Prediction of Heat Release Rate and Engine Emissions Using an Unsteady Flamelet Model Approach for a...

Introduction: process and hence are crucial from the modeling

point of view. Accurate prediction of ignition delay Application of computational fluid dynamics (CFD) requires proper chemical reaction modeling. There has recently grown very popular as a means to are four different approaches to specify chemical investigate various in-cylinder processes. Along kinetic mechanisms and they include detailed with the main combustion event, there are many mechanisms, skeletal mechanisms, reduced physical processes that need to be described mechanisms and global mechanisms [2]. The carefully to predict proper mixture formation detailed mechanisms involve all those chemical process. The mixture formation can affect the species and reactions which are pertinent but the combustion efficiency and hence the pollutant application of these detailed mechanisms in formation. One approach is to use empirical internal combustion engines is limited due to two relationships to describe different physical aspects reasons. Primarily, it is attributed absence of the of the combustion events. There is a drawback in proven mechanisms of those hydrocarbons, such as this approach as the assumptions of the steady state diesel, that involve a large number of homologous conditions are less likely to be valid for transient series . Secondly, the requirements for conditions as encountered in compression ignition computational resource for such simulations are engines [1]. The breakup of the fuel stream into large. The skeletal mechanism provides an droplets followed by the evaporation of these alternative course. In skeletal mechanism, the droplets are critical in the mixture formation

Prediction of Heat Release Rate and Engine Emissions Using an

Unsteady Flamelet Model Approach for a Compression Ignition

Engine 1, 2 1 3 1 1 1S. Imran , F. Noor *, R. Shad , A. Hussain , Z. Anwar , G. Ahmad

Abstract

Diesel Unsteady Flamelet Model (DUFM) approach along with probability density function (PDF) has been

used to investigate the effect of breakup length on the in-cylinder pressure and the rate of heat release. Two spray

breakup models, WAVE and Kelvin-Helmohltz Rayleigh Taylor (KHRT), have been investigated by varying the

magnitude of the breakup constants. The optimized set of parameters are used to predict the in-cylinder

pressure, the rate of heat release and NOx emissions in a direct injection (DI) engine. A chemical mechanism of

n-heptane with 29 species and 52 reactions has been used.

Keywords: Chemical kinetics, Computational combustion, unsteady flamelet model, spray and combustion,

compression ignition,

Submitted: 06/03/2015, Accepted: 30/03/2015, Online: 07/04/2015

1.Faculty of Mechanical Engineering, University of Engineering and Technology Lahore, Pakistan

2.School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, E1 4NS, UK

3.Department of Mechanical Engineering, University of Central Punjab, Lahore , Pakistan

*Corresponding author; Fahad Noor ([email protected])

JPIChE 43 (1) 2015: 21-36

journal homepage: www.piche.org.pk/journal

Journal of Pakistan Institute of Chemical Engineers

218-985-1 RV

21

Journal ofThe Pakistan Institute of

Chemical Engineers

Vol. XXXXIII 2015 ISSN 1813-4092

reduction in the number of species and the chemical limits burns quickly and as this process is primarily

reactions and hence the elimination of the faster governed by reaction kinetics, it is named as

premixed combustion. Diffusion or non-premixed reactions by categorizing them on the basis of their

combustion describe the slow burning of the relative significance within the full mechanism.

remaining unmixed or non-evaporated fuel which This is the easiest way to achieve mechanism

burns once properly prepared and as this reduction, but still insufficient to be adopted for

preparation is strongly dependent on mixing, this heavy hydrocarbons as diesel. Reduced

stage of combustion is generally referred as mixing mechanisms can further simplify the mechanism

controlled. For any fuel sprayed in this manner into complexity. To achieve this mechanism

the compression ignition environment, the ignition simplification (reduction), the sensitivity analysis

delay is the sum of both the physical delay as well as is carried by the assuming the steady state

the chemical delay [2]. The ignition delay can be assumptions. The sensitivity analysis analysis is

measured by using equation 2.used to eliminate the species with less contribution.

The last approach to achieve mechanism reduction (2)

is through the use of the global mechanisms.

Minimization of the number of relevant variables where is the ignition delay, P and T are the

makes these global mechanism approaches very average in-cylinder pressure and temperature

attractive especially to the CFD studies. A global before ignition. E is the activation energy whereas Amechanism can be represented by the following R is the universal gas constant. The experimental uequation,constants are represented by A and n. The above

(1)relationship shows that the ignition delay is a

strong function of temperature and pressure as

decreases when the temperature and pressure are Fuel and oxidizer mass fractions are represented by

increased. This equation has been successfully [F] and [O] whereas A, n and EA are typical

applied in number of studies. Some other Arhenius constants. n-Heptane is generally used as

parameters have also been investigated for their a diesel surrogate because of the comparable octane

possible e?ects on ignition delay. They include fuel number [3].

air equivalence ratio [46], the cetane number [7] Ignition Delay: and the engine speed [8]. Following relationship [Eq

The combustion process in a diesel engine is a 3] was proposed by Livengood and Wu [9] and used

combination of pre-mixed and diffusion combustion in many CFD codes [3].

processes. Liquid fuel such as diesel is injected into

the hot stream of air at the end of the compression

(3)stroke. Disintegration of the diesel fuel into smaller

droplets is followed by processes like evaporation Eq. 3 can be written as leading towards the formation of fuel vapor mixture

with in the combustion chamber. The time delay (4)

between the injection and the preparation of the

fuel for burning is referred as physical ignition When the value of the above integral (Eq. 4) exceeds

delay. Some low emperature reactions have been unity, combustion mode is activated.

reported to take place during and after the physical Spray Modelsignition delay leading to an additional delay that is

In dense sprays, the radial growth of sprays can be known as chemical delay. Auto-ignition is a

affected by the following factors [10],phenomenon in which a portion of the fuel which is

mixed with air su?ciently and is within combustible - Droplet Collisions

22 Journal of the Pakistan Institute of Chemical Engineers Vol. XXXXIII

)exp(][][][

TREOFATdt

FduA

ban -=

)/exp()( TREAP uAn-=t

11

1

0

=ò=

-

dtt

tt

1)/exp(

11

0

)(=ò

=

-

-dt

TREAP

t

t uAn

- Droplet Dispersion force. The following second order differential

equation is used to represent the TAB analogy- Levels of turbulence at the spray edge

Droplet collisions are important because they can (6)serve as a mechanism for droplet growth as well as

can contribute to droplet break up. Apart from

droplet collisions and coalescence, droplet Are the terms representing initiating dispersion can be another important factor affecting restoring and damping forces divided by the mass of spray growth. Droplet dispersion (Droplet-gas the body, whereas the instantaneous displacement phase turbulence interaction) that affects of the body from the equilibrium position is turbulence kinetic energy (k) and its dissipation described by x. The corresponding counterparts of rate (å) and hence may serve as mechanism for these three terms in liquid breakup environment droplet growth. Due to high slip velocity between are represented in the following equationthe droplet and the gas phase, the turbulence level

at the edge of spray can be high. This injection

(7)related high levels of turbulence can affect the

Substituting dimensionless y=x/C r, the above bradial growth of the spray. Apart from WAVE spray equation (Eq. 6) for acceleration takes following model, Taylor Anology Breakup (TAB) and Kelvin form,Helmohltz Rayleigh Taylor (KHRT) are the other

two spray model available for use in FLUENT.

Weber number is the main parameter that is used to (8)

define the breakup physics. It is defined as Orourke and Amsden [11] analytically solved this

the above second order differential equation [8]. (5)

Total fragmentation of the parent drop into a

number of daughter dropletss is resulted in TAB injWhere W , , u , d and are weber number, e g inj model but the model does not give any information

density, uniform velocity of the undistributed jet, about their numbers and sizes. Energy balance is

nozzle diameter and surface tension of the liquid used to estimate the number daughter droplets and

droplet, respectively. An analogy of spring mass their size. Under prediction of the droplet sizes of

system is used to describe the oscillation of the full cone diesel spray while using TAB model has

distorting droplets. The restoring force, the been reported [12, 13]. Park et al [14] reported that

external force and the damping force are the TAB model underestimates the penetration

represented by liquid surface tension, droplet drag when combined with Blob-method. Reitz [15]

and liquid viscosity respectively. The Taylor presented the KH breakup model based on the

Analogy Break up model (TAB model), originally Kelvin-Helmohltz instability . The basis for this

proposed by ORourke and Amsden [11], uses a breakup model is a fact that sinusoidal waves are

forced oscillating spring-mass system to describe setup on the surface of the liuid as it passes through

the behavior of an an oscillating drop that the nozzle hole. As the liquid jet enters into the

traversing through a gaseous atmosphere. The chamber, the interaction between the liquid and gas

aerodynamic forces deforming the droplet by a force phases help the sinusoidal waves to grow as a result

F that initiates the oscillations. The liquid surface of different aerodynamic factors. The growth rate .

tension responsible to keep the spherical shape of At which a wave grows on the droplet surface and

the droplet intact and resist the droplet deformation wave length of these waves can be expressed as

is represented by restoring force of the spring. The

viscosity effects resulting in the friction forces (9)

inside the droplet are represented by the damping

232015

23

2

,,lr

Cm

d

lrC

m

K

lr

guC

m

F ldk

relF

r

m

r

s

r

r==

sr inj

injge

duW 2

)(=

xm

dx

m

K

m

F&,,

ylr

Cylr

Cr

u

lC

Cy l

dkrelg

b

F &&&232

2

r

m

r

s

r

r--=

)4.11)(1(

38.034.0][

7.0

5.15.0

30

TZ

Wer gl

++

+=W

s

r

S. Imran, F. Noor, R. Shad, A. Hussain, Z. Anwar, G. Ahmad

24 Journal of the Pakistan Institute of Chemical Engineers

(10) generally used in combination with Rayleigh-

Taylor (RT) method to represent secondary breakup

of the droplet. Instability can be induced along the Where Z and T are the Ohnesorge number and the

normal to the interface between the two fluid of Taylor number respectively whereas r is the radius 0

different densities if the interface experience any of the jet before distribution. These two numbers

acceleration or deceleration [17]. Rayleigh-Taylor are functions of Reynolds number Re and wave

(RT) model is based on the Taylor's work of number W can be expressed ase instability. On a liquid-gas interface, if the

acceleration is directed into liquid, the interface is

(11) stable but disturbances (waves) can be setup if the

acceleration is directed into the gaseous medium. The breakup of a parent droplet of radius r can also The growth rate at which these waves grow and be modeled by applying the wave theory as proposed the wave length of these waves can be expressed asby Reitz [15]. Due to the assumption that child

droplet is formed by shearing of the surface of the

parent droplet, the radius of the child droplet is (14)

proportional to the wave length of the parent

droplet (15)

(12) The droplet is only allowed to breakup if its is

small than its diameter. Similar to the adjustable The KH model of spray breakup differs from the

constant B1 [Eq. 13] for the KH breakup model, RT TAB model in way that unlike TAB model, the

model has an adjustable constant in the form of C3. former approach does not allow complete breakup of

Both of these constants serve the same purpose and the droplet. In this approach, the droplet loses its

take into account the effect of initial conditions like mass continuously as it is penetrating into the

turbulence and cavitation on the secondary droplet gaseous medium. The rate at which the droplet

breakup. In order to overcome the deficiencies radius reduces is function of the original (parent)

reported in the two spray models (KH and RT), droplet radius, child droplet radius and

these two are generally applied in combined form as characteristic breakup time .bu

KH-RT spray model. In KH-RT model, both KH and

RT models compete are allowed to calculate (13)

unstable waves. If the breakup is predicted by RT B0 in equation [12] is a model constant whose

model with actual time step, the whole droplet values is fixed at 0.61 whereas B1 in equation [13] is

breakup occurs according to RT model. Otherwise an adjustable parameter whose value can range

the child droplets and reduction in diameter is between 1.73 [15] and 60 [16]. B1 takes into account

obtained through KH the influence of nozzle geometry (any turbulence

created) on the spray breakup. It has been

suggested that a higher value of B1 shall reduce the

droplet breakup and increase the penetration

length whereas a smaller value can increase the

spray disintegration and result in better fuel mixing

and also reduced penetration. One of the reported

drawback of this method of spray is that it results in

droplets with bigger than the KH radius in areas

near the nozzle tip. This is why this model is

model. If RT breakup model is

applied to the spray portion immediately after

nozzle exit, the diameter reduction is too fast.

Therefore it is only applied after a certain length

and only KH breakup is allowed near the nozzle exit

[18].

Droplet Drag Modeling:

When the droplet interacts with the gas inside the

combustion chamber, they exchange their

momentum. As a result the droplet decelerates and

Vol. XXXXIII

g

cl

WeTR

WeZ == ,

)(

)]([

33

22/3

gl

gla

rr

rr

s -

-=W

)(

323

glaC

rr

sp

+=L

6.067.1

7.05.0

0 )865.01(

)4.11)(45.01(02.9

gWe

TZ

r +

++=

L

L= 0Brnew

25

the gas phase accelerates due to difference in their

velocities before the exchange. The droplet (18)experiences a drag force. A spherical droplet of

radius r moving with a relative velocity u shall rel When y=0, it behaves as a sphere and when y=1 it experience a drag FD given by the following behaves as a disk.equation

Modeling NOX

(16) NO is a generic name given to a three different X

compounds; Nitric oxide (NO, the major

contributor), nitrogen dioxide (NO ) and nitrous 2A is the frontal area of the sphere. The drag f

oxide (N O). The NO formation can be attributed to 2 Xcoefficient CD for the sphere depends upon following chemical kinetics processesReynolds number for the gas phase Reg for low

- Thermal NO formation Reynolds number (Re<1000). X

Prompt NO formation X

(17) Fuel NO formationX

For Re>1000, a constant value of 0.424 is used [19]. Thermal NO X

The assumption that the droplet maintains its The oxidation of nitrogen present in the air is shape as a sphere does not hold when it interacts responsible for thermal NO formation. Extended Xwith gas with a sufficiently large Weber number. It Zeldovich mechanism is generally used to is deformed. The drag coefficient becomes a function determine the formation of thermal NO . These Xof Re as given in equation 17 as well as of its

reactions are highly temperature dependent.amplitude of oscillation. The drag coefficient of a

distorting drop can be modeled as lying between the

CD of a sphere, the lower limit, and the CD of a of (19)

disk.

(20)

(21)

The original Zeldovich mechanism consists of only

two reactions (Eqs 19 and 20). Once the third

reaction (Eq. 21) is included, it becomes an extended

Zeldovich mechanism. The third reactions has been

reported to contribute towards thermal NOX

formation when operating in rich mixtures [3]. The

net rate of reaction for the three reactions involved

in the Zeldovich extended mechanism can be

expressed as

-

-

2015

Fig. 1: Illustration of dynamic drag on a fuel droplet

)632.21(, yCC sphereDD +=

]][[]][[]][[]][[]][[]][[ 3,2,1,3,22,21, HNOKONOKNNOKOHNKONKNOKdt

NOfrrfff ---++=

(22)


2

232

3

4

2 dt

xdrACuF lfDrel

gD pr

r==

]6

Re1[

Re

243/2

,g

g

sphereDC +=

NONNO +Û+ 2

NNOON +Û+2

NOHOHN +Û+


where K and K represent the forward and reason why NO formation is highly temperature f r X

backward reaction rate constants respectively. The dependent. Nitrogen atom has small activation

first reaction in Zeldovich mechanism involves an energy and in fuel-lean flame (when there is enough

N molecule. The two nitrogen molecules are bonded oxygen), the rate of nitrogen consumption becomes 2

equal to its formation.together through a triple bond with a dissociation Hence a quasi-steady state can be assumed. Eq. 22 energy of 941 KJ/gmol. This step is a rate limiting can be written as

step in Zeldovich mechanism. This is the main

The dependence of the rate of NO formation on the (25)X

oxygen concentration and the temperature is clear

from the Eq 23. The concentrations of two [O] and For partial equilibrium approach, the eq. 25 can be

[OH] radicals are required apart from the written as

concentration of the two stable species O2, N . 2

(26)Various modeling strategies are adopted to

The partial equilibrium approach has generally determine the concentration of [O] and [OH] been reported to result in higher NO formation rate. radicals [3]. Equilibrium, Partial equilibrium and The predicted local concentration approach uses an local concentration are the three approaches that advanced chemistry model and takes [O] from the can be applied to determine the concentration of [O] local O species mass fraction. radical.

Conservation Equations Slower kinetics of the NO formation when X

The continuity equation can be written ascompared to the rate hydrocarbon oxidation

suggests that the thermal NO are formed after the X

(32) completion of the main combustion event. The

Using Einstein's notation, the continuity equation equilibrium approach calculates the formation of can expressed as the thermal NO after decoupling it from the main X,

(33) combustion process, by assuming that the

combustion reaction has attained equilibrium. The

following equation provides the equilibrium where D , Dt is substantial derivative of . For

concentration of the oxygen atom.incompressible flows, is constant. The continuity

equation reduces to(24)

One problem with the equilibrium approach for the (34)

determination of [O] radical concentration is the Using the same notations as for the continuity assumption itself. The concentration of [O] radical equation, the momentum equation can be expressed is usually more abundant than the equilibrium aslevels. The remedy to this problem is to assume the

concentration of [O] radical in partial equilibrium. (35)

As an improvement to the equilibrium approach, a

third body reaction can be included in to the The energy equation can be expressed as:

dissociation-recombination of oxygen

Vol. XXXXIII

)./(

][][

][1

][][

][1

]][[2 3

3,22,

1,

22,21,

22,1,

21, smg

OHkOk

NOk

OkNk

NOkk

NOKdt

NO

ff

r

ff

rr

f

+

-

=(23)

)/(][64.36][ 3/271232/12

2/1 mgmoleOTO T-=

0)( =¶

¶+

¶

¶u

xt i

rr

0=¶

¶+

i

i

x

u

Dt

Dr

r

0)(. =¶

¶==Ñ

i

i

x

uudivu

j

i

ij

ji

ji

jj fxx

p

x

uu

t

u

Dt

Du+

¶

¶+

¶

¶-=

¶

¶+

¶

¶=

trr ][

2/12 ][][ OkO p=

MOOMO ++Û+

27

(36) at a suitable time. A probability density function

table is generated at every fractional time step. This

table provides the flow field properties for he next Methodology

fractional time step [3].Unsteady Flamelet Approach

Pdf Approach:In the finite rate chemistry approach, the chemical

Being highly turbulent in nature, the combustion in source term is calculated by applying Arhenius

IC engines is governed by Navier Stokes equations. equation which does not take into account the

Various methods are employed to solve these eddies produced as a result of turbulence. The finite

Navier Stokes equations as the direct solution of rate chemistry model is more suitable for laminar

these equations computationally expensive. flames but it can also be applied to the situations

Reynolds averaging of these equations is one way to where there is small chemistry turbulence

solve these equations. For turbulent chemistry in interactions. The unsteady flamelet approach

IC engines, the Reynolds averaging approach achieves significant reduction in calculation time

results in two unknown terms for turbulent scalar when compared to the finite rate chemistry

flux and mean reaction rate. ANSYS FLUENT uses approach. This model solves the flamelet species

gradient diffusion to model turbulent scalar flux and energy equations at the same time it solves the

and treats turbulent convection as enhanced flow equation. The solution of the flamelet and the

diffusion. Laminar Eddy Dissipation Concept flow equations is advanced simultaneously. For

(EDC) and finite rate chemistry models are used to every fractional step, the properties of the flow are

model the mean reaction rate [3].used to calculate the properties of the flamelet

A transport equation for single-point, joint which in turn provide the input to calculate the flow Probability Density Function (PDF) can properties for that fractional. The initial flamelet alternatively be derived instead of Reynolds distribution is mixed but unburnt. Different averaging of the species and energy equations. The variables including temperature, pressure as well pressure and temperature of all the species present as scalar dissipation are volume-averaged scalar. at every time step are reflected in this PDF. For N The values of these variables for both the fuel as species the PDF has N+2 dimensions (N arises due well as the oxidizer are first calculated in a a flow to the number of species and +2 arises from the solver. The output of the flow solver serves as input temperature and pressure). Based on Pope's work to flame solver. This is repeated for every fractional [23], the following transport equation for PDF has step. The compression results in the flamelet been derived [3].temperature increase leading towards the ignition

Where is density, P and u are Favre averaged PDF expectation of X occurring provided that Y has i

occurred. The three terms on the right hand side of composition and mean fluid velocity, Ø and S are k

the eq. 37 represent unsteady rate of change of PDF, the composition space vector and rate of reaction for change of PDF due to convection arising from the species k respectively. and Ji. k are vectors

mean velocity field and the change of PDF due to representing fluctuation in fluid velocity and chemical reactions. All the terms are closed and molecular diffusion flux respectively. The two terms hence do not require any modeling. The closure of on the right hand side involves expectation and this heavily nonlinear term representing chemical conditional probability and can be summarized in reactions is a great advantage. Changes in PDF due the following analogy: < X | Y > represents the

2015

321

)().(dxdxdx

QuyuT

Dt

De s

xi

j&

&& +¶

¶+Ñ-ÑÑ= tlr

]1

[]/[)()()( , Px

J

pPu

xPSPu

xP

t i

ki

ki

k

k

i

i ¶

¶

Y¶

¶+Y¢¢

¶

¶-=

Y¶

¶+

¶

¶+

¶

¶rrrr

(36)



to turbulent scalar flux and molecular diffusion are solution becomes time expensive. Theoretically, the

represented by the terms on the right hand side of pre-tabulation of chemical results can help to avoid

the eq. 37. The two terms on right hand side are not integration via lookup tables but practically the

closed and hence require modeling. The composition scheme has many pitfalls. Any table constructed in

vector which is a function of mass fraction of this manner would have N+3 dimensions, where N

different species, temperature and pressure can be stands for the number of species and 3 is for

expressed as follows pressure, temperature and time. If each dimension

has X points, the total number of data points will be (38) XN+3. For 10 points in each direction and 10

where YN is the mass fraction of the nth species. species, the table would have 1013 data entries.

Integrating the reaction source term through Another problem with this pre-tabulation is that it

reaction fraction step results in following equation. stores data on some reactions that are at unrealistic

conditions, i.e., a data entry for OH radical at 300K.(39)

Computational Models

oA 90 sector mesh is used to take advantage of the Where S is the chemical source term. Some symmetry of the four equally spaced injector nozzle chemical reactions are fast and has a time scale of holes. ICEM-CFD, a state of the art mesh 10-10 seconds whereas other reactions may be generation package, was used to generate the mesh. considered slow and has a time scale of 10-3 With piston at the bottom dead center (BDC), the seconds. The difference in these time scales of mesh consists of 26788 cells. The mesh is moved results in numerical stifness. Direct or pre-from BDC to the crank angle where intake valve integration of chemical results are others options. closes. This is done through the dynamic mesh An earlier study [4] in the group has used pre-utility.integration approach to map the combustion

response in IC engines. This study used SENKIN, a Numerical Scheme and Selection of Models

sub-program in CHEMKIN-II to calculate the Unsteady flamlet model (UFM) has been used to detailed chemical kinetic reactions of air/fuel predict in-cylinder pressure, the rate of heat release mixtures at different temperatures, pressure and and different emissions. Two different spray compositions. These calculations were done prior to breakup models have been used in the UFM the engine simulations. The reaction results were approach; WAVE breakup model and KHRT. Three decoupled from their chemical time scales (order of different values of each breakup constant were used

-10about 10 and then integrated and saved in ) for the parametric study conducted to assess the 5physical time scale (order of about 10 ) in a database effect of the breakup constants on ignition delay,

file. The reactions results of different initial rate of pressure rise and the maximum in-cylinder conditions (temperature, pressure and composition) pressure. A bigger time step is used during are stored in different zones. The zones were compression of the in cylinder mixture. When

oindexed using their respective reaction conditions. injection starts, the time step is reduced to 0.1 CA These reaction results were retrieved from this for injection and combustion events. All reactions database file when needed during the simulation. It are switched on. The different physical aspects of took 29 days to generate the database file. the fluid are modelled as follows:

For a simulation containing 40,000 cells and 15

particles per cell, if the convergence is achieved in 81500 iterations then 10 stiff ordinary differential

equations are required to be solved. If each

integration is done in a few milli seconds, the

Vol. XXXXIII

),,......,,( 321 pTYYYY N=f

ò+=dt

Sdt0

01 ff

29

-

-

-

-

-

-

-

-

been used due to 3-D nature of the

computational domain. It provides general

shape of the spray.

Secondary breakup model: Both WAVE and

KHRT536 breakup models have been utilized

as described in the following section.

Droplet deformation: Dynamic drag model has

been used due to its ability to capture droplet

deformation540 due to aerodynamic forces.

Droplet collision and coalescence: Droplet

collision and coalescence models have been

considered. These models capture head-on

collision, side collision and multi-body collision

and coalescence. If these models are not used,

the prediction of particle breakup due to

collision is not captured.

Wall-film: This model is used to predict the

formation of thin fuel film at contact regions.

This model takes into account the particle

splashing, convective heat transfer from wall

to fuel film and the evaporation of the fuel film. Turbulence: RNG k-å has been used. It takes

into account swirling flow. Its computational NO : Extended Zeldovich mechanism has been X

cost is lower than LES model. used to model the formation of NO . Thermal X

and prompt NO have been predicted. The Discrete Phase: Langrangian approach has X

effect of turbulence on the formation of NO has been used to track individual droplets. It X

requires smaller computing resource and been considered. Temporal fluctuation of

simulation runtime. temperature and species concentration result

from the turbulence.Primary breakup: Solid cone injection type has

2015

Fig. 2: Computational Mesh used in the study

Fig. 3: General numerical scheme used in the study



ignition delay for the two lower values of the Results and discussion

breakup constant B and a longer ignition delay 1

Parametric Study when B was set at 50 can be explained on this basis. 1

Three values (10, 25 and 50) of the breakup model All three cases of UFM with different values of B 1

constant B are used. Three values (10, 30 and 50) of 1 have captured the ignition delay trend. The peak

the KHRT breakup model constant C are used. pressure occurs at the same crank angle position for 3

When unsteady flamlet model (UFM ) uses WAVE all three cases. This can explain the higher rate of

model for the secondary break, the effect of pressure rise when the ignition delay is maximum

variation in B is significant. Ignition, rate of at B =50. With shorter breakup length, the fuel is 1 1

pressure rise as well the maximum in-cylinder atomised and combustion commences earlier but

pressure are all affected by any change in this the dispersion of the fuel may not cover the whole

breakup constant. As the value of this breakup volume of high temperature air available at that

constant is increased, ignition is slightly delayed particular crank angle (reduced air utilization).

and a higher rate of pressure rise as well as higher With longer breakup length, the fuel atomisation

peak in-cylinder pressures are observed. The and hence ignition is delayed but air utilization is

minimum value of B produces the best agreement improved. Hence a larger proportion of the fuel is 1

consumed at the same time leading to higher rate of with the experimental data. Theoretically, a higher

pressure rise and hence increased heat release rate. value of B shall reduce the breakup and hence 1

When UFM uses KHRT model to simulate the increase the penetration length. On the other hand,

secondary breakup model, a very good agreement is a smaller value of B results in increased spray 1

noted between the experimental and the atomisation. The increased spray atomisation computational results.results in better fuel/air mixing. Relatively shorter

Vol. XXXXIII

Initial and Boundary Conditions

Table 1 summarizes the initial boundary conditions used in the simulations.

Table 1: Initial and boundary conditions used in the simulation

Sr No. Initial boundary conditionso1 Start crank angle -140 BTDC

o2 Stop crank angle 130 ATDCo3 Time step during compression stroke 0.5o4 Time step during injection, ignition and combustion 0.1

5 Temperature of cylinder wall 545 K

6 Temperature of cylinder head 610 K

7 Temperature of cylinder piston 650 K

8 Initial pressure 0.16 MPa

9 Fuel inlet temperature 370 K

10 Pressure discretization scheme Standardnd11 Turbulent dissipation rate discretization scheme second 2 Order Upwind

312 Density for diesel 840 kg/m

13 Saturation vapour pressure scheme Piecewise Linear

14 Droplet surface tension calculation Piecewise Polynomial

31

The effect of change in C on ignition delay, rate of value of C . Larger diameter droplets shall take 3 3

pressure rise and the peak in-cylinder pressure is longer to evaporate and hence result in slower rate

less pronounced when compared to the effect of of pressure rise. For the largest C value, the 3

change in WAVE breakup model constant B . For pressure drops more rapidly in the expansion stroke 1

the two smaller values of C , no difference was of the cycle.3

observed in terms of ignition delay, rate of pressure In-Cylinder Pressure and Rate of Energy rise and the peak in-cylinder pressure. When C was 3 Releaseset a very higher number, smaller rate of pressure

Figures 4 and 5 show computationally predicted in-rise and lower peak in-cylinder pressure were

cylinder pressure using UFM approach utilizing the obtained. According to the model, the breakup will

WAVE and KHRT breakup models respectively. An only occur if the wavelength of the wave growing on

overall better agreement is achieved with UFM the surface of the liquid droplet is smaller than the

approach when KHRT622 breakup model is used. droplet diameter.

Figures. 6 and 7 show computationally predicted A larger value of C shall reduce the breakup and 3 rate of energy release using UFM approach result in larger droplet diameter. This can explain utilizing the WAVE and KHRT breakup models the smaller rate of pressure rise with increasing respectively.

2015

Table 2: Effect of Wave breakup constant B on peak combustion pressure1

Chosen value of B Peak Combustion Pressure/ Mpa1

10 6.085

25 6.261

50 6.47

Fig. 4: Comparison of In-cylinder pressure for different values of breakup constant B using wave breakup model1



Figure 5: Comparison of In-cylinder pressure for different values of breakup constant C using KHRT breakup model3

oFrom Figures 6 and 7, it is clear that the occurs 1 CA before the corresponding peak for the

experimental rate of energy release rises first experimentally obtained rate of energy release

compared to the computational trend line which curve. All predicted results produced higher second

refrects that the model does not predict the ignition rate of energy release peak when compared to the

behavior well but the start of the main combustion experimental results. For the different values of

event is well predicted. This may be due to limited breakup constants tested within the different

knowledge of the injection mass profile, differences models used, B = 10 (WAVE model) and C = 30 1 3

between fuel surrogate and the real diesel, (KHRT model) give better prediction of in-cylinder

cavitation in the injector, pressure changes in the pressures and the rate of energy release. Hence

injector, fuel residuals and injector dribble. With these two values have been chosen to be used for the

UFM, two rate of energy release peaks are observed. FRC model.

The first predicted rate of energy release peak

Fig. 6: Comparison of rate of energy release for different values of breakup constant B using wave breakup model1

33

Prediction of Emissions used. Due to this reason this combination has been

chosen to predict three of the in cylinder emissions. Figures 8, 9 and 10 show comparison of The computational results for three emissions were experimentally and numerically obtained lower than the levels collected experimentally but emissions of specific NO , CO and CO respectively. X 2

the UFM approach has captured the trends. The Of all combinations of combustion and spray models agreement between the computational and the tried with different breakup constants, the UFM experimental results improved as the equivalence produces the best estimate of the in-cylinder ratio was increased.pressure and the rate of energy release when KHRT

spray model with a breakup constant (C ) set at 30 is 3

2015

Fig. 7: Comparison of rate of energy release for different values of breakup constant C using KHRT breakup model3

Fig. 8: Comparison of experimentally and numerically obtained specific NOX emissions



Fig. 9: Comparison of experimentally and numerically obtained specific CO emissions2

Fig. 10: Comparison of experimentally and numerically obtained specific CO emissions

The computationally predicted specific NO was experimentally obtained specific CO emissions X 2

12% lower than the experimentally obtained values range between 8 to 10 % across a range of

at an equivalence ratio of 0.5. The agreement equivalence ratios. The CO emissions were the least

between the computationally and experimentally well predicted. The agreement between the

obtained specific NO was improved and lie within computationally and experimentally obtained X

specific CO is 15%, 7% and 12% at the three 10% of each other with an equivalence ratio of 0.68.

equivalence ratios tested.The agreement between the computationally and

Conclusions: the rate of energy release.

The study investigated a set spray and combustion Computationally, the results of different

models to obtain an optimized set of these models. emissions are under-predicted for the cases

The optimized set was used to predict in cylinder tested but the trends have been well captured.

pressure, rate of heat release and various engine Nomenclatureemissions. The conclusions of the study are

Abbreviations summarized as follows,

CAD crank angle degrees When unsteady flamelet model is used in CI compression ignition combination with WAVE breakup model, the

DI direct injectionignition, the rate of pressure rise and the

References:maximum in-cylinder pressure are all affected

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Table 3: Percentage variation in the predicted emissions when compared to the experimental data across three different equivalence ratios using KHRT breakup model (C = 30) and unsteady3

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