Upload
others
View
9
Download
2
Embed Size (px)
Citation preview
1 PCI-1-2, 2018
Internal Combustion Engines I: Fundamentals and Performance Metrics
Prof. Rolf D. Reitz,
Engine Research Center, University of Wisconsin-Madison
2018 Princeton-Combustion Institute Summer School on Combustion
Course Length: 9 hrs (Mon.- Wed., June 25-27)
Copyright ©2018 by Rolf D. Reitz. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Rolf D. Reitz.
Hour 2: 1-D modeling, Charge Preparation
2 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Short course outline:
Internal Combustion (IC) engine fundamentals and performance metrics, computer modeling supported by in-depth understanding of fundamental engine processes and detailed experiments in engine design optimization.
Day 1 (Engine fundamentals)
Hour 1: IC Engine Review, Thermodynamics and 0-D modeling Hour 2: 1-D modeling, Charge Preparation Hour 3: Engine Performance Metrics, 3-D flow modeling
Day 2 (Computer modeling/engine processes)
Hour 4: Engine combustion physics and chemistry Hour 5: Premixed Charge Spark-ignited engines Hour 6: Spray modeling
Day 3 (Engine Applications and Optimization) Hour 7: Heat transfer and Spray Combustion Research Hour 8: Diesel Combustion modeling Hour 9: Optimization and Low Temperature Combustion
Mass conservation:
( )( )0cv
A A dxt
ρ ρ∂ = + ∇ ⋅ ∂ ∫ V
1g = / ) 0SystemdMg dt =
( ) ( ) 0A AVt x
ρ ρ∂ ∂+ =
∂ ∂
21 2 / 0V V PV fV Dt x xρ
∂ ∂ ∂+ + + =
∂ ∂ ∂
Momentum conservation:
Energy conservation:
Divergence theorem
1.
2.
3.
cv fixed
2/ / 2wf Vτ ρ=
P=ρRT
Supplementary:
e=cvT
5 unknowns U: ρ, V, e, P, and T 5 equations for variation of flow variables in space and time
4.
5. State
1-D compressible flow
)system relcv cssystem
dMg d dgd gd g dAdt dt dt
ρ ρ ρ= ∀ = ∀ + ⋅∫ ∫ ∫ V n
d Adx∀ =
dx
Reynolds Transport Equation
Anderson, 1990
3 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
In 1-D models friction factors are used to account for losses at area change or bends by applying a friction factor to an “equivalent” length of straight pipe
R Flow losses
Apply experimentally or numerically determined Loss Coefficient to equivalent straight pipe
2 / 2PP C Vρ∆ =
4 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
L
τ=L/c=1 m/330 m/s = 3 ms
1-D Modeling Codes
1-D codes (e.g., GT-Power, AVL-Boost, Ricardo WAVE) predict wave action in manifolds At high engine speed valve overlap can improve engine breathing inertia of flowing gases can cause inflow even during compression stroke.
Variable Valve Actuation (VVA) technologies, control valve timing to change effective compression ratio (early or late intake valve closure), or exhaust gas re-induction (re-breathing) to control in-cylinder temperatures.
Residual gas left from the previous cycle affects engine combustion processes through its influence on charge mass, temperature and dilution.
AVL Boost, Ricardo WAVE, GT-Power 1 ca deg = 0.1 ms @ 1800 rev/min 5 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
6 PCI-1-2, 2018
∆xi
i = 1, 2, 3, 4, …….. , M-1, M
To integrate the partial differential equations: Discretize domain with step size, ∆x Time marches in increments of ∆t from initial state 0 and: , , , ,n n n n n
i i i i i iU V e P Tρ
1( , )( , ) n ni i i
i i
U x n dt U UU x tx x x
+∆ ⋅ −∂= =
∂ ∆ ∆
1( , )( , ) n ni i iU x n dt U UU x t
t t t
+∆ ⋅ −∂= =
∂ ∆ ∆
Considerations of stability require the Courant-Friedrichs-Levy (CFL) condition
min( /(| | )n ni i it x V c∆ ≤ ∆ +
t=n∆t n=0, 1, 2, 3, ....
niU
Numerical solution
Hour 2: 1-D modeling, Charge Preparation
t - ti
me
x – distance along duct
P: particle-path
Wave diagram
dx Vdt
=slope
V
V
dx V cdt
= −slope
slope dx V cdt
= +
L: left-running wave
R: right-running wave
All points continuously receive information about both upstream and downstream flow conditions from both left and right-running waves. These waves originate from all points in the flow.
7 PCI-1-2, 2018
Analytical solutions – Method of Characteristics
Hour 2: 1-D modeling, Charge Preparation Anderson, 1990
t - ti
me
x – distance along duct
P: particle-path
Wave diagram
dx Vdt
=slope
V
V
dx V cdt
= −slope
slope dx V cdt
= +
L: left-running wave
R: right-running wave
min( /(| | )n ni i it x V c∆ ≤ ∆ +
t∆
x∆
R:, L:, P:, are called Characteristic Lines in the flow
8 PCI-1-2, 2018
Analytical solutions – Method of Characteristics
Hour 2: 1-D modeling, Charge Preparation Anderson, 1990
P: Slope nP
dx Vdt
=
∆t
∆x
1 2 3
4
R P L Time level n
Time level n+1
t
x
Slope n nR R
dx V cdt
= +
Slope n nL L
dx V cdt
= −
V
dP cdV Fdtρ+ = dP cdV Gdtρ− = 2/d dp c Hdtρ − =Along R: Along L: Along P:
( ), , , , ln /F G H Functionsof q f A dx=
2( )P Pc dP cdS d Hdtc
ρρ ρ
= − =
Note: from Gibbs’ equation
The discrete versions are:
4 4( ) ( ) ( )R R R RP P c V V F tρ− + − = ∆
4 4( ) ( ) ( )L L L LP P c V V G tρ− − − = ∆
4 42
1( ) ( )P P PP
P P H tc
ρ ρ − − − = ∆
3 equations to solve for
4 4 4and, V Pρ(Solution variables known)
9 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Moody, 1989
Flow velocities in IC engine cylinders are usually << than the speed of sound. Lagrange ballistics shows that cylinder pressure and density is the same at all points within the combustion chamber.
X
x
Vpiston
head
For dV<<c relative density change is small– density and pressure changes only in time
4 ( ) ( )R R piston RP P c V Vρ= − −R: 2
4 4( ) / )P P PP P cρ ρ= + −P:
4 ( ) (0 )L L LP P c Vρ= + −L:
~dP cdVρ
Pressure increases by dP each wave reflection (dV<0) in order to alternately ensure that the flow meets the boundary conditions: V=0 at head, and V=Vpiston at piston. Order of magnitude analysis of L:, R:, and P: gives
~d dVc
ρρ
pistondxSlope Vdt
=
and
t
x
Lagrange ballistics
10 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Thompson, 1972
Steady Compressible flow – A review
/Tds dh dp ρ= −
dh VdV= −
Gibbs
Energy
Euler dP VdVρ= −
2
2
(1 )dA M dPA Vρ
−=
0d dA dVA V
ρρ
+ + =AV Constρ =
2( 1)dA dVMA V
= −
for M<1 for M>1 Subsonic nozzle Subsonic diffuser Supersonic diffuser Supersonic nozzle dA<0 dA >0 dA <0 dA >0 from ρAV dV>0 dV <0 dV <0 dV >0 from Euler dP<0 dP >0 dP >0 dP <0 kinetic energy pressure recovery kinetic energy
Traffic flow behaves like a supersonic flow!
11 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Anderson, 1990
Area-velocity relations
201
1
112
T MT
γ −= + 2 10
11
1(1 )2
P MP
γγγ −−
= +
P0 P=Pb
P/P0 Pb
0
1
x
0.528
reservoir ambient
M=1 Manifold pressure, P1 cmHg
m
Choked
WOT
ψ
Ex. Flow past throttle plate
Choked flow for P2 < 53.5 kPa = 40.1cmHg
40.1 76
1
Isentropic nozzle flows
ψ
0
12 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Anderson, 1990
P1 P0
Model passages as compressible flow in converging-diverging nozzles
A*/A
0 P/P0 0 1
1
0.528
Subsonic Supersonic
0 ∞ M 1
reservoir throat exit
2 solutions for same area
P0 A*
1*2( 1)
1 00
2( )1Mm P A
RT
γγ γ
γ
+−
= =+
With M=1: Fliegner’s formula
1/ 20 0 0
0
( / ) /( / )
P Vm AV A RTRT c
P AM P P T TRT
ρ γ
γ −
= =
=
Choked flow, M=1
Minimum area point
1/ 211 11
*0 0
2 1( ) 1 ( )1 2
A P PA P P
γγγγ γ γ
γ
+−−
+ = − −
12( 1)
2*
1 2 ( 1)(1 )1 2
A MA M
γγγ
γ
+− −
= + +
Area Mach number relations
13 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Anderson, 1990
M=1 M=1
Application to turbomachinery
Reduced flow passage area
P0 /P Total/static pressure ratio
1/0.528=1.89 1.0
Choked flow
Increased speed
0
0
//ref
ref
m T TP P
Variable Geometry Compressor/ turbine performance map
“Corrected mass flow rate”
A measure of effective flow area
1*2( 1)
1 00
2( )1Mm P A
RT
γγ γ
γ
+−
= =+
Fliegner’s Formula:
14 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Anderson, 1990
M=1
15 PCI-1-2, 2018
Turbocharging
Improved
Hour 2: 1-D modeling, Charge Preparation
Pulse-driven turbine was invented and patented in 1925 by Büchi to increase the amount of air inducted into the engine. - Increased engine power more than offsets losses due to increased back pressure - Need to deal with turbocharger lag
Turbocharging Purpose of turbocharging or supercharging is to increase inlet air density, - increase amount of air in the cylinder.
Mechanical supercharging - driven directly by power from engine.
Turbocharger - connected compressor/turbine - energy in exhaust used to drive turbine.
Supercharging necessary in two-strokes for effective scavenging: - intake P > exhaust P - crankcase used as a pump
Some engines combine engine-driven and mechanical (e.g., in two-stage configuration).
Intercooler after compressor - controls combustion air temperature.
16 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Turbocharging Energy in exhaust is used to drive turbine which drives compressor Wastegate used to by-pass turbine
Charge air cooling after compressor further increases air density - more air for combustion
17 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Regulated two-stage turbocharger Duplicated Configuration per Cylinder Bank
EGR Cooler
EGR Cooler
EGR Valve
EGR Valve
LP stage Turbo-Charger with Bypass
LP stage Turbo-Charger with Bypass
HP stage Turbo charger
HP stage Turbo charger
Regulating valve
Regulating valve Charge Air Cooler
Charge Air Cooler
Compressor Bypass
Compressor Bypass
LP TURBINE
Regulating Valve
LP Stage Bypass
HP TURBINE Compressor Bypass
GT-Power R2S Turbo Circuit
18 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Centrifugal compressor typically used in automotive applications Provides high mass flow rate at relatively low pressure ratio ~ 3.5 Rotates at high angular speeds - direct coupled with exhaust-driven turbine - less suited for mechanical supercharging Consists of: stationary inlet casing, rotating bladed impeller, stationary diffuser (w or w/o vanes) collector - connects to intake system
Automotive compressor
19 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
P 0
P 3 T
S
P 1
P 2
P 0 3
= P 0,in
= P out
V 1 2 / 2 c P
Air at stagnation state 0,in accelerates to inlet pressure, P1, and velocity V1.
Compression in impeller passages increases pressure to P2, and velocity V2.
Diffuser between states 2 and out, recovers air kinetic energy at exit of impeller producing pressure rise to, Pout and low velocity Vout
Compressor
( )1
0,
1
a
aa
c a out in
a P in out
c in
W m h h
m c T pWp
γγ
η
−
= −
⋅ ⋅ = −
c
)()(
inout
inisenoutc TT
TT−
−= −η
Heywood, Fig. 6-43
Heywood, 1988
20 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Note: use exit static pressure and inlet total pressure, because kinetic energy of gas leaving compressor is usually not recovered
Compressor maps Work transfer to gas occurs in impeller via change in gas angular momentum in rotating blade passage
Surge limit line – reduced mass flow due to periodic flow reversal/reattachment in passage boundary layers. Unstable flow can lead to damage
At high air flow rate, operation is limited by choking at the minimum area point within compressor Pressure ratio evaluated
using total-to-static pressures since exit flow kinetic energy is not recovered
Non-dimensionalize blade tip speed (~ND) by speed of sound
Speed/pressure limit line
Supersonic flow
Shock wave
Heywood, Fig. 6-46 21 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation Heywood, 1988
Compressor selection
To select compressor, first determine engine breathing lines. The mass flow rate of air through engine for a given pressure ratio is:
= IMP = PR * atmospheric pressure (no losses)
= IMT = Roughly constant for given Speed
η
22 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Engine breathing lines
Engine Breathing Lines1.4L Diesel, Air-to-Air AfterCooled, Turbocharged
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000
Intake Mass Flow Rate (lb/min)
Com
pres
sor P
ress
ure
Rat
io
Torque Peak (1700rpm)
Trq Peak Operating Pnt
Rated (2300rpm)
Rated Operating Pnt
Parameter Torque Peak Rated UnitsHorsepower 48 69 hp
BSFC 0.377 0.401 lb/hp-hrA/F 23.8 24.5 none
23 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
Compressor maps
0.5
0.6
0.7
0.8
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Corrected Air Flow (kg/s)
Efficiency (T/T)
35000 40000 50000 70000
90000 110000 130000 150000
170000 180000 190000
35000 4000050000 70000
90000110000
130000
150000
170000
180000
190000
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Corrected Air Flow (kg/s)
Pressure Ratio (t/t)
GM 1.9L diesel engine
Serrano, 2008
24 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
P
V
TDC BDC
Pexhst Pintake
Compression
Expansion
Available work (area 5-6-7)
Blowdown
Automotive turbines
P-V diagram showing available exhaust energy - turbocharging, turbocompounding, bottoming cycles and
thermoelectric generators further utilize this available energy
1
2
3 4
5
6 7 8
9
Pamb 6’
Naturally aspirated: Pintake=Pexhst=Patm (5-7-8-9-1) Boosted operation: Negative pumping work: P7<P1 – but hurts scavenging
6’’
Compressor Turbine
0,( )t g in outW m h h= −
1
0,1
g
goutt g P in t
in
PW m c T
P
γγ
η
− = −
Reitz, 2007
25 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
c
Turbochargers
out
Radial flow – automotive; axial flow – locomotive, marine
0
3
0
3
0
3
TTNN
pp
TT
mm
corrected
gcorrected
=
=••
T
S
P 1
P 2
P 0 3
P 0 = P 0,in
P 3 = P out
V 1 2 / 2 c P
)()(
inisenout
inoutt TT
TT−
−=
−
η
26 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
( )
11
3
4
1
3
1
2 111
−
−⋅⋅
+
⋅⋅
+=
−
•
•aa
g
g
pp
m
mTCpTCp
pp
mechct
air
fuel
a
g
γγ
γγ
ηηη
Wt = Wc
Heywood, 1988
27 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
. .
Summary
1-D models/codes based on thermodynamic models are available, and they are very useful for understanding charge preparation and engine breathing. But, 1-D models require calibration against engine or theoretical data. Turbocharging increases overall engine efficiency by using available energy in exhaust and by reducing pumping work.
28 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
29 PCI-1-2, 2018
Hour 2: 1-D modeling, Charge Preparation
1-2:3,7-9,11-14 J. D. Anderson, Modern Compressible Flow (With Historical Perspective), McGraw-Hill (2nd or 3rd Edition), 1990.
1-2:5 1-1:34-36 http://www.ricardo.com/en-GB/What-we-do/Software/Products/WAVE
1-2:9 F.J. Moody, Introduction to Unsteady Thermofluid Mechanics, John Wiley & Sons, 1989.
1-2:10 P.A. Thompson, Compressible Fluid Dynamics, McGraw-Hill, 1972.
1-2:20-21,27 J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw Hill, 1988.
1-2:24 Serrano J.R., Arnau F.J., Dolz V. , Tiseira A., and Cervello C., “A model of turbocharger radial turbines appropriate to be used in zero- and one-dimensional gas dynamics codes for internal combustion engines modeling”, Energy Conversion and Management,49 (2008) 3729–3745, 2008.
1-2:25 Reitz, R.D., and Hoag, K.H., "Reciprocating Engines (Diesel and Gasoline)," Encyclopedia of Energy Engineering and Technology (EEE), B. Capehart, Editor, Marcel Dekker Publishing, New York, 2007.
References