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Atomization, Drop Breakup/Coalescence

Atomization, Drop Breakup/Coalescence 17
Part 5: Atomization, Drop Breakup/Coalescence Reciprocating Internal Combustion Engines Prof. Rolf D. Reitz Engine Research Center University of WisconsinMadison 2014 PrincetonCEFRC Summer School on Combustion Course Length: 15 hrs (Mon. Fri., June 23 – 27, 2014) Copyright ©2014 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 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Short course outine: Engine fundamentals and performance metrics, computer modeling supported by indepth understanding of fundamental engine processes and detailed experiments in engine design optimization. Day 1 (Engine fundamentals) Part 1: IC Engine Review, 0, 1 and 3D modeling Part 2: Turbochargers, Engine Performance Metrics Day 2 (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, Aftertreatment and Controls Part 10: Vehicle Applications, Future of IC Engines 2 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Resolution – predictive models 10 cm Finite difference 4 1D 10 grid points mesh 12 3D 10 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 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Amsden,1997 Governing Equations f = f (x, v, r, T ; t) d Gas phase x, v, r, Td Liquid phase Gas void fraction and drop number density Turbulence 4 3 Lagrangian Drop, q 1 ( r f drdvdT d)dVol/ Vol   Eulerian Fluid (LDEF) models 3 Vol Current LDEF spray TwoPhase Flow Regimes models: – drops Computational cell occupy no volume q 0.9 Drop parcels Thin Intact Churning Thick Very thin 4 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Dukowicz, 1980 LDEF Spray Modeling • Concept of using “drop parcels” For typical heavyduty diesel, injected fuel per cycle (75 load): 0.160 g One spray plume: m =0.160/6=0.0267 g fuel 10 If average SMD=10 mm  m =3.8x10 g drop 7 of drops in the domain=0.0267g/m =7.1x10 drop Impractical to track individual fuel drops – group identical drops into ‘parcels’ What you see in graphs: drop nozzle Grid size parcel 5 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Amsden,1997 Eulerian Gas Phase Mass conservation (species)  2 (u) 4r R f drdvdT l d  t R = dr/dt Vapor source Momentum conservation u 2 s  (uu)p(k) Fg 3 t Turbulent and viscous stress Rate of momentum gain due to spray – drop drag 6 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Amsden,1989 Gas Phase (2) Combustion Internal energy conservation heat release I c s +   uI = P u J +  + Q + Q t Turbulence Energy due to dissipation Spray vaporization Heat flux JTD h( /)  m m m Equations of state p RT / W  m m m Specific heat, enthalpy from JANAF data 7 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Amsden, 1997 Liquid Phase . Spray drop number conservation f = f (x, v, r, T , y, y; t) d . . . . f +  fv +  fF + (fR) + fT + fy + fy = f + f x v d coll bu trTyy d F=dv/dt R = dr/dt Drop Drop breakup, drop drag Vaporization and distortion coalescence heating Spray exchange functions s ' 3 2 F = f 4/3 r F + 4r Rv dv dr dT dy dy d d s 1 2 ' 2 3 ' Q = f 4r R I + vu + 4/3 r c T + F vuu dv dr dT dy dy d l l d d 2 s ' 3 ' Work done by drop drag forces W = f 4/3 r Fu dv dr dT dy dy d d 8 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Amsden, 1997 Lagrangian drop liquid phase Discrete Drop Model u' u drop position dx  v dt drop velocity l dv  F v dt drop size dr  R Spray submodels provide: dt F Drag, R – Vaporize . . f +  fv +  fF + (fR) + fT + fy + fy = f + f breakup/collide x v Turbulence model d coll bu trTy t y t+dt d provides: l, u’ Initial data: v, r, T – Atomization model d 9 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Amsden, 1997 Turbulence Model (RANS) Kinetic energy Dissipation   km 2 s . Ý  (uk) k u u ( )kW 3   t Pr   k Production due Rate of work to to mean flow disperse drops Dissipation rate m 2 +   u = C C u +   13 3 Pr t  s  + C :u C  + C W 12 s k Turbulence diffusivity Eddy size Turbulence intensity 2 3/2 D C k / m 2 l = C k / u’ = (2 k/3) 10 CEFRC35, 2014 UWERC Multidimensional CFD models Submodel Los Alamos UWUpdated References intake flow assumed initial flow compute intake flow SAE 951200 heat transfer lawofthewall compressible, unsteady SAE 960633 turbulence standard k RNG k /LES CST 106, 1995 nozzle flow none cavitation modeling SAE 1999010912 atomization Taylor Analogy surfacewavegrowth SAE 960633 Kelvin Hemholtz SAE 980131 Rayleigh Taylor CST 171, 1998 drop breakup Taylor Analogy Rayleigh Taylor Atom. Sprays 1996 drop drag rigid sphere drop distortion SAE 960861 wall impinge none reboundslide model SAE 880107 wall film/splash SAE 982584 collision/coalesce O’Rourke shattering collisions Atom. Sprays 1999 vaporization single component multicomponent fuels SAE 2000010269 low pressure high pressure SAE 2001010998 ignition Arrhenius reduced chemistry SAE 2004010558 combustion Arrhenius CTC/GAMUT SAE 2004010102 reduced kinetics SAE 2003011087 NOx Zeldo’vich Extended Zeldo’vich SAE 940523 soot none Hiroyasu Surovkin SAE 960633 Nagle Strickland oxidation SAE 980549 11 ERC RCCI Research 11 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1982 Atomization models (Single hole nozzle) Four main jet breakup regimes: Rayleigh, first windinduced, second windinduced and atomization a.) Rayleigh breakup Drop diameters jet diameter. Breakup far downstream nozzle b.) First windinduced regime Drop diameter jet diameter. Breakup far downstream of nozzle c.) Second windinduced 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 • Jet breakup known to depend on nozzle initiates liquid breakup design details. • Need to start by considering flow in the injector nozzle passage 12 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Sarre, 1999 Cavitation inception Cavitation Initial r/d Account for effects of region D nozzle geometry C c U mean 2 Cavitation if P P vena 1 v l/d Yes No P / P 2 1 Noncavitating flow Cavitating flow 1.0 1 C c  2 2(C  C ) 0.9 c c sharp inlet 0.8 nozzle Contraction coefficient (Nurick (1976) 0.7 1 21/2 C ( )11.4r / d c 0.62 0.6 0.00 0.04 0.08 0.12 0.16 r/d 13 CEFRC35, 2014 c c Part 5: Atomization, Drop Breakup/Coalescence Sarre, 1999 ERC Nozzle Flow Model Cavitating flow Noncavitating flow Yes No P / P 2 1 Nozzle discharge coefficient Nozzle discharge coefficient Lichtarowicz (1965) p p 1 v C C l d c C 0.827 0.0085 d p p d 1 2 Effective injection velocity Effective injection velocity 2(P P ) 1 2 2C P P (1 2C )P u C c 1 2 c v eff d u eff C 2(P P ) c 1 v   Effective nozzle area Effective nozzle area 2 2C (P P ) c 1 v A A eff A A eff 2C P P (1 2C )P c 1 2 c v 14 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Lee, 2010 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  Theory (γ) α=0 for pure liquid l  1.4 (Adiabatic) α=1 for pure vapor  l v 1.0 (Isothermal)  1 1   (1)  v l 2 2 2 a  a a  v v l l (Wallis, 1967) (2) Equation of State of mixture Void fraction, α pure pure 2 : by integrating dP a d (Schmidt, 1997) liquid vapor 2  Sonic velocity in bubbly air/water  a sat v v l v l P P P log  l vl 2 2 2 mixture at atmospheric pressure  a a a  l v v v v l l Brennen (1995) 2 2 2 2   a a  a sat sat v v l l v l v v P P P P log vl 2 2 2 2 l v vl 2 2  a a  a v v l l  l l 15 CEFRC35, 2014 Sonic Velocity (m/sec) Part 5: Atomization, Drop Breakup/Coalescence Lee, 2010 Nozzle flow cavitation 3 min. density at exit, g/cm max velocity at exit, cm/s Max ρ Max V (sec) (sec) density and streamline and exit velocity isosurface 3 (ρ=0.35g/cm ) 16 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 Eulerian flow models Nozzle diameter Spray Angle Bubbles Liquid Core Nozzle Walls Droplets Nozzle Length Inlet rounding Breakup Length Develop a CFD Model that: 1) Simulates internal nozzle flow and external sprays simultaneously; 2) Models the thermodynamic states of the compressible liquid and gas; 3) Is able to simulate flows with large pressure and density ratios (1000:1); nd 4) Predicts phase change based on the 2 Law of Thermodynamics; 5) Offers the capability of EulerianLagrangian transition for dispersed sprays; (EulerianLagrangian Spray and Atomization (ELSA) Model) 6) Models the subgrid liquidgas interface area density for the ELSA Model. 17 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 7Equation model Eulerian Fluid Solver Relaxation terms Gas Liquid LiquidVaporAir (7) 3phase mixture A Stiffened Gas Equation of State: L V 18 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 Equations solved with hybrid Rusanov HLLC scheme 19 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 Submerged Liquid Jet Chamber water density vapor mass fraction pressure velocity Water injected into water: Cavitation is generated over entire length of nozzle walls. Engine Research Center – University of Wisconsin Engine Research Center – University of Wisconsin Large region of cavitated fluid (bubble cloud) appears in chamber. 5 20 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Chamber water Submerged Liquid Jet Water injected into water: Cavitation generated over portions of nozzle passage. Large region of cavitated fluid (bubble cloud) appears in chamber. 21 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 Cavitating Liquid Jet Noncondensible air vapor mass fraction density pressure velocity Air mass fraction Low pressure (vapor pressure) regions seen within entire nozzle 6 22 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 Noncondensible air Cavitating Liquid Jet 23 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1982 Atomization “Wave” breakup model Taylor Hoyt, 1983 High speed photograph of water jet close to nozzle exit (at top) in the second windinduced breakup regime showing surface wave instability growth and breakup KelvinHelmholtz Jet Breakup Model  h + t = R e h h w ikz 0 Linear Stability Theory: Cylindrical liquid jet issuing from a circular orifice into a stationary, incompressible gas. Relate growth rate, w, of perturbation to wavelength 2/k 24 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1982  t hh e  2B  0 Linearized analysis r U = Jet velocity 2a Surface waves breakup on jet or "blob" Z 1 2 + t = R e h h w ikz 0 U(r) Equation of liquid surface: r = a+h, Axisymmetric fluctuating pressure, axial velocity, and radial velocity for both liquid and gas phases.  u 1  i  ( rv )  0 Fluctuations described by continuity equation i  z r  r plus linearized equations of motion for the liquid and the gas, 2  u  u dU 1  p m  u 1    u  Axial:  i i i i i i i  U ( r )  v     r   i i 2    t  z dr   z   z r  r  r   i i 25 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1982 Analysis (Cont.) 2  v v 1  p m  v  1  rv   i i i i i i Radial:  U ( r )     i 2      t  z   r   z  r r  r   i i Gas is assumed to be inviscid U(r) = U slip With h a, the gas equations give the pressure at the interface r = a w K (ka ) 2 0 p   (U  i ) kh 2 2 k K ( ka ) 1 Boundary conditions Kinematic, tangential and normal stress at the interface:  h u  v 1 1 v  w  ,   1 t  r z 2 v  s  h 2 1  p  2 n   ( h  a )  p  0 1 1 1 2 2 2  r a  z 26 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1988 Dispersion relationship ' ' 2 2 I ka 2 1 I ka I ka I la s k 2 l k 2 1 1 1 2 kl 2 = 1 k a w + 2 v k w 1 2 2 2 I ka 2 2  a 0 1 I ka I ka I la l + k 0 0 0 k + l 2 2  I ka K ka 2 2 2 1 0 l k + U i w /k k  2 2 1 I ka K ka 0 1 l + k 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  27 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1988 Curvefits of dispersion equation 0.5 0.7 0.5 1.5 3 1 + 0.45 1 + 0.4 Z T  a  1 0.34 + 0. 38 We 2 = 9.02  = a 0.6 1.67 s 0.6 1 + 0.87 We 2 1 + Z 1 + 1. 4 T 2 2 0.5  U a  U a We 0.5 2 1 Ua 1 where Z= ; T= Z We ; We = ; We = ; Re = 2 1 2 1 s s v 1 Re 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 2 2 28 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1988 “Wave” atomization model Drop size: r B 1 Breakup time:   v   q U Spray angle prediction:  v 1 g 1 / 2 2 Tan q   4  ( ) f ( T ) U A  1 l Breakup length of the core (Taylor, 1940): T=  3 1 L  C a / f ( T ) fT1 exp10T where  6 2 29 CEFRC35, 2014 f(T)= Part 5: Atomization, Drop Breakup/Coalescence Gao, 2010 Xray Phasecontrast imaging of highpressure sprays ANL SynchrotronBased Ultrafast (150 ps) SingleShot images Surface instability waves produce ligaments Breakup sensitive to injection pressure, fuel properties (Hydroground nozzle, biodiesel, 1 ms injection duration in quasisteady state) 30 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Beale, 1999 Rutland, 2011 Deshpande, 2013 ERC spray modeling LDEF RANS Approach LDEF – LES Approach Pure Eulerian DNS Approach Trujillo Reitz Rutland Track liquidgas interface with VOF method 31 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang, 2013 15 ELSA model Modeling liquidgas surface area density 2/15 • : LiquidAir surface area per unit mass:  3/5 2/5 Y  s l t rC eq 11/15 3/5 k L   m t u a 1    2   t Sc vr  eq  l eq We C O 1  eq s LiquidGas Surface Area 5 Density : Comparing Modeling and DNS 32 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang, 2013 15 ELSA model Modeling liquidgas surface area density • EulerianLagrangian transition in the dispersed spray region Control Volumes Droplet size: based on the local surface area density transition Droplet number: based on droplet size, as well as the liquid mass inside the cell Parcel Droplet Eulerian Liquid Mass • 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 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang, 2013 15 ELSA model Modeling liquidgas surface area density • AxiSymmetric Round Nozzle • L=1.025 mm, D = 139 μm • Injection Pressure: 400 bar, Chamber Pressure: 20 bar • Sharp corner at inlet, rounded corner at inlet with r/R=1 34 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Liu, 1997 Drop breakup 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 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Liu, 1993 Gas Low velocity drop breakup Liquid injection orifice 1.27 Nozzle Liquid drop Fig. 2 Schematic diagram of liquid drop breakup with the transverse gas jet 36 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Hwang, 1996 High speed drop breakup mechanism Double pulse images Air jet RT waves Drops  RT KH waves Rayleigh Taylor  KH  Breakup 3 2   g 2 t l g  RT Product  3s l g drops g = acceleration  g t t l g RT 3s 37 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Lee, 2001 Drop breakup regimes Breakup Deformation or Breakup process Weber number References stages breakup regimes First Air (1) D eformation 12 breakup We and flattening stage   12 We 100 Air (including the (b) Bag breakup Pilch and Erdman BagandStamen Bag growth Bag burst breakup) Rim burst Air Ranger and 80 (c) Shear breakup We Nicolls 1969 Second breakup stage (d) Stretching and Air   thinning 100 350 We Liu and Reitz 1997 breakup Air (e) Catastrophic  350 Hwang et al. 1996 We breakup Flattening RT KH waves and thinning waves 38 CEFRC35, 2014 l Part 5: Atomization, Drop Breakup/Coalescence O’Rourke, 1981 Drop collision modeling Collision frequency 2 n N(r r ) E v v /Vol 12 2 1 2 12 1 2 1 r 1 v 2 2 v 1 Number of collisions from Poisson process n Collision efficiency nt 12 p(n) = ent /n 12 2  K  E 1 12   K1/ 2 0 p 1 random number 2  v v r 2 l 1 2 2 K 9m r g 1 39 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Munnannur, 2007 Georjon, 1999 Drop collision and coalescence 1. Reflexive vs. surface energy 2. Kinetic energy of unaffected part vs. surface energy 3. Drops cannot expel trapped gas film (bounce apart) 4. Drops form combined mass (coalesce) 1 2 3 4 δ d s b b u u l l U U u u s s 2 d 2b s ρ U d L sΔ B We d , (d d ) , l s l σ d l 40 CEFRC35, 2014 B= Part 5: Atomization, Drop Breakup/Coalescence Ashgriz, 1990 Drop coalescence Grazingcoalescence boundary Drops fly apart if rotational energy of colliding pair exceeds surface energy of combined pair 11 3 6 1 2 2 1  12   2 3 3 x 1 1 B  3   5We 1   0 B x 1  random number B 41 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence 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 42 CEFRC35, 2014 Part 5: Atomization, Drop Breakup/Coalescence Ashgriz, 1990 ²=1 Reflexive separation   ²=0.75 0.25  ²=0.5 Tennison, 1998 Coalescence 0.2 2 2 We  6 2 3 3 hh 3 4 1 7 1 0  1 2 2  3 0.15   1  1 2 2 2 0.1 h 21 1 1  1 1 0.05 2 2 2 2 3 h 2  Reflexive separation 2 0 1 0 10 20 30 40 50 60 70 80 90 100 with x1 B /2 2 2We B 43 CEFRC35, 2014 xPart 5: Atomization, Drop Breakup/Coalescence Reitz, 2014 Summary The Lagrangian Drop/Eulerian Fluid (LDEF) Discrete Drop model is the work horse approach in commercial codes for simulating 2phase 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, 2009; XRay imaging: Liu SAE paper 2010010877 LES: Villiers Gosman, LES Primary Diesel Spray Atomization, SAE 2004010100 DNS: Near field spray modeling (Trujillo ERC) Reitz, Pickett Trujillo, 2014 44 CEFRC35, 2014
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