Atomization and sprays

atomization and sprays lefebvre free download and atomization in powder metallurgy
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Part 5: Atomization, Drop Breakup/Coalescence Reciprocating Internal Combustion Engines Prof. Rolf D. Reitz Engine Research Center University of Wisconsin-Madison 2014 Princeton-CEFRC 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 CEFRC3-5, 2014 Part 5: Atomization, Drop Breakup/Coalescence 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 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, After-treatment and Controls Part 10: Vehicle Applications, Future of IC Engines 2 CEFRC3-5, 2014 Part 5: Atomization, Drop Breakup/Coalescence Resolution – predictive models 10 cm Finite difference 4 1-D 10 grid points mesh 12 3-D 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 CEFRC3-5, 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 Two-Phase Flow Regimes models: – drops Computational cell occupy no volume q 0.9 Drop parcels Thin Intact Churning Thick Very thin 4 CEFRC3-5, 2014 Part 5: Atomization, Drop Breakup/Coalescence Dukowicz, 1980 LDEF Spray Modeling • Concept of using “drop parcels” For typical heavy-duty 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 CEFRC3-5, 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 CEFRC3-5, 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 CEFRC3-5, 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 + v-u + 4/3 r c T + F v-u-u 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 CEFRC3-5, 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 CEFRC3-5, 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 CEFRC3-5, 2014 UW-ERC Multidimensional CFD models Submodel Los Alamos UW-Updated References intake flow assumed initial flow compute intake flow SAE 951200 heat transfer law-of-the-wall compressible, unsteady SAE 960633 turbulence standard k- RNG k- /LES CST 106, 1995 nozzle flow none cavitation modeling SAE 1999-01-0912 atomization Taylor Analogy surface-wave-growth 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 rebound-slide model SAE 880107 wall film/splash SAE 982584 collision/coalesce O’Rourke shattering collisions Atom. Sprays 1999 vaporization single component multicomponent fuels SAE 2000-01-0269 low pressure high pressure SAE 2001-01-0998 ignition Arrhenius reduced chemistry SAE 2004-01-0558 combustion Arrhenius CTC/GAMUT SAE 2004-01-0102 reduced kinetics SAE 2003-01-1087 NOx Zeldo’vich Extended Zeldo’vich SAE 940523 soot none Hiroyasu & Surovkin SAE 960633 Nagle Strickland oxidation SAE 980549 11 ERC RCCI Research 11 CEFRC3-5, 2014 Part 5: Atomization, Drop Breakup/Coalescence Reitz, 1982 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 • Jet breakup known to depend on nozzle initiates liquid breakup design details. • Need to start by considering flow in the injector nozzle passage 12 CEFRC3-5, 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 Non-cavitating 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 CEFRC3-5, 2014 c c Part 5: Atomization, Drop Breakup/Coalescence Sarre, 1999 ERC Nozzle Flow Model Cavitating flow Non-cavitating 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 CEFRC3-5, 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 CEFRC3-5, 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 iso-surface 3 (ρ=0.35g/cm ) 16 CEFRC3-5, 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 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, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 7-Equation model - Eulerian Fluid Solver Relaxation terms Gas Liquid Liquid-Vapor-Air (7) 3-phase mixture A Stiffened Gas Equation of State: L V 18 CEFRC3-5, 2014 Part 5: Atomization, Drop Breakup/Coalescence Wang,, 2014 Equations solved with hybrid Rusanov HLLC scheme 19 CEFRC3-5, 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 CEFRC3-5, 2014
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