An Improved Prediction of Pre-Combustion Processes, Using the Discrete Multicomponent Model

sustainability

Article An Improved Prediction of Pre-Combustion Processes, Using the Discrete Multicomponent Model

Islam Kabil 1 , Mansour Al Qubeissi 2,* , Jihad Badra 3, Walid Abdelghaffar 1, Yehia Eldrainy 1,4, Sergei S. Sazhin 5, Hong G. Im 6 and Ahmed Elwardany 1,7,*

1 Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt; [email protected] (I.K.); [email protected] (W.A.); [email protected] (Y.E.) 2 Faculty of Engineering, Environment and Computing, Coventry University, Coventry CV1 2JH, UK 3 Fuel Technology Division, R&DC, Saudi Aramco, Dhahran 34465, Saudi Arabia; [email protected] 4 Mechanical Engineering Department, Arab Academy for Science, Technology and Maritime Transport, Alexandria 1029, Egypt 5 Sir Harry Ricardo Laboratories, School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4GJ, UK; [email protected] 6 Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia; [email protected] 7 Fuels and Combustion Engines Laboratory, Energy Resources Engineering Department, Egypt-Japan University of Science and Technology, New Borg El-Arab 21934, Egypt * Correspondence: [email protected] (M.A.Q.); [email protected] (A.E.); Tel.: +44-247-7658060 (M.A.Q.) Abstract: An improved heating and evaporation model of fuel droplets is implemented into the Citation: Kabil, I.; Al Qubeissi, M.; commercial Computational Fluid Dynamics (CFD) software CONVERGE for the simulation of sprays. Badra, J.; Abdelghaffar, W.; Eldrainy, The analytical solutions to the heat conduction and species diffusion equations in the liquid phase for Y.; Sazhin, S.S.; Im, H.G.; Elwardany, each time step are coded via user-deﬁned functions (UDF) into the software. The customized version A. An Improved Prediction of of CONVERGE is validated against measurements for a single droplet of n-heptane and n-decane Pre-Combustion Processes, Using the mixture. It is shown that the new heating and evaporation model better agrees with the experimental Discrete Multicomponent Model. data than those predicted by the built-in heating and evaporation model, which does not consider Sustainability 2021, 13, 2937. https:// the effects of temperature gradient and assumes inﬁnitely fast species diffusion inside droplets. The doi.org/10.3390/su13052937 simulation of a hollow-cone spray of primary reference fuel (PRF65) is performed and validated

Academic Editor: against experimental data taken from the literature. Finally, the newly implemented model is tested Laurencas Raslaviˇcius by running full-cycle engine simulations, representing partially premixed compression ignition (PPCI) using PRF65 as the fuel. These simulations are successfully performed for two start of injection Received: 19 December 2020 timings, 20 and 25 crank angle (CA) before top-dead-centre (BTDC). The results show good agreement Accepted: 1 March 2021 with experimental data where the effect of heating and evaporation of droplets on combustion phasing Published: 8 March 2021 is investigated. The results highlight the importance of the accurate modelling of physical processes during droplet heating and evaporation for the prediction of the PPCI engine performance. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in Keywords: combustion; computational ﬂuid dynamics; droplet evaporation; engine simulation; spray published maps and institutional afﬁl- iations.

1. Introduction In the pursuit of higher engine thermal efﬁciency and lower emissions, partially Copyright: © 2021 by the authors. premixed compression ignition (PPCI) draws considerable attention [1,2]. This is mainly Licensee MDPI, Basel, Switzerland. ascribed to the low-temperature combustion following this process. In such engines, This article is an open access article manipulation of the degree of stratiﬁcation of injected fuel into the engine cylinder by late distributed under the terms and injection at the end of the compression stroke controls the start of combustion. conditions of the Creative Commons Accurate simulation of the performance of PPCI engines mandates the proper descrip- Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ tion of the physical processes and properties. Spray dynamics dictate how the combustion 4.0/). process is going to develop during engine cycles [3]. These include a number of physical

Sustainability 2021, 13, 2937. https://doi.org/10.3390/su13052937 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 2937 2 of 12

processes which range from jet/droplet heating and evaporation to the breakup, collision, and coalescence of droplets. Amsden et al. [4] have proposed a computationally efﬁcient fuel droplet heating and evaporation model, which is implemented into CONVERGE as a zero-dimensional approach. This model, however, ignores the important effect of temperature gradients in droplets, which leads to an overprediction of droplet evaporation times [3]. This drawback in the latter model has stimulated the development of a more advanced model that takes into account the effects of temperature gradient, species diffusion, and recirculation inside a droplet [5,6]. The discrete multicomponent (DMC) model (see [7–9] for details) was a response to those drawbacks. A distinctive feature of this model is that it considers the effects of temperature gradient, species diffusion, and recirculation inside droplets using the effective thermal conductivity (ETC) and effective diffusivity (ED) models [10–13]. In three-dimensional engine simulations, an earlier effort to implement the ETC model into KIVA CFD code was made by Abdelghaffar et al. [14]. They investigated the effects of heating and evaporation (using the DMC model) on the predicted amounts of fuel vapour and in-cylinder pressure in a diesel engine. This implementation was important for single component fuels but lacked the inclusion of the effects of liquid species diffusion in the case of multicomponent fuels. To our knowledge, there have not been any modelling studies to describe the characteristics of multicomponent droplets into CFD codes for a full-cycle simulation. In recent studies [15,16], the DMC model was used for the analysis of single droplet and spray evaporation, with the implementation of the ETC/ED models into ANSYS Fluent. The ETC/ED models form an important part of the DMC model, in which each component is accounted for without approximation. These studies motivated the work on this paper to perform a similar analysis for a wider range of fuels and for a full combustion cycle. The results of the implementation of the DMC model into CONVERGE are reported in this paper. The customised version of this software, with the new ETC/ED models implemented via the user-deﬁned function (UDF), is applied to the analysis of droplet heating and evaporation and the dynamics of hollow-cone sprays. The new software has been successfully used for performing engine simulations, with an emphasis on the accurate analysis of fuel sprays under PPCI engine conditions.

2. The Models The ETC/ED models used in our analysis are described in [10,17]. The transient heat and species diffusion equations are solved analytically for a spherically symmetric droplet:

∂T ∂2T 2 ∂T = α + , (1) ∂t l ∂r2 r ∂r

∂Y ∂2Y 2 ∂Y li = D li + li , (2) ∂t l ∂r2 r ∂r

where T = T(r, t) is temperature; α = kl is the liquid thermal diffusivity; ρ , k , and c are l cl ρl l l l the liquid density, liquid thermal conductivity, and speciﬁc heat capacity, respectively; r is the distance from the droplet centre; t is time; Yli = Yli(r, t) is the mass fraction of species i; and Dl is the liquid species diffusivity calculated using the Wilke–Chang approximation [5]. The thermal and mass diffusivities were replaced by the effective thermal/mass diffusivity to consider the recirculation inside the liquid droplet [18]. The droplet mass evaporation . rate, md, is calculated as [18]: . md = −2πRdDvρgBM Shiso, (3)

where ρg is the density of the mixture of vapour and air, assumed to be independent of the distance from the droplet surface; BM is the Spalding mass transfer number; and Shiso is the isolated droplet’s Sherwood number, estimated following Abramzon and Sustainability 2021, 13, x FOR PEER REVIEW 3 of 13

where 휌푔 is the density of the mixture of vapour and air, assumed to be independent of Sustainability 2021, 13, 2937 the distance from the droplet surface; 퐵푀 is the Spalding mass transfer number; and 3Sh of푖푠표 12 is the isolated droplet’s Sherwood number, estimated following Abramzon and Sirignano [19]; and 퐷푣 is the vapour binary diffusion coefficient calculated using the Wilke–Lee formula [5,20]. Sirignano [19]; and Dv is the vapour binary diffusion coefficient calculated using the 3.Wilke–Lee Results formula [5,20]. 3. ResultsThe model described in Section 2 has been implemented into CONVERGE via the user-defined function (UDF). The customised version of this software has been tested by The model described in Section2 has been implemented into CONVERGE via the comparing its predictions with the experiments performed by Daif et al. [21] using multi- user-defined function (UDF). The customised version of this software has been tested component fuel droplets. The results of the simulation of a hollow-cone spray of PRF65 by comparing its predictions with the experiments performed by Daif et al. [21] using fuel (65% iso-octane/35% n-heptane) will be presented, using the conventional version of multicomponent fuel droplets. The results of the simulation of a hollow-cone spray of CONVERGE based on the Amsden et al. model [4] and the customised version of this PRF65 fuel (65% iso-octane/35% n-heptane) will be presented, using the conventional software. The full-cycle simulation of a PPCI engine is conducted, and the late injection version of CONVERGE based on the Amsden et al. model [4] and the customised version timingsof this software.are presented, The using full-cycle the customi simulationsed version of a PPCI of the engine software is conducted, with the new and heating the late andinjection evaporation timings model are presented, implemented using into the customised it. version of the software with the new heating and evaporation model implemented into it. 3.1. Single Droplet 3.1. SingleAs a first Droplet step, the customised version of CONVERGE was used to reproduce the conditionsAs a firstof the step, experiment the customised described version by ofDaif CONVERGE et al. [21]. wasIn this used experiment, to reproduce the the initial con- dropletditions ofradius the experiment was 743 µm described; the initial by Daif mass et al.fractions [21]. In of this n- experiment,heptane and the n- initialdecane droplet were 21.3%radius and was 78.7%, 743 µ respectivelym; the initial; droplet mass fractions relative ofvelocity n-heptane was and3.1 m/s n-decane; and its were initial 21.3% temper- and ature78.7%, was respectively; 294 K, with droplet ambient relative pressure velocity and temperature was 3.1 m/s; equal and its to initial 0.101 temperatureMPa and 348 was K, respectively.294 K, withambient pressure and temperature equal to 0.101 MPa and 348 K, respectively. TheThe results results predicted predicted by by CONVERGE CONVERGE with with the the new new model model,, implemented implemented via via UDF, UDF, forfor the the conditions conditions of of this this experiment experiment were were compared compared with with experimental experimental data dataand the and pre- the dictionspredictions of the of model the model described described in [4] in, which [4], which was wasimplemented implemented in the in conventional the conventional ver- sionversion of CONVERGE. of CONVERGE. The The results results of this of this comparison comparison are are shown shown inin Figure Figure 1.1 .In In [4] [ 4,], it it is is assumedassumed that that the the temperature temperature and and species species distribution distribution inside inside droplets droplets are are homogeneous, homogeneous, althoughalthough they they can can change change with with tim time.e. As can As canbe seen be seenfrom fromFigure Figure 1, the1 ,predictions the predictions made bymade CONVERGE by CONVERGE with the with new theheating new and heating evaporation and evaporation model are modelvery close are veryto the close exper- to imentalthe experimental data. On the data. other On hand, the otherthe predictions hand, the of predictions this software of thiswith software the conventional with the evaporationconventional model evaporation show lower model eva showporation lower rates evaporation yielding rateslarger yielding droplets. larger This droplets. clearly demonstratesThis clearly demonstrates an improvement an improvement in CONVERGE in CONVERGE prediction when prediction the effects when that the effectswere pre- that viouslywere previously ignored are ignored taken areinto taken account. into account.

0.6

0.5

) 0.4

0.3

(mm

R Measurements [21] 0.2 CONVERGE 0.1 CONVERGE+UDF

0.0 0 5 10 15 20 Time (s)

FigureFigure 1. 1. PPredictedredicted and and measured measured squared squared radii radii of of the the fuel fuel droplet dropletss versus versus time time.. 3.2. Spray Simulation The customized version of CONVERGE was used to analyse a PRF65 hollow-cone spray. Its predictions were compared with the experimental data presented by Wang et al. [22]. A Lagrangian discrete parcel method was used, in which droplets of similar properties are grouped into parcels [23]. These parcels are then injected into the computational domain. Sustainability 2021, 13, 2937 4 of 12

For turbulence modelling, the Reynolds averaged Navier-Stokes (RANS)-based renormalization group (RNG) k-ε model was used. The O’Rourke turbulent dispersion model, which accounts for fluctuating velocities, was used to model the effect of turbulent flow on the spray droplets. To describe the spray formation process, the modified Kelvin–Helmholtz and Rayleigh–Taylor (KH–RT) droplet breakup models were used, taking into account the contribution of the breakup length of the liquid jet Lb; droplets were formed and allowed to breakup when the jet reached Lb. Moreover, the dynamic drag model was used along with the no-time-counter (NTC) collision method, taking into account the post-collision regimes for better accuracy [24]. Injection velocities and droplet diameters are commonly calculated based on the nozzle diameter and mass flow rate [25]. This is the case for a solid-cone spray. However, an outwardly opening hollow-cone injector requires a more careful description of the process. The shape and area of the nozzle exit depend on the needle lift, which influences the injection velocities and droplet diameters (see Sim et al. [25] for the details). For the heating and evaporation of the droplet in spray, two models were used: that of Amsden et al. [4] (using the standard CONVERGE CFD tool) and the new model, which was implemented into CONVERGE via the UDF. A property that is commonly targeted for spray behaviour is spray penetration length. PRF65 under 100 bar of pressure was injected into a chamber with an ambient pressure and temperature of 1 bar and 298 K, respectively [22]. This spray was modelled assuming that it was injected into still air in a cylindrically shaped constant volume chamber with a height of 106.5 mm and a diameter of 150 mm. For computational efficiency, a 4 mm base mesh size was used with an adaptive mesh refinement (AMR) to maintain the minimal cubic cell size of 0.125 mm. Fixed AMR embedding was maintained at the nozzle exit, while dynamic AMR was triggered by flow fields based on temperature and velocity gradients. The injection actuation duration was 0.3 ms, and the start of the injection was 0.012 ms after the end of this actuation. The whole injection took 0.36 ms, which includes an opening period of 0.02 ms and a closing period of 0.06 ms (these were observed experimentally [25,26]). The total injected mass was 10 mg. The ambient temperature and pressure were 298 K and 1 bar, respectively. The breakup parameters in both the conventional and new versions of CONVERGE were adjusted to reach a good agreement between our predicted spray penetration and the experimental data of [22], as shown in Figure2. These versions of CONVERGE used the same parameters, except for the evaporation models. A slight difference in penetration length was observed. The new version of CONVERGE predicted slightly shorter penetration. This was demonstrated in [12] where different fuels were tested for hollow-cone spray setup using the two evaporation models. In contrast, a larger difference is revealed in the vapour masses predicted by two versions of CONVERGE, as shown in Figure3. As expected from the single droplet simulations performed in the previous section, the total masses of PRF65 vapour predicted by both versions of CONVERGE turned out to be significantly different. The version with the new model predicts higher evaporation rates due to the fact it predicts higher surface temperatures for the fuel droplets. This highlights the influence that the choice of droplet heating/evaporation model has on simulations of fuel sprays. An accurate prediction of the fuel vapour mass flow rate would allow the users to have a clearer idea of the start of combustion in mixing-controlled engines, which operate at relatively lower temperatures, as in the case of PPCI engines. Sustainability 2021, 13, 2937 5 of 12 Sustainability 2021,, 13,, xx FORFOR PEERPEER REVIEWREVIEW 5 of 13

Measurements [22] 20 CONVERGE CONVERGE+UDF 15

Spraypenetration [mm]

Spraypenetration [mm] 0 0.0 0.1 0.2 0.3 0.4 0.5 Time [ms]

Figure 2. Measured sprayspray axialaxial penetrationpenetration lengthlength andand the the values values predicted predicted by by the the conventional conventional and customisedand customi versionssed versions of CONVERGE of CONVERGE for PRF65 for PRF65 (primary (primary reference reference fuel). fuel).

1.5 CONVERGE CONVERGE+UDF 1.0

0.5

Vapourmass [mg]

Vapourmass [mg] 0.0 0.0 0.1 0.2 0.3 0.4 0.5 Time [ms]

Figure 3. Comparison of the total vapour masses versus time for PRF65 calculated using the two Figure 3. Comparison of the total vapour masses versus time for PRF65 calculated using the two versions of CONVERGE. versions of CONVERGE. 3.3. Engine Simulation 3.3. Engine Simulation 3.3. EngineWe investigated Simulation the effect of the accurate modelling of the heating and evaporation of fuelWe droplets investigated on the the values effect of the chamber accurate pressure modell asing predicted of the heating by CONVERGE. and evaporation The simulationof fuel droplets results on were the values compared of chamber with the pressure results of as experiments predicted by (inferred CONVERGE. from [ 3The]) using sim- aulation PPCI engineresults runningwere compared on PRF65. with Those the results experiments of experiments were conducted (inferred on from a single [3]) cylinder using a compressionPPCI engine ignitionrunning researchon PRF65. engine Those with experiments a compression were ratioconducted of 17:1, on with a single speciﬁcations cylinder ascompression shown in Tableignition1. Injection research wasengine performed with a compress as a singleion ratio pulse of of 17:1, fuel with with specifications an injection pressureas shown of in 300 Table bar 1 from. Injection a seven-hole was performed Bosch diesel as a single injector pulse with of a fuel 0.18 with nozzle andiameter injection andpressure a BTDC of 300 (before bar from top-dead-centre) a seven-hole 142Bosch◦ spray diesel angle. injector To achievewith a 0.18 PPCI, nozzle two diameter injection timingsand a BTDC were tested:(before 20top◦ and-dead 25-◦centre)CA (crank 142° angle)spray BTDC.angle. To The achieve masses PPCI, of the injectedtwo injection fuels weretimings 9.6 were mg and tested: 10.3 20 mg,° and respectively, 25° CA (crank with angle) an initial BTDC. fuel The temperature masses of of the 360 injected K. Injection fuels durationswere 9.6 mg were and 5.04 10.3 CA mg and, respectively 5.41 CA,,respectively. with an initial Changing fuel temperature the SOI (startof 360of K. injection) Injection fromdurations 25 to were 20 BTDC 5.04 CA was and used 5.41 to CA, evaluate respectively. the effect Changing of delayed the SOI injection (start onof injection) partially premixedfrom 25 to combustion. 20 BTDC was At used early to injection evaluate timings, the effect the of air–fuel delayed mixture injection is considered on partially mostly pre- homogeneousmixed combustion. and combustion At early injection in this casetimings is kinetically, the air–fuel controlled. mixture For is lateconsidered injections mostly with lowhomogeneous ambient temperatures, and combustion however, in this heating case is andkinetically evaporation controlled. processes For late in fuel injections sprays with play alow vital ambient role in controllingtemperatures, the however, start of combustion. heating and evaporation processes in fuel sprays play a vital role in controlling the start of combustion. Sustainability 2021, 13, x FOR PEER REVIEW 6 of 13

Sustainability 2021, 13, 2937 6 of 12 Table 1. Engine specifications used in our model.

Description Specification Table 1. Engine speciﬁcationsBore used in our model. 85 mm Stroke 90 mm Description Speciﬁcation Connecting Rod Length 138 mm Bore 85 mm Compression ratio 17:1 Stroke 90 mm ConnectingIntake Rodpressure Length 138100 mm KPa IntakeCompression temperature ratio 17:1298 K EngineIntake displacement pressure 1000.51 KPa Litre IntakeBowl temperature depth 29810 mm K Engine displacement 0.51 L NumberBowl depth of valves 2 intake, 10 mm 1 exhaust IntakeNumber valve of open valves (IVO) 2 intake,30 CA 1 exhaustBTDC Intake valve valve open close (IVO) (IVC) 3045 CACA BTDC ATDC ExhaustIntake valve valve close open (IVC) (EVO) 4550 CA CA ATDC BBDC Exhaust valve open (EVO) 50 CA BBDC Exhaust valvevalve close close (EVC) (EVC) 2525 CA CA ABDC ABDC

TheThe geometry geometry of of the the computational computational domain domain was was that that of of a a real engine with the base gridgrid chosen chosen as as 4 4 mm with fixed fixed AMR embedding at the nozzle exit and dynamic AMR embeddingembedding in in the the fluid fluid flow flow area, area, controlled controlled by by the the velocity and and temperature temperature gradients, gradients, leadingleading to to a a minimum minimum cell cell size size of of 0.125 0.125 mm mm (see Fig Figureure 44)).. ThisThis isis thethe samesame setupsetup asas inin previousprevious studies of the same engine and injector [3,27 [3,27]]..

FigureFigure 4. 4. MeshMesh used used for the single cylindercylinder engineengine duringduring spray spray event event showing showing AMR AMR (adaptive (adaptive mesh meshreﬁnement) refinement) reﬁning refining the grid. the grid.

TheThe RANS RANS-based-based renormalization renormalization group group (RNG) (RNG) k k--εε modelmodel was used for turbulence modemodelling.lling. For For spray spray model modelling,ling, the the modified modiﬁed KH KH–RT–RT breakup breakup model and NTC collision modelmodel were were used. used. For For heating heating and and evaporation, evaporation, the version the version of CONVERGE of CONVERGE with the with Ams- the denAmsden et al. et model al. model [4] and [4] and the thenew new model model were were tested. tested. The The multizone multizone detailed detailed chemistry chemistry combustioncombustion sub-model sub-model ofof SAGE SAGE was was used used [28 [28]], with, with a reduced a reduced PRF chemical PRF chemical kinetic kinetic mech- mechanismanism composed composed of 56 of species 56 species and 168 and reactions 168 reactions developed developed by Liu by et Liu al. [et29 ],al. representing [29], repre- sentinggas-phase gas combustion-phase combustion kinetics. kinetics. TThehe equi equivalencevalence ratio ratio and and temperature temperature contours contours at at various crank crank angle locations in thethe vicinity vicinity of of the the piston piston are are shown shown in Figures 55 andand6 6.. Figure Figure5 5shows shows that that ignition ignition starts starts forfor the the case case of of SOI SOI 20 20 right right at at the the piston piston bowl bowl surface. surface. This This is is attributed attributed to to the the high high thermal thermal conductivityconductivity of of the the hot hot piston piston surface surface and and the the swirling of air inside its bowl. As such such,, a highhigh concentration concentration of of the the fuel fuel vapo vapourur (high (high equivalence ratio) ratio) is is expected in in this region (point A). Combustion starts at point A and spreads to the regions near the piston bowl surface where fuel vapour is abundant within ﬂammability range. In Figure6, the contours of the temperature inside the engine cylinder are shown for the case of SOI 25. It is shown that ignition starts at a region near the piston bowl Sustainability 2021, 13, x FOR PEER REVIEW 7 of 13

(point A). Combustion starts at point A and spreads to the regions near the piston bowl Sustainability 2021, 13, 2937 surface where fuel vapour is abundant within flammability range. 7 of 12 In Figure 6, the contours of the temperature inside the engine cylinder are shown for the case of SOI 25. It is shown that ignition starts at a region near the piston bowl surface surface(point (pointB). Ignition B). Ignition is predicted is predicted to start to earlier start earlierin the incase the of case SOI of25 SOI than 25 SOI than 20. SOI This 20. is Thisattributed is attributed to the toearlier the earlier injection injection,, which whichallows allowsfuel vapo fuelur vapour to diffuse to diffuseinto the into air thetrapped air trappedinside the inside cylinder the cylinder to form to a mixture form a mixture ready to ready react to once react heated once heatedto its combustion to its combustion temper- temperature.ature. Before Beforeperforming performing combustion combustion simulations, simulations, matching matching with the with motoring the motoring curve of curvethe unfired of the unﬁred engine engineat 1250 at rpm 1250 was rpm achieved was achieved by adjusting by adjusting the compression the compression ratio ratioof the ofengine the engine to 15.7:1. to 15.7:1. This Thisadjustment adjustment was wasmade made to consider to consider the thecontribution contribution of ofresidual residual ex- exhausthaust gases gases and and blow blow-by.-by. This allowed us toto achieveachieve anan almostalmost perfect perfect agreement agreement of of the the modelmodel predictions predictions and and experimental experimental measurements, measurements, as as shown shown in in Figure Figure7. 7.

Temperature of piston bowl Equivalence ratio

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Figure 5. Cross-sections of the engine cylinder showing the temperature and equivalence ratio for SOI (start of injection) 20; the customised version of CONVERGE was used. Figure 5. Cross-sections of the engine cylinder showing the temperature and equivalence ratio for SOI (start of injection) 20; the customised version of CONVERGE was used.

Temperature Equivalence ratio

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Sustainability 2021, 13, 2937 8 of 12 Figure 5. Cross-sections of the engine cylinder showing the temperature and equivalence ratio for SOI (start of injection) 20; the customised version of CONVERGE was used.

Temperature Equivalence ratio

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Figure 6. Cross-sections of engine cylinder showing the temperature and equivalence ratio for SOI 25; the customised version of CONVERGE was used. Figure 6. Cross-sections of engine cylinder showing the temperature and equivalence ratio for SOI 25; the customised version of CONVERGE was used. Simulations were performed from the exhaust valve opening to the end of the expan- sion stroke of the cycle, using the same setup in both cases. Only the start of injection time and the injected50 mass were changed; these were taken from the experimental data. Cases run using both versions ofMeasurements CONVERGE could [3] reasonably accurately capture the start of combustion as40 shown in Simulation Figures8 and9. At the same time, the peak in-cylinder pressure

Pressure[bar] 10

–120 –80 –40 0 40 80 120 CAD

Figure 7. Matching between the experimental motoring curve and that predicted by CONVERGE with the new model implemented into it via UDF (user-defined functions).

Simulations were performed from the exhaust valve opening to the end of the expan- sion stroke of the cycle, using the same setup in both cases. Only the start of injection time and the injected mass were changed; these were taken from the experimental data. Cases run using both versions of CONVERGE could reasonably accurately capture the start of combustion as shown in Figures 8 and 9. At the same time, the peak in-cylinder pressure is predicted much more accurately by the software with the new model, compared to its standard version (see Figures 8 and 9). These results are in good agreement with the results of Bertoli and Na Migliaccio [30] based on KIVA-2 simulations for a mono-component diesel spray and the ones presented in [14]. One can see that the difference in peak pressures predicted by the two CONVERGE versions is larger for the early injection stage than for the late injection. This agrees with our findings presented in [12] and highlights how important the new model is in the simulation of combustion processes in PPCI engines. Sustainability 2021, 13, 2937 9 of 12 Sustainability 2021, 13, x FOR PEER REVIEW 9 of 13

is predicted much more accurately by the software with the new model, compared to its standard version (see Figures8 and9). These results are in good agreement with the results of Bertoli and Na Migliaccio [30] based on KIVA-2 simulations for a mono-component diesel spray and the ones presented in [14]. One can see that the difference in peak pressures predicted by the two CONVERGE versions is larger for the early injection stage than for the late injection. This agrees with our ﬁndings presented in [12] and highlights how important the new model is in the simulation of combustion processes in PPCI engines. Liquid fuel mass versus time as predicted by both versions of CONVERGE are shown in Figure 10. The software with the new model predicts more fuel vapour, which leads to lower in-cylinder temperatures due to evaporative cooling. This is linked with the relatively low peak in-cylinder pressures, as predicted by the software with the new model compared with the software with the Amsden et al. model, as shown in Figures8 and9. The difference in predicted vapour mass for both models increases at longer times, as shown in Figure 11. This agrees with the numerical predictions for vaporising sprays at different ambient conditions presented by Kabil et al. [12] using both heating and evaporating models. In the latter analysis, a spray of ﬁve-component light naphtha fuel Figure 6. Cross-sections of engine cylinder showing the temperature and equivalence ratio for SOI 25; the customised version of CONVERGE was used. surrogate at engine-like conditions was modelled.

50 Measurements [3] 40 Simulation

Pressure[bar] 10

–120 –80 –40 0 40 80 120 CAD

Sustainability 2021, 13, x FOR PEER REVIEWFigure 7. Matching between the experimental motoring curve and that predicted by CONVERGE10 of 13 Figure 7. Matching between the experimental motoring curve and that predicted by CONVERGE withwith the thenew new model model implemented implemented into it intovia UDF it via (user UDF-defined (user-deﬁned functions) functions)..

Simulations were performed from the exhaust valve opening to the end of the expan- 70 sion stroke of the cycle, using the same setup in both cases. Only the start of injection time and the injected mass Measurements were changed [3] ; these were taken from the experimental data. Cases 60 CONVERGE run using both versions CONVERGE+UDF of CONVERGE could reasonably accurately capture the start of combustion50 as shown in Figures 8 and 9. At the same time, the peak in-cylinder pressure is predicted much more accurately by the software with the new model, compared to its standard40 version (see Figures 8 and 9). These results are in good agreement with the results of Bertoli and Na Migliaccio [30] based on KIVA-2 simulations for a mono-component diesel30 spray and the ones presented in [14]. One can see that the difference in peak

pressuresPressure[bar] predicted by the two CONVERGE versions is larger for the early injection stage 20 than for the late injection. This agrees with our findings presented in [12] and highlights how important10 the new model is in the simulation of combustion processes in PPCI engines. 0 –40 –20 0 20 40 CAD

Figure 8. Comparison of in-cylinder pressures inferred from the experimental results, and the results Figure 8. Comparison of in-cylinder pressures inferred from the experimental results, and the re- sultsof of the the simulation simulation using using the the standard standard and and customised customised versions versions of of COVERGE COVERGE at at SOI SOI 20 20 (CAD) (CAD crank) crankangle angle in degreesin degree BTDCs BTDC (before (before top-dead-centre). top-dead-centre).

70 Measurements [3] 60 CONVERGE CONVERGE+UDF 50

Pressure[bar] 20

0 –40 –20 0 20 40 CAD

Figure 9. The same as Figure 8 but for SOI 25 CAD BTDC.

Liquid fuel mass versus time as predicted by both versions of CONVERGE are shown in Figure 10. The software with the new model predicts more fuel vapour, which leads to lower in-cylinder temperatures due to evaporative cooling. This is linked with the relatively low peak in-cylinder pressures, as predicted by the software with the new model compared with the software with the Amsden et al. model, as shown in Figures 8 and 9. The difference in predicted vapour mass for both models increases at longer times, as shown in Figure 11. This agrees with the numerical predictions for vaporising sprays at different ambient conditions presented by Kabil et al. [12] using both heating and evaporating models. In the latter analysis, a spray of five-component light naphtha fuel surrogate at engine-like conditions was modelled.

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70 Measurements [3] 60 CONVERGE CONVERGE+UDF 50

Pressure[bar] 20

0 –40 –20 0 20 40 CAD

Sustainability 2021, 13, 2937 Figure 8. Comparison of in-cylinder pressures inferred from the experimental results, and the re-10 of 12 sults of the simulation using the standard and customised versions of COVERGE at SOI 20 (CAD) crank angle in degrees BTDC (before top-dead-centre).

70 Measurements [3] 60 CONVERGE CONVERGE+UDF 50

Pressure[bar] 20

Sustainability 2021, 13, x FOR PEER REVIEW 11 of 13 0 –40 –20 0 20 40 Sustainability 2021, 13, x FOR PEER REVIEW 11 of 13 CAD

FigureFigure 9. The 9. The same same as Figure as Figure 8 but8 but for for SOI SOI 25 25CA CADD BTDC. BTDC. 4.0 4.0 (a) Liquid fuel mass versus time as predicted by(b) both versions of CONVERGE are shown 3.5 3.54.0 4.0 in Figure CONVERGE 10. The software with the new model predicts more CONVERGEfuel vapour, which leads to (a) 3.0 (b) CONVERGE+UDF 3.03.5 CONVERGE+UDF 3.5 lower CONVERGEin-cylinder temperatures due to evaporative cooling. This CONVERGE is linked with the rela- 2.5 CONVERGE+UDF 2.53.0 tively CONVERGE+UDFlow peak in-cylinder pressures, as predicted3.0 by the software with the new model 2.0 2.02.5 compared with the software with the Amsden2.5 et al. model, as shown in Figures 8 and 9. The difference in predicted vapour mass1.5 for both models increases at longer times, 1.52.0 2.0

as shown in Figure 11. This agrees withLiquid mass[mg] the numerical predictions for vaporising sprays Liquid mass[mg] 1.0 1.01.5 1.5 at different ambient conditions presented by Kabil et al. [12] using both heating and evap-

Liquid mass[mg] 0.5 Liquid mass[mg] 0.51.0 orating models. In the latter analysis, a spray1.0 of five-component light naphtha fuel surro- 0.0 0.00.5 gate at engine-like conditions was modelled.0.5 –20 0 20 –20 0 20 0.0 CAD 0.0 CAD –20 0 20 –20 0 20 CAD CAD Figure 10. Predicted liquid mass of fuel for: (a) SOI 20; (b) SOI 25 CAD BTDC. Figure 10. Predicted liquid mass of fuel for: (a) SOI 20; (b) SOI 25 CAD BTDC. Figure 10. Predicted liquid mass of fuel for: (a) SOI 20; (b) SOI 25 CAD BTDC.

100 100 (a) (b) 100 100 80 (a) 80 (b) CONVERGE 80 CONVERGE 80 60 CONVERGE+UDF 60 CONVERGE+UDF CONVERGE CONVERGE 60 60 CONVERGE+UDF 40 CONVERGE+UDF 40

40 40

Evaporatedmass [%] 20

Evaporatedmass [%] 20 0 0 –20 0 20 –20 0 20 0 CAD 0 CAD –20 0 20 –20 0 20 CAD Figure 11. PredictedCAD evaporated fuel mass for: (a) SOI 20; (b) SOI 25 CAD BTDC. Figure 11. Predicted evaporated fuel mass for: (a) SOI 20; (b) SOI 25 CAD BTDC. Figure4. Conclusions11. Predicted evaporated fuel mass for: (a) SOI 20; (b) SOI 25 CAD BTDC. 4. ConclusionsA new heating and evaporation model based on the analytical solutions to transient heat4. Conclusions transferA new and heating species and diffusion evaporation equations model was based implemented on the analytical into the solutions commercial to transient CFD softwareheat transferA CONVERGE.new heating and species and The evaporationdiffusion model was equations validatedmodel based was in theimplemented on analysisthe analytical of into the solutionsthe heating commercial and to transient evap- CFD orationsoftwareheat transfer ofa CONVERGE. single and droplet.species The diffusion The model results wasequations predicted validated was byin implemented CONVERGEthe analysis intoof with the the heating the commercial new and model evap- CFD orationsoftware of CONVERGE. a single droplet The. modelThe results was validated predicted in by the CONVERGE analysis of thewith heating the new and model evap- wereoration found of a to single be closer droplet to the. The experimental results predicted measurements by CONVERGE than those with based the on new the model built- inwere version found based to be on closer the Amsdento the experimental et al. model. measurements than those based on the built- in versionThe customi based onsed the version Amsden (using et al. the model. ETC/ED models) and original version (using the AmsdenThe etcustomi al. model)sed version of CONVERGE (using the were ETC/ED applied model to analys) andse original PRF65 hollowversion-cone (using spray the penetrationAmsden et al.length. model) The of prediCONVERGEctions of were both applied versions to of analy CONVERGEse PRF65 hollowwere found-cone sprayto be similar,penetration although length. some The discrepanc predictionsies of between both versions the predictions of CONVERGE of the two were versions found of to this be softwaresimilar, although were shown some in discrepanc the vapouiesr mass between time thehistory; predictions the customized of the two version versions of ofCON- this VERGEsoftware predicted were shown higher in therates vapo of evaporation.ur mass time history; the customized version of CON- VERGEThe predicted simulation higher of a PPCIrates ofengine evaporation. at late fuel injection timings was performed. The customiThes edsimulation CONVERGE of a toolPPCI allowed engine usat lateto better fuel injectioncapture the timings peak winas-cylinder performed pressure. The thancustomi thes originaled CONVERGE version oftool the allowed software. us toThis better was capture ascribed the to peakthe fact in- cylinderthat the pressureETC/ED modelthan thes could original predict version the ofsize the history software. of fuel This droplets was ascribed more accuratelyto the fact thanthat thethe ETC/EDoriginal softwaremodels could tool (usingpredict the the Amsden size history et al. of model fuel droplets). It also morepredict accuratelyed higher than droplet the originalsurface temperaturessoftware tool, (usingwhich theenhance Amsdend their et al.breakup. model )The. It alsoresults predict of oured numericalhigher droplet simulations surface temperatures, which enhanced their breakup. The results of our numerical simulations Sustainability 2021, 13, 2937 11 of 12

were found to be closer to the experimental measurements than those based on the built-in version based on the Amsden et al. model. The customised version (using the ETC/ED models) and original version (using the Amsden et al. model) of CONVERGE were applied to analyse PRF65 hollow-cone spray penetration length. The predictions of both versions of CONVERGE were found to be similar, although some discrepancies between the predictions of the two versions of this software were shown in the vapour mass time history; the customized version of CONVERGE predicted higher rates of evaporation. The simulation of a PPCI engine at late fuel injection timings was performed. The customised CONVERGE tool allowed us to better capture the peak in-cylinder pressure than the original version of the software. This was ascribed to the fact that the ETC/ED models could predict the size history of fuel droplets more accurately than the original software tool (using the Amsden et al. model). It also predicted higher droplet surface temperatures, which enhanced their breakup. The results of our numerical simulations highlight the importance of properly describing the physical processes in fuel and biofuel sprays, especially in partially premixed combustion engines.

Author Contributions: Conceptualisation, A.E. and I.K.; methodology, I.K.; software, I.K., Y.E.; validation, I.K., J.B., H.G.I.; formal analysis, A.E.; investigation, J.B.; resources, I.K.; data curation, M.A.Q.; writing—original draft preparation, I.K.; writing—review and editing, M.A.Q., A.E., S.S.S.; visualization, M.A.Q.; supervision, A.E., W.A.; project administration, W.A.; funding acquisition, M.A.Q., S.S.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the European Commission and the British Council, grant numbers: 2018-1-UK01-KA107-047386 and 2020-1-UK01-KA107-078517 (M.AQ.) and UK EPSRC, grant number: EP/M002608/1 (S.S.S.). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors are grateful to Convergent Science for providing a CONVERGE license. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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