Reciprocating Internal Combustion Engines

Transcription

1 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., Fri., June 7-9) Hour 4 Copyright 01 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 CEFRC4 June 8, 01

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) Hour 1: IC Engine Review, 0, 1 and 3-D modeling Hour : Turbochargers, Engine Performance Metrics Hour 3: Chemical Kinetics, HCCI & SI Combustion Day (Spray combustion modeling) Hour 4: Atomization, Drop Breakup/Coalescence Hour 5: Drop Drag/Wall Impinge/Vaporization Hour 6: Heat transfer, NOx and Soot Emissions Day 3 (Applications) Hour 7: Diesel combustion and SI knock modeling Hour 8: Optimization and Low Temperature Combustion Hour 9: Automotive applications and the Future CEFRC4 June 8, 01

3 Resolution predictive models Finite difference mesh 10 cm 1-D 10 4 grid points 3-D 10 1 grid points 10 m Models will not be entirely predictive over next decade 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 CEFRC4 June 8, 01

4 Governing Equations Gas phase Liquid phase Turbulence Hour 4: Atomization, Drop Breakup/Coalescence Two-Phase Flow Regimes x, v, r, Td Computational cell 1 ( f = f (x, v, r, T d ; t) 4 3 r3 f drdv dtd Amsden et al Gas void fraction and drop number density Vol Current spray models: drops occupy no volume>0.9 )dvol / Vol Drop parcels Intact Churning Thick Thin Very thin 4 CEFRC4 June 8, 01

5 Spray Modeling Dukowicz 1980 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=10m 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 CEFRC4 June 8, 01

6 Eulerian Gas Phase Amsden et al Mass conservation (species) t (u) l 4r R f drdv dt d R = dr/dt - Vapor source Momentum conservation u (uu )p( 3 t Turbulent and viscous stress k )F s g Rate of momentum gain due to spray drop drag 6 CEFRC4 June 8, 01

7 Gas Phase () Amsden et al Internal energy conservation I t Heat flux Equations of state Combustion heat release +ui = -Pu -J ++ Q c + Q s JTD h m ( m /) m prt m / W m Specific heat, enthalpy from JANAF data m Turbulence dissipation Energy due to Spray - vaporization 7 CEFRC4 June 8, 01

8 Liquid Phase Hour 4: Atomization, Drop Breakup/Coalescence Spray drop number conservation f t + xfv + v ff + r (fr ) +. f = f (x, v, r, T d, y, y; t). Amsden, T d ft 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 4/3r 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 ' d v dr d T d dy d y Work done by drop drag forces W s = - f d 4/3r 3 F ' u ' dv dr dt d dy dy 8 CEFRC4 June 8, 01

9 Lagrangian drop - liquid phase Amsden, 1997 Discrete Drop Model drop position dx dt v drop velocity l u u' dv dt F drop size dr dt R Turbulence model provides: l, u t t+dt v Spray submodels provide: F - Drag, R Vaporize.. f coll + f bu - breakup/collide Initial data: v, r, T d Atomization model 9 CEFRC4 June 8, 01

10 Turbulence Model (RANS) Kinetic energy Amsden, 1997 Dissipation k t (uk) kuu(. )k 3 Pr k Ý W s Dissipation rate Production due to mean flow Rate of work to disperse drops +u= - t C 1 - C 3 u + 3 Pr + k C 1:u - C + C s W s Turbulence diffusivity DC k / Eddy size l = C k 3/ / Turbulence intensity u = ( k/3) 10 CEFRC4 June 8, 01

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 CEFRC4 June 8, 01

12 Review of atomization models (Single Hole Nozzle) Reitz & Bracco, 198 Four main jet breakup regimes: Rayleigh, first wind-induced, second wind-induced and atomization Growth of small disturbances initiates liquid breakup 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. 1 CEFRC4 June 8, 01

13 P sat v av l v l PP l P vl log lv av v av lal vl 1 a l 1 (1 ) v l v l al v v Hour 4: Atomization, Drop Breakup/Coalescence Nozzle flow - cavitation Lee & Reitz, 010 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 l al v v a a a v α=0 for pure liquid α=1 for pure vapor v l l l va (Wallis, 1967) () Equation of State of mixture : by integrating dpa d (Schmidt, 1997) P sat l Sonic Velocity (m/sec) sat v av P v P vl log l al pure liquid Theory (γ) 1.4 (Adiabatic) 1.0 (Isothermal) Void fraction, α pure vapor Sonic velocity in bubbly air/water mixture at atmospheric pressure Brennen (1995) 13 CEFRC4 June 8, 01

14 Nozzle flow - cavitation Lee & Reitz, 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 ) 14 CEFRC4 June 8, 01

15 Cavitation Inception Account for effects of nozzle geometry r/d Cavitation region Initial D Cavitation if P < P v U mean C c 1 vena Yes P / P 1 No l/d Sarre SAE Cavitating flow 1 ( C C ) Contraction coefficient (Nurick (1976) c c Non-cavitating flow c c C c sharp inlet nozzle C 1 c [( ) 11. 4r / d ] / CEFRC4 June 8, 01 r/d

16 ERC Nozzle Flow Model Cavitating flow Yes P / P 1 No Non-cavitating flow Nozzle discharge coefficient C d C c p p 1 1 p p Effective injection velocity v Nozzle discharge coefficient Lichtarowicz (1965) C l d d Effective injection velocity u eff C P1 P( 1 C ) P C ( PP ) c c v c 1 v u eff C d ( P 1 P ) Effective nozzle area Effective nozzle area A eff Cc ( P1 Pv ) C PP ( 1 C ) P A c 1 c v A eff A Sarre SAE CEFRC4 June 8, 01

17 Atomization - Wave breakup model 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 Reitz & Bracco, 198 Kelvin Helmholtz Jet Breakup Model Linear Stability Theory: Cylindrical liquid jet issuing from a circular orifice into a stationary, incompressible gas. = R 0 e ikz+t Relate growth rate,, of perturbation to wavelengthk 17 CEFRC4 June 8, 01

18 e t B 0 Linearized analysis r 1 Z Equation of liquid surface: r = a+, 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 a U(r) U = Jet velocity = R 0 e ikz+t u i z 1 r plus linearized equations of motion for the liquid and the gas, Reitz & Bracco, 198 r (rv i )0 Axial: u i t U (r) u i i z v i du i dr 1 p i u 1 i i r u i z z rr r i i 18 CEFRC4 June 8, 01

19 Analysis (Cont.) Reitz & Bracco, 198 Radial: v i t U i (r) v i z 1 i p i r i i v i z 1 r r rv i r Gas is assumed to be inviscid U(r) = U - slip With<<a, the gas equations give the pressure at the interface r = a Boundary conditions- p (Ui k ) k K 0 (ka) K 1 (ka) Kinematic, tangential and normal stress at the interface: v 1 w t, u 1 r v 1 z p v 1 r a ( a z ) p 0 19 CEFRC4 June 8, 01

20 Dispersion Relationship Reitz, v 1 k I 1 ' ka I 0 ka - kl I1 ka k +l I 0 ka I1 ' la I 0 la = k 1a 1 - k a l - k l + k I 1 ka I 0 ka + 1 U - i/k k l - k l + k I 1 ka K0 ka I 0 ka K1 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 0 CEFRC4 June 8, 01

21 Curvefit of Dispersion Equation a = Z T We a Reitz, 1988 = We Z T 0.6 where Z= We Re 1 ; T=ZWe 0.5 ; We1= 1 U a ; We = U a ; Re 1= Ua v1 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 1 CEFRC4 June 8, 01

22 Wave atomization model Reitz, 1988 Drop size: r B Breakup time:~ v ~ U Spray angle prediction: v Tan U 1 A 4( g l ) 1 / f (T ) Breakup length of the core (Taylor, 1940): f(t)= LC a 1 / f (T ) where f T 1 exp 10T 6 3 T= CEFRC4 June 8, 01

23 X-ray Phase-contrast imaging of high-pressure sprays 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) Gao, CEFRC4 June 8, 01

24 Drop breakup Hour 4: Atomization, Drop Breakup/Coalescence 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) (x) Delplanque & Sirignano Atom Sprays (1994) Stretching and thinning drop distortion - Liu and Reitz IJMF (1997) 4 CEFRC4 June 8, 01

25 Hour 4: Atomization, Drop Breakup/Coalescence Low velocity drop breakup Liu & Reitz, 1993 Gas Liquid injection orifice 1.7 Nozzle Liquid drop 5 CEFRC4 June 8, 01

26 Hour 4: Atomization, Drop Breakup/Coalescence High speed drop breakup mechanism Double pulse images Air jet RT waves KH waves RT KH Drops Rayleigh Taylor Breakup RT Product drops gt = acceleration Hwang, g RT 3 t l g l g g t l g 3 CEFRC4 June 8, 01

27 Hour 4: Atomization, Drop Breakup/Coalescence Drop Breakup Regimes Breakup stages First breakup stage Deformation or breakup regimes (1) Deformation and flattening (b) Bag breakup Breakup process 1 We 100 (including the Bag-and-Stamen breakup) Pilch and Erdman Air We 80 Ranger and Nicolls 1969 Air 100 We 350 Liu and Reitz 1997 Air 350 We Hwang et al Air Bag burst Rim burst (e) Catastrophic breakup l Second breakup stage (d) Stretching and thinning breakup References We 1 Air Bag growth (c) Shear breakup Weber number Flattening and thinning RT waves KH waves Lee & Reitz, CEFRC4 June 8, 01

28 Hour 4: Atomization, Drop Breakup/Coalescence O Rourke PhD thesis 1981 Drop collision modeling Collision frequency 1 N (r 1 r ) E 1 v 1 v / Vol 1 r1 v v1 Number of collisions from Poisson process p(n) = e - 1 t 1 t n /n! Collision efficiency K E1 ~ 1 K 1 / 0 < p <1 random number l v1 v r K 9 g r1 8 CEFRC4 June 8, 01

29 Hour 4: Atomization, Drop Breakup/Coalescence Drop collision and coalescence Munnannur, 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) B= δ We ρlu d s σ b B, ( d s d l ), 9 d Δ s dl CEFRC4 June 8, 01

30 Hour 4: Atomization, Drop Breakup/Coalescence Drop coalescence Ashgriz & Poo, 1990 Grazing-coalescence boundary Drops fly apart if rotational energy of colliding pair exceeds surface energy of combined pair We 1 3 Bx 11 0 < Bx <1 random number B 30 CEFRC4 June 8, 01

31 Hour 4: Atomization, Drop Breakup/Coalescence Grazing - Stretching Separation Ashgriz & Poo, 1990 Energy and angular momentum conservation: Grazing drops move in same direction but at reduced velocity Coalescence mass average properties of colliding drops B 31 CEFRC4 June 8, 01

32 Hour 4: Atomization, Drop Breakup/Coalescence Reflexive Separation ²=1 ²=0.75 ²= Tennison, SAE We with Coalescence Reflexive separation 0 1 Bx 1 / *We Ashgriz & Poo, 1990 B 3 CEFRC4 June 8,

33 Hour 4: Atomization, Drop Breakup/Coalescence Summary 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, CEFRC4 June 8, 01