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Effect of inter-stage phenomena on the performance
prediction of two-stage turbocharging systems
Authors:
Calogero Avola a +, Colin Copeland a, Richard Burke a and Chris Brace a
a Department of Mechanical Engineering, University of Bath, Claverton Down, Bath BA1 2PB, UK
Corresponding Author:
Calogero Avola+ Email address: [email protected]
AbstractThe paper analyses the influence of aero-thermal inter-stage phenomena on the
performance prediction of two-stage sequential turbocharging systems. A novel methodology to
measure performance of two-stage turbocharging systems into equivalent maps has been
implemented and detailed. Investigation of a two-stage sequential turbocharging system has been
performed in a steady turbocharger gas-stand, obtaining thermodynamic properties of the complete
turbocharging system. The measurement of equivalent maps and the combination of stand-alone HP
and LP turbochargers maps have led to the quantification of inter-stage effects and the influence on
performance predictions of the two-stage systems.
In this study, equivalent two-stage and combined HP and LP stand-alone maps are compared
in order to quantify the variation of performance affecting the two-stage system. Specifically, a
simplified 1D model of the two-stage system flow path is developed for the investigation. In order to
quantify the influence of inter-stage effects, heat correction of the diabatic compressor and turbine
maps has been implemented. In conclusion, in comparison to equivalent two-stage maps, combined
stand-alone maps predict a significantly higher pressure ratio and efficiency for the compressor
system at conditions of low equivalent speed, while the turbine net efficiency is missed by about
10% at elevated corrected mass flow operations.
Keywords: Two-stage; Turbocharger; Compressor; Turbine; Equivalent map; Heat transfer;
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Nomenclaturem Mass flow rate [Kg/s]
1D One-dimensional
app Apparent
c Compressor
CBP Compressor By-Pass
corr Corrected
eff Effective
EGR Exhaust Gas Recirculation
eq Equivalent
HP High Pressure
in Inlet
is Isentropic
LP Low Pressure
MAF Mass Air Flow
N Speed [rpm]
NA Not Available
P Pressure
PR Pressure ratio
PRT Platinum Resistance Temperature
Q Specific mass flow heat [KJ/Kg]
ref Reference
s Static
T Temperature
T Total
t Turbine
TBP Turbine By-Pass
TC Thermocouple
TIT Turbine Inlet Temperature
T-s Total-to-static
T-T Total-to-Total
VGT Variable Geometry Turbine
WC Water-cooling
γ Ratio of specific heats
η Efficiency
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1. IntroductionThe increasing demand for cleaner automobiles is leading the efficiency improvement and
harmful emissions reduction of internal combustion engines with the adoption of key strategies,
such as high pressure (HP) and low pressure (LP) exhaust gas recirculation (EGR) [1, 2], turbocharging
approaches [3] and waste heat recovery solutions [4]. Furthermore, the reduction of engine swept
volume and number of cylinders is able to improve thermal efficiency of internal combustion
engines, through the decimation of friction losses [5]. Therefore, the adoption of boosting
technologies is a necessary action to restore rated power of downsized internal combustion engines
at steady [6] and transient [7] operations. In this scenario, two-stage turbocharging systems are able
to impact positively on the engine pumping losses [8] and powertrain system flexibility [9]. In fact,
the choice of a two-stage system results in a wider flow range operation, generating high levels of
boost at every engine speed, as the maximum pressure ratio is not delivered by a single
turbocharger [10]. In this way, reduction of mechanical and thermal stresses on the single
turbocharger is reduces [11]. However, two-stage turbocharging systems lead to a rise of system
complexity in regards to powertrain control [12].
In these boosting technology, high pressure (HP) and low pressure (LP) turbochargers are
connected sequentially and regulated via by-pass valves [13]. In fact, exhaust gases of the internal
combustion engine are ingested by the HP turbine, incurring a first expansion phase, and the LP
turbine, being subjected to the last expansion phase. As well as turbines, the air is compressed
sequentially by LP (high mass flow and rotating inertia) and HP (low mass flow and rotating inertia)
compressors. In conditions of elevated engine speed, exhaust flow is diverted away from the HP
turbine inlet through the turbine by-pass (TBP) valve, in order to expand exhaust gasses in LP turbine
and reduce engine back-pressure. Additionally, the HP compressor by-pass (CBP) valve is activated at
high mass flows to avoid choking of the HP compressor and performance disruption of the two-stage
system. Furthermore, the sequence of HP and LP turbochargers can generate aero-thermal effects,
causing a variation of performance maps of two-stage systems [14].
Analysis of turbochargers performance in two-stage regulated systems has stated that
performance changes in high pressure (HP) compressor and low pressure (LP) turbine can occur [15].
Specifically, reduction of swallowing capacity and pressure ratio of LP turbine and HP compressor,
respectively, can be recorded in comparison to the stand-alone maps. Moreover, LP turbine and HP
compressor are seemed to deliver lower efficiencies in two-stage regulated systems [15]. In this
scenario, it is important to focus on the cause of performance distortion of the turbomachine in
sequential systems. In fact, the presence of complex ducting geometries at the inlet of HP and LP
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compressors causes a variation of the performance map measured with straight ducts as in gas-
stands [16, 17]. In the case of radial turbines, swirling flows generated at the HP turbine outlet cause
vortexes at the LP turbine inlet, resulting in a variation of LP turbine efficiency [18]. As well as
turbines, the presence of pre-whirl can distort pressure ratio and efficiency of compressors in two-
stage systems [19]. Additionally, in diabatic operations of the two-stage system, heat transfer from
turbines to compressors influences thermodynamic boundary conditions of the turbomachinery [20,
21].
The performance evaluation of two-stage turbocharging systems in equivalent maps has
reduced the inaccuracy of performance data, particularly, at low loads [22]. In addition, thermal
effects at inter-stage ducts due to intercooling and heat transfer can be incorporated in the
equivalent map. In this scenario, equivalent performance variables for compressor and turbine
systems would have to be considered, as well as, an equivalent two-stage speed term [23]. In this
paper, the focus is on the variation of turbochargers performance in two-stage turbocharging
systems. Equivalent maps of a regulated two-stage turbocharging system are measured in a steady
turbocharger gas-stand, in order to account for inter-stage phenomena and performance variations
of HP compressor and LP turbine. Subsequently, stand-alone maps of HP and LP turbochargers are
measured and combined in order to quantify the inter-stage effects and the influence on the two-
stage system performance. In order to diversify flow motions and heat transfer effects, internal heat
transfer in turbocharger is evaluated through adiabatic and diabatic operations of the two stand-
alone turbochargers with a turbine inlet temperature (TIT) of 773K. Furthermore, the presence of a
water-cooling loop at the LP compressor is analysed and influences on two-stage system is
investigated through the implementation of maps corrections.
2. Experimental setting
2.1 Steady turbocharger gas-standIn order to quantify the performance of HP and LP turbochargers in stand-alone and
equivalent two-stage system configurations, experiments on a specifically built steady turbocharger
gas-stand have been performed. In this scenario, performance maps for compressors and turbines
can be generated through the monitoring of mass flow rates, pressure and temperature of air path
in compressors and turbines. In addition, the turbocharger gas-stand is equipped with eddy current
sensors for evaluating rotational speeds at the compressor casing. In order to investigate adiabatic
and diabatic operations, the turbocharger gas-stand of figure 1 is able to generate hot and
pressurised steady flows at the turbine inlet, due to the presence of two 44KW electric heaters
(element 9 of figure 1) and a 7bar pressurised air source controlled via a regulator (element 2 of
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figure 1). In addition, the facility consists of separate ducting systems for compressor and turbine
sides. In order to perform experiments on the turbocharger, load on the compressor is controlled
through a back-pressure valve (element 13 of figure 1). Due to lubrication and, in the case of the LP
stage, cooling requirements of turbochargers, oil (element 15 of figure 1) and water-cooling
(element 16 of figure 1) control units are available, maintaining the loops at the desired temperature
and pressure.
Figure 1. Steady turbocharger gas-stand for investigating automotive turbochargers
SENSOR RANGE ACCURACY
PRT -50 to +200 degC ±0.3 + 0.005*T
1.5mm K type TC -200 to 1260 degC 0.0075*T
V-cone mass flow 0 to 1200 Kg/h ±0.5%
Pressure 0 barA to 6 barA 0.25%
Turbo speed 0 to 400,000 rpm 0.1%
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Table 1. List of sensors adopted in the steady turbocharger gas-stand, including measuring range and
accuracy. Response and sampling frequency is not reported due to steady state tests being
performed
Compressor and turbine performance maps are generated, as pressure, temperature, mass
flow and speed of the turbomachine are measured with sensors listed in table 1. The positioning of
the sensors in the turbocharger gas-stand has been performed accordingly to ASME [24] and SAE
standards [25, 26]. Specifically, pressure is measured through a transducer monitoring conditions at
four points along a radial section of the duct, as in figure 2a, in order to reduce obtain an averaged
value across the single section of the duct. A similar approach is applied for the temperature
estimation. At compressor inlet, depths of two platinum resistance temperature (PRT) sensors are
oppositely positioned at 1/3 of the duct diameter, while, four PRTs are placed at 1/4, 1/3 and 1/2 of
the diameter at the compressor outlet, as in figure 2b. As well as the compressor, turbine inlet and
outlet temperatures are measured through four thermocouples positioned in a similar way as
represented in figure 2b. Importantly, in the case of PRT sensors, the presence of a long sensing
element at the PRT sensor tip (up to 20mm for PRTs with 150mm long steam) brings to slightly
deeper protrusion of sensor tip within the flow, when compared to K-type thermocouples with
sensing elements in the order of few millimetres.
Figure 2. Pressure measurement at four radial positions of a measurement section (a) and
temperature measurement at four radial positions of a measurement section with sensors tips
placed at 1/4, 1/3 and 1/2 of the diameter (b)
The turbocharger speed is monitored through Eddy current sensors, counting the passing of
compressor blades. Moreover, in the experimental investigation, temperature of lubricating oil is
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controlled downstream of the bearing housing at about 360K, maintaining a pressure of about 2.4-
3bar varying directly with the turbocharger speed. In case of water-cooled LP compressor housing, a
temperature of 360K is controlled downstream the compressor with a water flow of 10l/min. it is
important to notice that the measuring sections in the gas-stand are fully insulated to avoid heat
transfer between the flow and test cell ambient, introducing errors in the estimation of compression
and expansion efficiencies [27].
2.2 Full two-stage system and stand-alone turbochargersIn order to perform the study, a two-stage sequential turbocharging system with regulating
valves has been experimentally investigated. In this system layout, HP and LP turbochargers are
connected in series with compressor by-pass (CBP) and turbine by-pass (TBP) valves controlling the
operation across a vast range of mass flows through compressors and turbines. In fact, the two
turbochargers have different sizes in order to be able to generate elevated levels of boost at low and
high mass flow rates. Specifically, as in table 2, HP and LP compressors have wheel diameters of
approximately 35cm and 60cm, respectively. Clearly, in figure 3, pressure at point 3 is varied in order
to control the expansion ratio in the turbine stages. Meanwhile, load at HP and LP compressors is
generated though a back-pressure valve at point 2 in the turbocharger gas-stand.
Compressor size Turbine size Maximum speed VGT position
HP stage 34cm 36cm 260Krpm 50% shut
LP stage 60cm 47cm 186Krpm 50% shut
Table 2. Characteristics of HP and LP turbochargers, including compressor and turbine sizes,
maximum rotating speed and VGT position
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Figure 3. Schematic of two-stage turbocharging system with regulating valves: turbine by-pass (TBP)
and compressor by-pass (CBP), as installed in the turbocharger gas-stand
In according to the definition of equivalent two-stage map [23], turbine and compressor
equivalent maps are evaluated across the two stages, as in figure 3, using the definitions of pressure
ratio (PR), mass flow rate (m) and efficiency (η) for compressor and turbine in equations 1-6,
respectively. In this scenario, the two-stage system is treated as a single turbocharger with
compression and expansion processes. The equivalent mass flow rate of compressor and turbine are
corrected for pressure (Pref ¿ and temperature (T ref ), being equivalent to 298K and 1bar for
compressor and 288K and 1atm for turbine.
PRT−T=P2T /P1T (1)
mccorr=mc √T 1T /T refP1T /Pref
(2)
ηT−T=T 1T∗(PRT−T
γ−1γ )
T2T /T 1T(3)
PRT−s=P3T /P4 s (4)
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mtcorr=mt √T 3T /T refP3T /Pref
(5)
ηnet=PowercPoweris t
(6)
Due to the dependency between the performance of the turbocharging system and the
speeds of HP and LP stages, an equivalent two-stage system speed [23] has been defined in equation
7 and corrected for inlet total temperature (T ¿t) of turbine or compressor in equation 8. Accordingly
to the definitions in equations 1-8, the equivalent two-stage system maps can be generated in the
steady turbocharger gas-stand, treating the turbocharging system as a single turbocharger.
N eq=N LP∗( N LP
NHP ) (7)
N eq corr=N eq √T ref /T¿T (8)
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Figure 4. On the left hand-side, the two-stage turbocharging system installed in the steady
turbocharger gas-stand. The LP turbocharger is positioned on top, while, the HP turbocharger is
connected at the bottom of the exhaust manifold. On the right hand-side, LP and HP stage in stand-
alone configuration
In the proposed study, in order to focus on the effect of inter-stage phenomena on two-
stage system performance prediction, the TBV valve is constrained to the fully shut position, as well
as, the variable geometry turbines (VGT) at both HP and LP stages fixed at 50% between minimum
and maximum allowable opening area. Due to the complexity of the turbocharging system design,
difficulties persist in the estimation of the effect of VGT on the opening area of HP and LP turbines.
Therefore, HP and LP turbochargers have been treated as fixed geometry turbines with a reduction
of the operating range, reducing the VGT to 50%. In conjunction with the testing of the full two-stage
system, stand-alone HP and LP turbochargers have been investigated in the steady turbocharger gas-
stand, as shown in figure 4.
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2.3 Experimental campaignBoth HP and LP turbochargers have been mapped under adiabatic and diabatic conditions in
order to quantify the heat correction of the turbochargers. Due to the presence of a water-cooling
housing in the LP compressor, tests w/ and w/o cooling effects have been performed in both the
two-stage system and the LP turbochargers in stand-alone configurations. In details, in case of
adiabatic maps, compressor outlet and turbine inlet temperatures are matched, although the
bearing housing is controlled at an oil outlet temperature of 360K. Although, this setting may not
represent complete adiabatic conditions of the turbocharger [28], the dependency of compressor
and turbine power from friction changes between adiabatic and diabatic maps is reduced [29].
Furthermore, in case of diabatic maps, the TIT is maintained at 773K for both LP and HP
turbochargers whilst lubricating oil temperature is controlled at 360K. In summary, the experimental
campaign for the study is reported in the test matrix of table 3.
Adiabatic Diabatic at 773K TIT w/o water-
cooling
Diabatic at 773K TIT w/ water-
cooling at 360K
HP stage √ √ NA
LP stage √ √ √
Two-stage NA √ √
Table 3. Test matrix for HP and LP turbochargers and the full two-stage system. The adiabatic test is
performed matching compressor outlet and turbine inlet temperature. Lubricating oil temperature is
controlled equally across the experiments at 90degC downstream the bearing housing
3. Experimental results
3.1 Equivalent two-stage mapsIn figure 5, equivalent two-stage maps for compressor and turbine are generated in the
turbocharger gas-stand w/ and w/o water-cooling at the LP compressor. In the case of compressor
cooling, the downstream compressor coolant temperature is maintained at 360K. It is important to
notice that the corrected speed lines in figure 5 relates to the equivalent speed term of equation 8.
As visible, the equivalent two-stage compressor and turbine maps have been limited to 46Krpm and
28.3Krpm, respectively, corresponding to 200Krpm and 100Krpm of HP and LP turbochargers,
respectively.
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Figure 5. At the top, equivalent performance map for the two-stage compressors. At the bottom,
equivalent performance map for the two-stage turbines. Two cases w/ and w/o water-cooling at the
LP compressor are considered
The adoption of a water-cooling system at the LP compressor has a negative effect on the
equivalent compressor T-T efficiency, due to the downstream compressor water temperature
controlled at 360K. In this scenario, the water-cooling system can extract and introduce heat to the
LP compressor flow due to the constantly controlled temperature of 360K. However, as visible at the
top right corner of figure 5, compressor efficiency is lower in the presence of water-cooling for the
vast majority of speed lines. In addition, a small reduction of available pressure ratio in the two-
stage system is obtained in comparison to the case of the uncooled LP compressor. The increase in
turbine net efficiency (ηnet) for the case w/ water-cooling could be supported by an increase in
apparent compressor work due to the lower compressor T-T efficiency. Meanwhile, the effect of
water-cooling LP compressor housing shows a small change in turbine swallowing capacity at low
pressure ratios.
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3.2 Stand-alone turbochargers mapsIn order to analyse the influence of inter-stage effects on the prediction of two-stage system
performance, stand-alone turbochargers maps would have to be measured, resembling operating
conditions of the complete system. In conjunction with the equivalent two-stage maps generated in
the turbocharger gas-stand at diabatic conditions, stand-alone maps for HP and LP turbochargers
would have to be investigated at similar conditions of heat transfer. However, it is important to
consider that temperature at inlet of HP compressor would be higher than ambient, while TIT of LP
turbine could lower than 773K [14].
The investigation of adiabatic and diabatic compressor maps is able to provided correct
estimation of heat transfer and effective efficiencies of compressors and turbines [20]. For both LP
and HP turbochargers, the quantification of the heat transfer term to the compressor is possible,
assuming that the heat source is added to the flow following the adiabatic compression. Meanwhile,
the heat transfer term is included at the turbine entry, due to the temperature dependency of the
expansion processes on the turbine efficiency. In this way, heat corrected efficiencies for LP and HP
compressors and turbines can be estimated, as shown in figures 6 and 7.
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Figure 6. At the top, HP compressor performance maps at adiabatic and diabatic (773K TIT) are
shown. At the bottom, HP turbine performance maps at diabatic conditions (773K TIT) are shown.
The heat correction is applied to both compressor and turbine apparent efficiencies for the
estimation of effective efficiencies
Figure 7. At the top, LP compressor performance maps at adiabatic and diabatic (773K TIT) are
shown. At the bottom, LP turbine performance maps at diabatic conditions (773K TIT) are shown.
The heat correction is applied to both compressor and turbine apparent efficiencies for the
estimation of effective efficiencies
In figures 6 and 7, variations in compressor T-T efficiency can be noticed between adiabatic
and diabatic (773K TIT) conditions for both HP and LP turbochargers. Specifically, the diabatic
efficiency decreases significantly at low corrected compressor mass flow rates in comparison to the
adiabatic efficiency. In the case of turbines, the adiabatic map could not be generated due to varying
TIT and corrected speed terms. Furthermore, heat corrected efficiencies have been calculated for
both turbine and compressor. As visible in both figures 6 and 7, compressor T-T efficiency is closer to
adiabatic operations when heat corrections are applied. On the other side, a reduction of turbine net
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efficiency is obtained with heat correction due to lower power required by HP and LP compressors,
in figures 6 and 7, respectively.
Figure 8. At the left hand-side, LP compressor performance map for adiabatic and water-cooled
conditions at 90degC (WC 360K). At the right hand-side, apparent LP compressor T-T efficiency for
diabatic (773K TIT) and water-cooled conditions at 360K (WC 360K)
Due to the experienced variation of equivalent two-stage compressor efficiency in figure 5,
the effect of water-cooling on LP compressor performance has been analysed. In figure 8, the
maximum speed line tested on the LP compressor has shown a rise in pressure ratio in comparison
to adiabatic conditions. In fact, a significant increase in compressor efficiency is recorded in the
presence of water-cooling. Specifically, the apparent compressor efficiency reaches values higher
than 0.8 at 133.7Krpm. Meanwhile, peak efficiency at 54.2Krpm reduces from 0.6 in diabatic
operations to 0.4 in water-cooled conditions. However, in order to evaluate the effects of heat
transfer from water-cooling on the effective compressor power (Power eff) in equation 9, heat
sources from hot turbine (Power heat) and compressor water-cooling effect (Power cool) would have
to be considered from the apparent compressor power measured in the gas-stand (Power app).
Power eff=Power app−Power heat−Power cool (9)
Applying the correction for heat and cooling power to the temperature related LP
compressor efficiency (apparent) in the gas-stand can lead to the analysis of water-cooling effects on
the compression process. In figure 9, the variation of compressor efficiency due to water-cooling
system controlled at a downstream water-flow temperature of 360K is shown. As visible in figure 9,
the efficiency corrected for water-cooling power (Cool Corr) is higher than adiabatic and heat
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corrected efficiency values at mass flow operations lower than peak efficiency points at 116.4Krpm
and 133.7Krpm. At lower speeds of the LP turbocharger, the water-cooling system is not able to
extract heat from the compression process due to compressor outlet temperatures unable to reach
360K. In addition, owing to a more efficient compressor, the cool corrected turbine net efficiency is
affected.
Figure 9. At the left hand-side, adiabatic and heat corrected compressor T-T efficiency is compared
with effective compressor efficiency in the presence of water-cooling (Cool Corr) for the LP
compressor. At the right hand-side, heat and cool corrected turbine net efficiency for the two
highest LP turbine corrected speeds tested in gas-stand
3.3 Map correctionThe turbocharger gas-stand is extremely important for the performance evaluation of
compressors and turbines. However, the characteristic design of a turbocharger can cause the
measurement of diabatic compression and expansion processes, in case of heat sources introduced
at the turbine inlet [30]. In this scenario, corrections of performance would have to be performed, in
order to distinguish between heat and thermodynamic work. The evaluation of adiabatic maps in the
turbocharger gas-stand reduces the requirements for heat transfer models [31]. However, adiabatic
and diabatic maps would have to measured experimentally in the steady gas-stand, increasing the
testing time. It is important to state that the focus of the investigation regards the comparison of
equivalent and combined maps for two-stage turbocharging systems and the map correction
procedure is adopted to differentiate between turbocharger shaft power and heat. Therefore, after
assuming the total energy balance across the turbocharger operating in adiabatic operations, the
friction power can be calculated for HP and LP turbochargers. Specifically, the turbochargers are
non-insulated and a small amount of heat is able to escape to ambient.
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Figure 10. Relationship between adiabatic friction power and turbo speed for HP and LP
turbochargers. Best-fit curves for HP and LP turbochargers as dashed lines
The difference in turbocharger sizes has resulted in a different magnitude of friction losses,
as presented in figure 10. Specifically, although the HP turbocharger is tested at rotating speeds of
about 220Krpm, the friction losses account for about 2.5KW. In the case of LP turbocharger, the
same amount of friction power is achieved at about 100Krpm. Moreover, the relationship between
shaft speed and friction power develops differently for the two turbochargers. In this way, the heat
corrected turbine power can be calculated by joining the friction power to the heat corrected
compressor power. In this scenario, the assumption of friction independency from variation of axial
trust is stated, although, this could differ between adiabatic and diabatic operations [32].
Furthermore, adiabatic and diabatic (773K TIT) maps have allowed for the calculation of
specific heat flow to the compressor, assuming that heat addition to the compressor is occurring
after the compressor. In figures 11 and 12, the relationship between compressor and turbine heat
and mass flow for HP and LP turbochargers is shown. It is visible that the specific heat flow is
significantly higher in magnitude in the LP compressor, achieving about twice the amount HP
compressor energy at 0.02Kg/s. Additionally, the specific heat flow consists of 2KJ/Kg at about
0.07Kg/s in the HP compressor and 0.14Kg/s in the LP compressor. A different trend is observed for
the specific heat flow escaping the turbine. In fact, the amount of heat is similar between HP and LP
turbines, although a shift towards higher mass flows is recorded for the LP compressor.
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Figure 11. Relationship between specific compressor heat flow and compressor mass flow for HP and
LP turbochargers. Best-fit curves for HP and LP turbochargers as dashed lines. Positive specific heat
flow is transmitted to the compressor
Figure 12. Relationship between specific turbine heat flow and turbine mass flow for HP and LP
turbochargers. Best-fit curves for HP and LP turbochargers as dashed lines. Positive specific heat flow
is escaping the turbine
In order to evaluate the changes in compressor efficiency with the introduction of water-
cooling systems at the LP compressor housing, the multiple effects of heat and cooling flow would
have to be subtracted from the measured compressor efficiency in the gas-stand (equation 9). In this
perspective, the cooling power is analysed from availability of friction and effective turbine powers.
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Specifically, the calculation of maps correcting factors can be analysed in the appendix A.1.
Moreover, the cooling capacity of the LP compressor along the entire mapped operations is shown
in figure 13. In this graph, significant benefits on compressor efficiency from the water-cooling
system can be achieved at mass flow operations below 0.12Kg/s, as supported by results in figure 9.
However, at mass flow ranges between 0.06 and 0.12Kg/s, heat can be provided by the water-
cooling system in conditions of compressor outlet temperatures below 360K.
Figure 13. Relationship between compressor cooling power and compressor mass flow for LP
turbocharger. Positive power values represent cooling action of water on compressor outlet flow
4. Two-stage performance prediction
4.1 Equivalent and combined mapsIn order to evaluate the gap in performance prediction of the two-stage turbocharging
system, analysis of equivalent two-stage and combined stand-alone HP and LP maps could provide
accurate information. In fact, inter-stage phenomena occurring between HP and LP turbochargers
could affect the performance of the entire two-stage system. In this scenario, the equivalent two-
stage maps for compressors and turbines generated under diabatic conditions should be compared
to combined maps of the two turbochargers. The process of maps combination is performed into a
1D model of the steady turbocharger gas-stand with performance maps of HP and LP turbochargers.
It is important to consider that inter-stage components have been included in the mapping
procedures of stand-alone HP and LP turbochargers. Specifically, measured HP and LP turbochargers
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speeds are imposed and performance across the two turbochargers are calculated, as shown in the
diagram in figure 14. For this reason, speed values of HP and LP turbochargers may be different
between measured stand-alone maps and conditions in the combined map. Therefore, extrapolation
of unmeasured speed values is done through quadratic fits to regions of the speed lines via least
squares regression. Furthermore, heat correction of stand-alone HP and LP measured at 773K TIT
conditions are implemented and compared to equivalent two-stage maps, as in figure 15.
Figure 14. Diagram resembling the combination process of stand-alone HP and LP maps occurring
into a steady 1D model
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Figure 15. At the top, compressor performance maps of equivalent two-stage system at diabatic
conditions (Equivalent 773K TIT), combined stand-alone HP and LP stages at diabatic conditions w/
and w/o heat corrections. At the bottom, turbine performance maps obtained in the same
conditions
The results of figure 15 show a significant different in both pressure ratio and efficiency
predictions for the compressors system. In particular, equivalent two-stage compressor map
measures a lower pressure ratio at 12.5Krpm and 18Krpm in comparison to combined maps w/ and
w/o heat correction, as visible at the top left corner of figure 15. The change in pressure ratio
prediction is nearly absent at equivalent speeds equal and higher than 23Krpm. Additionally, a
similar trend is recorded in the estimation of compressor T-T efficiency. In these conditions, a
maximum change in efficiency for about 0.05 is monitored at 12.5Krpm between equivalent and
combined compressors. Furthermore, combined map estimate a difference in the swallowing
capacity of the two-stage turbines in relation to the equivalent two-stage map measured directly in
the turbocharger gas-stand. Differently from the compressors case, the turbine net efficiency
obtained by the combination of HP and LP maps is overestimated at high equivalent speed values, as
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visible in figure 15. Above all, the implementation of heat correction to diabatic operations of HP and
LP turbochargers is not able to significantly improve predictions of two-stage system performance.
Figure 16. Compressor performance maps of equivalent two-stage system with water-cooling at LP
stage (Equivalent w/ WC), combined stand-alone HP and water-cooled LP stages w/ and w/o cooling
corrections
Moreover, the heat and cooling correction of the LP compressor map is able to improve the
prediction of the two-stage system performance, in relation to the equivalent configuration, as
visible in figure 16. In fact, in the case of equivalent compressor pressure ratio, combination of HP
and LP maps with cooling corrections can reduce the gap with the measured equivalent map at low
rotating speeds. Accordingly, compressor efficiency estimation is generally improved with the
adoption of cooling power correction at the LP stage. Specifically, higher efficiency is monitored for
the two-stage in the gas-stand at low mass flows across the analysed speed lines. However, the
absence of cooling correction factors at the LP stage is not able to predict compressor efficiency at
12.5Krpm. Furthermore, it is important to notice that the combination of stand-alone turbochargers
maps is unable to confidently predict two-stage turbocharging performance at low operating speeds
and pressure ratios.
In order to analyse the effect of heat and cool corrections to stand-alone maps, HP and LP
compressors powers are investigated in combined two-stage maps. Figure 16 shows the relationship
between HP and LP powers under diabatic conditions w/ and w/o water-cooling at the LP
turbocharger. Moreover, the introduction of heat and cooling power corrections in relation to the
two diabatic cases highlights variation of trends in figure 16. Accordingly to plots in figures 15 and
16, a higher influence to compressors power is achieved in the implementation of corrections of the
water-cooled LP turbocharger. In fact, in conjunction to the low speed operations analysed in figure
17, LP compressor power is reduced with correction for heating effects by the water-cooling system
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controlled at 360K. Moreover, the application of correction for heat flux from the turbine to the
compressor reduces both HP and LP compressor powers, although a smaller effect is recorded in
figure 17.
Figure 17. Relationship between HP and LP compressor power in combined stand-alone maps at
diabatic conditions (773K TIT), with water-cooling at LP stage (w/ WC), with heat and cooling
corrections
5. ConclusionsIn this study, the influence of inter-stage effects on the performance of two-stage
turbocharging systems is investigated. Equivalent two-stage maps of compressors and turbines are
measuring performance of the complete two-stage regulated system. In order to focus on the inter-
stage effects, CBP and TBP valves are maintained closed with VGT actuators at 50% for HP and LP
turbochargers. In this scenario, stand-alone turbochargers are mapped in the turbocharger gas-stand
at adiabatic and diabatic conditions with TIT of 773K. Combinations of these maps w/ and w/o heat
corrections are performed and analysed against the equivalent two-stage system map. Similarly, the
comparison between combined and equivalent two-stage performance is discussed in the presence
of water-cooling of the LP compressor. Conclusively, the main findings of this research paper can be
listed as:
First of all, the equivalent performance definition of the two-stage system has been
possible. The equivalent speed definition has been able to capture constant speed
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trends and complete operation of turbochargers in the system. The change in
measured compressor efficiency between diabatic operation w/ and w/o water-
cooling is visible, reaching about 0.1 at 12.5Krpm. Importantly, the equivalent
mapping approach is able to incorporate the aero-thermal effects occurring
between stages which could modify the behaviour of turbochargers.
Moreover, the approach for predicting two-stage system performance based on the
combination of stand-alone HP and LP maps for compressor and turbines could
match system performance in the case of negligible inter-stage effects. The results in
figure 15 suggest significant influence of inter-stage effects at compressor speeds of
12.5Krpm and 18Krpm in the two-stage system. As heat correction for each of the
stages is implemented, it is clear that the difference between combined and
equivalent maps could be caused by flow distribution between stages. In relation to
turbines, dependency from inter-stage phenomena of two-stage swallowing capacity
is reduced.
Furthermore, the presence of water-cooling system, targeting 360K water-flow
downstream the compressor case, is able to worsen and improve compressor
apparent efficiency at low and high LP speeds, respectively. In the two-stage system
map, the efficiency is reduced in the presence of the water-cooling loop, as visible in
figure 5. The combination of stand-alone turbochargers maps can be improved at
low equivalent speeds with the adoption of cooling correction factors for the LP
compressor. In this scenario, inter-stage phenomena are still causing a change in
two-stage performance predictions at low equivalent speeds.
Finally, the investigation for a correct estimation of two-stage system performance
suggests that equivalent two-stage maps would be preferred, due to the low speed
compressor behaviour. However, in order to measure two-stage system maps,
decision on the complete package would have to be made. This is not always
available at an early stage of development and the equivalent two-stage maps
would have to be considered useful, to serve as a reference of boost prediction table
in control systems. Additionally, the combination of stand-alone map refers mostly
to extrapolated operations due to the limited number of tested conditions for each
turbocharger.
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Acknowledgement The Authors would like to acknowledge the technical staff at the Powertrain and Vehicle
Research Centre for the support received in implementing the experimental facility and researchers
Tomasz Duda and Ramkumar Vijayakumar for the support in running the experimental facility. The
Authors would like to acknowledge the University of Bath and the TurboCentre2 consortium for the
financial support.
Appendix A
A.1 Map heat transfer correctionIn the case of diabatic operations with TIT of 773K, the heat correction is performed,
considering compressor and turbine performance measured at both adiabatic and diabatic
conditions. Due to heat transfer, the compressor power at diabatic operations (Power cdia) results
higher than the adiabatic compressor power (Power cadia). Therefore, the change in power can be
estimated as in equations A.1 and A.2. The heat from turbine to compressor (Qc) is evaluated for HP
and LP turbochargers as in equation A.3.
Heatc=Power cdia−Power cadia (A.1)
Power c=mc(h2−h1) (A.2)
Qc=Heat c/mc (A.3)
In order to calculate the total heat escaping the turbine (Qt ¿, the same process of equations
A.1-3 is implemented, as reported in equations A.4-6.
Heat t=Powert dia−Power t adia (A.4)
Powert=mt (h3−h4) (A.5)
Qt=Heat t /mt (A.6)
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