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Drop Drag/Wall Impinge/Vaporization/Sprays

Drop Drag/Wall Impinge/Vaporization/Sprays 18
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Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays 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 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays 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 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Beale, 1999 RT Model ERC Spray modeling  1 LCa / f(T) Breakup length  2 Blob injection model Kelvin-Helmoltz Rayleigh Taylor R/D Linearized instability analysis L/D r=B 0 t = e 0  KH Model Spray Models Nozzle flow/cavitation Jet atomization KH-RT Drop breakup Drop collision/coalescence Discrete drop Drop drag model Multi-component fuel evaporation Spray-wall impingement 3 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Liu, 1993 Droplet drag modeling Steady-state Stokes viscous drag, added-mass and Basset history integral dv t ' dv 1 4 3 2 ' dt dv/dt = F 6r v (r ) 6r dt g g g 2 3 ' 0 dt tt General form 2  U g  V dv/dtC A U / U L d D f 2 1 2/3  24Re (1 Re / 6), Re 1000  d d d C  d 0.424, Re1000   d • Drop distortion (TAB model) 2 yy82  U l rel y5 2 3 2  r r 3 r l d l d l d C C (1 2.632y) d d ,sphere 4 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Gosman, 1981 Turbulence & drop dispersion Vortex structure • Monte Carlo method St 1  u u  u  St 1 3/2 2 St 1 G(u )4 / 3k exp(3u  / 4k) Stokes St=t /t Drop-eddy interaction time e p Eddy life time Residence time t l / u v t l / 2k / 3 p e 3/ 4 3/ 2  = l l = C k /  t min(t ,t ) int e p 5 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Wachters, 1966 Spray wall impingement At low approach velocities (We) drops rebound elastically With hot walls cushion of vapor fuel forms under the drop As approach velocity is increased, normal velocity component decreases and drop may break up 2  d/2 U n  We  Beyond We = 40 liquid spreads into surface layer At high temperatures film boiling takes place We=- 0.678We exp( 0.088We ) o i i   We 40 We 40 6 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Naber, 1988 Dry wall impingement models Stick - drops stick to the wall Reflect - drops rebound Slide/Jet - incident drop leaves tangent to the surface From mass and momentum conservation: p yb =- ln1- p(1- exp(- ) b where 0 p 1 random number exp(b )+1 2 sina=+ ( ) /1 (p /b ) exp(b )- 1 7 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Senecal, 1997 Lippert, 2000 ERC wall impingement models • Rebound or slide based on We • Enhanced breakup due to drop destabilization B = 1.73 1 3 2.5 2 1.5 1 measured (Naber et al.) predicted (present) 0.5 measured (Booth) predicted (present) 0  B 3 1 B 40 1 0 0.5 1 1.5 2 2.5  time (ms) B 3 1 B 40 1   We 40 We 40 8 CEFRC3-6, 2014 radial penetration (cm)Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Deng, 2014 Wet wall impingement – grid independent model Saffman lift force on splashed drops 2  U g  V dv / dt C A U / U F L d D f Saff 2 Fd1.61 Uv - Re Saff g g  du g 2 H w Re d g  dy g Wall Jet Model R w (b) Glauert analytical solution Drop splash criterion u real 1 22 E We E 3,330 L,i crit h 1 1 o u min( ,1) m 2 d Re Li , Splash mass ratio v y 1/ 4 drop 1 2  C  u  We m h Li ,  o m 0.1 0.4min( ,1) y  m d  2 Ud L inj noz u CFD C We L,inj  9 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Deng, 2014 H w R w 40 40 R R w Without Wall Jet Model 0.25 mm With Wall Jet Model w 0.25 mm 0.5 mm 0.5 mm 1.0 mm 1.0 mm 30 30 2.0 mm 2.0 mm exp exp 20 20 10 10 0 0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time / ms Time / ms 10 CEFRC3-6, 2014 Wall Spray Radius / mm Wall Spray Radius / mmPart 6: Drop Drag/Wall Impinge/Vaporization/Sprays Deng, 2014 Effect of ambient pressure 8 8 H w H w Pa = 7.5 bar Pa = 5 bar 0.25 mm 0.25 mm 0.5 mm 0.5 mm L = 24 mm L = 24 mm 1.0 mm 1.0 mm 6 6 2.0 mm 2.0 mm exp exp 4 4 2 2 0 0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time / ms Time / ms 8 8 H H w w Pa = 10 bar Pa = 15 bar 0.25 mm 0.25 mm 0.5 mm L = 24 mm 0.5 mm L = 24 mm 1.0 mm 1.0 mm 6 6 2.0 mm 2.0 mm exp exp 4 4 2 2 0 0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time / ms Time / ms 11 CEFRC3-6, 2014 Wall Spray Height / mm Wall Spray Height / mm Wall Spray Height / mm Wall Spray Height / mmPart 6: Drop Drag/Wall Impinge/Vaporization/Sprays Sirignano, 1999 Law, 1976-77 Aggarwal, 2000 Drop Vaporization – well understood for single component, low ambient pressure 2 – D Law Liquid-Vapor Interface: Tinf Equilibrium or YR Non-equilibrium T Drop Y Yinf R TR Mass transfer with Internal circulation and surroundings: vaporization, r profiles: temperature, condensation, gas solubility concentration, velocity Heat transfer to drop: convection (conduction), radiation Relative Drop Motion 12 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Amsden, 1989 Lefebvre, 1989 KIVA vaporization models Frossling correlation Rdr /dtDBSh/ (2r) Y 1 1 Mass transfer number Y 1 r B (YY ) /(1Y ) 1 1 1 Sherwood number ln(1B) 1/ 2 1/ 3 Sh (2.0 0.6 Re Sc ) d B Fuel mass fraction at drop surface p Y W / WW (1) 1 1 1 0 p (T ) v d Vapor pressure P from thermodynamic tables v 13 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Amsden, 1989 Lefebvre, 1989 Drop heat-up modeling Change in drop temperature from energy balance 4 3 2 2 r c T 4r RL(T ) 4r Q d d d d d 3 Rate of heat conduction to drop from T ∞ Ranz-Marshall correlation Q (T T )Nu / 2 r T d r dd where ln(1 B) 1/ 2 1/3 Nu (2.0 0.6Re Pr ) d B 14 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Ra, 2003 Vaporization regimes q q o o m m Boiling Flash boiling q q i i heating cooling T T d d q o q T T o T s s ∞ m m T T T T b b Tq q T amb i i s T T d d T d T T T T d s T s s ∞ r r T T Normal Normal T ∞ T evaporation evaporation d T =T s b heating cooling T =T s b T d r r 15 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Ra, 2003 Vaporization regimes Normal evaporation energy balance  C m P  mL(T ) h (TT ) (TT ) s i,eff d s s  2r C m C (y y ) Sh o P A F Fs exp1  Nu Nu  mass balance y y Fs F  m g ln(1 B ) g ln(1 ) m M m 1 y Fs Boiling evaporation (T from Clausius Clapeyron equation) b  C m P  mL(T ) (h )(TT ) (TT ) b i,eff sh d b b  2r C m C (y1) Sh o P A F exp1  Nu Nu T TT  d b  m 0.26 Superheated   0.76T (0T 5) sh h ,  t droplet  i,eff e eff e 2.33  correlation  0.027T (5T 25) e T T (Adachi et al., s 0.39 d 1997) 13.8T (25T )  q 16 CEFRC3-6, 2014 distribution or mole fraction % Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Ra, 2003 Lippert, 1997 Multi-component fuel modeling Diesel Gasoline d dies iese el l A A d dies iese el B l B A Ar rom omati atic c % % 34 34 16 16 S Su ulfu lfur r ppm ppm 10.5 10.5 7.3 7.3 P Para arafin fins s % % 33 33 42 42 N Nap apth then enes es % % 33 33 42 42 O Olef lefin in % % 0.2 0.2 0.3 0.3 C Cetan etane e 43 43 47 47 C C/H /H r rati atio o 7.014 7.014 6.393 6.393 1.6 50 gasoline composition Discrete g (mw ) 1.4 p i iso-octane approximation Common automotive fuels are 40 1.2 Single comp approx multi-component 1 30 Components: Various molecular 0.8 weights and chemical structures 20 Continuous f (I) 0.6 Three approaches; p i) single component approximation 0.4 10 ii) continuous multi-component 0.2 iii) discrete multi-component 0 0 0 50 100 150 200 250 300 molecular weight 17 CEFRC3-6, 2014 distribution or mole fraction %Yi, 2001 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Ra, 2003, 2009 Multi-component model formulation Continuous Multi-Component Discrete Multi-Component  Continuous system of a liquid phase +  Discrete system of a liquid phase + Semi-continuous mixture system of Discrete mixture system of vapor vapor phase fuel and ambient gas: phase fuel and ambient gas: N N N F s p p p p G (I) x f (I) x (I I ) G (I) x (I I ) x (I I ) p F p s s  p F F s s s1 F1 s1 continuous phase discrete phase discrete phase of fuel discrete phase of air/fuel mixture  Vapor phase transport equation,   Vapor phase transport equation, n n  I f (I)dI (n 0, 1, 2,) p p  0  y y v(Dy ) s i i i i g,i   n n n t   v  I J dI S f v f v I g  0 t    - func  Assumed distribution function :  1 y y v(Dy ) S (I ) (I ) F F F g f (I) exp t  () 2 2   ,  18 CEFRC3-6, 2014 Part 6: Drop Drag/Wall Impinge/Vaporization/Sprays Ra, 2009 DMC model tests 0.030 Diesel A Modeled species contents 0.025 species MW Mass fraction 0.020 Diesel A (US narrow-cut Diesel) 0.015 c14h30 198 0.6253 0.010 c12h26 170 0.0559 0.005 c16h34 226 0.3025 c18h38 254 0.0163 0.000 0 50 100 150 200 250 300 350 Diesel B (Euro Diesel) molecular weight g/mol c14h30 198 0.2376 0.012 Diesel B ic8h18 114 0.0153 0.010 c10h22 142 0.0807 0.008 c12h26 170 0.1863 0.006 c16h34 226 0.1984 0.004 c18h38 254 0.2817 0.002 0.000 0 50 100 150 200 250 300 350 molecular weight g/mol 19 CEFRC3-6, 2014 probabilty density probabilty densityPart 6: Drop Drag/Wall Impinge/Vaporization/Sprays Ra, 2009 Fuel component distributions MW=199.61 MW=196.06 0.0025 0.0120 0.0100 0.0020 0.0080 0.0015 0.0060 0.0010 0.0040 0.0005 0.0020 0.0000 0.0000 ic8h18 c10h22 c12h26 c14h30 c16h34 c18h38 ic8h18 c10h22 c12h26 c14h30 c16h34 c18h38 Diesel B MW =200 ini CA=-14 ( first ignition timing) 20 CEFRC3-6, 2014 mass fraction mass fraction