Copyright 15 SAE International 15-4-463 Aspects of Numerical Moelling of Flash-Boiling Fuel Sprays Christopher Price, Arash Hamzehloo an Pavlos Aleiferis University College Lonon, UK Davi Richarson Jaguar Lan Rover, UK ABSTRACT Flash-boiling of sprays may occur when a superheate liqui is ischarge into an ambient environment with lower pressure than its saturation pressure. Such conitions normally exist in irect-injection spark-ignition engines operating at low incyliner pressures an/or high fuel temperatures. The aition of novel high volatile aitives/fuels may also promote flashboiling. Fuel flashing plays a significant role in mixture formation by promoting faster breakup an higher fuel evaporation rates compare to non-flashing conitions. Therefore, funamental unerstaning of the characteristics of flashing sprays is necessary for the evelopment of more efficient mixture formation. The present computational work focuses on moelling flash-boiling of n-pentane an iso- Octane sprays using a Lagrangian particle tracking technique. First an evaporation moel for superheate roplets is implemente within the computational framework of STAR- CD, along with a full set of temperature epenent fuel properties. Then the computational tool is use to moel the injection of flashing sprays through a six-hole asymmetric injector. The computational results are valiate against optical experimental ata obtaine previously with the same injector by high-spee imaging techniques. The effects of ambient pressure (.5 an 1. bar) an fuel temperature ( 18 C) on the non-flashing an flashing characteristics are examine. Effects of initial roplet size an break-up submoels are also investigate. The computational methoology is able to reprouce important physical characteristics of flashboiling sprays like the onset an extent of spray collapse. Base on the current observations, further improvements to the mathematical methoology use for the flash-boiling moel are propose. INTRODUCTION Flash-Boiling Atomization Flash-boiling is the rapi phase transition from liqui to vapor when a liqui spray is ischarge into an ambient environment with lower pressure than the saturation pressure of the fuel. Uner this conition fuel roplets are superheate an enter a Page 1 of 3 metastable state, where the latent heat is consume by bubble nucleation within the liqui. Bubbles create at nucleation sites can continue to grow or collapse epening on the local fuel conitions surrouning each bubble an the size of the vapor bubble itself. Many forms of bubble nucleation an flashing can occur incluing: heterogeneous nucleation where bubbles form on surfaces an iscontinuities, homogeneous nucleation where bubbles form everywhere insie the liqui, combination of internal an external flashing, etc. The type of flashing an its characteristics epen on various parameters incluing: nozzle geometry, fuel properties an environmental conitions. Internal nucleation an bubble growth/bursting in fuel injectors can form a gaseous phase within the nozzle volume which may then create an uner-expane jet of fuel vapor at the nozzle exit (with embee liqui roplets). This occurs ue to the high injection pressures typically use with gasoline irect injection, currently up to bar. On the other han, external flashing occurs when the majority of bubble growth an bursting occurs just past the nozzle exit. The conitions in which a flash-boiling spray may form, can occur in irect-injection gasoline engines when operating at low-loa warm conitions with early intake stroke injection strategies to promote mixture homogeneity (i.e. injection of high-temperature fuel into low in-cyliner pressure). Particular engine operating strategies such as early intake valve closure (which can lea to a partial in-cyliner vacuum) can promote flashing conitions [1]. Highly booste ownsize engines can transfer a higher amount of heat into the fuel via heat transfer through the injector, increasing the latent heat, an in turn proucing further flashing mechanisms []. It is worth mentioning that uner the aforementione conitions flashboiling may occur uner conventional gasoline fuelling ue to the existence of high volatile components such as n-pentane. A strong initiative to use cleaner an more sustainable alternative fuels is an essential path for future internal combustion (IC) engine evelopment ue to the ever increasing cost of conventional hyrocarbon fuels, the global obligation to reuce carbon-base emissions an the current fuel supply uncertainty [3]. The majority of novel fuels an aitives have high volatilities, which can influence the spray formation in a similar way to increasing fuel temperature or reucing ambient pressure. For example, the aition of
ethanol to gasoline can have a significant influence on the spray formation ue to an increase evaporation rate or flashing phenomena, even at low blening ratios [4] [9]. With the inevitable increase in global consumption of new fuel blens, it is essential to unerstan the effect of flash-boiling on spray formation with a range of components. A typical pump-grae gasoline contains very many iniviual fuel components, each comprising of ifferent thermophysical properties. The variation in volatility, as well as properties such as surface tension, specific heat an viscosity of each component, can influence the formation of the spray as single components can flash-boil iniviually an affect the behaviour of roplets. Previous experimental stuies [9] whereby both single an multi-component fuels were injecte into a quiescent chamber at superheate conitions, have shown that high volatility single components like n-pentane can be use to represent the behavior of gasoline since it is these components within gasoline s multicomponent blen that rive the spray s collapsing mechanism. Flash-boiling of liqui fuel sprays can play a beneficial role in mixture formation, as increase evaporation rates an enhance atomization can prouce a more homogeneous fuel mixture, which may result in more efficient an cleaner combustion. The roplet sauter mean iameter (SMD) of a flashing spray is significantly smaller than a non-flashing spray at the same injection pressure ratio [1], [11]. This generally causes a reuction in spray penetration ue to smaller roplets having less inertia. However, epening on the number of injection holes an proximity of plumes from iniviual holes, effects may involve severe plume merging an increase axial momentum, hence longer axial overall spray penetration. The shortene or elongate penetration may reuce or exacerbate roplet-wall impingement which in turn can affect the formation of tailpipe emissions such as particulates an unburnt hyrocarbons. The majority of work carrie out on flash-boiling sprays over the last four ecaes has been experimental, as the unerlying mechanisms are extremely ifficult to unerstan on a funamental level an moel appropriately. Sher an Elata [1] were among the first to evelop empirical moels to preict bubble growth rates an roplet sizes cause by flashboiling. A relationship between average roplet size, nozzle pressure ratio an fuel properties was evelope an valiate against flashing sprays forme using a pressure-can apparatus. Kitamura et al. [13] went on to quantitatively preict the critical superheat for the onset of flashing in superheate liqui jets. It was foun that the critical superheat for a complete flashing spray was well above the bubble-point an epene on several parameters incluing injection velocity an nozzle iameter. Numerous other parameters have since been characterize by Sher et al. [14], specifically fuel surface tension, fuel viscosity, nozzle surface roughness, injection pressure an nozzle geometry. Another important aspect in numerical moelling of flashboiling is the effect of the superheate conition on the rate of Page of 3 heat an mass transfer. Aachi et al. [15] measure an theoretically erive relationships regaring the evaporation of superheate sprays. Using an infrare extinction/scattering technique, fuel vapor concentrations were characterize, an use to successfully valiate the theoretical heat an mass transfer moels evelope. It was conclue that a more homogenous mixture was prouce with a significant increase in the evaporation rate when flash-boiling was observe. One of the first attempts to numerically moel the atomization an vaporization of a flash-boiling spray was conucte using the classical nucleation theory [16]. The numerical moel inclue bubble nucleation, bubble growth, vapor formation an roplet formation. Bubble size an roplet sizes were estimate, an coincie with experimental ata reasonably well. However, a computational flui ynamics (CFD) approach was not unertaken an spatial/temporal spray structures were not moelle. Ra an Reitz [17] focuse on roplet evaporation of a single roplet, at temperatures ranging from normal to flashboiling conitions. Here an unsteay internal heat flux an surface temperature moel were propose. The moifie evaporation moel evelope was use with both multicomponent gasoline an iso-octane fuel sprays, whereby the KIVA-3V coe was use to simulate a hollow-cone injector at relatively low in-cyliner pressures. It was foun that multicomponent fuel moels can prouce a large variation in vapor istribution when compare to single component fuel moels for a hollow cone spray. The evise surface temperature calculation an internal heat flux moel offere an improvement in preicte evaporation rates. Present Contribution The funamental mechanism of flash-boiling fuel sprays is still uner ebate ue to the ifficulty associate with experimentally quantifying areas of ense spray close to the nozzle exit an flow properties insie working injectors. Limitations also lie with current empirical moels as they have been evelope for a specific range of liquis an operating conitions [18]. Currently there is very limite computational work available in the literature that has iscusse methos for successfully moelling multi-hole flashing sprays uner engine-like conitions, as well as capturing the mechanism of spray collapse that can lea to quite complex spray structures an affect the in-cyliner mixture formation. The current stuy attempts to formulate an valiate a computational framework for flash-boiling fuel spray moelling base on a two-phase Lagrangian particle tracking (LPT) methoology. The main objectives of the present work can be summarize as follows: To implement in a CFD coe an evaporation moel which incorporates aitional evaporation cause by superheate roplets an stuy its effects. To conuct a preliminary valiation of the numerical framework against optical experimental ata obtaine
previously in-house with a specific multi-hole injector using fuels of ifferent volatilities. To use the evelope flash-boiling spray moel to investigate the influence of auxiliary sub-moels incluing roplet break-up an roplet collision moels on spray characteristics. To examine the effect of various spray parameters, like the initial roplet iameter an plume cone angle, on the formation of flash-boiling sprays an the associate mechanism of spray collapse. NUMERICAL METHODOLOGY Moelling Approach A flash-boiling evaporation moel was implemente into STAR-CD using its FORTRAN-base user-coing capability which is ocumente later in this paper. A couple Lagrangian-Eulerian framework was use to enable numerical moelling of a isperse multi-phase flow. A Lagrangian particle tracking technique was use whereby governing equations (i.e. the conservation of mass, momentum an energy) are solve for the iniviual elements of the isperse phase (using the stochastic parcel approach where iniviual roplets are groupe into parcels an assume to have ientical physical properties). The continuous phase which is expresse in Eulerian form is solve in the same manner; it incorporates source terms in orer to allow for mass, momentum an energy transfer with the isperse phase, hence a couple two-phase flow framework. The PISO pressure-velocity coupling algorithm is use as originally propose by Isaa [19], along with the secon-orer Monotone Avection an Reconstruction Scheme (MARS) for both momentum an turbulence of the Eulerian phase. The Lagrangian phase is moelle using first-orer orinary ifferential equations. Turbulence was moelle using a Reynols-average Navier- Stokes (RANS) approach by employing an ey viscosity moel. Specifically the k-ε/rng (Re-Normalization Group) moel evelope by Yakot et al. [] was selecte. This moel has shown goo accuracy for non-fuelle in-cyliner flow moelling work by one of the authors of the current work [1]. Therefore, it was chosen to maintain consistency with future moelling of fuelle in-cyliner flow an mixture formation using the evelope framework. With the high velocity flow fiel an shear layers generate by high pressure injection, turbulent ispersion was inclue in the moelling approach by a ranom walk technique []. Two single-component fuels were investigate, namely iso- Octane an n-pentane, to represent a meium an high volatility component of gasoline, respectively. Temperature epenent polynomial relationships for the thermo-physical properties of those fuels were taken from the Yaws atabase [3] an implemente via user coing as well. The fuel properties moelle inclue; surface tension, viscosity, latent Page 3 of 3 heat of vaporization, ensity, specific heat capacity, saturation pressure an thermal conuctivity. The polynomials are ocumente in Appenix A. Vapour ensities were moelle by the ieal gas law. Flash-Boiling Evaporation Moel Numerical moelling of superheate fuel injection requires an evaporation moel which can account for heat transfer from the surrouning environment an from the superheate roplet itself. Here the flash-boiling evaporation moel implemente is escribe. The following assumptions were mae: 1) the roplet is spherical, ) at superheate conitions the roplet surface temperature is equal to the saturation temperature of the fuel an 3) the type of flash-boiling being moelle is external flash-boiling as ispute by Reitz [4]. Also, consiering the small ratio of length/iameter of the nozzle hole use in the current investigation [8], [5], [6], bubble bursting an consequent flashing occurs close-to or ownstream of the nozzle exit plane. Displaye in Figure 1 is a schematic showing the irection of heat transfer an surface evaporation for a superheate roplet. At superheate conitions, heat from the surrouning environment (referre to as subcoole evaporation from hereafter), as well as heat from the roplet center (referre to as superheat evaporation from hereafter), contribute to the roplet surface evaporation. At subcoole conitions heat transfer from the center of the roplet is assume to be negligible. External Heat transfer from surrounings Evaporation Internal heat transfer from superheate fuel Figure 1. Schematic of heat-transfer at roplet temperatures above an below the boiling temperature of the fuel. The subcoole roplet evaporation term, M sc1 can be calculate as follows [7]: M sc ShDi P P 1 v AP ln t Tf Rf D P P (1) s where A is the surface area of the roplet, P the ambient pressure, Sh is the non-imensional Sherwoo number, D i the binary iffusivity coefficient, T f the temperature of the vapor film assume to be the average of the roplet temperature an surrouning gas temperature, R f the specific gas constant of
the vapor film, D the roplet iameter an P v an P s the partial vapor pressure in the cell an saturation pressure of the fuel, respectively. Formulation of non-imensional numbers use in the current work can be foun in Appenix A. A secon formulation of an evaporation moel was also implemente an compare to the moel ocumente in Equation 1. The subcoole evaporation rate is given as [8]: Page 4 of 3 M t sc ShDi AP T R D f f 1Y ln 1Ys where Y is the instantaneous mass fraction of vapor in the cell an Y s is the fuel vapor mass fraction at the roplet surface, given as: Y s s v s a () Ps mv P m ( P P ) m (3) Here m v an m a represent the molecular weight of fuel an air, respectively. The formulation of M sc1 is base on the mole fraction whereas M sc is calculate using mass fraction as seen in Equation. Then a superheate roplet evaporation term, M sh, was implemente in the coe. This term was originally suggeste by Aachi et al. [9] an can be summarize as follows: M t sh A T (4) H where T is the egree of superheat, α is a heat transfer coefficient an H V is the latent heat of the fuel. The heat transfer coefficient α is given by empirical functions that have been formulate from experimental investigations that employe a pintle injector an n-pentane [15]: 76T 7T. 6. 33 138T V when T 5 when 5 T 5. 39 when T 5 in W/m K. The egree of superheat is calculate using the boiling temperature of the fuel at the specific ambient pressure, efine as: where T b is the boiling tem (5) T T T b (6) perature an T the instantaneous roplet temperature. A vapor film surrouning the roplet is incorporate into the evaporation equations, this vapor film is calculate base on the mixture fraction of fuel vapor an ambient air properties. This vapor film incorporates the reuction in the rate of evaporation with an increase in partial vapor pressure (cause by a vapor film subsiing in the immeiate area surrouning the roplet). The total evaporation rate M t is calculate by the accumulation of the subcoole, M sc1 or M sc, an superheate, M sh, evaporation rates, i.e.: M t t M t sc1 M t It shoul be note that at subcoole conitions the superheat evaporation term is equal to zero. The aitional evaporation cause by internal roplet heat transfer increases linearly with superheat egree, an the heat transfer coefficient increases non-linearly at three specific superheat egrees, resulting in an ever increasing non-linear superheat evaporation rate. An increase mass transfer rate ue to flash-boiling subsequently causes an increase in heat transfer. The conservation of energy law is use to etermine the heat transfer of the isperse phase at both non flashing an flashing conitions, whereby heat transfer is calculate irectly from surface heat transfer an phase-change mass transfer: mc p T t Ah sh M t T T T H where h is the heat transfer coefficient which is a function of the Nusselt number, originally erive by Wakil et al. [3] an T is the ambient gas temperature. Droplet Break-Up an Collision Moels Droplet Break-Up In orer to moel roplet break up, an essential part of atomizing sprays, the Reitz-Diwakar roplet break-up moel was applie [31]. Two break-up regimes are moelle, namely bag break-up an stripping break-up, both of which are cause by aeroynamic forces acting upon the roplet surface. Using non-imensional values, namely the Weber an Reynols numbers (ocumente in Appenix A), an empirical moel constants, the onset of roplet break-up is etermine an moelle. The overall break-up rate is calculate as a function of the stable roplet iameter, which is a roplet iameter that can withstan the current aeroynamic forces acting upon it, remaining intact. A breakup timescale is also incorporate along with the instantaneous roplet iameter. The break-up rate is given in Equation 9. b V (7) (8) D D t D,stable (9) t τ
Here τ b is the break-up timescale, D the instantaneous roplet iameter an D,stable the stable roplet iameter. The stable roplet iameter an break-up timescales are calculate separately for each regime an compete where the smallest values are applie in orer to calculate the break-up rate. The equations use in both the bag break-up an stripping breakup are as follows [31]: Bag break-up: Stripping break-up: u u D We b,stable 1/ 3/ bρ D 1 4 σ / C where U 1, is the relative velocity between two roplets, u 1 an u are roplet velocity vectors an X 1 an X are the roplet position vectors. The secon conition is that the roplets Page 5 of 3 b1 (1) C τ (11) C b s We (1) Re C s1 D u u (13) The stable roplet iameter an break-up timescale for each regime are calculate base on the empirical constants C b1, C s1, C b an C s erive by Reitz an Diwakar [31], the efault values are isplaye in Table 1. Table 1. Reitz-Diwakar roplet break-up moel constants. C b1 C s1 C b C s 6.5 3.1416 The influence of the moel constant values of C b1 an C b on spray characteristics are also investigate in the current paper. Droplet Collisions Droplet collisions are moelle base on O Rourke s statistical approach [3] with a spee up algorithm evelope by Schmit an Rutlan [33]. Two funamental conitions must be met if roplets are to collie [34]. The first is that the roplets must be moving towars each other, state in the following equation: X X 1 U 1, u1 u (14) X X1 must be moving at a spee which results in a relative isplacement (within one time step) equal to or greater than the istance between them. Which is numerically escribe as follows: KU 1, t X X1 r1 r (15) where K is the relative motion factor (set to the efault value of unity in this investigation), t is the time step an r 1 an r are the raii of the roplets. If these are not met, collisions may not occur within the current time step. If these two prerequisites are met, then a statistical approach is applie where roplets may collie. The statistical approach assumes roplets are istribute evenly over the entire cell an a Poisson istribution is applie in etermining the number of collisions occurring in the current time step. Once the number of collisions have been calculate, the most appropriate regime is selecte via the roplet Weber number. Three regimes are available namely: coalescence, separation an bouncing. The bouncing regime moels two roplets which o not coalesce, instea they are consiere as two soli spheres which collie, exchanging only momentum with no restitution factor. In the case of separation, momentum is also only exchange. However, this regime is use to moel two roplets which coalesce but possess too great a momentum to permanently remain attache, hence the roplets separate. Coalescence is where two roplets collie an coalesce to form a single larger roplet, here momentum, mass an energy are exchange. O Rourke s [3] roplet-roplet collision moel can be improve by inclusion of submoels for further moes of collision that have been foun beneficial to the preiction of ense iesel sprays [35]. However, this was not consiere necessary within the immeiate objectives of the current stuy, albeit part of our work in progress for the gasoline injection system uner stuy here. Simulation Setup A cubic omain of 8 mm 3 was create an a gri consisting of hexaheral elements was prouce. A number of cell sizes ranging from.5 mm to 3 mm in size were stuie to ientify an optimum resolution for this gri. The final resolution was consiere on the basis of limitations associate with the LPT; specifically, this requires a sufficient resolution for the assumption that a Lagrangian parcel isplaces no Eulerian phase to remain applicable. This assumption is acceptable when the volume fraction of the isperse phase is kept relatively small. In orer to o this a cell size of 1 mm was chosen as cells of.5 mm ten to generate an unstable simulation as the volume fraction limit of.4 coul be reache in the ense regions of the spray. 1 mm cells were also compatible with the future application of the methoology to engine simulations, where 1 mm cells have been eeme small enough for in-cyliner flow simulations (e.g. when valiate
against PIV ata [1]) an they also allowe reasonable CPU times within the computational power bouns available to the authors. Therefore, finally, 51 cells of 1 mm size fille the computational omain an an initially quiescent environment of rie air at T = C was consiere. A time step of 1 μs was employe. This selection was again base on future application to engine simulations an computational power availability; for reference, 1 μs correspons to ~.1 crank angle egree (CAD) resolution at 15 RPM. The simulations were set up on the basis of an asymmetric sixhole gasoline injector, isplaye with full geometrical etails in Appenix B. The injector consiste of six holes each of μm in internal iameter an iniviual plume cone angles θ of about 15. A large atabase of spray images is available with this injector with various fuels for valiation purposes (incluing gasoline, alcohols, high an meium volatility hyrocarbon components, etc.), both in quiescent injection chambers an in-cyliner [9], [36]. A constant mass flow rate of g/s was use throughout the test cases of the current stuy. This was measure for the same injection system at an injection pressure, P inj of 15 bar, e.g. see [5], [6]. A variation in mass flow rate of less than 5% was seen in the experimental ata at varying ambient conitions, hence it was ecie to fix the flow rate at all conitions within the bouns of the current stuy. Table isplays all test cases use in the current moelling stuy. Table. Non flash-boiling an flash-boiling spray cases. obtaine using the same nozzle set-up. Specifically, the spray preictions were compare to spray images obtaine by highspee shaowgraphy an Mie scattering techniques, as well as against penetration lengths obtaine by image processing [1], [36]. Both evaporation moels were quantitatively compare using two fuels, namely iso-octane an n-pentane. The two moels prouce very similar fuel sprays with almost ientical characteristics at subcoole conitions; their roplet iameters an spray penetrations ha a ifference in the region of %. No contribution existe from the superheate evaporation term M sh (Equation 4) as this was equal to zero at subcoole conitions. From here on the results presente correspon to the total evaporation term M t that incorporate M sc1 an M sh, unless otherwise state. Figure isplays a comparison between the results of the computational moel an spray images at subcoole conitions of P = 1. bar an T f = C for both iso-octane an n-pentane fuels. It can be observe that the numerical moel was able to reprouce quite well the general spray characteristics an shape of spray plumes. 11. 167. 1. 77. 3. Spray No. T f [ C] P [bar] Fuel T b [ C] T [ C] 1 1. n-pentane 36.1. 1. iso-octane 99.. 3 1 1. n-pentane 36.1 83.9 4 1 1. iso-octane 99. 1. 5 9 1. n-pentane 36.1 53.9 6 1.5 n-pentane 16. 14. 7 1.5 iso-octane 78. 4. 8 9.5 n-pentane 16. 74. 9 18.3 n-pentane 3. 177. 1 18.3 iso-octane 6. 117. 11. 167. 1. 77. 3. iso-octane RESULTS AND DISCUSSION Subcoole Conitions n-pentane The two evaporation moel terms M sc1 an M sc (Equations 1 an ) were compare an valiate both quantitatively an qualitatively at subcoole conitions against experimental ata Page 6 of 3 Figure. Computational spray results an experimental spray images of iso-octane an n-pentane at P = 1. bar an T f = C.
To stuy the effects of fuel on preicte spray characteristics at subcoole conitions, a irect comparison is mae between the highly volatile n-pentane an the lower volatility iso- Octane. The size an ensity of roplets at the tips of all the spray plumes in Figure are ifferent between the two fuels, with n-pentane exhibiting smaller roplets. The preicte sauter mean iameter (SMD) of the roplets uring injection is compare for the two fuels in Figure 3. The ifference in SMD between the two fuels at 4 μs after start of injection (ASOI) is foun to be 1.. The higher volatility of n- Pentane results in faster evaporation as well as a smaller stable roplet size. The higher evaporation rates associate with n- Pentane can be seen in Figure 4, where fuel vapor mass fraction is plotte on the central axis of the injector. The effect of fuel properties is clearly isplaye, with iso-octane proucing a vapor mass fraction of approximately % of that prouce by n-pentane. SMD [] 5 15 1 5 iso Octane n Pentane Spray No. 1+ 4 6 8 1 1 Figure 3. SMD of n-pentane an iso-octane at P = 1. bar an T f = C. experiments, this was achieve by incluing the injector river s elay uration (typically aroun 3 µs) to the computational results [37]. Penetration [mm] 6 5 4 3 1 iso Octane iso Octane Experiment n Pentane n Pentane Experiment Spray No. 1+ 4 6 8 1 1 Figure 5. Plume penetration of n-pentane an iso-octane at P = 1. bar an T f = C. The computational penetration curves isplaye in Figure 5, for both n-pentane an iso-octane fuels contain a ifference to experiment of 1% an 3% at 8 µs ASOI, respectively. It shoul be note here that the initial injection velocity of each fuel is ifferent, ue to a constant mass flow rate being applie an fuel properties varying. The injection velocities at this conition are 91.64 ms -1 an 11.6 ms -1 for iso-octane an n- Pentane, respectively, proucing higher penetrations for n- Pentane. The relatively small ifference in penetration length gives confience in the implementation of the evaporation moel an accuracy of the simulation set-up. A similarly small ifference was quantifie uring experimentation an the experimental spray penetration curves reflect this ifference. 1 -.133.98.65.33 1-1.655.491.38.164 It is note here that, in orer for the preicte penetrations to precisely match those of the experiments, the break-up moel constants an initial roplet properties coul be tweake. This was examine systematically an is ocumente in the following sections. Break-up Moel.. Figure 4. Vapor mass fraction of iso-octane (left) an n- Pentane (right) at P = 1. bar an T f = C. The newly implemente evaporation moel with flash-boiling capabilities was further valiate at subcoole conitions by comparing the penetration length of plumes 1 an 6 (see Appenix B for reference) to experimental ata. The penetration is calculate by importing iniviual parcel geometry into an in-house MATLAB coe. The penetration was calculate at multiple time steps, an was irectly compare to experimental ata as shown in Figure 5. The reaer shoul be aware that the computational results have been moifie to incorporate the injection elay witnesse in Page 7 of 3 The Reitz-Diwakar [31] roplet break-up moel relies on the calculation of a stable roplet iameter to preict roplet break-up by aeroynamic forces. The calculations ultimately rely on fuel properties, pressures an temperatures, which can result in the efault moel constants being unsuitable, especially at extreme conitions corresponing to superheate liquis in the case of high-pressure fuel injection. Razzaghi [38] stuie the effect of superheating on the break-up of a flashing spray, etermining a critical superheat egree whereby break-up ue to thermal mechanisms ominate. It is this conclusion which suggests that the break-up moel can be a significant an useful tool in builing a numerical framework capable of preicting suitable roplet sizes an spray characteristics of a flash-boiling spray. However, the
aim of this investigation is to efine the potential to replicate the enhance roplet break-up from thermal effects, in a flashboiling spray. The influence of break-up moel coefficients on spray formation, of which are ocumente in Table 1, were stuie at subcoole conitions. Both the bag break-up an stripping break-up weber number constants were ajuste simultaneously, ultimately resulting in a steay reuction in stable roplet iameter. The break-up timescale constants (C b an C s ) were kept unchange at the efault values to give a irect comparison between stable roplet iameters. Figure 6 represents the plume penetration with reucing moel constants from the efault values given by Reitz an Diwakar [31]. A clear effect on the plume penetration was observe, whereby a smaller stable roplet iameter followe an expecte tren, proucing a spray with smaller roplets. An exact match between the numerical solution an experimental ata can be achieve through ajusting the roplet break-up moel constants. However, this trial an error approach is not always applicable. Penetration [mm] 7 6 5 4 3 1 Cb1 6. Cs1.5 Cb1 5. Cs1.4 Cb1 4. Cs1.3 Cb1 3. Cs1. Cb1. Cs1.1 Experiment Spray No. 4 6 8 1 1 14 Time [μs] Figure 6. Effect of break-up moel constants on plume penetration of iso-octane at P = 1. bar, T f = C. Flash-boiling sprays prouce significantly smaller roplets when compare to non-flashing sprays, a byprouct of both high evaporation rates an enhance aeroynamic break-up ue to fuel properties (such as surface tension an viscosity), iminishing with temperature. A superheate flash-boiling spray may also contain a thermal break-up mechanism cause by bubble nucleation an growth insie of liqui roplets, which is currently not implemente into the current computational framework. The reuction in SMD cause by a reuction in break-up criterion is isplaye in Figure 7. The SMD is reuce from 57. to 4.7 at 1 µs ASOI when using the outer-most values, a tren which can commonly occur in flash-boiling sprays ue to the enhance break-up mechanism. The value associate with the break-up timescale was clearly visible from the SMD plot of Figure 7, as the inception of break-up occurre at approximately µs, where the effect of moel constants became prominent. For completeness, it is note here that the SMD of iso-octane s spray roplets measure at a location of mm from the nozzle exit within plume 1 using phase Doppler anemometry was of the orer 15 at C, 1. bar, i.e. closer to the lower en of preicte values in Figure 7. SMD [μm] 5 15 1 5 Spray No. 4 6 8 1 1 Time [μs] Figure 7. Effect of break-up moel constants on the SMD of iso-octane at P = 1. bar an T f = C. The capability of moifying current break-up moels to replicate enhance thermal break-up mechanisms is a potential solution in avancing the computational framework towars an accurate flash-boiling numerical moel. This may well involve the Jakob number to inclue superheat effects. Inclusion of such effects was not part of the immeiate objectives of the current stuy, neither was tuning of the efault break-up moel constants to match the experimental curves over a range of superheate conitions, since that woul be a purely practical tuning exercise without much sophistication. Therefore, with the acquire knowlege of sensitivity to these constants for the injector uner stuy, it was ecie to use the efaults constants, as liste in Table 1, for the rest of the work. This was to maintain universality by ecoupling tuning effects from any funamental unerstaning that coul be gaine. It is envisage though that the knowlege gaine from this section an subsequent ones will be applie to future refinement of the evelope coe. Flash-Boiling Sprays Cb1 6. Cs1.5 Cb1 5. Cs1.4 Cb1 4. Cs1.3 Cb1 3. Cs1. Cb1. Cs1.1 The current section investigates the behavior of the flashboiling evaporation moel at superheate flash-boiling conitions. Firstly, an initial comparison was mae between spray preictions an experiments obtaine from the literature where a Laser-inuce Exciplex fluorescence (LIEF) technique was use to visualise the vapor phase in a similar multi-hole gasoline injector to that use in the current stuy [39]. It was foun that the vapor phase prouce with the implemente superheate evaporation term was qualitatively comparable to that measure by the LIEF experiments, with clear epenency on fuel type (however, this is not shown for brevity ue to the qualitative nature of the comparison an the exact experimental injector geometry of LIEF being unknown). Then a secon investigation was carrie out to observe the results obtaine with the two subcoole evaporation moels, M sc1 an M sc, an with the total Page 8 of 3
evaporation flash-boiling moel, M t (with M Sc1 contribution), an at conitions equivalent to the available in-house experimental spray ata. Various conitions were moelle using both n-pentane an iso-octane, ranging from superheat conitions of 83.9 C an 1. C respectively (Spray No. 5 an 6) to severe superheat conitions of 165 C an 111. C, respectively (Spray No. 11 an 1). Specifically, conitions of initial fuel temperature of T f = 1 C an atmospheric pressure of P = 1. bar were initially use (Spray No. 5 an 6). A irect comparison between the total flash-boiling evaporation moel M t an the two subcoole evaporation moels M sc1 an M sc was mae by plotting the vapor mass fraction of iso-octane an n-pentane at 4 µs ASOI on the central injector plane looking from the sie, as illustrate in Figure 8. It is clear that the implemente superheat term prouces a higher evaporation rate at superheate conitions in comparison to the subcoole moels. The subcoole moels prouce vapor concentrations with comparable values, where M sc was seen to preict the smallest evaporation rate. Figure 8. Vapor mass fraction of iso-octane (top) an n- Pentane (bottom) at T f = 1 C an P = 1. bar, using M sc1 (left), M sc (center) an M t (right). Vapor Footprint Area [mm ].5.169.113.56..8.6.4.. 1 8 6 4 Figure 9. Vapor footprint area of iso-octane an n-pentane at T f = 1 C an P = 1. bar. Page 9 of 3 Msc1 n Pentane Msc n Pentane Mt n Pentane Msc1 iso Octane Msc iso Octane Mt iso Octane 4 6 8 1 1 To quantify the effect of the ae superheat evaporation term, the footprint area of the vapor phase on the central axis plane as shown in the vapor plots in Figure 8 is isplaye in Figure 9. The more rapi evaporation at the beginning of injection preicte by the implemente superheat term, prouce a larger footprint of vapor suggesting a promotion of homogeneity which is reporte by Aachi et al. [15]. The increase mass of fuel in gaseous state at superheate expane conitions coul act as a potential source of promoting jet tip vortices (e.g. see [4] for a iscussion on high-spee gaseous fuel jets), causing recirculation of vapor an a wiening of the vapor footprint. This effect may also have an influence on spray collapse. At severe flashing the reuce inertia of small roplets prouces a spray which is more susceptible to air entrainment, in turn increasing iniviual plume interactions, roplet collisions an spray collapse. The velocity fiel of the Eulerian gas phase is plotte in Figure 1. The spray tip vortices are clearly visible in the twoimensional velocity vector plot of the Eulerian phase, which was plotte on the centerline of the injector relative to the sie view. Vortices similar to that foun in a PIV stuy by Zhang et al. [41] on a flash-boiling multi hole injector were foun. Zhang et al. foun that flashing prouce stronger vortices in terms of velocity magnitue, an the increasing strength pushe the plumes towars the central axis, eventually contributing to collapse. 1.7 m/s 9.53 6.35 3.18. Counter Rotating Vortices Tip Vortex Figure 1. Sie view of velocity vectors of the Eulerian phase, using n-pentane at T f = 1 C an P = 1. bar. The same vortex mechanism is capture in the Lagrangian particle tracking metho employe here, however this technique may not be able to accurately moel the tip vortices in the Eulerian phase, as the interaction between roplets an the surrouning vapor/air mixture are not irectly resolve. Lagrangian/Eulerian momentum transfer was moele with many limitations, such as perfectly spherical roplets, an momentum issipation over the entire computational cell, resulting in a coarse representation an inaccurate issipation of the Eulerian phase velocity. This limitation of the moel may uner-preict the strength of these vortices, potentially
limiting the preiction of spray collapse with the current computational framework. Sher et al. [11] suggest that the vapor phase leaving the nozzle coul have a velocity which is significantly higher than the liqui phase an coul increase the velocity within the bulk spray surrouning. The average roplet iameter of a flashing spray was foun to be smaller than a non-flashing spray, ue to the rapi evaporation upon exit of the nozzle. The SMD of the flashboiling evaporation moel was compare to the subcoole moel components an is illustrate in Figure 11. SMD [] SMD [] 5 15 1 5 5 15 1 5 Spray No. 3 Msc1 Msc 4 6 8 1 1 Spray No. 4 4 6 8 1 1 Figure 11. Comparison between the SMD of n-pentane (top) an iso-octane (bottom) at P = 1. bar an T f = 1 C. A reuction in SMD was observe for the flash-boiling moel at the state superheate conitions for n-pentane. Specifically, an SMD at 4 µs ASOI of 56.4 was calculate, compare to 8.9 at C shown earlier in Figure 3. This also illustrate the ae contribution of the superheate roplet moelling term of the implemente total evaporation flash-boiling moel, where the aitional heattransfer from superheat contribute to surface evaporation an further reuction in roplet size. Once the aitional thermal energy was expene through surface evaporation, the roplet temperature fell below its boiling point. The evaporation rate then returne to its subcoole value, where the ifference between the flash-boiling moel an the subcoole moels remaine constant thereon. However, it is clearly note that the contribution of the superheate evaporation term, using the publishe empirical constants, is not as isruptively large as Mt Msc1 Msc Mt one may have initially expecte for a high volatility fuel like n-pentane. In the case of iso-octane the effect of the implementation of a flash-boiling evaporation term appeare insignificant at the much lower egree of superheat experience by this fuel at these conitions. The penetration lengths of plumes 1 an 6 are isplaye in Figure 1 for both n-pentane an iso-octane fuels with superheat of 83.9 C an 1. C, respectively (Spray No. 5 an 6). Penetration [mm] Penetration [mm] 7 6 5 4 3 1 7 6 5 4 3 1 Msc1 Msc Mt Experiment 4 6 8 1 1 14 Msc1 Msc Mt Experiment Spray No. 3 Spray No. 4 4 6 8 1 1 14 Figure 1. Plume penetration of n-pentane (top) an iso- Octane (bottom) at P =1. bar an T f = 1 C using M sc1, M sc an M t in comparison to experiments. It can be seen that for these flash-boiling conitions, the flashboiling evaporation moel M t cause a small reuction in penetration for n-pentane in comparison to M sc only, pushing the preicte results closer to the experiment, but only by a little. This is clearly a eficiency; more to the point, it is note that the experiments showe a egree of spray collapse, as isplaye in the spray image ajacent to Figure 1, but no type of such spray collapse behavior was preicte using the existing moel settings. In the case of iso-octane where the superheat egree i not breach the highest criteria in the calculation of the heat transfer coefficient of Equation (5), no significant effect of the aitional evaporation term was observe. Here the experiments showe no spray collapse which allowe the computational penetration to lie overall closer to the experiment (small iscrepancies between M t an M sc terms past 1 ms ASOI stem from the preiction of isolate Page 1 of 3
single large roplets at the tip of spray plume an require further stuy). Another interesting observation is the ifference between M sc1 an M sc at superheate conitions. The evaporation limit of M sc is lower than that of M sc1, isplaye as larger SMD values, an larger penetration lengths for n-pentane. The variance comes from ifferences in the formulation, where a smaller saturate evaporation limit is seen for M Sc. 1 -.133.98.65.33 1-1.655.491.38.164 4 mm vapor mass fractions at 4 µs ASOI are isplaye in Figure 13, which are plotte on a plane cutting through the central axis of the injector. The aition of a flash-boiling evaporation moel was implemente an the limitation of the current computational framework was apparent, where complex spray structures in the form of plume merging an collapse coul not be preicte with the chosen settings. In orer to further investigate this limitation a sensitivity stuy of the results to the initial roplet size an plume angle, as well as the empirical constants of the superheate heat transfer parameter of Equation (5), was carrie out as etaile in the next section. Parametric Stuies.. Initial Droplet Diameter.4.168.11.56..533.399.67.133..883.663.44.1. Figure 13. Vapor mass fraction of iso-octane (left) an n- Pentane (right) at T f = C an P = 1. bar, T f = 1 C an P =.5 bar, T f = 1 C an P =.5 bar an T f = 18 C an P =.3 bar. To stuy the effect of injection temperature an ambient pressure on evaporation, the vapor mass fraction was plotte at numerous conitions using both fuels (Spray No. 1,, 3, 4, 6, 7, 9 an 1). This was carrie out by varying the fuel injection temperature an ambient pressure separately. The Page 11 of 3 iso-octane.81.69.46.3..84.618.41.6..99.717.496.48. n-pentane Droplet-roplet collision moels can significantly influence the spray preicte by the numerical coe an the number an type of collisions can vary epening on spray properties. Superheate sprays were moelle an the initial roplet iameter an iniviual spray plume angle were varie inepenently in orer to attempt to preict the interaction between iniviual plumes. The proximity of iniviual plumes of multi-hole injector can hugely influence the subsequent spray formation, as inter-plume interactions can prouce merge plumes, in-turn proucing a collapsing spray an complex roplet clou structures [1], [4] that can subsequently affect in-cyliner mixing, wall wetting, combustion an emissions. The flash-boiling phenomena can resie both internally an externally in the region of the nozzle orifice, epening on a number of factors incluing in-nozzle an atmospheric conitions, as well as fuel properties [8], [5]. At high superheat egrees, the spray is eeme to be fully flashing as the flow exiting the nozzle can consist alreay of a large amount of fuel vapor clou housing liqui roplets. The size of these liqui roplets iminishes as the severity of flashboiling increases, resulting in the initial roplet iameter becoming much smaller than the nozzle iameter for highly superheate fuels [1]. The influence of initial roplet size on spray formation was investigate for both n-pentane an iso- Octane at superheate conitions where the onset of plume merging was witnesse, T f = 9 C, P = 1. bar, an T f =1 C, P =.5 bar, respectively. A number of initial roplet iameters were stuie, ranging from the nozzle orifice of D = own to D =. The effect of those sizes on the spray formation of n-pentane is isplaye in Figure 15. It is clear that the initial roplet size influences the subsequent roplet momentum an roplet collisions mechanism, leaing to graual merging of the spray s plumes. Large initial roplets of prouce no plume merging or spray collapse at these superheate conitions, whereas the smallest stuie initial roplets of lea clearly to spray plumes fully merging. When compare to experiments, it seems that
there is an optimum nominal initial roplet iameter that allows the computational framework to preict the global spray shape. Specifically, at these conitions, 1 initial roplets lea to a egree of plume merging that agrees well with the experiment. In practice, to make such a reverseengineering parametric exercise useful, a valiate thermophysical relationship woul nee to be evelope that woul automatically preict the correct initial roplet iameter for a range of fuels an conitions. 1. 157. 113. 69. 5. 57.5 46.95 36.4 5.8 15.3 1 5 19. 85.75 6.5 47.5 16. 4.7 34.53 6.35 18.18 1. Experiment penetration as isplaye in Figure 16. It was foun that the merging process cause by reuce initial roplet iameter resulte in a reuce plume penetration length. This effect is somewhat ue to smaller roplets carrying less inertia, however, the collapsing mechanism also prouces smaller penetrations because part of the roplets axial velocity is converte into raial velocity from roplet interactions an the subsequent plume merging process. Penetration [mm] SMD [] 7 6 5 4 3 1 5 1 Experiment 4 6 8 1 1 Figure 16. Penetration of n-pentane with varying initial roplet iameter at P = 1. bar an T f = 9 C. 5 15 1 Spray No. 5 Spray No. 5 1 5 5 Figure 15. Spray formation of n-pentane C with varying initial roplet iameter at P = 1. bar an T f = 9. Another interesting fining from the current numerical stuy was the change in SMD over time of each spray, which is shown in Figure 17 for flashing n-pentane. The initial SMD is typically equal to the initial roplet iameter. It was foun that inepenent of initial roplet iameter, the SMD at 1 µs consiste of a small variation of 4.9 between the largest an smallest initial roplet iameters. The small ifference is cause by the larger, weaker roplets unergoing ropletbreakup as oppose to smaller more robust roplets resiing uner the stable roplet iameter limit. A slight increase in SMD can be seen for initial roplet sizes of ; this may be cause by some of these small initial roplets completely evaporating an remaining ones participating in roplet coalescence phenomena overcoming the reuction cause by evaporation. The effect of initial roplet iameter on the spray characteristics was also investigate through plume 4 6 8 1 1 Figure 17. SMD of n-pentane with varying initial roplet iameter at P = 1. bar an T f = 9 C. The same effect of initial roplet iameter was apparent in iso- Octane, however its lower volatility cause the effect to be somewhat retare, ue to the roplet evaporation rate being smaller an hence resulting in larger roplets ownstream of the nozzle. The spray formation of iso-octane is isplaye in Figure 18. It can be seen that there is less recirculation of roplets at the leaing ege, cause by the larger iniviual roplet mass as oppose to the n-pentane spray case. In terms of penetration a very similar effect is foun, where smaller roplets an plume merging prouce a smaller plume penetration length, isplaye in Figure 19. The SMD is isplaye in Figure. A shallower graient was prouce in the case of iso-octane fuel which is a clear inication of the smaller evaporation rate. The fuel is also less susceptible to break-up as it has a higher surface tension an viscosity, resulting in a larger stable roplet iameter. Page 1 of 3
1. 161.5 11.5 81.75 4. 74. 61.77 1 115.8 94.8 73.83 5.84 31.85 5 44.4 36.5 Iniviual Plume Cone Angle Displaye in Figure 1 is the spray formation of superheate n-pentane at P =.5 bar an T f = 9 C using an initial roplet iameter of D =. It is clear that the spray formation calculate containe the collapsing mechanism, proucing a spray with broaly similar characteristics to those of the experiment. Plumes an 3, as well as 4 an 5, fully collapse an the cone angle of plumes 1 an 6 iminishe to an angle of θ = 13 (an angle of 15 is illustrate). A curvature of the plumes is also apparent. 49.55 37.33 5.1 Experiment 8.6.7 1.8 3.5 6.88 1.5 15.6 θ = 15 Droplet recirculation 1. Merging plumes Figure 18. Spray formation of iso-octane with varying initial roplet iameter at P =.5 bar an T f = 1 C. Penetration [mm] 7 6 5 4 3 1 4 6 8 1 1 14 Figure 19. Penetration of iso-octane with varying initial roplet iameter at P =.5 bar an T f = 1 C. SMD [] 5 15 1 5 4 6 8 1 1 Figure. SMD of iso-octane with varying initial roplet iameter at P =.5 bar an T f = 1 C. Page 13 of 3 3 5 1 Experiment Spray No.6 Spray No. 6 1 5 Figure 1. Spray formation of n-pentane at P =.5 bar an T f = 9 C using an initial roplet iameter of. An aitional factor affecting the spray formation was the iniviual plume cone angle. It is evient from literature an experimental ata that two-phase flows rapily expan upon the nozzle exit, cause by a suen reuction in pressure an simultaneous bubble growth/bursting. The current computational framework uses a constant user specifie cone angle, which will not moel the increasing angle with increasing superheat. Here, an initial stuy was carrie out to investigate the effect of iniviual cone angle, with the scope to implement a moel for automate calculation of this cone angle over a range of conitions base on empirical ata as future work. The spray experiments with this injector have illustrate the mechanism of graual wiening of the plumes at the nozzle exit at superheate conitions [1], [5]. Aitionally, other stuies with single-hole injection nozzles have foun that increasing the superheat an flashing of a spray cause a significant wiening of the cone angle at the nozzle exit, in some cases it reache angles in the orer of 1 [43]. Figure shows the spray formation of n-pentane at P =.5 bar an T f = 9 C with an increase cone angle of θ = 3 an θ = 45 as oppose to the original angle of θ = 15. It was foun that increasing the cone angle to θ = 3 prouce a larger tip spreaing of the plumes, an qualitatively a closer match to the collapse experimental spray at the same conitions. The amount of collapse remaine similar to that of θ = 15. However, a larger number of roplets surrouning the bulk liqui were observe. This effect was also witnesse when further increasing the cone angle to θ = 45, where a larger number of roplets resie in the area surrouning the bulk spray. An interesting comparison of footprint shape was
mae between the numerically moelle spray an experiment. The general tren of plumes 1 an 6 was capture, where the two plumes are rawn together. The influence of flash-boiling is also somewhat capture in plumes, 3, 4 an 5, whereby plumes an 3, an 4 an 5 merge into two istinct plumes. These two merge plumes begin to collapse together, creating a large sprea of roplets over a wie angle which was observable in the high-spee image of the severely flash-boiling gasoline spray. 33.5 7.88.5 16.63 11. 3 45 initial roplet iameter from D = to D =, proucing a length of 46 mm an 38 mm at 8 µs ASOI, respectively. The penetration is further reuce with an increase in iniviual cone angle from θ = 15 to 3 an 45. The fact that the iniviual cone angle can have a substantial effect on plume penetration was further stuie by simulating the most extreme flash-boiling conition whereby an injection temperature of T f = 18 C an an ambient pressure of P =.3 bar were simulate. The iniviual cone angles were varie from θ = 45 to θ = 6. Droplet initial iameters of were applie with both n-pentane an iso-octane fuels. The spray formation preicte is isplaye in Figures 4 an 5. 16.9 1.68 45 6 8.45 4.3 Figure. Spray formation of n-pentane at P =.5 bar an T f = 9 C using an iniviual cone angle of 3 an 45 with initial roplet iameter of. Penetration [mm] 7 6 5 4 3 1 Figure 3. Penetration of n-pentane with varying initial roplet iameter an plume cone angle at P =.5 bar T f = 9 C. The spray penetrations are plotte against experimental ata in Figure 3. The influence of iniviual plume cone angle is isplaye for n-pentane fuel. The preiction of spray collapse alongsie roplet iameter cause a substantial reuction in penetration, coinciing with experimental ata, which isplaye a smaller penetration for a collapse spray. A substantial reuction in penetration is seen for the change in Page 14 of 3, θ = 3, θ = 45 Experiment Spray No. 7 4 6 8 1 1 Experiment Figure 4. Spray formation of n-pentane at T f = 18 C an P =.3 bar with iniviual plume cone angle of 45, 6. In the case of n-pentane, a significant amount of roplet recirculation is capture, cause by the rapi evaporation an subsequent minute roplets resiing at the leaing ege of the plume, which ecelerate quickly an are overtaken by larger roplets. The increasing cone angle results in a large sprea of roplets, an the inner most roplets are seen to almost merge to prouce a single collapse spray with respect to the sie view. The footprint view is also isplaye in Figure 4 an shows plumes 1 an 6 fully merging at both θ = 45 an 6, which is also the case for plumes, 3, 4 an 5. The same effect is foun in flash-boiling iso-octane fuel sprays in Figure 5, where an increase cone angle promotes ropletroplet interaction an encourages plume merging an collapse. The resultant severe flashing spray formation foun in the case of iso-octane isplaye less collapse, when compare to n-pentane. This is expecte ue to the superheat egree being consierably smaller.
3 45 6 35. 6.5 D = μm x =.39 x = 1.5 x = 3. 17.5 18. 11.5 9.5 5.75 1. 1..75.5.5 Experiment. Figure 6. Effect of heat transfer exponent on spray of n- Pentane at P =.5 bar, T f = 9 C, with initial roplet iameter. Figure 5. Spray formation of iso-octane at T f = 18 C an P =.3 bar with iniviual plume cone angle of 45, 6. Heat Transfer Coefficient 1. 81.5 6.5 43.75 5. D = 1 μm x =.39 x = 1.5 x = 3. The final parameter investigate is the heat transfer coefficient α in Equation (4). The original empirical relationships of Equation (5) were evelope by the work of [15], []. An initial investigation was carrie out here by changing the highest regime coefficient x, as isplaye in Equation 16, from the efault value of.39 to 1.5 an then 3.. To keep this exercise simple, 138 was kept fixe espite the change in x an it was consiere that α maintaine units of W/m K. Page 15 of 3 138 T x when T 5 (16) Three initial roplet iameters were moelle at each x value, at a collapsing conition of n-pentane, specifically P =.5 bar an T f = 9 C. Displaye in Figures 6, 7 an 8 are spray characteristics incluing roplet iameter, spray shape an vapor mass fraction. It was clear that the increase in exponent x significantly affecte the evaporation rate at flash boiling conitions above the 5 C superheat threshol. Figure 6 isplays the effect of increasing x on a flash-boiling spray with initial roplet iameter roplets of D =. It shoul be note that 8% of roplets completely evaporate in the case of x = 3.. In terms of spray formation a more significant collapse was seen with an increase in evaporation, a result of smaller roplets cause by rapi evaporation upon exit of the nozzle in the extreme case of x = 3.. A smaller effect is seen when x = 1.5, ue to roplets remaining relatively large in comparison to x =.39. The istribution of vapor in the quiescent chamber was seen to cover a substantially larger area cause by large evaporation rates close to the nozzle exit. 1..75.5.5. Figure 7. Effect of heat transfer exponent on spray of n- Pentane at P =.5 bar, T f = 9 C, with initial roplet iameter 1.. 15.5 15. 57.5 1. 1..75.5.5. D = μm x =.39 x = 1.5 x = 3. Figure 8. Effect of heat transfer exponent on spray of n- Pentane at P =.5 bar, T f = 9 C, with initial roplet iameter.