Reciprocating Internal Combustion Engines

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Reciprocating Internal Combustion Engines Prof. Rolf D. Reitz Engine Research Center University of Wisconsin-Madison 014 Princeton-CEFRC Summer School on Combustion Course Length: 15 hrs (Mon.

1 Reciprocating Internal Combustion Engines Prof. Rolf D. Reitz Engine Research Center University of Wisconsin-Madison 014 Princeton-CEFRC Summer School on Combustion Course Length: 15 hrs (Mon.- Fri., June 3 7, 014) Copyright 014 by Rolf D. Reitz. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Rolf D. Reitz. 1 CEFRC3-5, 014

2 Short course outine: 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) Part 1: IC Engine Review, 0, 1 and 3-D modeling Part : Turbochargers, Engine Performance Metrics Day (Combustion Modeling) Part 3: Chemical Kinetics, HCCI & SI Combustion Part 4: Heat transfer, NOx and Soot Emissions Day 3 (Spray Modeling) Part 5: Atomization, Drop Breakup/Coalescence Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Day 4 (Engine Optimization) Part 7: Diesel combustion and SI knock modeling Part 8: Optimization and Low Temperature Combustion Day 5 (Applications and the Future) Part 9: Fuels, After-treatment and Controls Part 10: Vehicle Applications, Future of IC Engines CEFRC3-5, 014

3 Resolution predictive models Finite difference mesh 10 cm 1-D 10 4 grid points 3-D 10 1 grid points 10 mm Models will not be entirely predictive for decades Accurate submodels will be needed for detailed spray processes (e.g., drop drag, drop turbulence interaction, vaporization, atomization, drop breakup, collision and coalescence, and spray/wall interaction) 3 CEFRC3-5, 014

4 Amsden,1997 Governing Equations Gas phase Liquid phase Turbulence Lagrangian Drop, Eulerian Fluid (LDEF) models Two-Phase Flow Regimes x, v, r, Td q 1 ( Computational cell f = f (x, v, r, T d ; t) Gas void fraction and drop number density Vol 4 3 r 3 f drdv dtd )dvol/ Vol Current LDEF spray models: drops occupy no volume q >0.9 Drop parcels Intact Churning Thick Thin Very thin 4 CEFRC3-5, 014

5 Dukowicz, 1980 LDEF Spray Modeling Concept of using drop parcels For typical heavy-duty diesel, injected fuel per cycle (75% load): g One spray plume: m fuel =0.160/6=0.067 g If average SMD=10 mm m drop =3.8x10-10 g # of drops in the domain=0.067g/m drop =7.1x10 7 Impractical to track individual fuel drops group identical drops into parcels nozzle drop What you see in graphs: Grid size parcel 5 CEFRC3-5, 014

6 Amsden,1997 Eulerian Gas Phase Mass conservation (species) t (u) l 4r R f drdv dt d R = dr/dt - Vapor source Momentum conservation u t (uu) p ( 3 k) Fs g Turbulent and viscous stress Rate of momentum gain due to spray drop drag 6 CEFRC3-5, 014

7 Amsden,1989 Gas Phase () Internal energy conservation I t Heat flux Equations of state Combustion heat release + ui = -Pu - J + + Q c + Q s J T Dh m ( m / ) p RT m m m / W m Specific heat, enthalpy from JANAF data Turbulence dissipation Energy due to Spray - vaporization 7 CEFRC3-5, 014

8 Amsden, 1997 Liquid Phase Spray drop number conservation. f = f (x, v, r, T d, y, y; t) f t + x fv + v ff + r (fr) + ft d + T d y fy + y fy = f coll + f bu.... F=dv/dt drop drag R = dr/dt Vaporization and heating Drop distortion Drop breakup, coalescence Spray exchange functions F s = - f d 4/3 r 3 F ' + 4r Rv dv dr dt d dy dy Q s = - f d 4r R I l + 1 v-u + 4/3 r 3 c l T d + F ' v-u-u ' dv dr dt d dy dy Work done by drop drag forces W s = - f d 4/3 r 3 F ' u ' dv dr dt d dy dy 8 CEFRC3-5, 014

9 Amsden, 1997 Lagrangian drop - liquid phase Discrete Drop Model drop position dx dt v drop velocity dv dt F drop size dr dt R + v ff + r (fr) + Turbulence model provides: l, u l u ft d + T d y fy + t y fy = f coll + f bu t+dt u' v Spray submodels provide: F - Drag, R Vaporize.. - breakup/collide Initial data: v, r, T d Atomization model 9 CEFRC3-5, 014

10 Amsden, 1997 Turbulence Model (RANS) Kinetic energy Dissipation k t (uk) k u. m u ( )k 3 Pr k W Ý s Dissipation rate t Production due to mean flow + u = - 3 C 1 - C 3 u + m Pr Rate of work to disperse drops + k C 1 :u - C + C s W s Turbulence diffusivity D C m k / Eddy size 3/ l = C k / Turbulence intensity u = ( k/3) 10 CEFRC3-5, 014

UW-ERC Multidimensional CFD models Submodel Los Alamos UW-Updated References intake flow assumed initial flow compute intake flow SAE 95100 heat transfer law-of-the-wall compressible, unsteady SAE

11 UW-ERC Multidimensional CFD models Submodel Los Alamos UW-Updated References intake flow assumed initial flow compute intake flow SAE heat transfer law-of-the-wall compressible, unsteady SAE turbulence standard k- RNG k- /LES CST 106, 1995 nozzle flow none cavitation modeling SAE atomization Taylor Analogy surface-wave-growth SAE Kelvin Hemholtz SAE Rayleigh Taylor CST 171, 1998 drop breakup Taylor Analogy Rayleigh Taylor Atom. Sprays 1996 drop drag rigid sphere drop distortion SAE wall impinge none rebound-slide model SAE wall film/splash SAE collision/coalesce O Rourke shattering collisions Atom. Sprays 1999 vaporization single component multicomponent fuels SAE low pressure high pressure SAE ignition Arrhenius reduced chemistry SAE combustion Arrhenius CTC/GAMUT SAE reduced kinetics SAE NOx Zeldo vich Extended Zeldo vich SAE soot none Hiroyasu & Surovkin SAE Nagle Strickland oxidation SAE ERC RCCI Research 11 CEFRC3-5, 014

Reitz, 198 Atomization models (Single hole nozzle) Four main jet breakup regimes: Rayleigh, first wind-induced, second wind-induced and atomization a.) Rayleigh breakup Drop diameters > jet diameter.

12 Reitz, 198 Atomization models (Single hole nozzle) Four main jet breakup regimes: Rayleigh, first wind-induced, second wind-induced and atomization a.) Rayleigh breakup Drop diameters > jet diameter. Breakup far downstream nozzle b.) First wind-induced regime Drop diameter ~ jet diameter. Breakup far downstream of nozzle c.) Second wind-induced regime Drop sizes < jet diameter. Breakup starts close to nozzle exit d.) Atomization regime Drop sizes << jet diameter. Breakup at nozzle exit. Growth of small disturbances initiates liquid breakup Jet breakup known to depend on nozzle design details. Need to start by considering flow in the injector nozzle passage 1 CEFRC3-5, 014

13 Cavitation inception Account for effects of nozzle geometry r/d Cavitation region Sarre, 1999 Initial D Cavitation if P < P v U mean C c 1 vena Yes P / P 1 No l/d Cavitating flow 1 ( C C ) Contraction coefficient (Nurick (1976) c c Non-cavitating flow c c C c sharp inlet nozzle C c 1 [( ) 114. r / d] / r/d 13 CEFRC3-5, 014

14 Sarre, 1999 ERC Nozzle Flow Model Cavitating flow Yes P / P 1 Non-cavitating flow No Nozzle discharge coefficient Nozzle discharge coefficient u C eff d C c p p 1 1 p p v Effective injection velocity C P P ( 1 C ) P C ( P P ) c 1 c v c 1 v C u Lichtarowicz (1965) d eff l d Effective injection velocity C d ( P 1 P ) Effective nozzle area Effective nozzle area A eff Cc ( P1 Pv ) C P P ( 1 C ) P A c 1 c v A eff A 14 CEFRC3-5, 014

15 Sonic Velocity (m/sec) 1 a l Part 5: Atomization, Drop Breakup/Coalescence Nozzle flow - cavitation Homogeneous Equilibrium Model - single phase mixture of vapor and liquid - considers variable compressibility of mixture. (1) Sonic Speed of mixture : function of void fraction l v α=0 for pure liquid α=1 for pure vapor 1 (1 ) v l v lal va Theory (γ) 1.4 (Adiabatic) 1.0 (Isothermal) Lee, 010 P sat vav l v l P Pl Pvl log l vav vav lal vl : by integrating dp a d (Schmidt, 1997) va v v a lal v v l a l l (Wallis, 1967) () Equation of State of mixture P sat l sat v av Pv Pvl log l al pure liquid Void fraction, α pure vapor Sonic velocity in bubbly air/water mixture at atmospheric pressure Brennen (1995) 15 CEFRC3-5, 014

16 Nozzle flow - cavitation Lee, 010 max velocity at exit, cm/s min. density at exit, g/cm 3 Max V Max ρ (sec) (sec) streamline and exit velocity density and iso-surface (ρ=0.35g/cm 3 ) 16 CEFRC3-5, 014

17 Eulerian flow models Bubbles Nozzle diameter Spray Angle Wang,, 014 Inlet rounding Nozzle Walls Nozzle Length Liquid Core Droplets Breakup Length Develop a CFD Model that: 1) Simulates internal nozzle flow and external sprays simultaneously; ) Models the thermodynamic states of the compressible liquid and gas; 3) Is able to simulate flows with large pressure and density ratios (1000:1); 4) Predicts phase change based on the nd Law of Thermodynamics; 5) Offers the capability of Eulerian-Lagrangian transition for dispersed sprays; (Eulerian-Lagrangian Spray and Atomization (ELSA) Model) 6) Models the sub-grid liquid-gas interface area density for the ELSA Model. 17 CEFRC3-5, 014

18 Wang,, Equation model - Eulerian Fluid Solver Relaxation terms Gas Liquid Stiffened Gas Equation of State: (7) Liquid-Vapor-Air 3-phase mixture L A V 18 CEFRC3-5, 014

19 Wang,, 014 Equations solved with hybrid Rusanov HLLC scheme 19 CEFRC3-5, 014

$density vapor mass fraction pressure velocity Water$ injected into water: Cavitation is generated over

Large region of cavitated fluid (bubble cloud)

20 Wang,, 014 Submerged Liquid Jet Chamber water density vapor mass fraction pressure velocity Water injected into water: Cavitation is generated over entire length of nozzle walls. Large region of cavitated fluid (bubble cloud) appears in chamber. Engine Research Center University of Wisconsin 5 0 CEFRC3-5, 014

21 Submerged Liquid Jet Chamber water Water injected into water: Cavitation generated over portions of nozzle passage. Large region of cavitated fluid (bubble cloud) appears in chamber. 1 CEFRC3-5, 014

$fraction pressure$ (vapor pressure) regions

22 Wang,, 014 Cavitating Liquid Jet Non-condensible air density vapor mass fraction pressure velocity Low pressure (vapor pressure) regions seen within entire nozzle Air mass fraction CEFRC3-5, 014 6

23 Wang,, 014 Cavitating Liquid Jet Non-condensible air 3 CEFRC3-5, 014

Atomization - Wave breakup model Reitz, 198 Taylor & Hoyt, 1983 High speed photograph of water jet close to nozzle exit (at top) in the second wind-induced breakup regime showing surface wave

24 Atomization - Wave breakup model Reitz, 198 Taylor & Hoyt, 1983 High speed photograph of water jet close to nozzle exit (at top) in the second wind-induced breakup regime showing surface wave instability growth and breakup Kelvin-Helmholtz Jet Breakup Model Linear Stability Theory: Cylindrical liquid jet issuing from a circular orifice into a stationary, incompressible gas. Relate growth rate, w, of perturbation to wavelength /k h = R h 0 e ikz + w t h 4 CEFRC3-5, 014

25 Reitz, 198 hh e t B 0 Linearized analysis r Equation of liquid surface: r = a+h, Surface waves breakup on jet or "blob" Axisymmetric fluctuating pressure, axial velocity, and radial velocity for both liquid and gas phases. Fluctuations described by continuity equation u i z 1 r plus linearized equations of motion for the liquid and the gas, Axial: 1 u i t Z a u U ( r ) i i z U(r) v i du i dr 1 i U = Jet velocity p i z h = R h 0 e ikz + w t m i i u i z r ( rv i ) 0 1 u r i r r r 5 CEFRC3-5, 014

26 Analysis (Cont.) Part 5: Atomization, Drop Breakup/Coalescence Reitz, 198 Radial: v i t U i ( r ) v i z 1 i p i r m i i v i 1 rv i z r r r Gas is assumed to be inviscid U(r) = U - slip With h <<a, the gas equations give the pressure at the interface r = a Boundary conditions- p ( U i w k ) k h K ( ka ) 0 K 1 ( ka ) Kinematic, tangential and normal stress at the interface: v 1 w h t, u 1 r v 1 z p 1 n 1 1 v 1 r s a ( h a h z ) p 0 6 CEFRC3-5, 014

27 Reitz, 1988 Dispersion relationship w + v 1 k ' I w 1 ka I 0 ka - kl I 1 ka k + l I 0 ka ' I 1 la I 0 la = s k 1 a 1 - k a l - k l + k I 1 ka I 0 ka + 1 U - i w / k k l - k I 1 ka K 0 ka l + k I 0 ka K 1 ka Weber Ohnesorge Maximum wave growth rate characterizes fastest growing waves which are responsible for breakup (as a function of Weber and Ohnesorge numbers) Maximum wave growth rate and length scale: and 7 CEFRC3-5, 014

28 Curvefits of dispersion equation Reitz, 1988 a = Z T a 3 s We 0.5 = We Z T 0.6 where Z = We Re ; T = Z We ; We 1 = 1 U a s ; We = U a s ; Re 1 = Ua v 1 Maximum growth rate increases and wavelength decreases with We Increased viscosity reduces growth rate and increases wave length Wavelength Ohnesorge number, Z growth rate Weber number, We Weber number, We 8 CEFRC3-5, 014

29 f(t)= Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1988 Wave atomization model Drop size: r B Breakup time: ~ 1 q v ~ U Spray angle prediction: Tan q v U 1 A g 4 ( ) 1 / f ( T ) 1 l Breakup length of the core (Taylor, 1940): L C a 1 / f ( T ) where f T 1 exp 10T 6 3 T= 9 CEFRC3-5, 014

X-ray Phase-contrast imaging of high-pressure sprays

Single-Shot images Surface instability waves produce

fuel properties (Hydroground nozzle, biodiesel, 1 ms

30 X-ray Phase-contrast imaging of high-pressure sprays Gao, 010 ANL Synchrotron-Based Ultrafast (150 ps) Single-Shot images Surface instability waves produce ligaments Breakup sensitive to injection pressure, fuel properties (Hydroground nozzle, biodiesel, 1 ms injection duration in quasi-steady state) 30 CEFRC3-5, 014

31 Beale, 1999 Rutland, 011 ERC spray modeling Deshpande, 013 LDEF - RANS Approach LDEF LES Approach Pure Eulerian DNS - Reitz - Rutland Approach - Trujillo Track liquid-gas interface with VOF method 31 CEFRC3-5, 014

32 ELSA model Modeling liquid-gas surface area density [1-5] Liquid-Gas Surface Area Density [5] : Comparing Modeling and DNS Part 5: Atomization, Drop Breakup/Coalescence Wang, 013 : Liquid-Air surface area per unit mass: m t u a 1 t Sc eq 3/5 /5 s l t req C k 3/5 Y /15 11/15 L l v req Weeq C O s 1 3 CEFRC3-5, 014

33 Wang, 013 ELSA model - Modeling liquid-gas surface area density [1-5] Eulerian-Lagrangian transition in the dispersed spray region Control Volumes transition Droplet size: based on the local surface area density Droplet number: based on droplet size, as well as the liquid mass inside the cell Eulerian Liquid Mass Parcel Droplet Advantages: Naturally works with RANS and does not require expensive mesh resolution. Criterion for transition: (A) Liquid volume fraction is less than a threshold value; (B) Liquid mass in the cell is larger than a threshold value 33 CEFRC3-5, 014

34 Wang, 013 ELSA model Modeling liquid-gas surface area density [1-5] Axi-Symmetric Round Nozzle L=1.05 mm, D = 139 μm Injection Pressure: 400 bar, Chamber Pressure: 0 bar Sharp corner at inlet, rounded corner at inlet with r/r=1 34 CEFRC3-5, 014

35 Drop breakup Part 5: Atomization, Drop Breakup/Coalescence Liu, 1997 Mechanisms of drop breakup at high velocities poorly understood - Conflicting theories Bag, 'Shear' and 'Catastrophic' breakup regimes Breakup due to capillary surface waves Hinze Chem Eng (1955) and Engel Nat. Bureau Stds (1958) Boundary Layer Stripping due to Shear at the interface Ranger and Nicolls AIAA J. (1969) Reinecke and Waldman AVCO Rep (1970) d(x) Delplanque & Sirignano Atom Sprays (1994) Stretching and thinning drop distortion - Liu and Reitz IJMF (1997) 35 CEFRC3-5, 014

36 Liu, 1993 Low velocity drop breakup Gas Liquid injection orifice 1.7 Liquid drop Nozzle Fig. Schematic diagram of liquid drop breakup with the transverse gas jet 36 CEFRC3-5, 014

37 High speed drop breakup mechanism Air jet Hwang, 1996 Double pulse images RT waves RT Drops Product drops KH waves KH Rayleigh Taylor Breakup RT 3 g t = acceleration g RT s g t t l l l 3s g g g 3 37 CEFRC3-5, 014

38 l Part 5: Atomization, Drop Breakup/Coalescence Lee, 001 Drop breakup regimes Breakup stages Deformation or breakup regimes Breakup process Weber number References First breakup stage (1) Deformation and flattening Air We < 1 (b) Bag breakup Air Bag growth Bag burst Rim burst 1 We 100 (including the Bag-and-Stamen breakup) Pilch and Erdman Second breakup stage Air (c) Shear breakup We < 80 Ranger and Nicolls 1969 (d) Stretching and thinning breakup Air 100 We 350 Liu and Reitz 1997 (e) Catastrophic breakup Air Flattening and thinning RT waves KH waves 350 We Hwang et al CEFRC3-5, 014

39 O Rourke, 1981 Drop collision modeling Collision frequency n 1 N (r 1 r ) E 1 v 1 v /Vol 1 r 1 v Collision efficiency E 1 v 1 K K 1/ K l v 1 v r 9 m g r 1 ~ 1 Number of collisions from Poisson process p(n) = e -n 1t n 1 t n /n! 0 < p <1 random number 39 CEFRC3-5, 014

surface energy 3. Drops cannot expel trapped gas film (bounce apart) 4.

40 B= Part 5: Atomization, Drop Breakup/Coalescence Munnannur, 007 Drop collision and coalescence 1. Reflexive vs. surface energy. Kinetic energy of unaffected part vs. surface energy 3. Drops cannot expel trapped gas film (bounce apart) 4. Drops form combined mass (coalesce) Georjon, b δ d s u l U We ρ L U d s σ b B, ( d s d l ), Δ d s d l u s 40 CEFRC3-5, 014 d l

41 Ashgriz, 1990 Drop coalescence Grazing-coalescence boundary Drops fly apart if rotational energy of colliding pair exceeds surface energy of combined pair x B 1 5 We < B x <1 random number B 41 CEFRC3-5, 014

42 Ashgriz, 1990 Grazing - stretching separation Energy and angular momentum conservation: Grazing drops move in same direction but at reduced velocity Coalescence mass average properties of colliding drops B 4 CEFRC3-5, 014

Ashgriz, 1990 Reflexive separation Tennison, 1998 We 6 h 1 h 1 3 3 41 7 1 3 3 0 0.5 0. 0.15 Coalescence ²=1 ²=0.75 ²=0.

43 Ashgriz, 1990 Reflexive separation Tennison, 1998 We 6 h 1 h Coalescence ²=1 ²=0.75 ²=0.5 h h 1 3 with / 1 B x Reflexive separation *We B 43 CEFRC3-5, 014

Summary Part 5: Atomization, Drop Breakup/Coalescence Reitz, 014 The Lagrangian Drop/Eulerian Fluid (LDEF) Discrete Drop model is the workhorse approach in commercial codes for simulating -phase

44 Summary Part 5: Atomization, Drop Breakup/Coalescence Reitz, 014 The Lagrangian Drop/Eulerian Fluid (LDEF) Discrete Drop model is the workhorse approach in commercial codes for simulating -phase flows. Detailed models are available for use in engine CFD models to describe the effects of injector nozzle flow, and liquid and gas properties on spray formation and drop breakup physics. Due to the importance of sprays in applications, research is still needed. Recent experimental and modeling work can be accessed through ILASS and ICLASS conference papers and the Atomization and Sprays journal. Significant progress is being made using LES/DNS spray modeling with high resolution experimental diagnostics to validate engine CFD spray models. Ballistic imaging: Linne, 009; X-Ray imaging: Liu SAE paper LES: Villiers & Gosman, LES Primary Diesel Spray Atomization, SAE DNS: Near field spray modeling (Trujillo - ERC) Reitz, Pickett & Trujillo, CEFRC3-5, 014

Reciprocating Internal Combustion Engines

Reciprocating Internal Combustion Engines Prof. Rolf D. Reitz, Engine Research Center, University of Wisconsin-Madison 01 Princeton-CEFRC Summer Program on Combustion Course Length: 9 hrs (Wed., Thur.,