Internal Combustion Engines I: Fundamentals and Performance Metrics

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1 Internal Combustion Engines I: Fundamentals and Performance Metrics Prof. Rolf D. Reitz, Engine Research Center, University of Wisconsin-Madison 08 Princeton-Combustion Institute Summer School on Combustion Course Length: 9 hrs (Mon.- Wed., June 5-7) Copyright 08 by Rolf D. Reitz. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Rolf D. Reitz. PCI--, 08

2 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 (Engine fundamentals) Hour : IC Engine Review, Thermodynamics and 0-D modeling Hour : -D modeling, Charge Preparation Hour 3: Engine Performance Metrics, 3-D flow modeling Day (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 PCI--, 08

3 Anderson, 990 -D compressible flow Mass conservation: g = dmg / dt ) = 0 System Reynolds Transport Equation dmg d d = ρgd ρgd ρg da dt dt = + dt V n ) system rel cv cs system dx. ( ρ A) 0 = + cv t ( ρa) ( ρav ) + = 0 t x ( ρ AV) Momentum conservation:. cv fixed dx V V P + V + + fv D = t x ρ x Energy conservation: 3. Divergence theorem / 0 Supplementary: d = Adx P=ρRT f e=c v T =τ ρv State w / / 5 unknowns U: ρ, V, e, P, and T 5 equations for variation of flow variables in space and time 3 PCI--, 08

of straight pipe Flow losses R Apply experimentally or numerically

4 In -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 Flow losses R Apply experimentally or numerically determined Loss Coefficient to equivalent straight pipe P= C ρv / P 4 PCI--, 08

, 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

5 -D Modeling Codes -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. L τ=l/c= m/330 m/s = 3 ms AVL Boost, Ricardo WAVE, GT-Power ca deg = rev/min 5 PCI--, 08

Numerical solution To integrate the partial differential equations: Discretize domain with step size, x Time marches in increments of t from 0 n n n n n initial state U : ρ, V, e, P,and T i i i i i i

6 Numerical solution To integrate the partial differential equations: Discretize domain with step size, x Time marches in increments of t from 0 n n n n n initial state U : ρ, V, e, P,and T i i i i i i t=n t n=0,,, 3,... n U i x i i =,, 3, 4,.., M-, M U(,) xt U ( x, n dt) U U = = x x x n n i i+ i U(,) xt U ( x, n dt) U U = = t t t i n+ n i i i Considerations of stability require the Courant-Friedrichs-Levy (CFL) condition i n n t min( x /( V + c ) i i i 6 PCI--, 08

7 Anderson, 990 Analytical solutions Method of Characteristics R: right-running wave slope dx V c dt = + Wave diagram V t - time L: left-running wave dx slope V c dt = P: particle-path slope dx dt = V V x distance along duct 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--, 08

8 Anderson, 990 Analytical solutions Method of Characteristics dx R: right-running wave slope V c dt = + Wave diagram V t - time L: left-running wave dx slope V c dt = P: particle-path slope dx dt = V t V x x distance along duct R:, L:, P:, are called Characteristic Lines in the flow n n t min( x /( V + c ) i i i 8 PCI--, 08

9 Moody, 989 Along R: dp + ρcdv = Fdt Along L: dp ρcdv = Gdt Along P: d ρ dp / c = Hdt ( ) F, G, H = Functions of q, f,ln A/ dx Time level n+ t t Slope dx n VL dt = 4 c n L Slope P: Slope dx n VR dt = + dx V dt = c n R n P The discrete versions are: ( P P ) + ( ρc) ( V V ) = F t 4 R R 4 R R ( P P ) ( ρc) ( V V ) = G t 4 L L 4 L L ( ρ ρ ) ( P P ) = H t 4 P 4 P P c P 3 equations to solve for Time level n (Solution variables known) 3 R P L x V x ρ, V and P Note: from Gibbs equation cp dp cp ds = ( dρ) = Hdt ρ c ρ 9 PCI--, 08

10 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. t head x Hour : -D modeling, Charge Preparation Thompson, 97 Lagrange ballistics X V piston dx Slope V dt = piston L: R: P: P4 = PL + ( ρc) L(0 VL) P4 = PR ( ρc) R( Vpiston VR ) ρ = ρ + ( P P )/ c ) 4 P 4 P P 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=V piston at piston. Order of magnitude analysis of L:, R:, and P: gives x dp ~ ρcdv and dρ ~ ρ dv c For dv<<c relative density change is small density and pressure changes only in time 0 PCI--, 08

11 Steady Compressible flow A review Gibbs Energy Tds = dh dp / ρ dh = VdV Euler dp = ρvdv Hour : -D modeling, Charge Preparation Anderson, 990 Area-velocity relations for M< for M> ρ AV = Const da A d ρ da dv ρ + A + V = = M ( ) dv V 0 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 da ( M ) = dp A ρv Traffic flow behaves like a supersonic flow! PCI--, 08

12 Anderson, 990 Isentropic nozzle flows T T 0 γ = + M P0 P γ γ γ = ( + M ) Ex. Flow past throttle plate P 0 ψ P 0 P 0 P=P b Choked flow for P < 53.5 kpa = 40.cmHg reservoir ambient WOT Choked P/P 0 P b m M= ψ Manifold pressure, P cmhg x PCI--, 08

13 Anderson, 990 Model passages as compressible flow in converging-diverging nozzles P V m = ρav = A γrt RT c γ = P AM ( P / P ) /( T / T ) RT0 With M=: Fliegner s formula / A* Minimum area point P 0 Choked flow, M= m γ + ( γ ) γ M = = ( ) 0 M= γ + RT0 M= PA * A*/A Subsonic Supersonic Area Mach number relations A * A ( γ ) = + M γ + + A ( P ) ( P γ γ γ γ = ) * A P 0 γ P0 ( M ) γ + ( γ ) γ + γ / 0 solutions for same area reservoir 0.58 throat exit P/P M 3 PCI--, 08

14 Anderson, 990 Application to turbomachinery Fliegner s Formula: m γ + ( γ ) γ M = = ( ) 0 M= γ + RT0 PA * Variable Geometry Compressor/ turbine performance map Increased speed Corrected mass flow rate A measure of effective flow area m T 0 ref P / P / T ref 0 Reduced flow passage area Choked flow.0 /0.58=.89 P 0 /P Total/static pressure ratio 4 PCI--, 08

- Increased engine power more than offsets losses due to increased

15 Turbocharging Pulse-driven turbine was invented and patented in 95 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 Improved 5 PCI--, 08

Turbocharging Hour : -D modeling, Charge Preparation Purpose of turbocharging or supercharging is to increase inlet air density, - increase amount of air in the cylinder.

16 Turbocharging Hour : -D modeling, Charge Preparation 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. 6 PCI--, 08

17 Turbocharging Hour : -D modeling, Charge Preparation 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 7 PCI--, 08

Turbo Circuit EGR Valve EGR Cooler HP TURBINE Compressor Bypass Charge Air Cooler Compressor Bypass Regulating

18 Regulated two-stage turbocharger Duplicated Configuration per Cylinder Bank LP stage Turbo-Charger with Bypass Compressor Bypass HP stage Turbo charger Charge Air Cooler Regulating valve EGR Cooler EGR Valve GT-Power RS Turbo Circuit EGR Valve EGR Cooler HP TURBINE Compressor Bypass Charge Air Cooler Compressor Bypass Regulating valve HP stage Turbo charger LP stage Turbo-Charger with Bypass Regulating Valve LP TURBINE LP Stage Bypass 8 PCI--, 08

Automotive compressor Centrifugal compressor typically used in automotive applications Provides high mass flow rate at relatively low pressure ratio ~ 3.

19 Automotive compressor 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 9 PCI--, 08

Heywood, 988 T Compressor η ( Tout ( T isen c = out Tin) T ) in P 0 3 P 3 P = P out Heywood, Fig. 6-43 Air at stagnation state 0,in accelerates to inlet pressure, P, and velocity V.

20 Heywood, 988 T Compressor η ( Tout ( T isen c = out Tin) T ) in P 0 3 P 3 P = P out Heywood, Fig Air at stagnation state 0,in accelerates to inlet pressure, P, and velocity V. V / c P P 0 P = P 0,in Compression in impeller passages increases pressure to P, and velocity V. Diffuser between states and out, recovers air kinetic energy at exit of impeller producing pressure rise to, P out and low velocity V out ( ) W c = m a hout hin S γ a m a a cp T γ Note: use exit static pressure and inlet total a in p out W = pressure, because kinetic energy of gas c η c p 0, in leaving compressor is usually not recovered 0 PCI--, 08

Heywood, 988 Compressor maps Work transfer to gas occurs in impeller via change in gas angular momentum in rotating blade passage Surge limit line

Unstable flow can lead to damage Pressure ratio evaluated using total-to-static pressures since exit flow kinetic energy is not recovered Speed/pressure

21 Heywood, 988 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 Pressure ratio evaluated using total-to-static pressures since exit flow kinetic energy is not recovered Speed/pressure limit line Non-dimensionalize blade tip speed (~ND) by speed of sound At high air flow rate, operation is limited by choking at the minimum area point within compressor Supersonic flow Shock wave Heywood, Fig PCI--, 08

22 Compressor selection To select compressor, first determine engine breathing lines. The mass flow rate of air through engine for a given pressure ratio is: η = IMP = PR * atmospheric pressure (no losses) = IMT = Roughly constant for given Speed PCI--, 08

Engine breathing lines 3.8 Engine Breathing Lines.4L Diesel, Air-to-Air AfterCooled, Turbocharged 3.6 3.4 3.

.8.6.4. Parameter Torque Peak Rated Units Horsepower 48 69 hp BSFC 0.377 0.40 lb/hp-hr A/F 3.8 4.5 none 0.000.

23 Engine breathing lines 3.8 Engine Breathing Lines.4L Diesel, Air-to-Air AfterCooled, Turbocharged Torque Peak (700rpm) Trq Peak Operating Pnt Rated (300rpm) Rated Operating Pnt 3 Compressor Pressure Ratio Parameter Torque Peak Rated Units Horsepower hp BSFC lb/hp-hr A/F none Intake Mass Flow Rate (lb/min) 3 PCI--, 08

24 Serrano, 008 Compressor maps GM.9L diesel engine Pressure Ratio (t/t) Efficiency (T/T) Corrected Air Flow (kg/s) Corrected Air Flow (kg/s) PCI--, 08

25 Reitz, 007 Automotive turbines Naturally aspirated: P intake =P exhst =P atm ( ) Boosted operation: Negative pumping work: P 7 <P but hurts scavenging P 3 4 W = m ( h h ) W t g in 0, out P = mct η P t g P in t 0, out in γ g γ g Compressor P intake P exhst 9 8 Expansion 5 Compression 7 Blowdown Available work (area 5-6-7) 6 6 Turbine 6 P amb TDC BDC P-V diagram showing available exhaust energy - turbocharging, turbocompounding, bottoming cycles and thermoelectric generators further utilize this available energy V c 5 PCI--, 08

26 Turbochargers Hour : -D modeling, Charge Preparation Radial flow automotive; axial flow locomotive, marine T V / c P P 0 = P 0,in P P P 03 m corrected N corrected = m g = p T N T3 T T p 0 0 out P 3 = P out η = t ( T ( T out out isen Tin ) T in ) S 6 PCI--, 08

27 ( ) = a a g g p p m m T Cp T Cp p p mech c t air fuel a g γ γ γ γ η η η W t = W c Heywood, PCI--, 08 Hour : -D modeling, Charge Preparation..

28 Summary -D models/codes based on thermodynamic models are available, and they are very useful for understanding charge preparation and engine breathing. But, -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. 8 PCI--, 08

29 References -:3,7-9,-4 J. D. Anderson, Modern Compressible Flow (With Historical Perspective), McGraw-Hill (nd or 3rd Edition), :5 -: :9 F.J. Moody, Introduction to Unsteady Thermofluid Mechanics, John Wiley & Sons, :0 P.A. Thompson, Compressible Fluid Dynamics, McGraw-Hill, 97. -:0-,7 J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw Hill, :4 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 (008) , :5 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, PCI--, 08

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan