse, Figure 8. The point of peak pressure coincides more or less with maximum energy and mass
flow rate into the turbine. From this point through and continuing on the downhill side, the
measured efficiency starts to differ to a greater extent and has a value well above the efficiency
from steady-flow performance maps. The turbine efficiency characteristic derived from
measurements and that from using steady-flow efficiency performance maps, describe quite
different behavior of the turbine.
The provided steady flow efficiency data for TB1 and TB2 differs quite a lot when looking at the
maximum efficiency level. Sensitivity to measurement installation might be a cause of it. Even
though measured efficiency for turbocharger 1 shows better agreement with tabulated steady flow
data than turbocharger 2 does, it is clear that the on-engine instantaneous efficiency, for both
turbochargers and load points, is significantly higher on the “downhill side” of each exhaust pulse.
The measured turbine efficiency shows a hysteretic effect with an unrealistically high efficiency for
decreasing mass flow rate after pulse peak.
To investigate if the region of high measured instantaneous efficiency (not considering the lower
energy part of the pulse) will have any affect on the cycle averaged efficiency compared to results
obtained using efficiency performance maps, the time spent by the turbocharger in this region of
the exhaust pulse is important. For TB1 at 1300 rpm the efficiency is plotted against crank angle
instead of blade speed ratio, Figure 9.
47
Figure 9 Comparison between instantaneous turbine efficiency based on measurements and results from using tabulated
steady-flow efficiencies versus crank angle. The figure includes isentropic power at turbine inlet and markers on the
efficiency curves showing the points exceeding 2 kW.(top figure, a). BR versus CAD. Both figures are for TB1 at 1300 rpm
and wide open throttle (lower figure, b).
Figure 9 shows the efficiency together with turbine inlet isentropic power versus crank angle for
TB1 at 1300 rpm. The figure also shows how the blade speed ratio varies during the same crank
angle interval. According to Figure 9 the crank angle interval of the pulse indicating large
discrepancy between measured and quasi steady flow efficiency can be expected to be important as
the energy is still at moderate levels (region of decreasing mass flow rate following upon pulse
peak). It will have an effect on the time and mass averaged efficiency during an engine cycle and
the importance it may have on turbocharger matching.
4.1.3 Accuracy of the calculated turbine efficiency
Results related to the effect of different measurement errors on the calculated efficiency are
presented in this section. Only steady-state errors are considered for the individual measurement
errors, they do not include inaccuracies due to the pulsating conditions. For simulated parameters
as temperature and mass flow rate, errors from differences in measured and simulated cycle
averaged values are added to the instrumentation error.
48
The variables in eqn. 5 are all marred by measurement errors. The uncertainty in the calculated
turbine efficiency depends on these individual measurement errors. The variance for the calculated
total-to-static turbine efficiency 2TSη
σ can be estimated with the use of Gauss’ approximation
formulas, describing the laws for error propagation of non-linear measurement equations
[10].Using Gauss’ approximation formula gives the expression for the variance of the turbine total-
to-static efficiency:
∑ ⋅⎟⎟⎠
⎞⎜⎜⎝
⎛∂∂N=i
=i ixi
η σxη
=σ1
2
TSTS
22 (46)
where σ2xi is the variance for the measured parameter xi. The instantaneous total-to-static efficiency
as a function of the individual independent variables (4):
( ) ( 403exh04030201airtcrotorTS P,P,m,T,T,T,T,m,N,Jf=Xf=η && ) (47)
Figure 10 shows the instantaneous efficiency together with its crank angle resolved variance during
one exhaust pulse. The individual measurement error contributions to the efficiency variance are
also shown.
Figure 10 Turbine efficiency, efficiency variance and the different individual measurement error contributions. TB1 at
1300 rpm and wide open throttle.
49
It is clear that the accuracy of the measured efficiency is mainly determined by the measurement
error of the turbine shaft speed. The pressure before and after the turbine are also important. The
efficiency variance goes to infinity as the energy of the pulse vanishes. The sensitivity of all the
other measured parameters is very low. It must be pointed out that the dynamic errors are not
accounted for and also the sensitivity of the phasing of different parameters in equation (5) is not
considered, for example the phase shift between mass flow rate and shaft power. The pressure
trace after the turbine was difficult to simulate correctly and according to Figure 6 in the
calibration section, there are some discrepancy in the upward peaks between measurement and
simulation. This can affect the instantaneous mass flow rate used in the efficiency calculations since
they are simulated averaged values between the exhaust gases flowing into and out of the turbine at
each instant. If the pressure trace after the turbine suffers from difference in phase between
measurement and simulation, it is possible the instantaneous mass flow rate will do that as well.
Phasing of the mass flow rate was shown to be very critical when calculating the efficiency using
equation (5).
4.2. CFD modeling of pipe flows The primary purpose for introducing the CFD modeling was to integrate full CFD calculations on
the exhaust manifold of a turbocharged SI engine passenger car with 1D engine calculations on the
rest of the engine. The question at issue was if the inlet conditions to the turbine would be
affected by taking the multidimensional flow effects in the upstream exhaust manifold into account
in the 1D model. However, the operating points considered where such that problems as reverse
flow at the outlet of the CFD-domain made this task difficult to realize due to the limitations in
applying appropriate boundary conditions in the commercial code. This was even true for the case
with extension volumes added at both the inlet and outlet end of the domain. As stated above, it is
not self evident that the coupled system can have a solution for small but finite incompatibility
between the 1D and 3D models. Thus, the attempt of extending the domain may not be adequate
to prevent oscillations or divergence of the process due to the instability of the interfacing at the
1D/CFD boundaries.
The focus was instead on comparing the results between 1D and CFD analysis of the exhaust
manifold, both under steady-state and pulsating flow conditions. For the pulsatile flow case the
flow showed a considerable separation bubble after the strong bend just upstream of the end of the
computational domain (i.e. the outlet boundary). In addition, it was difficult to draw direct
50
conclusions from the different results as the effects of the error introduced by creating a 1D model
from the 3D manifold geometry was difficult to estimate.
Thus, in order to gain a better understanding of the different problems, a set of simpler cases have
been studied. These geometries have been used to assess the effects of the 1D assumption and the
discrepancy between the 1D and 3D results in terms of losses.
4.2.1 Methods
For the different geometries modeled in STAR-CD the equations of fluid motion has been solved
using the Reynolds Averaged Navier Stokes equations (RANS) together with a εκ − RNG
turbulence model. A second-order MARS scheme was used for spatial discretization and a full
implicit first order scheme was used for temporal discretization. For the steady state problems the
SIMPLE solution algorithm has been used to solve the final discretized FV equations and for the
transient problems the PISO algorithm. From the decoupling of the equation for each dependent
variable and their linearization, the resulting large sets of linear algebraic equations are solved with
an algebraic multigrid approach (AMG). A numerical accuracy study performed by Hellström on a
single and double bent pipe [28] showed that the order of accuracy of the STAR-CD code is
between 1 and 2, depending on the flow case and on the discretization schemes used.
The near wall boundary is modeled with a standard wall function and the wall boundary is treated
as smooth and adiabatic. For simplicity the flow study has not concerned heat transfer issues.
4.2.2 Bent pipe geometries
The study on gas flow through bent pipes comprised 5 geometries, all 10 mm in diameter with
circular cross sectional area. Case 1 was a straight pipe; Cases 2, 3, and 4 consisted of a 15 diameter
long straight part followed by a single bend of 30, 60, or 90 degree and finally another 10 diameter
long straight section. Case 5 was a double bent pipe having a straight inlet of 12 diameters
followed by two 90 degree bends separated by a 2 diameter straight section and then ending up
with a 6 diameter long straight part. The five geometries are described in more detail in Table 1.
51
Table 1 Description of bent pipe geometries modeled in 1D and CFD
Case/
Geometry
Length
of first
straight
part
(mm)
Angle of
first
bend (°)
Radius of
curvature
for first
bend (mm)
Length of
second
straight
part (mm)
Angle
of
second
bend
(°)
Radius of
curvature for
second bend
(mm)
Length
of third
straight
part
(mm)
Number
of cells
1 180 - - - - - - 130 000
2 150 30 10 100 - - - 155 000
3 150 60 10 100 - - - 150 000
4 150 90 10 100 - - - 160 000
5 120 90 10 20 90 15 60 185 000
Geometries 4 and 5 are shown in Figure 11 below.
Figure 11 Case 4 with a single 90 degree bend and Case 5 with two 90 degree bends having different radius of curvature.
The case 5 geometry was the same as that one used in the work by Hellström [28]. He performed
numerical computations on steady and pulsatile flow in both a single and a double bent pipe.
STAR-CD was used for this purpose and both the RANS technique with the εκ − RNG
turbulence model and the LES approach was tested and the results compared to measured data. A
numerical accuracy study was performed and Hellström concluded that using RANS and for the
finest grid of the double bent pipe (185 188 cells), the mean numerical uncertainty was 0.02%,
9.6%, and 5.3% at three different evaluation stations. The evaluated parameter was the phase
averaged streamwise velocity component.
52
4.2.2.1 Steady flow
For the steady flow conditions a symmetric fully developed turbulent velocity profile, from using a
power law relation, is imposed as shown in Figure 12.
Figure 12 Velocity profile imposed on the inlet to the computational domains.
The normal component of the inlet velocity is adjusted to maintain the mass flow rate at a constant
value. The mass flow rate corresponded to a mean flow velocity at the inlet of about 240 m/s and a
Re number of 36 000. The outlet to the domain was defined by a pressure boundary at atmospheric
pressure and a zero gradient assumption for the temperature and turbulence parameters.
The secondary flow structure developed over the bends is a pair of counter rotating vortices, the so
called Dean vortices. As the flow enters the bend it is accelerated near the inner wall and
decelerated close to the outer wall due to the adverse pressure gradient (which is when the static
pressure increases in the direction of the flow). In areas where the fluid is decelerated and its
velocity pressure is converted to static pressure a lot of turbulence is produced and significant
energy is dissipated. The pressure difference across the pipe induces a fluid motion from the outer
wall towards the inner. Further into the bend centrifugal forces comes into play, acting on the fluid
in the direction from the centre of the pipe and outward, inducing a fluid motion in the same
direction. A secondary flow structure in the form of a single pair of counter rotating vortices is
formed, in a plane normal to the primary flow direction. The effect of the secondary flow is to
53
transport energy to the inner wall region where low energy fluid is accumulated. Strong secondary
flows thereby prevent flow separation which can occur because of the adverse pressure gradient on
the inner wall at the bend outlet. Secondary flow causes losses due to mixing in the turning section
and in the outlet pipe downstream of a bend. Although the strength of the secondary flow weakens
further downstream, a significant part of the losses connected to turning flows occur in the
redevelopment region of the flow downstream of the bend outlet. The results show that the
secondary flow structure is still present at 10 diameters downstream. Figure 13 shows the mean
axial flow velocity and the secondary flow structure for the 60 degree bent pipe at bend inlet, bend
outlet, and at two sections downstream of the bend (located at one and three diameters
downstream of the bend outlet).
Figure 13: Mean flow axial velocity (contoured area) and secondary flow structure (arrows) at bend inlet (upper left), bend
outlet (upper right) and at one and three diameters downstream of the bend outlet (lower left and lower right respectively).
In addition to the formation of the two vortices, the mean axial velocity profile has changed as
compared to that upstream of the bend. The axial velocity profile is distorted and non axis-
54
symmetric. It has a higher velocity closer to the outer wall, more or less c-shaped. As the strength
of the vortices weakens, so does also the velocity profile even out further downstream. The radial
pressure distribution at cross sections upstream and downstream of the bend is affected by the
presence of the bend and is non-uniform. The pressure distribution across planes from the 60
degree bend outlet and downstream is shown in Figure 14.
Figure 14: Absolute static pressure at the 60 degree bend outlet and 0.5, 1, 1.5, and 2 diameters downstream of the bend
(minimum and maximum value for the local static absolute pressure is 0.97 bar and 1.07 bar respectively).
The pressure difference across the pipe is nearly 0.1 bar at the bend outlet, one pipe diameter
downstream it has decreased to one tenth of that. Performing on-engine pressure measurements it
is very important not to place the transducers in or near a bend, especially when investigating low
speed and load conditions as the radial distribution might be of importance. Due to the narrow
space on an engine this may still not be possible but nevertheless it must be considered. Figure 15
shows the maximum pressure difference over sections, normalized with the mean pressure across
the main flow direction, from 3 diameters upstream of the bend to 3 diameters downstream of it
for the 60 and 90 degree bent geometries.
55
Figure 15 The difference between maximum and minimum pressure is normalized with the average pressure across the
main flow direction at sections located from upstream to downstream of the 60 and 90 degree bends of Case 3 and 4.
The pressure distribution at sections located at the same distance upstream and downstream of the
bend is quite different. The pressure distribution is quite uniform a half to one diameter upstream
of the bend, the pressure at corresponding sections downstream of the bend is still quite unevenly
distributed. Figure 16 shows how the pressure distribution differs for planes located at 0.5 and 1
diameter upstream and downstream of the 90 degree bend respectively.
Figure 16 Absolute static pressure at sections 0.5 and 1 diameter upstream (left figure) and downstream (right figure) of
the 90 degree bend.
56
To study how the pressure changes along the flow direction the pressure gradient is considered.
The gradient of the mass averaged static pressure for sections along the straight inlet part to Cases
3, 4, and 5 are shown in Figure 17.
Figure 17 The gradient of the mass averaged (MAV) static pressure along the straight part upstream of the single 60 and
90 degree bend (left figure), and upstream of the first bend and between the two bends of the double bent pipe (right
figure). The value for the straight pipe is included in both figures and the bend inlet is positioned at 0 mm.
The gradient along the straight pipe, Case 1, is constant and has a value of near (minus) 20 Pa/mm.
This figure can be considered a reference value. The corresponding gradient for the single bent
pipe geometries is more or less constant and equal to the reference value up to 0.5-1 pipe diameters
upstream of the bend. This also applies to the first of the bends for the double bent pipe (right
figure). Closer to the bend the gradient for the average pressure increases. For the single bent pipes
the results show that the sharper the bend the greater the gradient and also the further upstream it
has an affect. For the straight part between the two 90 degree bends the pressure gradient is very
high close to the first bend outlet, about 10 times that for the straight pipe, and it reduces to the
reference level at approximately one pipe diameter downstream. The pressure gradient is not that
57
affected by the second bend until very close to the inlet. The gradient along the straight part
downstream of the different bends are shown in Figure 18.
Figure 18 The gradient of the MAV pressure along the straight part downstream of the single 60 and 90 degree bend and
the two 90 degree bends of the double bent pipe. The bend outlet is positioned at 0 mm.
It can be seen that the gradient of the mass averaged cross sectional pressure is large in the vicinity
of each bend outlet and that the effect of the bend remains almost one pipe diameter downstream
of it.
The two bends of Case 5 is just about 2 diameters apart and they will most certainly interact with
each other and thereby affecting the losses compared to two isolated bends. The pressure gradient
after the second 90 degree bend is almost 50% higher compared to the straight pipe still at several
pipe diameters downstream, 30 Pa/mm compared to 20 Pa/mm. The velocity and pressure
distribution at 1 diameter downstream of the two bends in Case 5 is shown in Figure 19.
58
Figure 19 The pressure and velocity distribution at cross-sectional planes one diameter downstream of the first 90 degree
bend (leftmost figures) and the second bend (rightmost figures) of Case 5.
The pressure distribution is much more uniform downstream of the second bend compared to the
outlet of the first. The secondary flow structure shows a swirling motion compared to the counter
rotating vortices downstream of the first bend. This has to do with the skewed velocity profile of
the flow entering the second bend. Nearly all the low energy fluid follows the same path, the
shortest path between the inside of the first bend to the inside of the other, creating the swirling in-
plane flow structure.
4.2.2.1.1 Three-dimensional CFD results compared to 1D
The geometries according to Table 1 have been modeled in 1D with the same boundary conditions
as for the CFD case. The mass flow rate was kept constant at the inlet, the walls were treated as
smooth and adiabatic and the outlet pressure was set to atmospheric pressure. The mass flow rate
for the double bent pipe was somewhat lower than for the single bent pipes, but equal for the 1D
59
and CFD case. The modeled gas properties as molecular weight, specific heat capacity, and
dynamic viscosity were set to constant and equal values in both codes. In the CFD code a turbulent
velocity profile was imposed at the inlet and in the 1D code a turbulent profile is assumed for
values of Re corresponding to turbulent flow. The code accounts for the fact that a turbulent
profile has a larger velocity gradient close to the wall, creating additional friction.
The absolute pressure at locations along the different geometries is compared for the 1D and 3D
CFD calculations, Figure 20.
Figure 20 The absolute static pressure at pipe inlet, bend inlet, bend outlet and pipe outlet for the single bent geometries
(left figure, 30, 60, and 90 degree bend) and the double bent geometry (right figure, to 90 degree bends).
The outlet pressure is set to 1 bar and the upstream pressure for the different pipe geometries is
seen to differ for the 1D and CFD calculations. It is quite obvious that the biggest discrepancies
are introduced over the bends where the pressure drop is for all cases higher for the 1D code. To
make an estimation of the discrepancies introduced on the upstream inlet pressure for the same
outlet pressure using the 1D flow assumption together with the use of correction factors and CFD
calculations, a non-dimensional pressure parameter is defined according to:
out
outiND p
ppp
−= (48)
60
This parameter is calculated at the inlet to the geometries using the results from the 1D and CFD
calculations and is plotted in Figure 21:
Figure 21 Calculated dimensionless pressure parameter from 1D and CFD results at pipe inlet for the different Cases.
The relative difference increases with increasing angle of the bend. The discrepancy between the
1D and CFD computational results is highest for the second bend of Case 5. The difference for the
calculated non-dimensional pressure coefficients using 1D or 3D computational results is not zero
even for the straight pipe.
To understand the different upstream results for the pressure using 1D and CFD calculations of
flow through these geometries we consider the differences in the pressure gradients along the
pipes. The calculated pressure gradient in the 1D code for the simple case of the straight pipe is
plotted in Figure 22:
61
Figure 22 Pressure gradient along straight pipe modeled with the 1D code.
The results show that the code actually has a problem with the number of significant digits. It is
not possible as a user to set that parameter and with a small discretization length of 1 mm as used,
“pressure jumps” appears over the pipe length. The value for the pressure gradient is just about the
same as the value for the gradient of the averaged cross sectional pressure in the CFD calculations,
about 20 Pa/mm. The 1D flow approximation for a straight pipe is shown to be very good and
more or less as expected. The calculated pressure gradient for all straight parts of the geometries in
Table 1 is exactly the same as for the straight pipe modeled alone. This means that modeling a
straight part next to a bend in 1D, a distance of 0.5-1 diameter upstream or downstream of that
bend will have a calculated pressure gradient that is lower compared to 3D computations. The 1D
code does not account for the presence of a neighboring bend.
It is seen in Figure 20 that the largest differences between the calculated upstream pressure for
Cases 1 to 5 is the pressure drop over the bends. The results for the pressure drop over the various
bends from 1D and CFD calculations are shown in Figure 23.
62
Figure 23 The absolute pressure drop (left figure) and the average pressure gradient (right figure) over the bends of Cases
2, 3, 4, and 5.
The pressure drop is displayed as an absolute value in kPa over the entire length of the bend. Cases
1 to 5 correspond to the 30, 60, and 90 degree single bends and the two 90 degree bends of the
double bent pipe. The discrepancy between the two codes is quite big. A “global” mean value for
the pressure gradient from dividing the pressure drop over the bend by the length of the bend is
plotted in the right figure and displayed in Pa/mm (compare with the results shown for the
resolved pressure gradient of the straight parts connected to the bends, Figure 17-Figure 18).
The pressure gradient over the bent pipes is in all cases much higher in the 1D code compared to
the 3D code. As secondary flow structures develop through these pipes the 1D code relies on
correction of the pressure loss in the momentum equation by adding a semi-empirical pressure loss
coefficient . The coefficient is interpolated in a look-up table from the radius of curvature and
the length of the bend. According to support it is based on an average of a few published sources,
as they were not in complete agreement. The SW vendor is working on improving the model and is
adding a missing Re dependence. The pressure loss coefficients for the single bent geometries are
calculated according to equation (33) using 1D and 3D data and the result is plotted in Figure 24
together with the tabulated values used by the 1D simulation. Included in the diagram are also
pC
63
estimated values for the loss coefficients using bend performance charts from experiments by
Miller [43].
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
30 60 90Bend angle [degree]
Loss
coe
ffici
ent [
-]
1D calc from data
1D tabulated
3D bend inlet to bend outlet
3D bend inlet to 1d downstreamBend performance chart
Figure 24 Calculated loss coefficients for the single bent geometries using 1D and 3D data, the 3D case even for including
the losses up to 1 diameter of the downstream connected pipe. Tabulated loss coefficients used in the 1D simulation are
also displayed together with estimated values of the loss coefficients from using bend performance charts based on
experiments by [43].
Measurements are made on steady incompressible flow of a nearly Newtonian fluid flow through
various bends connected to long inlet and outlet pipes (more than 50 diameter long), the Re
number is in all cases 106. For a Newtonian fluid the relation between the shear stress and the
strain rate is linear, the viscosity being the proportionality constant. Basic loss coefficients for
bends based on these measurements are tabulated in a chart. The basic loss coefficients can then be
corrected to account for other values of the Reynolds number, the length of the inlet and outlet
pipe connected to the bend, surface roughness, bend-to-bend interactions, and even to
compressibility effects for Mach numbers above 0.2. The corrections that can be made are further
described in the Appendix.
Before commenting on the results it must be pointed out that, still writing this thesis, it is not
known exactly how the different variables were measured (how the velocity was measured / if the
64
velocity profile was measured) or any detailed description of the measurement installation system
that was used producing the tabulated values for the loss coefficient by [43].
The 1D tabulated loss coefficients are expected to be close to the values of the performance charts
as that kind of data is described as being used by the 1D software support. Why the performance
chart data estimates even higher losses over the bends is probably due to the correction factors that
have been used from the basic chart data. The tabulated values used in the 1D code are very close
the measured uncorrected loss coefficients. Compensating for the lower Re number has the affect
of increasing the basic loss coefficient (a factor of about 1.6 for these cases) and the correction for
the only 10 diameter long outlet pipe has the affect of decreasing the basic loss coefficient (a factor
between 0.6-0.9 for the different cases). Finally, compensating for compressibility effects has the
affect of decreasing the losses with a factor close to 0.94.
The 1D tabulated values and the calculated pressure loss coefficient using 1D result differ and the
latter is more close to the chart data.
There are large discrepancies found comparing the 1D tabulated coefficients and calculated values
using 3D data. To see if the 1D code perhaps overestimates the loss coefficient of a bend to
include the losses connected to the downstream pipe, the total loss coefficient of the bend plus 1
diameter of the pipe downstream of it, is calculated in 3D and displayed in the diagram, Figure 24.
Not even by including the losses one diameter downstream of the bend gives good agreement
between 1D and 3D results. Experimental observations by [43] on circular cross sectional 90°
bends show that the distribution of losses in the bend and its outlet pipe, for a radius of curvature
between 0.8 and 1.5, about 80% of all the losses occur in the bend and the first 2 pipe diameters
downstream of the bend outlet. As the bend angle is reduced below 90° the percentage of the total
loss occurs in the downstream pipe. For a 45° bend with a radius of curvature below 3, as much as
50% of the loss is connected to the downstream pipe.
It is not understood why the loss coefficients from performance chart data and 3D calculated result
differ that much. As mentioned it is not known how the measurements on the pipe bends were
performed and measurements on the same geometries as those being modeled in 1D and 3D is
needed to validate the simulation results for a deeper analysis (hopefully to be included in the
continuing work). Perhaps the loss coefficient calculations are not appropriate to use directly on
65
3D data because of the averaging process of the flow variables that must be carried out at the
cross-sectional planes at the bend inlet and outlet where the flow has a skewed velocity profile and
strong secondary flow.
The results for the loss coefficients for the two bends of Case 5, bend 1 and 2, is shown in Figure
25 .
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 2Bend nr [-]
Loss
coe
ffici
ent [
-]
1D calc from data
1D tabulated
3D bend inlet to bend outlet
3D bend inlet to 1d ds bendoutlet
Bend performance chart
Figure 25 Calculated loss coefficients for the 2 bends of geometry 5 using 1D and 3D data, the 3D case even for including
the losses up to 1 diameter of the downstream connected pipe. Tabulated loss coefficients used in the 1D simulation are
also displayed together with estimated values of the loss coefficients from using bend performance charts based on
experiments by [43].
The 1D code’s tabulated value for the loss coefficient of the second bend is lower compared to
that of the first bend, whereas the 3D results shows a small increase of the loss coefficient of the
second bend compared to the first. In the 1D simulation the velocity profile into the second bend
is identical to the one entering the first bend, no bend interactions are considered. This explains the
lower pressure drop for the second bend due to the larger radius of curvature compared to the first
bend. In the CFD simulation it is shown that the flow into to the second bend is not identical to
the inlet of the first bend and the velocity profile is asymmetric, Figure 19. The performance charts
result shows the same effect, that the loss over the second bend is higher than the first. This is
without using available correction factors on the loss coefficient for bend-bend interactions, only
66
for inlet and outlet pipe length which is different in this case. Interactions between two bends
occur if a second bend is located in the flow redevelopment region downstream of the first bend
and then the loss connected to that region is decreased. Also the velocity profile in the
redevelopment region is different to that of an isolated bend which will affect the second bend.
Direct interaction between two bends can both have the effect of decreasing and increasing the
pressure loss compared to isolated pipes [43].
Investigating the different terms in the expression for the pressure loss coefficient the same trends
are shown for the 1D and 3D computations except for the total pressure at the outlet of the
second bend. It is the dynamic pressure contribution to the total pressure at the outlet of the
second bend that gives the different results for the second bend of Case 5:
Figure 26 The dynamic pressure (multiplied by a factor 2) at the first and second bend outlet of Case 5.
The dynamic pressure in STAR-CD is calculated using the three components of the velocity vector
and it as the area averaged value over the section upstream/downstream of the bend. Mass
averaged values are used in the calculations displayed in Figure 24 and Figure 25 and they had a
little affect on the calculated loss coefficient. Even though the exact levels are not the same for the
1D and CFD, Figure 26 shows that the dynamic pressure shows the same “trend” at the bend inlet
and also at the outlet for the single bent geometries. The CFD results for the double bent pipe
67
show that the dynamic pressure at the outlet of the second bend is higher compared to the first
bend, a result that is contradictory to what the 1D results show.
One of the causes to the discrepancies between the calculated pressure gradient using 1D or 3D
CFD calculations is assumed to be secondary flow effects as they are not accounted for in the 1D
code, yet corrected for. The strength of the secondary flow close to the inlet and the outlet of the
bends to Cases 2, 3, 4, and 5 are calculated according to 222
22
wvuvu++
+ and are plotted in Figure
27.
Figure 27 Strength of secondary flow upstream and downstream of bends to Cases 2-5.
The strength of the secondary flow along the inlet to the various bends (left figure) is more or less
equal for all the cases except for the inlet to the second bend of Case 5 which is much higher. A
slight increase for a larger degree of bend is seen. The results are more spread along the outlet to
the bends (right figure) but still the strength of the secondary flow is higher for larger degree
bends. The secondary flow at the outlet to the second bend is shown to be much lower compared
to the outlet of the first 90 degree bend which in turn is more or less identical to the outlet of the
single 90 degree bend. The level of the secondary flow at the outlet to the second bend is even
lower than for the 60 bend case.
68
4.2.2.2 Pulsating flow
Case 5 in Table 1 is simulated with pulsating flow in both 1D and 3D. The mass flow rate at the
inlet boundary for the five computed engine cycles are shown below, the individual cycles are
displayed on top of each other:
Figure 28 Inlet boundary mass flow rate for each of the five engine cycles run, the individual cycles are laid on top of each
other.
The mass flow rate is imposed by providing boundary values for the inlet density and the inlet
velocity. The imposed velocity profile is fully turbulent and is a function of radius and time
according to Figure 29.
Figure 29 The inlet boundary normal velocity component as a function of radius and time given at the inlet boundary to
Case 5 for the pulsating flow case.
69
The Reynolds values are up to 70000 during the pulse. The results for the pulsating flow case is
presented in Figure 30 and Figure 31 where the secondary flow at sections immediately
downstream of the first and second bend is plotted at 4 different times during the pulse. To get a
better picture of the magnitude of the axial velocity the secondary flow is here defined
as2
22
wvu + .
Figure 30 The strength of the secondary flow at the first bend’s outlet at 4 different times during the pulse. These time
steps correspond to low (upper left), medium (upper right), high (lower left) and again low (lower right) mean axial
velocity.
70
The upper part of the planes depicted in the figure correspond the outer curvature of the bend and
the lower part the inner curvature. The secondary flow is less pronounced in regions where the axial
velocity is higher (having the C-shaped velocity profile out of the first bend in mind). At the outlet to
the second bend the results look somewhat different, Figure 31.
Figure 31 The relative strength of the secondary flow at second bend outlet at 4 different times during the pulse.
As was noted for the steady-state flow of Case 5 (Figure 27), the strength of the secondary flow
both upstream and downstream of the two bends is different from each other. With pulsating flow
the strength of the secondary flow is weaker downstream of the second bend compared to
downstream of the first bend. The upper part of the cross-section is the outer curvature and the
high velocity region is rotated to the right as compared to the first bend, Figure 27.
71
4.2.2.2.1 Full CFD results compared to 1D
To compare the results of the pulsating flow using 1D and CFD computations, the instantaneous
values of the calculated pressure drop over the two bends of Case 5 is plotted in Figure 32. The
mean axial velocity at the respective bend inlet is also displayed.
Figure 32 A comparison between the simulated instantaneous pressure drop over the first bend (left) and the second bend
(right) of Case 5 using 1D and CFD calculations. The axial velocity at the two bend inlets is shown as well (right y-axis in
the two plots).
As for the steady-state flow case, the 1D code estimates a higher pressure drop over each of the
two bends compared to the CFD code. The discrepancies between the 1D and CFD results are a
somewhat larger for the first bend.
4.2.3 Exhaust manifold
4.2.3.1 Steady flow
The exhaust manifold of the engine that has been analyzed both by on-engine measurements in
test cell and by 1D engine simulations will be studied with the aid of CFD computations. The
exhaust manifold geometry that we consider is shown in Figure 33:
72
Figure 33 The exhaust manifold geometry.
The exhaust manifold consists of two separate parts. They do not join before the turbine inlet. For
simplicity a first study was made only considering the two outer runners, the primary exhaust pipes
of cylinders 1 and 4. The mass flow rate was imposed at the two inlets and a constant pressure was
set at the outlet. The mass flow rate was 0.046 kg/s at one inlet and almost zero at the other, by
imposing the velocities and densities given at the boundaries. The corresponding Reynolds number
is about 90000. The outlet pressure was set to atmospheric pressure and the walls were considered
to be smooth and adiabatic.
A plug-flow profile was set at the inlet boundaries to the extension volumes added to the original
geometry. The computational domain was extended with the aim of allowing the flow to develop
naturally from the inlet; however, the extended inlets were not long enough to produce a fully
developed turbulent velocity profile at the original geometry’s inlet. Similar extension of the outlet
section was aimed at avoiding the formation of a separation bubble that extends up to the outlet
boundary. It has to be noted that such a separation bubble is formed due to the strong bend of the
exhaust manifold ahead of the inlet to the turbine. Separation of the flow gives flow losses due to
large scale mixing spreading through the main flow and results in a drop in total pressure. The
static pressure at a section across the computational domain is shown in Figure 34.
73
Figure 34 The absolute static pressure distribution (Pa) at a section across the outer exhaust runners.
There are large pressure variations across the right bend which is connected to cylinder 1. The
bend is about 75° and counter rotating vortices are seen downstream of the bend. At the outlet,
downstream of the junction joining the two pipes, the secondary flow structure is a swirling
motion. The axial velocity component is also very asymmetric, Figure 35.
Figure 35 Flow structure at the original outlet of the junction joining the outer runners to cylinders 1 and 4 (the CFD
domain outlet is extended 120 mm downstream of the original geometry). The axial velocity is shown as a contour plot
and the secondary flow components as vectors.
74
The strength of the secondary flow is locally as or even larger than the axial velocity component,
which is seen in, Figure 36, showing the secondary flow at the junction of the exhaust pipes of
cylinders 1 and 4.
Figure 36 The strength of the secondary flow at the junction outlet of cylinders 1 and 4.
4.2.3.1.1 CFD results compared with 1D results
The outer runners of the exhaust manifold are modeled in 1D with the same constant inlet mass
flow rate and outlet pressure as for the CFD model. The walls are assumed to be smooth and
adiabatic.
The calculated pressure drop, from the inlet of the runner blowing with high velocity to the
junction outlet, is 20% lower in the 1D calculations compared to the CFD calculations. From
previous investigation of the pressure losses over the various bent geometries under steady-state
flow conditions it was expected that the pressure loss calculated by the 1D code would be larger as
compared to the CFD results. The fact that the opposite is true for this particular geometry may
depend on differences in the problem set-up. For example GT-Power assumes a fully turbulent
velocity profile which do account for additional frictional losses to the wall, but since a plug flow is
75
used in the CFD calculations, there are large initial pressure gradients as the turbulent flow
develops. In addition, the flow itself is poorly modeled in 1D. The CFD geometry has not circular
cross sectional shape which is assumed by the 1D code and correction factors have not been used
in this case to account for other shapes. Also the bend angle is not easy to account for (as shown in
this thesis above). Handling the junction in the 1D model is very intricate and it is done by ad-hoc
fixes.
The pressure drop over the runner from cylinder 4 with almost zero mass flow rate is again larger
in the 1D calculations as compared to the CFD calculations. Running the CFD model with a
turbulent velocity profile at the two inlets would answer the question if the profile has that
significant effect on the pressure losses or if it is the conversion of a complex geometry with bent
pipes, irregular cross sectional area and junctions that is the main problem.
4.2.3.2 Pulsating flow
For the simulation of pulsating flow through the outer runners of the exhaust manifold, inlet
boundary condition is extracted from 1D engine simulations at pipe components located upstream
of the manifold, Figure 37.
76
Figure 37 Inlet boundary conditions at the two outer primary pipes of the exhaust manifold, velocity, density, and
temperature profiles. They are extracted from 1D engine simulations at 1300 rpm and wide open throttle.
The imposed pressure at the outlet is also extracted from 1D simulation and is time-dependent.
The shape of the inlet velocity profile contains only a constant axial component (i.e. plug flow) and
the Reynolds number varies between 0 and 200000 during the pulse. The figure below (Figure 37)
shows a plot of the axial velocity together with secondary flow vectors for low, medium and high
mass flow rates at the junction outlet.
77
Figure 38 Velocity field at the junction outlet. Axial velocity is shown as a contour plot and secondary flow components as
vectors.
At very low mass flow rates the flow detaches from the wall and reverses during the cycle. Thus,
the outlet boundary becomes an inlet boundary and that the temperature and velocity must be
given in addition to the pressure at the outlet boundary (from the 1D simulation). This may give
rise to sudden temperature changes on the boundary as the temperature drop is not identical in the
two codes. This is since the temperature on the outlet boundary is calculated by STAR-CD for
positive outflow and it is imposed, using temperatures from GT-Power simulations, for reverse
flow situations. An improved method for imposing the outlet temperature is desirable. For very
low mass flow rates the flow is dominated by the in plane velocities and for medium and high mass
flow rates the main flow normal to the boundary has a secondary flow structure of swirling motion.
78
The strength of the secondary flow varies and is shown for medium and high mass flow rates in
Figure 39.
Figure 39 Strength of the secondary flow velocity for medium and high axial velocity.
4.2.3.2.1 Flow in manifold versus 1D
The results from comparing the 1D and CFD “overall pressure drop”, from the inlet of the
primary exhaust pipe of cylinder 1 to the outlet of the junction, during one engine cycle is plotted
in Figure 40.
Figure 40 Comparison between 1D and CFD calculated time resolved pressure difference across the manifold (primary
pipe connected to cylinder one and outlet to junction of cylinder 1 and cylinder 4) over one engine cycle.
79
The results from several cycles are displayed on top of each other and the ripples on the pressure
curve are due to the start-up transients (initial conditions) in the CFD calculations during the first
cycle. The pressure drop is larger in the 1D calculations as compared to the CFD calculations
during period of the pulse when it is blowing from the two cylinders.
4.3. Integrated 1D/3D simulations Some effort was made trying to perform a code coupling between the exhaust manifold modeled in
STAR-CD and the rest of the engine system modeled in GT-Power.
To start with there were difficulties even to get the two softwares to communicate. The first
succeeded coupled simulation was a tutorial from Gamma Technologies. An inlet manifold was
modeled in STAR-CD and a 4-cylinder aspirated engine was modeled in GT-Power.
In the continuing work a simple case with a straight pipe upstream of the compressor was modeled
in STAR-CD and coupled to the 1D engine model of the turbocharged engine calibrated in test
cell. Five coupled engine cycles were performed. The 1D result for the instantaneous static
pressure located at 1 diameter upstream of the connected CFD pipe (using values from the last
cycle in the continuously updated 1D model during the code coupling) is compared with the
pressure from the five consecutive cycles in the CFD calculations, Figure 41.
Figure 41 The instantaneous pressure for the last coupled cycle at a section in the 1D model located 1 diameter upstream of the CFD modeled pipe together with the instantaneous pressure from the individual cycles from the CFD calculations at the inlet boundary to the pipe.
80
The first coupled cycle shows start-up transients for the pressure calculated by the CFD code from
the provided 1D boundary values. The results from cycles 3 and 4 are identical and the results can
be considered “converged”. As only a straight pipe was modeled in STAR-CD and the 1D code is
already a good approximation of the flow through these geometries, no significant differences are
seen when comparing the results for the 1D simulation alone and the 1D/3D integrated solution.
Then some effort was made on trying to couple a 3D model of the outer runners of the exhaust
manifold to the same calibrated 1D model. Usually the 3D computation would run for some time
steps, but always terminating with negative densities. This can happen if the mesh is of poor
quality, the time steps used are too large or because of numerical instabilities. Also, the engine
operating condition was such that the part of the exhaust manifold modeled had reverse flow at the
outlet. Reverse flow at the outlet boundary of the CFD domain may have been one reason for not
being able to obtain converged results. As pointed out it is not self evident that the combined
scheme has a solution at all and if it has, the coupling procedure must be such that it is stable. No
attempt has been made to address these basic issues.
4.4. Experimental results The experimental tests are performed on a 4 cylinder 2-liters standard production turbocharged SI
engine from 2004.
4.4.1 Operating conditions
The engine was run in test cell with two different turbochargers. The waste gates were in both
cases mechanically closed to assure that there was no gas slipping through the by-pass valve, this
way an uncertainty in the calibration of the 1D model is avoided. A restriction is that the boost
pressure is limited at high engine speeds and the measured full load curve is only run up to 1500
rpm, plotted in Figure 42.
81
Figure 42 Measured full load curve showing the engine brake torque from 1000 rpm to 1500 rpm.
The operating points in Figure 42 were used to calibrate the 1D engine model. In addition to these
operating points used for model calibration other operating conditions spanning the low energy
region of the engine, various part load conditions up to an engine speed of 5000 rpm, have been
run in test cell.
4.4.2 Measurement accuracy
The fuel flow is measured with an AVL Fuel Balance 733s [8]. The fuel consumption is determined
gravimetrically using a weighing vessel and the fuel mass flow rate can be determined with an
accuracy of 0.5%. The air to fuel ratio (AFR) is measured with an ECM AFRecorder 2000 [11] and
can be determined to an accuracy of 0.6% at stoichiometric conditions. The steady-state air flow is
therefore accurate within 1.1%.
The gas temperature is measured using (shielded) 3 and 4 mm K-type thermocouples [12] with
different insertion lengths. It was concluded [1] that the temperature measured by a long inserted
radiation shielded thermocouple is quite accurately that of the mass averaged temperature. The
accuracy of class 1 type K thermocouples is the larger of 1.5˚ and 0.4% of the measured
temperature.
The gas pressure was measured at different locations on the engine. On the intake side GEMS 2200
series steel diaphragm gauge pressure transducers [13] were used and on the exhaust side piezo-
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resisitive Kistler transducers 4045 [14]. The accuracy of the former are 0.25 % FS and of the latter
0.1%.
Turbine speed is measured with a Micro-Epsilon eddy current probe mounted in the compressor
housing. The probe is sensitive to disturbances since it can be interpreted as a blade passage, giving
a much higher turbine speed over the respective logged time interval than its actual value. The
error is reinforced by the interpolation to crank angle basis made including these erroneous turbine
speed points. In this work every cycle showing this kind of disturbance are withdrawn from the
collected measured data to get good accuracy and average values over the cycles. The accuracy of
the measured turbine speed is difficult to determine. One way is to study the speed and
acceleration for each single cycle (of the 300 consecutive cycles that are logged) and how these
differ from the averaged value at the different crank angles for the analogues measuring points. For
TB1 at 1300 rpm (turbine speed of 93600 rpm) it results in a relative standard deviation of about
0.1 for the speed.
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5. Summary and Conclusions
5.1. 1D computations The unsteady on-engine turbine efficiency has been calculated at two operating points in the
engine’s low speed and load region. The calculations are based on high frequency measurements of
turbine inlet and outlet pressure together with turbine shaft speed and acceleration. Unfortunately
it was not possible to measure the exhaust temperature and mass flow rate on a crank angle
resolved basis, only cycle averaged values are available. Instantaneous values for the temperature
and mass flow rate used in the computations were extracted from a calibrated 1D engine model of
the engine.
The computed efficiencies are compared with simulated values assuming a quasi-steady behavior of
the turbocharger. The results show that:
o The on-engine turbocharger is not well described by steady flow data.
o The on-engine efficiency shows a hysteretic effect over the exhaust pulse so that the
discrepancy between measured and quasi-steady values increases for decreasing mass flow
rate after a pulse peak.
One uncertainty with the calculated efficiency value is that temperatures and mass flow rates are
simulated and not measured and thereby it contains all the modeling errors. Another shortcoming
is that no phasing of the different measured/simulated quantities has been used in the efficiency
calculations to compensate for that the measured extracted turbine power results from the state of
the gas upstream of the turbine at an earlier time. This phase shifting is not trivial as the
propagation of the different transient pulses through the volute is complex, a mix of acoustic and
convective transmission.
The flow through a straight pipe, three single bent pipe geometries and a double bent pipe
geometry have been computed under steady flow conditions (Re number of 36000) and also under
pulsating flow for the latter geometry (Re number between 0 and 200000) , using the full 3D code.
The pressure gradient over the straight pipe and also over the straight parts of the bent geometries
is about 20 kPa /mm. In the 1D model, the pressure loss over a bend is calculated as that of a
85
straight pipe with the addition of an empirical pressure loss coefficient to account for the additional
losses due to the curvature. Tabulated values from non-named references of steady flow
measurements on bent pipe geometries are used by the code.
The pressure loss coefficient is defined as the ratio between the difference in total pressure across
the bend and the upstream velocity/dynamic pressure. In addition to the used tabulated values, the
loss coefficient was also calculated for each of the bends. The 1D results show that:
For the single bent pipes:
o Tabulated and calculated values differ between 20-30% for the tested cases, the
latter always being the larger value of the two.
o As expected, the greater the angle of the bend, for the same radius of curvature,
the pressure loss coefficient increases.
For the double bent pipe:
o For the same angle of bend, the pressure loss coefficient is lower for the bend with
the larger radius of curvature.
Comparing 1D tabulated and calculated loss coefficient to data from performance charts by [43],
the results show that:
o 1D tabulated loss coefficient values are close to the basic coefficients not being
corrected for the actual Re number, compressible flow affects etc.
5.2. CFD computations The flow through the same bent geometries that were computed with 1D were also computed with
CFD, under steady flow conditions for the single bent pipes and under steady and pulsating flow
conditions for the double bent pipe. The flow field downstream of each bend shows that the
initially symmetric velocity profile becomes distorted, having a higher velocity at the continuation
of the outer curvature part of the bend. A secondary flow structure is developed over the bends
and consists of a pair of counter rotating vortices which strength is higher for increasing angle of
the bend.
The gradient of the average cross sectional pressure in the straight pipe is near 20 kPa/mm. For the
straight pipe sections of the bent geometries, downstream of the individual bends, the 3D
computations show that:
86
o The calculated pressure gradient is much higher compared to that of the straight
pipe geometry at the same conditions.
For the single 90 degree bend the value for the pressure gradient is as much as one order of
magnitude higher compared to the referenced straight pipe in the vicinity of the bend outlet. The
high pressure gradient decreases to the value corresponding to that of the straight pipe at about
one pipe diameter downstream of the bend outlet.
o The pressure gradient in the straight pipe part upstream of the bend is also affected by the
presence of a bend but to a lesser extent and only for a more limited distance upstream.
For the double bent pipe the 3D results show that:
o The pressure gradient after the second 90 degree bend is almost 50% higher compared to
the straight pipe still at several pipe diameters downstream.
The velocity field downstream of the second bend becomes even more asymmetric compared to
that after the first bend and the high velocity region is rotated. The secondary flow structure is a
swirling motion and the strength of it is lower compared to the strength of the in plane velocities
after the first bend.
For the pulsating flow case the peak of the secondary flow downstream of the two bends varies
during the pulse and reverse flow is seen close to the inner walls.
Steady and pulsating flow through the outer runners of the engine exhaust manifold was also
computed with CFD. (Re number of about 90 000 in the former case and between 0 and 200 000
in the latter). For both cases a plug flow profile was set at the inlet and the velocity profile had not
time to become fully developed. This will have an effect on the pressure drop over the geometry
compared to using a fully developed velocity profile. For the pulsating flow case boundary values
from 1D simulations of the engine operating at 1300 rpm and full load conditions are used.
o The flow structures resemble to those of the double bent pipe which is expected due to the
geometry of the manifold.
87
Counter rotating vortices are formed after the first curvature (~ 75 °) and a swirling motion is
developed after the second turn where the two runners join. At the original geometry outlet the
strength of the secondary flow structure is locally even larger than the axial velocity component.
The latter of which is also very asymmetric. For the pulsating flow case it was shown that:
o During time of the pulse with very low mass flow rate the flow detaches from the wall and
reverses, both at the inlets and the outlet boundaries.
A better way of imposing the temperature at the junction outlet for times of reverse flow must be
performed, and also to set a fully developed turbulent profile at the inlet for better comparison
with the 1D results.
5.3. Comparison of 1D and 3D computations o The calculated pressure gradient for a straight pipe under steady flow conditions is similar
using either the 1D or CFD computational tool.
o There is a clear deviation between the 3D and 1D result near the bends and up to about
one diameter upstream and downstream of the bends. It seems that one can compensate
for the losses in the bent to some extent (e.g. steady flow) but it is difficult to make such a
compensation for general flows and geometries.
The pressure gradient in the 1D calculation is well predicted for a straight pipe whereas the
pressure gradient in the CFD calculations is larger than that for the 1D model in a straight pipe
close to a bend. This discrepancy is higher downstream of the bend compared to that upstream,
due to the slow decay of the secondary flow in the downstream direction. The difference between
the 1D and CFD computed pressure gradient in the straight part joining the two bends of the
double bent pipe is especially high; by as much as 50% larger in the CFD calculations.
For the various bends of the computed geometries the pressure loss coefficient from 1D and CFD
calculations is compared instead for the local pressure gradient.
o The calculated pressure loss coefficient for each individual bend of the single bent
geometries is always much higher for the 1D computation compared to the CFD
computation.
88
There may be many factors acting to give the large discrepancies between the 1D and the 3D
results, only possible reasons can be stated since no measurements have been performed on the
studied cases for validation. What differs between the two ways of modeling the flow is that the 1D
code does not model secondary flow or turbulence. Both contributes to flow losses and the 1D
code has to rely on empirical loss coefficients, from steady flow measurements performed on
perhaps not identical geometries and/or at the same flow conditions.
The pressure loss coefficient calculated by the two codes shows the same trend with increasing
value for an increasing angle of the bend. However, for the double bent pipe the result goes in
opposite direction.
o The pressure loss coefficient for the second bend of the double bent pipe calculated by the
1D code is lower compared to the first bend and the vice versa is true for the CFD code.
The discrepancy can be related to the difference in calculated dynamic pressure downstream of the
second bend. This is the effect due to the distorted flow into the second bend. Thus, it is difficult
to have a simple model to account for a sequence of bends in a 1D code.
89
90
6. Future work
To continue the work presented in this thesis it will be natural to analyze the behavior of the 1D
model in handling a junction geometry. The flow in such junctions can hardly be assumed to be
1D. Additionally, the flow is expected to depend on the geometrical details upstream of the
junction, in addition to the inlet flow profile and its frequency (and the periodicity of the flow) The
future analysis shall be for both steady and pulsating flow conditions so as to assess effects of the
flow unsteadiness. The comparison of the 1D to the 3D results and the projection of the 3D result
on the 1D model could be useful hopefully to introduce improvements in the 1D model. The
computed results are also to be compared to quantitative experimental wherever these are available.
91
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7. Acknowledgement
First of all I would like to acknowledge the Swedish National Energy Administration, STEM, for
financing this project.
I want to thank my supervisor Professor Hans-Erik Ångström for the support and for being
available for discussions and comments on the work at all times.
I would also like to thank my co-supervisor Professor Laszlo Fuchs for guidance during the project
and for sharing the knowledge in the fields of numerical computations to which I am quite new.
Fredrik Westin, thank you for thoroughly reading my thesis. The questions and comments on the
work were very valuable.
GM Powertrain Sweden AB is acknowledged for material support.
Börje Grandin, former employee at GM Powertrain Sweden AB, thank you for all the ideas
concerning my project (there were many in the beginning!) and for emphasizing the importance of,
on a daily basis, reminding yourself on the project’s goals to assure you are heading in the right
direction.
Thanks to you all, colleagues at KTH. I understand now that I have learnt a lot from the constant
discussions concerning engines.
I would also like to thank my mother for all the help with the children- you made it possible to
combine work and family!
Finally, but not the least, I would like to thank Jonas for all love and also our three children for the
patience they have shown throughout my years at KTH. I figure it cannot have been that bad in
the end as they say they will all study at KTH when they get older…
Stockholm, August 2008
Ulrica Renberg
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8. Nomenclature
κ : Mean ratio of specific heat for gas temperatures over turbine [-]
κ : Ratio of specific heat [-]
ρ : Density [kg/m3]
isρ : Density at the throat [kg/m3]
0ρ : Upstream stagnation density [kg/m3]
ijδ : Kronecker delta function,
TSη : Total-to-static turbine efficiency [-]
mechη :Turbine mechanical efficiency [-]
ip ,3Δ : Difference between instantaneous maximum and minimum pressure at turbine inlet [-]
ijτ : Viscous shear stress [N/m2]
ijΠ : Stress tensor consisting of normal stresses and shearing stresses applied on a fluid element
μ : Dynamic viscosity [kg/ms]
υ : Kinematic viscosity [m2/s]
Tυ : Turbulent viscosity [m2/s]
A : Cross-sectional flow area [m2]
AAV: Area averaged data
95
totA Heat transfer surface area [m2]
effA : Efficient flow area [m2]
RA : Reference flow area [m2]
BMEP: Break Mean Effective Pressure [Pa]
CAD: Crank angle degree [°]
DC : Discharge coefficient [-]
Cf: Skin friction coefficient [-]
Cf,s: Instantaneous friction factor using correlation for steady flow [-]
34,pC : Mean specific heat capacity for gas temperatures over turbine [J/kgK]
34,pC : Mean specific heat capacity for gas temperatures over turbine [J/kgK]
Cp the pressure loss coefficient [-]
Cs: Gas flow velocity after isentropic expansion through an ideal nozzle [m/s]
c: Speed of sound [m/s]
D: Pipe diameter [m]
e: internal energy [J/kg]
f: Friction factor [-]
if : Body force [N]
Funst : Instantaneous unsteady friction factor [-]
h : Specific enthalpy [J/kg]
96
hg: Heat transfer coefficient [J/m2Ks]
hr: Roughness height [m]
rotorJ :Turbine shaft moment of inertia [kgm2]
pK : Pulsation factor [-]
tk : Coefficient of thermal conductivity [J/mKs]
LES : Large Eddy Simulation
airm& : Air mass flow rate [kg/s]
exhm& : Exhaust mass flow rate [kg/s]
aexh,m& : Exhaust mass flow rate at turbine inner volute entry [kg/s]
bexh,m& : Exhaust mass flow rate at turbine outer volute entry [kg/s]
m& : Mass flow rate [kg/s]
MAV: Mass averaged data
Mconst: Constant global friction multiplier [-]
Munst : Global unsteady friction multiplier [-]
tcN :Turbine shaft rotational speed [rpm]
accP :Turbo shaft acceleration power [W]
comprP :Compressor power [W]
extrP :Extracted power [W]
97
isentrP :Maximum power for isentroic expansion through the turbine [W]
atmP : Atmospheric pressure [Pa]
totp : Total pressure [Pa]
RP Absolute pressure ratio, the static outlet pressure divided by the total inlet pressure [-]
03P : Turbine total inlet pressure [Pa]
a03,P Total pressure at turbine inner volute entry [Pa]
b03,P Total pressure at turbine outer volute entry [Pa]
4P : Turbine static outlet pressure [Pa]
i3,P : Turbine instantaneous pressure [Pa]
m3,P : Average turbine inlet pressure [Pa]
p : Pressure [N/m2]
q : Heat flux [J/m2 s]
Q& : Heat source [J/s]
R: The gas constant [J/kgK]
ijS : The “mean strain”.
cellloadTQ : Mean torque [Nm]
T : Temperature [K]
Twall: Wall temperature [K]
98
0T : Upstream stagnation temperature [K]
01T : Compressor inlet total temperature [K]
02T : Compressor total outlet temperature [K]
03T : Turbine total inlet temperature [K]
a03,T : Total temperature at turbine inner volute entry [K]
b03,T : Total temperature at turbine outer volute entry [K]
4T : Turbine static outlet temperature [K]
i3,T : Turbine inlet instantaneous temperature [K]
mT ,3 : Average turbine inlet temperature [K]
t : Time [s]
U: Velocity vector [m/s]
isU : Isentropic velocity at the throat [m/s]
Ur : Rotor tip speed [m/s]
U : Velocity vector for the mean flow [m/s]
u′ : Fluctuating velocity component vector [m/s]
321 u,u,u : Components of the velocity vector [m/s]
u: Mean axial velocity [m/s]
99
V : Volume [m3]
VGT: Variable Geometry Turbine
extW& : External work [J/s]
X : The position coordinate vector
321 x,x,x : Position coordinates
100
9. References
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Institute of Technology, Stockholm
2. WATSON N. AND JANOTA M.S. 1982 Turbocharging the internal combustion engine MacMillan Press
ISBN 0-933283-10-5
3. DALE A. AND WATSON N. 1986 Vaneless radial turbocharger turbine performance IMechE Paper no.
C110/86
4. BAINES N. C. Turbocharging the Internal Combustion Engine 2004 Concepts NREC
5. DALE A. AND WATSON N. 1988 The development of a turbocharger turbine test facility IMechE Paper
6. www.ueidaq.com
7. www.adlinktech.com
8. www.avl.com
9. www.micro-epsilon.de
10. ARNÉR M. Mätosäkerhet, kalibrering, felfortplantning och R&R studier 2002 Studentlitteratur ISBN
9789144041032
11. www.ecm-co.com
12. www.pentronic.se
13. www.gemssensors.com
14. www.kistler.com
15. EHRLICH D. A. 1998 Characterization of unsteady on-engine turbocharger turbine performance Doctoral
Thesis, Purdue University
16. WINTERBONE D.E. AND PEARSON R.J. 1998 Turbocharger turbine performance under unsteady flow-a
review of experimental results and proposed models IMechE Paper no. C554/031/98
17. CAPOBIANCO M. MARELLI S. 2007 Waste-gate turbocharging control on automotive SI engines: effect
on steady and unsteady turbine performance SAE Paper no. 2007-01-3543
18. CAPOBIANCO M. MARELLI S. 2007 Unsteady-flow turbine performance in turbocharged automotive
engines EAEC Conference Paper
19. CAPOBIANCO M. MARELLI S. 2006 Unsteady flow behavior of the turbocharging circuit in downsized SI
automotive engines FISITA Paper no. F2006P119
20. IWASAKI M., IKEYA N., MARUTANI Y., KITAZAWA T. 1994 Comparison of turbocharger
performance between steady flow and pulsating flow on engines SAE Paper no. 940839
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characterization SAE Paper no. 971565
22. RIEGLER U. AND BARGENDE M. 2002 Direct Coupled 1D/3D-CFD-Computation of the Flow in the
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0901
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23. BORGHI M., MATTARELLI E., L. MONTORSI L. 2001 Integration of 3D-CFD and Engine Cycle
Simulations: Application to an Intake Plenum SAE Paper no. 2001-01-2512
24. SINCLAIR R., STRAUSS T., SCHINDLER P. 2000 Code Coupling, a new Approach to Enhance CFD
Analysis of Engines SAE Paper no. 2000-01-0660
25. PEARSON R. J., WINTERBONE D. E., BASSETT M. D. 1999 Multi-Dimensional Wave Propagation in
Pipe Junction SAE Paper no. 1999-01-0213
26. COSTALL A. 2008 A one-dimensional study of unsteady wave propagation in turbocharger turbines Doctoral
Thesis, Imperial College, London
27. GROSE D. AND AUSTIN K. 2001 Coupling of One Dimensional and Three Dimensional Simulation
Models SAE Paper no. 2001-01-1770
28. HELLSTRÖM F. 2008 Numerical computations of the unsteady flow in a radial turbine Licentiate Thesis,
Royal Institute of Technology, Stockholm
29. RENBERG U. Instantaneous 2006 On-Engine Turbine Efficiency for an SI engine in the closed waste gate
region for 2 different turbochargers SAE Paper no. 2006-01-3389
30. LAM J. K.-W., ROBERTS Q. D. H., McDONELL G. T. 2002 Flow modeling of a turbocharger turbine
under pulsating flow IMechE Paper no. C602/025/2002
31. WALLACE F. J., BLAIR G. 1965 Performance of inward radial flow turbines under unsteady flow
conditions Proc.Instn.Mech.Engrs,Vol.184
32. WINTERBONE D. E., NIKOPOUR B., FROST H. 1991 A contribution to the understanding of
turbocharger turbine performance in pulsating flow IMechE Paper no. C433/011
33. KATSUYUKI O.,HIGASHIMORI H., MIKOGAMI T. 2002 Study on the Internal Flow of a radial Turbine
rotating blades for automotive turbochargers SAE Paper no. 2002-01-0856.
34. YEO J. H., BAINES N. C. 1990 Pulsating flow behavior in a twin-entry vaneless radial-inflow turbine IMechE
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inflow turbines IMechE Paper no. C484/006/94
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37. KARAMANIS N., MARTINEZ-BOTAS R. F., SU C. C. 2001 Mixed flow turbines: Inlet and exit flow under
steady and pulsating conditions ASME Journal of Turbomachinary, Vol. 123
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102
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103
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10.Appendix
Incompressible flow For incompressible flow, a component’s loss coefficient is defined as the non-dimensional
difference in total pressure between its two ends. To non-dimensionalize the pressure loss, the
convention is to use the component’s inlet velocity pressure, 2Uρ21
⋅⋅ .
The loss coefficient K is then given by:
2UρΔPK 2⋅
= (A1)
where ΔP is the difference in total pressure [Pa] over the component, ρ is the density [kg/m3] and
U is the mean upstream velocity [m/s].
To establish a loss coefficient it is important to have a long inlet and outlet pipe before the
component so that the friction gradient has time to develop before the component and that the
losses caused by flow redevelopment after the component are debited to the component.
Bend loss coefficients Kb vary with surface roughness, with connected pipe arrangements but to an
ever greater extent with Re. A basic loss coefficient K*b is defined at a Reynolds number of 106
(because many industrial flow systems operate at those Reynolds number) for bends with long and
smooth inlet and outlet pipes.
Correction factors can be applied to these basic loss coefficients to account for other Re, outlet
pipe length and surface roughness. When a bend is located close to another component,
corrections can be made for the interactions.
The corrected bend loss coefficient Kb is given by:
f0RE*bb CCCKK ⋅⋅⋅= (A2)
105
Kb* is the basic loss coefficient defined at a Reynolds number of 106 for bends with long and
hydraulically smooth inlet and outlet pipes or passages.
CRE is the Reynolds number correction
C0 outlet pipe length correction
Cf is the roughness correction factor
Compressible flow For the incompressible flow case the pressure loss coefficient was defined by non-dimensionalizing
the total pressure difference across a component by the velocity pressure. For the compressible
flow case the total pressure difference is instead non-dimensionalized using the dynamic pressure.
The dynamic pressure tends to the velocity pressure as the Mach number approaches zero. The
compressible total loss coefficient Kc is given by:
1t
ttc pp
ppK
1
21
−
−= (A3)
where pt1 and pt2 is the total pressure at the upstream and downstream location of the component
respectively, p1 is the static pressure upstream.
A chart diagram plots the ratio between the dynamic pressure and the velocity pressure as a
function of the Mach number. Ki can den be calculated using the chart value and the relation for
the incompressible total loss coefficient Ki:
2Uρ
ppK 2
tti
21
⋅
−= (A4)
106
