400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760

SAE TECHNICALPAPER SERIES 1999-01-0567

Evaporation of In-Cylinder Liquid Fuel Dropletsin an SI Engine: A Diagnostic-Based

Modeling Study

Robert Meyer and John B. HeywoodMassachusetts Institute of Technology

Reprinted From: Combustion in SI Engines(SP-1436)

International Congress and ExpositionDetroit, Michigan

March 1-4, 1999

The appearance of this ISSN code at the bottom of this page indicates SAEs consent that copies of thepaper may be made for personal or internal use of specific clients. This consent is given on the condition,however, that the copier pay a $7.00 per article copy fee through the Copyright Clearance Center, Inc.Operations Center, 222 Rosewood Drive, Danvers, MA 01923 for copying beyond that permitted by Sec-tions 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying such ascopying for general distribution, for advertising or promotional purposes, for creating new collective works,or for resale.

SAE routinely stocks printed papers for a period of three years following date of publication. Direct yourorders to SAE Customer Sales and Satisfaction Department.

Quantity reprint rates can be obtained from the Customer Sales and Satisfaction Department.

To request permission to reprint a technical paper or permission to use copyrighted SAE publications inother works, contact the SAE Publications Group.

No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior writtenpermission of the publisher.

ISSN 0148-7191Copyright 1999 Society of Automotive Engineers, Inc.

Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solelyresponsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published inSAE Transactions. For permission to publish this paper in full or in part, contact the SAE Publications Group.

Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE.

Printed in USA

All SAE papers, standards, and selectedbooks are abstracted and indexed in theGlobal Mobility Database

1 1999-01-0567

Evaporation of In-Cylinder Liquid Fuel Droplets in anSI Engine: A Diagnostic-Based Modeling Study

Robert Meyer* and John B. HeywoodMassachusetts Institute of Technology

Copyright 1999 Society of Automotive Engineers, Inc.

ABSTRACT

Liquid fuel behavior in the cylinder impacts SI engine HCemissions particularly during engine start-up. Inflow ofliquid fuel into the cylinder is largely determined by theflow and temperature environment in the intake port.Subsequent evaporation of fuel droplets in the cylinderprior to impact on the piston and cylinder liner reducesthe amount of liquid fuel in the cylinder that is likely tocontribute to HC emission and is therefore important.In this study, measurements of liquid fuel droplet charac-teristics in the vicinity of the intake valve of a firing SIengine were analyzed to estimate the amount and spatialdistribution of in-cylinder evaporation of liquid fuel prior todroplet impact on the cylinder liner or piston. A one-dimensional fuel droplet evaporation model was devel-oped to predict the amount of fuel evaporation givenmeasured fuel droplet sizes and velocities, intake portand valve temperatures during warm up, and cylindergeometry. Measurements of the liquid fuel droplet distribution enter-ing the cylinder were made around the circumference ofthe intake valve with open and closed valve port injectiontiming, during engine starting and warm up. Based onthese measurements the dependence of in-cylinder fuelevaporation on changing temperatures and droplet sizedistributions during engine warm-up has been assessed.The fraction of the liquid fuel entering the cylinder thatvaporizes before wall impact was found increase fromabout 20% at start-up to about 50% under warmed upconditions. This fraction proved to be most sensitive tothe intake port and valve temperature.

INTRODUCTION

Liquid fuel in the cylinder of automotive SI engines is alikely cause of increased HC emissions particularly dur-ing the period of engine starting and warm up. This sub-ject has drawn significant research efforts recently to

analyze the nature of liquid fuel transport into the cylin-der.The authors conducted a study in an optical single cylin-der engine [1] that revealed important details of themechanisms by which liquid fuel is transported into thecylinder under firing engine conditions and how thesemechanisms depend on fuel injection timing and enginewarm-up. The study was based on Phase Doppler(PDPA) measurements of fuel droplets in multiple loca-tions around the circumference of the intake valve in thecylinder of the firing engine. The present study analyzes the in-cylinder evaporation ofliquid fuel droplets that enter through the intake valve withthe characteristics (size and velocity) measured in thevalve vicinity. The magnitude of fuel droplet evaporationin the cylinder prior to impact on a surface (i.e. piston,cylinder liner and head) is likely to have a significantimpact on engine-out HC emissions. The evaporated fuelis more likely to burn completely during combustion. Thein-cylinder liquid fuel that does not vaporize prior to com-bustion may be stored in various locations in the cylinder(e.g. crevices, lubricating oil film) where it can be asource of HC emissions. The purpose of the study described in this paper was toestimate the amount of fuel evaporation from liquid fueldroplets that enter the cylinder prior to impact on sur-faces in the cylinder, as well as the spatial distribution ofthe impacting fuel in the cylinder. A one-dimensional fueldroplet evaporation model was developed that uses mea-sured characteristics of fuel droplets in the valve vicinityas an input to determine the amount of evaporation fromthese droplets. The sensitivity of fuel evaporation to injec-tion timing and to changes in the thermal environment ofthe engine during warm up was studied. The study is lim-ited to in-cylinder evaporation of liquid fuel droplets only.The behavior of any liquid fuel entering the cylinder as afuel film was not considered.

* Authors current affiliation: BMW AG

2MEASURED FUEL DROPLET CHARACTERISTICS

The experimental apparatus used to provide the initial in-cylinder fuel droplet characteristics is described in detailin [2]. A Phase Doppler Particle Analyzer (PDPA) wasused in a transparent single-cylinder square-pistonengine to measure the characteristics (size and velocity)of liquid fuel droplets in the vicinity of the intake valveunder firing conditions during starting and warm-up. Theengine has a flat cylinder head which provides good opti-cal access to the intake valve. Fuel droplet characteristicsas functions of time after engine starting and crank anglewere taken in seven angular locations on five planesbelow the cylinder head. The measurement positionswere located on half-circles 5 mm away from the perime-ter of the intake valve. The locations of the measurementpositions in the intake valve vicinity are shown in Fig. 1.

Figure 1. PDPA measurement locations in the intake valve vicinity

To visualize the geometrical structure of the liquid fuelspray entering the cylinder, a Planar Laser Induced Fluo-rescence (PLIF) technique was applied on the sametransparent engine. PLIF images were taken at variousengine cycle positions in a plane 10 mm from the centerline of the engine intake system. A sample image at max-imum valve lift is shown in Fig. 2. The cone structure ofthe fuel spray emerging from the intake valve as well asits separation into two jets due to the large valve lift canbe observed. Also it can be seen from this figure, that the5 planar PDPA measurement locations are sufficientlyspread out to cover the entire width of the curtain areaaround the intake valve through which liquid fuel entersthe cylinder. The PDPA and PLIF measurements were made duringengine starting and subsequent warm up. The enginewas first motored at constant speed. Fuel injection wasthen started to provide firing engine operation. To achieveprompt firing, the first injection pulse was enriched to pro-vide six times the amount of fuel of the subsequent injec-tions. The engine was then run for 90 seconds of enginewarm up. The engine operating conditions are summa-rized in Table1.

Table 1. Engine operating conditions for fired tests

Figure 2. PLIF setup and sample image at maximum valve lift

A procedure was developed and verified previously [1] toapproximate the volume of liquid fuel entering the cylin-der based on the PDPA and PLIF measurements. Theprocedure allowed to estimate the volume of liquid fuelentering the cylinder as a function of time and its spatialdistribution in the intake valve vicinity. Figure 3 displaysfor the open valve injection and the closed valve injectioncase the volume flow of liquid fuel into the cylinder duringa time interval of warm-up (t = 4 sec.) normalized by thevolume of liquid fuel injected during this time interval.

3Figure 3. Volume inflow of liquid fuel during warm-up

DROPLET EVAPORATION MODEL

Based on considerations found in [3], a fuel droplet evap-oration model was developed to predict the fate of in-cyl-inder liquid fuel droplets with their initial characteristicsobtained from the PDPA measurements. For simplicitythe droplets were assumed to be of spherical shape, anduniform temperature initially. Influence of the surroundingdroplets in the spray on the evaporation behavior of eachsingle droplet was neglected. Mass transfer of an evaporating droplet due to a speciesconcentration gradient (neglecting thermal diffusion)yields

(1)

where DS is the droplet diameter and k g and cpg are thethermal conductivity and the heat capacity of the sur-rounding gas phase respectively. BM is a mass transfernumber

(2)

with Ys being the fuel mass fraction at the droplet - airinterface. A heat transfer number BT is defined by :

(3)

where T

and TS are the ambient air temperature and thedroplet surface temperature, respectively, and L is thelatent heat of fuel vaporization corresponding to the fuelsurface temperature TS. BT denotes the ratio of the avail-able enthalpy in the surrounding air to the heat requiredto evaporate the fuel droplet. A balance of heat transfer to a droplet and heat removalthrough evaporation yields an expression for the instanta-neous change of droplet surface temperature:

(4)

The instantaneous change of droplet diameter follows as:

(5)

Balancing the aerodynamic and inertial forces exerted onthe droplet yields an expression for the instantaneouschange of droplet velocity under the influence of a sur-rounding airflow:

(6)

with the drag coefficient cD given by:

(7)

where the Reynolds number Re is based on the dropletdiameter and the relative velocity between droplet andsurrounding gas.

Figure 4. Simulated mean air velocity in the valve gap and in-cylinder gas temperature throughout the intake stroke

For adaptation of this model to the conditions in the testengine in which the PDPA droplet measurements wereobtained, the surrounding air temperature in the cylinder,and air velocity in the valve gap during intake, were cal-culated using a zero-dimensional engine cycle simulation

4code [4]. Both in-cylinder gas temperature and valve gapvelocity are plotted as a function of crank angle in Fig. 4. Initial conditions for ambient temperature and relativedroplet velocity are the cylinder gas temperature, and thedifference between valve gap velocity of the intake airflowand measured droplet velocity, respectively, at the cycleposition of droplet measurement. The initial droplet tem-perature at entry into the cylinder was assumed to be theaverage of the valve and the port wall temperatures. Bothtemperatures were measured as a function of time duringthe engine starting and warm up experiments (see Fig.5).

Figure 5. Measured intake valve and port temperatures during engine warm-up

Using the equations above the model allows an approxi-mate prediction of the diameter and position of a mea-sured fuel droplet as a function of engine cycle position.Using a given cylinder and valve geometry, the amount offuel evaporation from a droplet prior to its impact on thecylinder liner or piston, or prior to commencement ofcombustion, was determined.To best represent the conditions in the transparentengine used in this study, the piston position at each timestep was determined using the geometric dimensions(crank radius and connecting rod length). The engine cyl-inder was modeled with a circular geometry, with the cyl-inder bore such that the round cylinder cross-sectionequaled the square one. The distance from piston top tocylinder head at TC was set at 14 mm as in the transpar-ent engine. Droplet impact on either cylinder liner or pis-ton top surface was determined by considering the fueldroplet position at each time step of the calculation rela-tive to cylinder liner and piston top location at that timestep. Thus the droplets were modeled to follow the initialtrajectory as observed from the PLIF visualization results.Droplet redirection through interaction with the in-cylinderflow field was not considered. Such influences wouldbecome important especially near cylinder and pistonwalls, where the impinging intake air jet forms recircula-tion regions that would tend to carry drops first parallel toand then away from the wall surface. We can speculatethat small droplets of around 10 mm in diameter wouldfollow these flow features most easily and would hencecontribute less to wall impingement than predicted by the

model. These small droplets would be likely to stay sus-pended in air until start of combustion or complete evapo-ration.

DROPLET EVAPORATION AT ENGINE CONDITIONS

To better understand the sensitivity of droplet evaporationto the surrounding conditions it is helpful to analyze thedetails of the heat and mass transfer process to and froma single droplet during heat up and vaporization. Theevaporation process of a droplet is displayed schemati-cally in Fig. 6 as of a droplet diameter - time history. Adroplet suddenly exposed to a large enough temperaturedifference to allow vaporization, undergoes two distinctphases of evaporation [3]. As heat is first transferred tothe droplet, its temperature increases. Little mass trans-fer from the droplet occurs due to low fuel vapor concen-tration at the droplet surface. The droplet is heated up,similar to any other cold body, with a non uniform temper-ature profile that decreases from the droplet periphery toits center. This period of the evaporation process is calledthe heat up process. The decrease in droplet diameterduring this phase is minimal (and the heat up phase of adroplet is often approximated as a phase of constantdiameter). With increasing droplet temperature, heattransfer to the droplet is increasingly balanced by masstransfer away from the droplet surface. Droplet heat upcontinues until the droplet surface reaches the wet bulbtemperature at the surrounding conditions is. From thispoint, heat transfer to the droplet is completely balancedby mass transfer of vapor away from it. The droplet diam-eter undergoes a quadratic decease with time which isrepresented by the straight lines drawn in Fig. 6.

Figure 6. Droplet warm-up and evaporation (from [3])

Under engine conditions during start up, therefore thereare two main parameters that have major influence onthe in-cylinder fuel droplet evaporation process. One isthe initial droplet temperature at entry into the cylinder, asthis determines the amount of heat transfer necessarybefore substantial evaporation occurs at wet bulb temper-ature. The other is the in-cylinder gas temperature sincethe magnitude of heat transfer to the droplet is

5determined by the temperature difference between thein-cylinder gases and the droplet. The initial droplet tem-perature will be determined by the port and valve temper-ature in the intake. It can be shown that at the enginespeed used in this study (1100 rev/min), almost completeheat up of a fuel film of the thickness commonly occurringin intake ports is reached in a time interval of about 6degrees CA. Hence, the initial droplet temperature at cyl-inder entry was assumed to be the average of valve andport temperatures (liquid fuel was seen to be atomizedfrom both the valve and the port surface). The in-cylindergas temperature will be a function of cycle position as asizable fraction of high temperature residual gas ispresent in the cylinder at IVO. During intake, this residualgas will be diluted by mixing with intake air, so that thecylinder temperature decreases to close to the intaketemperature level. The mean cylinder temperature duringthe intake stroke was determined by a zero-dimensionalcycle simulation code (see Fig. 4).Model tests were run to quantify the impact of both vari-ables on droplet evaporation. For droplets of various size,the evaporation process was calculated for different initialin-cylinder temperatures. For a 50 m droplet, dropletsize histories are shown on a time scale relevant forengine circumstances in Fig. 7. The figure shows theeffect of a variation of both initial droplet temperature andcylinder gas temperature, respectively, while holding theother temperature constant. The maximum time of 0.01 sdisplayed on the graphs corresponds to the travel time ofthe slowest measured droplets (order of 10 m/s) to coverthe largest available distance in the cylinder (order of 10cm). It can be seen that the initial droplet temperaturehas a significant influence on the rate of droplet evapora-tion. The effect of the surrounding cylinder temperature isnegligible on the time scale considered. Due to the small travel distance in the cylinder (order ofcentimeters) the time scale of droplet travel before wallimpact does not extend substantially beyond the heat-upperiod of the fuel droplets. During heat up, heat transferto the droplet causes only a small changes in diameter.Thus increased heat transfer through increased cylindertemperatures does not result in faster evaporation.Increased initial temperature, however, determines thatless heat up is necessary for the droplet to reach wetbulb temperature. Hence, constant heat transfer to thedroplet results in increased mass transfer away from thedroplet through evaporation.Thus the amount of liquid fuel evaporated from the drop-lets subjected to heat transfer will be dependent on theinitial droplet temperature at entrance into the cylinder(i.e. the temperature of the engine during warm up).Changing cylinder gas temperature during the enginecycle is of minor influence.

Figure 7. Influence of cylinder gas temperature and initial droplet temperature on droplet evaporation

LIQUID FUEL EVAPORATION IN THE CYLINDER

Using the evaporation model, the fate of the in-cylinderliquid fuel droplets measured with the PDPA duringengine warm up was determined. The intake valve wasassumed to be placed in a round cylinder (as opposed tothe square geometry of the transparent engine). For eachPDPA measurement location around the circumferenceof the intake valve, the radial distance to the cylinder linerwas determined. This input was used to determine thetime and location of droplet impact on the cylinder liner orpiston.Four different locations of the intake valve in the cylinderhead were considered: a generic case with the valve inthe center of the cylinder head, two different configura-tions representative of 2-valve engines, and a configura-tion representative of a 4-valve engine. The fourconfigurations are shown in Fig. 8.Figure 9 displays the volume of liquid fuel that vaporizesin the cylinder after induction, normalized by the volumeof liquid fuel entering the cylinder as a function of timeafter start up, for the idealized case with the intake valve

6in the center of the cylinder head. In this case the avail-able travel distance for each drop before impact on thewall is equal at each measurement location. The fractionof the liquid fuel volume entering in each position thatvaporizes, hence depends mainly on the size distribu-tions of the droplets in each location. It can be seen thatthe fraction of liquid fuel that vaporizes increases withtime with both open and closed valve injection. Atwarmed-up engine conditions, after 90 seconds of opera-tion, about 50 % of the liquid fuel entering the cylindervaporizes before droplet impact on the cylinder wall orpiston. The amount of vaporization scales with the initialdroplet temperature at entry into the cylinder, i.e. theintake port and valve temperatures. This is due to thesensitivity of in-cylinder fuel droplet evaporation to initialdroplet temperature identified above.Additionally, evaporation increases more rapidly withclosed valve injection during engine warm up than with

open valve injection. While fuel droplet transport into thecylinder with open valve injection is primarily due to directcommunication between the injector and the cylinderthrough the open valve, droplets are stripped off a fuelfilm in the valve vicinity in the case of closed valve injec-tion. As shown in [5] the size distribution of fuel dropletsdue to this atomization process is strongly dependent onthe fuel film thickness in the valve vicinity. This film thick-ness diminishes with engine warm-up causing in-cylinderfuel droplet size to decrease with engine warm up. Withopen valve injection, the in-cylinder droplet size distribu-tion remains essentially constant during warm-up due tothe different mode of liquid fuel transport into the cylinderin this injection case. The reduction in droplet size distri-bution with closed valve injection with engine warm-up isreflected in the fuel evaporation improvements displayedin Fig. 9.

Figure 8. Modeled valve configuration cases

7Figure 9. Center valve location - Fraction of liquid fuel that vaporizes in the cylinder as a function of engine running time (averaged over valve circumference)

Figure 10 shows the fraction of the liquid fuel entering thecylinder that vaporizes prior to droplet impact on the cyl-inder liner or piston as a function of the valve circumfer-ential angle . The values displayed are averages over90 seconds of engine warm up. With both open andclosed valve injection, the fraction of entering liquid fuelthat vaporizes has a minimum at the location of maximumliquid fuel entry into the cylinder (where the maximumSMD occurs). Since in this valve configuration case thedroplet travel distances between the valve and the cylin-der wall are equal in all angular locations, differences inthe fraction of liquid fuel vaporizing can only be attributedto different size distributions of the initial droplet inflow.

Figure 10. Center valve location - Fraction of liquid fuel that vaporizes in the cylinder as function of valve angle (averaged over 90 s of engine operation)

Figure 11 displays the measured droplet size distribu-tions for closed valve injection in the angular locations = 45 and = 112.5. The size distribution at = 112.5shows a greater number of larger droplets. Evaporationof larger droplets proceeds slower due to the lower sur-face to volume ratio, so that a smaller fraction of liquidfuel was observed to vaporize.

Figure 11. Droplet size distribution at valve (closed valve injection - averaged over 90 seconds engine operation)

Figure 12. Fraction of initial size distribution that does not fully vaporize before liner impact during various stages of warm up

In Fig. 12, the droplet size distribution of the volume frac-tion impinging on the cylinder wall is displayed for bothpositions during three time intervals of engine operationafter start up (0 - 30 seconds, 30 - 60 seconds, and 60 -90 seconds). The increase of droplet evaporation withengine warm up results in the increasing minimum diam-eter of droplets impacting on the wall at later stages ofengine operation. The observed increase of the fractionof liquid fuel vaporized with engine warm up is thus aresult of increased initial droplet temperature, and thedecreasing droplet mean diameter caused by reducingfilm thickness in the intake port with engine warm-up.Due to the spray targeting in the intake port with closed

8valve injection, the positions around = 112.5 show alarge percentage of large droplets that are less likely tovaporize. With open valve injection, most injected fuel inthe intake port is carried forward by the intake flow whichresults in large droplet sizes in the front of the intake port(around the = 157.5 location). Consequently the frac-tion of in-cylinder liquid fuel vaporizing in this location hasa minimum in this injection timing case.Figure 13 shows the fraction of vaporized in-cylinder liq-uid fuel as a function of valve angle for the basic two-valve configuration (see Fig. 8). In this case the droplettravel distance before impact on the cylinder wall issmaller in the rear and larger in the front of the intake portcompared to the center valve configuration case. Conse-quently liquid fuel droplet evaporation prior to impact onthe cylinder wall increases in the front of the intake portand decreases in the back (relative to the center valvelocation case).

Figure 13. Basic 2 Valve configuration - Fraction of liquid fuel that vaporizes in the cylinder as function of valve angle (averaged over 90 s of engine operation)

To analyze the influence of available droplet travel dis-tance before wall impact, model calculations were carriedout with the measured droplet size distributions. Figure14 shows the droplet size distribution of the volume frac-tion impinging on the cylinder wall resulting from thedroplet size distributions measured in the = 45 and = 112.5 positions and assuming three different availabletravel distances (5 mm, 25 mm, and 50 mm). Withincreasing available travel distance, only larger diameterdroplets do not vaporize fully in the cylinder and impingeon the liner. This is very similar to the effect of increasinginitial droplet temperature during engine warm up that asdiscussed before. For droplets at wet bulb temperature,the droplet diameter decreases with the second power oftime due to evaporation, so that evaporation benefits canbe expected to be more than proportional to increasingtravel distance.

Figure 14. Fraction of initial size distribution that does not fully vaporize before liner impact for various available travel distances (averaged over 90 s of engine operation)

Figure 15. Basic 2 Valve configuration - Fraction of liquid fuel that vaporizes in the cylinder as function of engine running time (averaged over valve circumference)

Figure 15 displays the overall fraction of liquid fuel vapor-izing in the cylinder as a function of time with both openand closed valve injection for the basic two valve configu-ration. Compared to the center valve configuration case,more liquid fuel vaporizes in the cylinder with open valve

9injection and less with closed valve injection. This can beunderstood by considering the spatial distribution of theinflow of liquid fuel into the cylinder around the intakevalve. Due to targeting in the port, with closed valve injec-tion most fuel enters the cylinder through the sides of theintake port, whereas with open valve injection most fuelenters the cylinder through the front of the intake valvedue to interaction of the injected fuel with the intake air-flow (see [1]). The volume inflow distribution of liquid fuelin the vicinity of the intake valve as measured in [1] isshown in Fig. 16. Since most fuel enters the cylinder inthe front of the valve with open valve injection, theincrease of travel distance before impact on the wall fordroplets entering the cylinder in the front of the intakevalve leads to the observed improved evaporation of liq-uid fuel. In the case of closed valve injection, evaporationdecreases slightly due mainly to reduction of travel dis-tance in the = 90 location.

Figure 17 shows the fraction of liquid fuel vaporizing as afunction of valve circumferential angle on either side ofthe intake valve in the valve configuration cases repre-sentative of a multi-cylinder two valve in-line engine anda four valve engine (see Fig. 8). The effect of availabletravel distance on the fraction of liquid fuel that vaporizesin the cylinder is apparent in differences of fuel evapora-tion. Since with open valve injection most fuel enters thecylinder in a relatively confined area in the front of theintake valve, fuel evaporation is increased in valve orien-tations that provide the longest possible travel distance tothe cylinder wall. With closed valve injection, the reduc-tion potential is limited due to the fact that most liquid fuelenters the cylinder symmetrically through the sides of the

intake valve. Moving one side of the valve away from thecylinder wall reduces the droplet travel distance on theother side of the valve, so that changes in the amount offuel that vaporizes are minimal. Figure 18 shows theamount of liquid fuel vaporizing as a function of warm-uptime with open and closed valve injection in the two andfour valve configuration cases.

Figure 16. Spatial distribution of liquid fuel volume influx in the intake valve vicinity with open and closed valve injection (measured in [1])

Figure 17. Spatial distribution of in-cylinder liquid fuel evaporation (2 valve inline and 4 valve configurations)

10

FUEL IMPINGEMENT ON THE CYLINDER LINER

TOTAL AMOUNT OF LIQUID FUEL IMPINGEMENT Using the results of the in-cylinder liquid fuel evaporationmodel, a prediction of the amount of liquid fuel thatimpinges on the cylinder wall during warm up can bemade. The amount of impinging liquid fuel is obtained bymultiplying the amount of liquid fuel entering the cylinderby the fraction that does not vaporize according to modelprediction. The amount of liquid fuel that impinges on thecylinder liner during a given time interval during theengine warm-up process, normalized by the amount offuel injected into the port during that time interval, isshown in Fig. 19 for both open and closed valve injec-tion. The basic two valve configuration in Fig. 8 was usedfor this calculation. With both open and closed valveinjection, the volume fraction of in-cylinder liquid fuel thatvaporizes at start up is about 20%. This volumeincreases steadily with increasing engine temperature toreach about 50% under warmed up conditions after 90seconds of engine operation.

Figure 18. Dependence of in-cylinder fuel evaporation on valve orientation

With open valve injection, the volume of liquid fuel enter-ing the cylinder at start up is about 25 % of the injectedfuel. About 22 % of this amount would vaporize in the cyl-inder prior to impact on the liner in liquid form, so thatabout 20 % of the volume of injected fuel would impingeon the wall. Under warmed up conditions about 15% ofthe injected fuel enters the cylinder in liquid phase ofwhich about 55% would vaporize prior to impingement onthe cylinder liner (i.e. 7% of the injected fuel impinges onthe liner).

With closed valve injection the volume of liquid fuel enter-ing the cylinder at start-up is about 18 % of the injectedfuel. The fraction of this amount that vaporizes in the cyl-inder is about 18%, so that wall impingement of liquid fuelduring this phase can be expected to amount to about 15% of the injected fuel. Under warmed-up conditions, theamount of liquid fuel entering the cylinder equals about2% of the injected fuel, and about 50% of that fractioncan be expected to vaporize. Hence about 1% of theinjected fuel can be expected to impinge on the cylinderliner under warmed-up engine conditions. Maximuminflow of liquid fuel with closed valve injection equalsabout 38% of the injected fuel after about 15 seconds ofengine operation. At this stage of warm up, about 21% ofthe in-cylinder liquid fuel can be expected to vaporizeaccording to model prediction, so that the amount of liq-uid fuel impinging on the cylinder liner would equal 30%of the injected fuel.

Figure 19. Liquid fuel impinging on the cylinder liner and piston during warm-up according to model prediction

SPATIAL DISTRIBUTION OF LIQUID FUELIMPINGEMENT For the basic two valve configurationcase, an assessment of the spatial distribution of the liq-uid fuel at impingement on the cylinder liner was made.This valve configuration most closely resembles theactual valve configuration in the transparent test engine.For each PDPA measurement location in the circumfer-ence of the intake valve, the amount of liquid fuel mea-sured passing through it, reduced by the fraction thatvaporizes in the cylinder according to the model predic-tion, was projected onto the location of impingement onthe cylinder liner. The location of fuel impingement wasdetermined from the location of the PDPA measurementin the valve vicinity and the droplet flight trajectory. Fromthe PLIF images, a 45 degree orientation of the liquid fuelcone to the valve axis and an 11 degree spreading angleof the liquid fuel cone was observed.

11

Figure 20. Definition of cylinder angle and head distance

Figures 21 and 22 display the spatial distribution of theliquid fuel on the cylinder wall for both open and closedvalve injection. To display the distribution of liquid fuelimpinging on the cylinder wall, the liner surface is dis-played in cylindrical coordinates with the cylinder angleranging from 0 degrees in the back of the intake port to180 degrees in the front of the port, and the distancefrom the cylinder head starting at 0 at the cylinder headsurface (see Fig. 20). The diagrams presented in Fig. 21and 22 thus represent projections of half of the cylinderwall on a flat plane where the fuel impingement wasassumed to be symmetrical with respect to the intakeport axis. For each impingement location on the cylinderwall, the amount of impinging fuel was calculated. Leastsquares fitting was then used to produce a contour plot torepresent the spatial distribution of the impinging fuelamount. The relative quantity of impinging liquid fuel isrepresented by gray gradients, where darker areas repre-sent areas of increased fuel impingement. Since the spa-tial distribution of liquid fuel inflow in the vicinity of theintake valve does not vary during warm up with eitheropen or closed valve injection, the relative distribution offuel impingement on the cylinder wall stays essentiallyconstant during warm up. For a given point in time duringwarm up, the fuel distribution contour plot can be inte-grated to give the total amount of fuel impinging on thecylinder liner as represented in Fig. 19. Hence, a combi-nation of both figures can be used to estimate theamount of liquid fuel present on various parts of the cylin-der wall during warm up.

Figure 21. Spatial distribution of impinging liquid fuel on cylinder liner (open valve injection)

With both open and closed valve injection, it can be seenthat fuel impingement on the cylinder wall occurs furtheraway from the cylinder head surface in the front (higherdegrees cylinder angle - see Fig. 20) of the cylinder. Dueto the larger available droplet travel distance, liquid fuelimpinges about 40 mm below the cylinder head over anarea of about 20 mm width. With open valve injection,about 65% of the non-evaporating in-cylinder liquid fuelimpinges in an area around 135 degrees cylinder angle,due to the fact that, driven by interaction with the intakeairflow, with this injection timing most fuel passes throughthe front of the intake valve. With closed valve injection,impingement of liquid fuel on the cylinder liner is spreadout over a wider angular range. About 60% of the non-vaporizing in-cylinder liquid fuel impinges on an areaaround 60 degrees cylinder angle (the side of the intakeport). The more spread out appearance of the impingingliquid fuel on the cylinder wall with closed valve injectionis due to the fact that with this injection timing, the fuelspray in the intake port is not redirected through interac-tion with the intake airflow, and hence liquid fuel entryinto the cylinder is distributed according to spray target-ing in the port.

Figure 22. Spatial distribution of impinging liquid fuel on cylinder liner (closed valve injection)

CONCLUSIONS

A one-dimensional droplet evaporation model has beendeveloped to estimate the fraction of in-cylinder liquid fuelvolume (carried by fuel droplets) that vaporizes beforeimpact on the cylinder liner or piston. Inputs to the modelare droplet characteristics measured in the valve vicinityby a Phase Doppler (PDPA) technique as well as droplettrajectories observed from PLIF imaging. Measuredintake port and valve temperatures as well as in-cylindergas temperature and the mean air velocity in the valvegap as obtained from a zero-dimensional engine simula-tion code are used to account for the changing thermaland flow environment in the cylinder during engine warm-up and throughout the cycle.Several important trends in in-cylinder droplet evapora-tion were inferred from the model application to engineconditions. The fraction of in-cylinder liquid fuel that

12

vaporizes, scales with the increasing port and valve tem-perature during warm-up, and not with the decreasing in-cylinder gas temperature during the intake stroke asresiduals increasingly mix with fresh charge. This is dueto the fact that mass transfer from a droplet is not signifi-cant until the droplet wet bulb temperature is reached.Droplet travel distances in the cylinder are short, so thatincreased heat transfer to a droplet mainly results in atemperature increase of the droplet. In-cylinder liquid fuelevaporation improves with reduced droplet mean diame-ters and increased travel distance before wall impact.Hence, in-cylinder liquid fuel evaporation with open valveinjection is greater than with closed valve injection, ini-tially, since the mean droplet sizes are smaller in thiscase and most fuel enters the cylinder in the front of thevalve where the travel distances before liner impact arelongest. Evaporation increases more rapidly duringengine warm up with closed valve injection due todecreasing droplet size distributions with increasingengine temperature. With both open and closed valveinjection, the fraction of in-cylinder liquid fuel that vapor-izes prior to wall impact, according to model prediction,steadily increases from about 20% to about 50%. Notethat neither droplet interaction with spatial features of thecylinder flow field nor the effect of droplet interactions inthe spray on heat transfer were taken into account. Espe-cially, it is likely that small droplets (diameter 10 mm)would closely follow the in-cylinder flow features and stayairborne in the cylinder.

ACKNOWLEDGMENTS

This work has been supported by the Engine and FuelsResearch Consortium in the Sloan Automotive Labora-tory at MIT whose members are: Chrysler Corp., FordMotor Co., General Motors Corp., Mobil Corp., PeugeotS.A., Renault S.A., Shell Oil Co., and Volvo Car Corp..We would like to thank Brian Corkum and Peter Menardfor their help with the engine test cell setup

REFERENCES

1. Meyer R., Yilmaz E., and Heywood, J.B., Liquid Fuel Flowin the Vicinity of the Intake Valve in a Port Injected SIEngine, SAE Paper 982471, 1998

2. Meyer R., and Heywood, J.B., Liquid Fuel Transport intothe cylinder of a Firing Port-Injected SI Engine During StartUp, SAE Paper 970865, 1997, SAE Transactions Vol.107,1997

3. Lefebvre, A.H., Atomization and Sprays, HemispherePublishing Corp., 1989, pp. 309 - 364

4. Poulos, S.G., and Heywood, J.B., "The Effect of Combus-tion Chamber Geometry on S.I. Engine Combustion", SAEPaper 830334, SAE Transactions Vol.92, 1983

5. Meyer, R. and Heywood, J.B., Effect of Engine and FuelVariables on Liquid Fuel Transport into the Cylinder in Port-Injected SI Engines, SAE Paper, to be presented 1999

6. Watson, K.M., Prediction of Critical Temperatures andHeats of Vaporization, Ind. Eng. Chem., Vol. 23, No.4, pp.315-364, 1931

7. Vargaftik, N.B., Tables on the Thermophysical Probertiesof Liquids and Gases, Halsted Press, New York, 1975

8. Touloukian, Y., Thermal-Physical Properties of Matter,Plenum Press, New York, 1970

13

APPENDIX : DROPLET EVAPORATION MODEL EQUATIONS

The evaporation model follows an argumentation setforth in [3]. One evaporating droplet is treated as a singleobject. The influence of the surrounding spray isneglected. Mass transfer of evaporating fuel from a drop-let is driven by a concentration gradient of fuel near thedroplet surface. A mass transfer number is defined as:

where YFs is the fuel vapor concentration at the dropletsurface. It is calculated as

with MA and MF representing the molecular weights of airand fuel respectively and p the ambient pressure. Thefuel vapor pressure pFs at the droplet surface of tempera-ture Ts is calculated by a Clausius Clapeyron expression:

Values for a and b can be found in [3]. Heat transfer to the droplet is driven by a temperature dif-ference between the droplet surface and the surround-ings. A heat transfer number is defined relating theavailable enthalpy in the surrounding gas to the heatrequired to evaporate the fuel.

Where L denotes the latent heat of the fuel droplet at sur-face temperature, cpg the heat capacity of the gas sur-rounding the droplet (which consists of air and fuelvapor), and T

the temperature of the surrounding gas

sufficiently far away from the droplet surface. The latentheat at droplet surface temperature is determinedaccording to a correlation given in [6]:

where LTbn, Tbn, and Tcr can be found in [3]. The heatcapacity of the surrounding gas is calculated by:

with the reference values for temperature, concentrationof fuel, and concentration of air as

The heat capacities for air and fuel vapor (cpa and cpv)were calculated as functions of ambient temperature andpressure from linearizations of experimental data foundin [7]Using this set of equations the mass and heat transfernumbers (BM and BT) are calculated for each time step(t) of droplet evaporation. Mass transfer from the droplet(assuming a spherical droplet shape with diameter D)can be expressed as:

where the conductivity of the gas phase surrounding thedroplet (kg) is calculated as

where ka denotes the conductivity of air and kv the fuelvapor conductivity which is calculated according to [3] as:

with

An expression for the instantaneous change of dropletdiameter then yields:

The instantaneous change of droplet surface tempera-ture according to heat and mass transfer to and from thefuel droplet is calculated by:

14

Using the last two expressions, new values for dropletdiameter and surface temperature are calculated for thenext time stepA force balance of aerodynamic and inertial forces yieldsan expression for the instantaneous change of dropletvelocity under the influence of a surrounding airflow:

with

where the Reynolds number (Re) is based on the dropletdiameter D and the relative velocity (udrop- uair). Theinstantaneous change of droplet velocity is used to deter-mine the droplet velocity for the next time step. The drop-let position is determined using the magnitude of dropletvelocity and the droplet trajectory as observed in thePLIF imaging results. The equations for droplet velocityand those governing heat and mass transfer are coupledvia the droplet diameter.