Superheated Fuel Injections for Automotive

Size: px

Start display at page:

Download "Superheated Fuel Injections for Automotive"

Valentine Short
6 years ago
Views:

1 University of Bologna Ph.D. School in Industrial Engineering g The Prediction of Flash Evaporation in Superheated Fuel Injections for Automotive Applications 3 years program review Sergio Negro XXIII Cycle A.Y Ph.D. Research in: Mechanics and Advanced Engineering Sciences: Fluid Machines and Energy Systems Tutor: Prof. Piero Pelloni

2 THE PHYSICS BEHIND FLASH EVAPORATION TARGET OF THE PRESENT RESEARCH MODELING INTERNAL FLASHING MODELING EXTERNAL FLASHING MODELING THE METASTABILITY OF THE LIQUID JET CONCLUSIONS

3 The physics behind Flash Evaporation P Po a liquid b critical ii point The process a a represent a subcooled fuel injection: (aerodynamic breakup) The process b b represents a superheated dfuel linjection process. Ps(To) spinodal limit Thermodynamic non equilibrium: 1 difference of T between phases P1 Psat a1 b2 b metastable region b1 vapour 2 Evaporation delay time (metastability) t 3 Excess of enthalpy T1 T2 T Violent phase change What happens inside and outside the nozzle during a superheated fuel injection?

4 The physics behind Flash Evaporation Experimental evidence of effervescent atomization at nozzle exit in high pressure gasoline injections T=293 K T=325 K T=372 K p = 80 kpa p=55kpa p = 30 kpa (Chalmers University Internal Report 2005) Well known effects of increasing superheat on sprays: droplet size decreases intact jet length decreases spray cone angle increases? (more investigation is needed)

5 The physics behind Flash Evaporation For very high ratios of injection to discharge pressures the evaporation rate at the jet surface becomes very high and sonic conditions maybe reached outside the nozzle The jet structure changes completely External flashing with surface evaporation at nozzle exit Back Pressure Diminishes Pinj=2.6 bar T= 76 C Shock wave Vieira and Simoes Moreira, Kurschat, Chaves and Meier, and other authors provided experimental evidences of sonic structures around the liquid jet and put forth a theory of an evaporation wave (Simoes Moreira and Shepherd)

6 The physics behind Flash Evaporation According to experimental results, considering only thermal effects, four basic different behaviours of a liquid jet issuing a short nozzle can be assumed: bubble growth a) b) sub-cooled liquid flow In-flow nucleation of superheated liquid break-up metastable liquid core c) d) bubble nucleation and growth effervescent atomization absence of in-flow nucleation two-phase mixture A choking or limiting mass flow rate can be reached for a certain superheating degree of the liquid During choking conditions the mass flow rate becomes insensitive to backpressure P3

Fuel injection process: two main regimes are of interest: The physics behind Flash Evaporation

Internal flashing with effervescent atomization at nozzle exit High injection pressure High turbulence

7 Fuel injection process: two main regimes are of interest: The physics behind Flash Evaporation metastable liquid core c) d) bubble nucleation and growth effervescent atomization 1. Internal flashing with effervescent atomization at nozzle exit High injection pressure High turbulence Low rate heat transfer explosive evaporation In nozzle nucleation (irregular jet outside) absence of in-flow nucleation 2. External flashing with surface evaporation at nozzle exit Low injection pressure two-phase mixture Short nozzles High rate heat transfer gentle evaporation No in nozzle nucleation (unbroken jet) T=293 K T=372 K

8 The target of the present research TARGET OF THE PRESENT RESEARCH Develop l a 1D homogeneous model able to simultaneously l deal with hboth hinternall and external flashing Provide the model the capacity to deal with hydrocarbon fuels, in metastable states Investigate the sensibility of Flashing to main thermo fluid dynamic parameters Apply the 1D model to investigate i thermal effects on fuel injection i in GDI engines Use the 1D model to provide boundary conditions to 3D CFD spray simulations

9 Modeling Internal Flashing Mass 1 p ( ρu) Momentum a + ρu df + x 2 t x F 2 ( ρu) ( ρu + p) t + x ρu + F = 0 2 df = x Energy ( ρeo ) ( ρu( e0 + p / ρ )) ρu( e0 + p / ρ ) Vapour mass fraction M F HEM df + + = EV + E F t x F x ( ρy ) ( ρuy ) ρuy df + + = Γ +1+1 t x F x Nucleation Model The nozzle flow 5,279 Is function of the N = CN exp k Δϑ superheating degree HRM + 1 closure equations for R time Γ Y = ρ Y Θ e Homogenous Relaxation Model (HRM). A relaxation time is required to model the transition from non equilibrium to equilibrium Nozzle-Spray Coupling Atomization Model Relates the bubble diameter to the void fraction and the superheated degree at nozzle exit Spray Evaporation

10 The evaporation sub model: closure for the HRM Γ = Y Ye Θ ρ Θ = Θ 0α φ Evaporation rate Relaxation time (Downar Zapolskiet al.) l) Modeling Internal Flashing Θ 0 = φ = [ p sat p (T sat in (T 4 ) P ] in ) [s] Two Phase speed of sound: 1 ρa 2 = α ρ a v 2 v 1 α 1 + ρ la 2 ρ l ρv 1 Y ρl p Phase change occurs and this must be accounted for (Saurel et. al., Catania et al.) ρvρl ρ = Y ρ + l ( 1 Y ) ρv Mixture density ρ Y = α v ρ Vapour mass fraction The equation of state: P RT v b a( T ) v ( v + b ) + b ( v b ) = D.Y. Peng and D.B. Robinson, 1976

11 Modeling FLASH EVAPORATION Internal Flashing The Peng Robinson EOS describes real fluids behaviour, and hydrocarbons properties n-dodecane n-octane n-heptane methanol ethanol water Formula C12H26 C8H18 C7H16 CH4O C2H6O H2O The Peng Robinson EOS can get around the discontinuity of evaporation during isothermal expansion P P Ideal Isotherm Experimental Isotherm IDEAL GAS LAW B' Psat A o B saturation pressure Psat IDEAL GAS LAW A' CUBIC EOS Cubic-eos Ideal gas law EXPERIMENTAL ISOTHERM V V=b V

12 Modeling Internal Flashing The PR EOS can describe superheated and subcooled states as long as the mechanical stability criterion is respected P [Pa] Psat P ρ T Isotherm curve for T=540 K Saturation pressure vapour spinodal limit > 0 A A1 UNPHYSICAL SOLUTION P ρ T < 0 B1 P ρ B T > 0 liquid spinodal limit Rho [kg/m3] SATURATED VAPOUR DENSITY SATURATED LIQUID DENSITY

13 Modeling Internal Flashing The PR EOS can calculate saturation pressure, spinodal limits, real enthalpy f A Z B ln = Z 1 ln( Z B) ln P 2 2B Z 0.414B Fugacity at equilibrium: L f = Vapour pressure line n-octane Liquid Spinodal Vapour Spinodal f V supercritical region Tc=569.1 K h h* = da T a + + dt Z 2.44B RT ( Z 1) ln 2 2b Z 0.414B enthalpy departure function PR-EOS Enthalpy Ideal Enthalpy P [Pa] liquid region Enthalp py [J/kg] ideal enthalpy vapour enthalpy Ttp=216.4 K metastable metastable vapour region T [K] liquid enthalpy T [K] Tc

14 Atomization model Critical condition N d = 2N d Modeling Internal Flashing Senda et al. Nozzle Spray Coupling A modified K. Huh and A.D. Gosman model for flashing droplets: probability density function p(x) R d = R d (DTsh,ltk) Mono dispersed Cloud R d = R d (DTsh) R d, b = 3 3 V 4πN l d p( x) Φ( x) = C τ A (x) x F T λ = = R b R d = Rd, b ν F 0.75 l C L ε 1 K ( C ) R b = R λ is the most perturbing scale assumed dto be proportional to the Kolmogorov length scale b T

Results: FLASH EVAPORATION Internal Flashing The code has been validated versus the Rossmeissl and Wirth s experiment The test case consists of a

Fluid Injection pressure [bar] Inlet water temperature [K] Downstream pressure [bar] Deionised water 7 393 and 413 Ranging from 1 to 5 The test

15 Results: FLASH EVAPORATION Internal Flashing The code has been validated versus the Rossmeissl and Wirth s experiment The test case consists of a pressurized liquid vessel with stirrer and wall heating jacket linked with an orifice nozzle placed at the bottom of the vessel Operating conditions Fluid Injection pressure [bar] Inlet water temperature [K] Downstream pressure [bar] Deionised water and 413 Ranging from 1 to 5 The test provides experimental measurements of the mass flow rate of a superheated liquid. The model capability in capturing the mass flow rate choking has been checked.

16 Results: Internal Flashing Validation: mass flow rate and choking condition ] Mass Flo ow Rate [g/s] Psat=1,98 Psat=1.98 bar Choked flow Q experimental 4-Flash-63 ] Mass Flo ow Rate [g/s] Psat=3,61 Psat=3.61 bar Choked flow Q experimental 4Flash63 4-Flash T=393 K T=413 K Outlet Pressure [bar] Outlet Pressure [bar] 4 Flash code allows to accurately reproduce the overall experimental mass flow trends: the maximum 4 Flash code allows to accurately reproduce the overall experimental mass flow trends: the maximum error is below 3%

17 The same set of conservation equation is solved within the nozzle Two phase region The nozzle flow Modeling External Flashing Absence of in-flow Intact superheated nucleation liquid core Surface Evaporation Model Relates the nozzle-flow conditions to a superheated fast evaporating external jet The evaporation is normal to the surface of the outside liquid core (u U) Flow is stationary Target: to obtain a front kinetic closure using P1 and P2 liquid P0 nozzle P Surface evaporation front P2 P1 liquid jet cylindrical expansion U P3

18 Modeling External Flashing The evaporation is modelled as a wave like process: the evaporation wave is a discontinuity and is treated in the same fashion as a deflagration wave in a combustion process Evaporation wave (Flame front) Vapour (products) control volume mass [ ρw] = 0 2 momentum [ ρw + P] = 0 Energy stored in the metastable state (Energy of chemical bonds) u Superheated Liquid (reactants) U w 2 h + 2 energy = 0 the evaporation wave in a superheated liquid is an adiabatic phase transition the latent heat of vapotization is supplied by the energy stored in the metastable state: the process is self sustaining the velocity u is constant and is two order of magnitude smaller than the velocity at which the the velocity u is constant and is two order of magnitude smaller than the velocity at which the mixture is ejected in the low pressure enviroment [Le Me tayer et al., ]

19 Modeling External Flashing Isentropic assumption: using the pressure before and after the evaporation front [Saurel], the vapour travels at the local speed of sound Evaporation front velocity p ( p met p CJ ) ( pmet pcj ) c = = V f = ξ Π (liquid/vapour interface) ρ ( ρl ρ g ) ( ρl ρ g ) ξ = The evaporated mass: sum of the contributions of all the cylinders of fluid liquid P0 conical nozzle P1=P met P1 P P2=P CJ Vf j cylindrical evaporation j+1 j+n 1 j+n P3 U Vf liquid jet Dx=Udt The Liquid idjet Extinction i Length Le is calculated l and compared with experimental ldata from Low pressure flashing mechanisms in iso octane liquid jets [Vieira and Simoes Moreira] Le

20 Results: External Flashing Comparison between simulation results of Le/D plotted versus Ps/Po ratio and experimental values by Viera and Simoes Moreira with iso Octane,, for injection pressures respectively of Po=122 kpa and Po=500 kpa (Din=3 mm, Dout=0,31 mm, L=8 mm) 40 Po=122 kpa 40 Po=500 kpa Flash Vieira and Simoes-Moreira's experiment Flash Vieira and Simoes-Moreira's experiment Le/D P D Le P D Le Ps/Po Ps/Po

21 P Po FLASH EVAPORATION critical point a b Modeling Metastability of the Liquid Jet Is it possible to know the degree of metastability from initial superheating conditions? (how deep b1 is in the metastable region) Ps(To) liquid spinodal limit An important tfeature of a flashing jet tis the Evaporation delay time: Delay time without nucleation? P1 Psat a1 b2 b1 metastable region vapour Nucleation (T=cost) + Growth (P=cost) tn << tg Delay time is driven by HEAT TRANSFER T1 T2 T metastable liquid core c) d) effervescent atomization

22 Modeling Metastability of the Liquid Jet Heat transfer: from the superheated liquid to the evaporating interface (free surface considered in the same fashion as bubble interface) ) The thermodynamic system moves from non equilibrium to equilibrium, driven by a superheating degree, variables at relaxation end can be calculated. Relaxation equation: dt dt T(t ) = Θ T sat T( Θ ) Tsat (T 0 Relaxation Temperature T sat ) T [K] To Heat transfer equation:(conduction) dq sh dt k = Sε x SH (T(t( ) T Θ 2 ρlcpd = Heat transfer Θ 8Kε SH ) Relaxation Time T Tsat 1 ε SH = ξ α P r Rp β Ja γ t [s]

23 Results: Metastability of the Liquid Jet Assessment of the injection pressure influence on the degree of metastability Π = Θ Θ Degree of me etastability Degree of me etastability 0.9 T=330 K T=350 K Experimental from Vieira and Simoes-Moreira Calculated Injection pressure [kpa] 0.1 Experimental from Vieira and Simoes-Moreira Calculated Injection pressure [kpa] Increasing of injection pressure seems to have a direct influence on the relaxation time constant which Increasing of injection pressure seems to have a direct influence on the relaxation time constant, which as a result reduces the degree of metastability (changes the time scale)

24 Modeling Metastability of the Liquid Jet Metastable pressure: When the pressure is locked during choking conditions the orifice cannot reach any imposed outlet pressure. P = ( 1 Π )P 1 s Calculated Pressure e [kpa] Psat Po = 122 kpa Po = 250 kpa Po = 500 kpa Po = 750 kpa Calculated Metastable Pressures P Experimental metastable pressure [Pa] T [K] Assessment of the influence of the injection pressure on the metastable pressure: thelower the injection pressure, the deeper the liquid enters into the metastable state [10].

25 Conclusions An analytical and numerical 1D model for internal and external flash evaporation is presented Calculation of internal flashing and effervescent atomization is presented The evaporation model has been validated versus experimental data An approximated front kinetic closure for the HRM is provided Calculation of the evaporation front velocity and of extinction jet length is proposed A time constant, based on a steady formulation of the heat exchange problem, has been derived and used as closure for the HRM The degree of metastability and the metastable pressure at nozzle exit are obtained under a frozen flow assumption This approach solves the problem of introducing an arbitrary parameter for the flash evaporation triggered in homogeneous non equilibrium models. Furthermore, it grants the homogeneous flow model the capacity to detect choking conditions induced by external flashing (without solving the Riemann problem!)

Mass flow determination in flashing openings

Int. Jnl. of Multiphysics Volume 3 Number 4 009 40 Mass flow determination in flashing openings Geanette Polanco Universidad Simón Bolívar Arne Holdø Narvik University College George Munday Coventry University