modeling engine combustion spray

đánh giá tổng quan về hệ thống phun nhiên liệu trong động cơ đốt trong từ các loại tảo từ các công trình khoa học nghiên cứu trên thế giới. đây là tài liệu mang tính chất tham khảo để phục vụ học tập, nghiên cứu cao học, tiến sỹ

Modelling of Spray Combustion, Emission Formation and Heat Transfer in Medium Speed Diesel Engine

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Pertti Taskinen

Modelling of Spray Combustion, Emission Formation and Heat Transfer in Medium Speed Diesel Engine

Tampere University of Technology Publication 562

Tampereen teknillinen yliopisto - Tampere University of Technology

Tampere 2005

ISBN 952-15-1476-0 (printed) ISBN 952-15-1498-1 (PDF) ISSN 1459-2045

ABSTRACT

This thesis deals with the spray combustion, emissions (NOx and soot) formation and heat transfer theories of phenomena and their modelling related to medium speed diesel engines The modelling work was done with the Marintek A/S version of the open source code KIVA-II program by implementing new sub-models or by modifying old models of the phenomena into the code

The aim of the work has been to develop a simulation tool for medium speed diesel engines that can

be applied later in the optimisation process of the engine economy with the allowed pollution level

by computing different cases with the different engine parameters such as compression ratio, fuel injection timing, injection rate shaping, direction of injection, diameter of the nozzle hole etc In

developing work of the KIVA-II code main attention was focused on the following phenomena: the drop vaporisation under a high-pressure environment, the soot formation modelling by the Hiroyasu

TM models and the or the oxidation by the NSC model, the soot radiation modelling by the simplified model (pure emission) or the DOM, the convective heat transfer modelling and the spray turbulence modelling by the RNG/STD k-e turbulence models

The high pressure drop vaporisation model was developed based on the equality of the fugacity of the fuel in liquid and the vapour phase on the drop surface The mass fraction of fuel vapour in the drop surface is much larger with the high pressure model than with the original low-pressure model yielding a more realistic ignition of the fuel vapour and air mixture and the combustion

The original TM soot formation model of the code was a failure and this was rectified The Hiroyasu soot formation and the NSC soot oxidation model were added into the code and formulated into the source term form using either the computational cell average or the EDC-weighted values of the cell quantities in the soot transport equation The soot emissions after modifications were a more realistic level than in the case of the original formulation and the models Also the lack of an NSC soot oxidation model able to predict the soot oxidation rate correctly was taken into account by the extra constant in the model

The soot radiation was taken into account in the internal energy transport equation by the simplified model (optically thin radiant media), i.e pure emission from the radiant media or the RTE solved

by the DOM The radiant heat flux to piston top becomes the more realistic level with the DOM than with the simplified model compared to the experimental values of the slightly other type diesel

engine than the modelled medium speed diesel engine This shows that the absorption of soot radiation in the radiant region must also be taken into consideration Effect of the soot radiation on temperature of the gas appears only in the soot region, not in the fuel vapour reaction zone where the soot is not found Therefore the soot radiation does not reduce maximum temperatures of the gas in the fuel vapour reaction zone or in the nitrogen oxide (NOx) formation regions near the reaction zone and so influence in the NOx emissions from the engine

The original temperature wall function of the KIVA-II based on the modified Reynolds analogy under-predicts the heat flux to wall considerably The model was replaced by the model which was based on the use of a one-dimensional energy equation and the correlation of dimensionless temperature including an increasing turbulent Prandtl number near the wall The heat flux to piston top with the new model was a more realistic level than with the original model of the code compared to the experimental values of the other type diesel engine

The modified RNG k-epsilon model was developed based on the results obtained with the STD and the basic RNG k-e models According to the results mentioned above the STD model is too diffusive while the basic RNG is too less diffusive in the high rate of the strain region (spray region) and therefore the fuel vapour mixing (combustion) occurs in an un-satisfactorily way In the turbulence model developed the additional term of the epsilon equation was modified suitably and therefore the spray spreading and the combustion occur more realistically compared to either the basic RNG or the STD k-e turbulence model cases The gas turbulence intensity was reduced in the early phase of combustion and emphasized in the later phase of combustion compared to the situation with the STD model The cylinder pressure curve becomes by far the closest with the new turbulence model than either of both the models mentioned above In the work the failure of the basic RNG turbulence model of the KIVA-3V was found and rectified

PREFACE

This work has been carried out at the Institute of Energy and Process Engineering, Tampere University of Technology (TUT) The work has been funded by the PROMOTOR program (Mastering the Diesel Process (MDP)) of the National Technology Agency of Finland (Tekes) and the CFD Graduate school program of the Aerodynamic Laboratory of Helsinki University of Technology (HUT)

I wish to express my gratitude to Professor Reijo Karvinen, advisor of my dissertation for his guidance during this work I would also like to thank all the staff at the Institute of Energy and Process Engineering

Furthermore, I wish to extend my thanks to Dr Eilif Pedersen at the Marintek A/S Research Centre

of the Sintef Group, Trondheim, Norway for his unique guidance with the KIVA-II code and to Professor Martti Larmi at the Internal Combustion Engine Laboratory (ICEL) of Helsinki University of Technology for the discussions and meetings on the MDP project I would also like

to thank Mr Gösta Liljenfeldt at the Wartsila Diesel Company in Vaasa for the support during the entire co-operation time of the medium speed diesel engine process modelling and Mr James Rowland for the high quality reviewing the English of the manuscript

Finally, I must thank to my roommate Licentiate of Technology Vesa Wallen, for the interesting and inspiring discussions on the work

Tampere, May 2005

Pertti Taskinen

2.2.7 Heat transfer 49

3 AUTHOR’S IMPLEMENTED/DEVELOPED SUBMODELS AND

THEIR CONTRIBUTION TO THE MODELLING TOOL FOR

4 MODELLING RESULTS AND THEIR EXPERIMENTAL

APPENDIX A: Modelled engine specifications

APPENDIX B: Flow chart of numerical modelling tool

NOMENCLATURE

Latin

0

(f , T

M , F

fi

/

/1

r Radius of drop [ ]m

fu

32

f

,

/1

η Ratio of turbulent to mean-strain time scale [ ]−

HG Huh-Gosman

1 INTRODUCTION

1.1 General aspects

Medium speed diesel engines are used in ships and small power plants High reliability, efficiency (economy) and nowadays especially low nitrogen oxide (NOx) and particulate emissions are the desirable features of these engines (Taskinen et al., 1997, Taskinen et al., 1998, Taskinen, 2000, Taskinen, 2001, Weisser et al., 1997) Advantages of the diesel engine compared to the spark ignition (SI) engine are its high fuel economy and therefore its low carbon dioxide emissions as well as low un-burnt hydro-carbon emissions Correspondingly a major drawback of it has been the high particle (soot) matter emissions, but nowadays these harmful to health emissions have been succeeded to reduce by new fuel injection and exhaust gas after treatment techniques Nitrogen oxide emissions depend highly on the temperature of the gas in the cylinder and its residence time

at high temperature High speed diesel and typical SI engines produce almost the same level of nitrogen oxide emission, while medium or low speed diesel engines may produce much larger NOx emission due to the much longer residence (reaction) time of gas at high temperature

The improvement of the efficiency and reduction of emission formations of diesel engines can nowadays be done by a sophisticated numerical simulation tool and/or experimentally The numerical simulation of the spray combustion process of a medium speed diesel engine is quite a new field, whereas from a small engine field a lot of references/data are available The reason for this is that competition in the passenger car industry is so intensively keen to develop new engines that have both the best low emissions and economies possible The engine process modelling saves time and is an investment in the developing process to get the engine to the market A numerical simulation tool obtains solutions with the different engine construction parameters such as fuel injection timing, duration, spray direction, nozzle hole diameter, injection pressure, compression ratio, stroke/bore, etc The solutions data can be utilised in the optimisation process in order to find such a combustion system in which high efficiency is combined with the low emissions Purely by experiment this is not possible However, experiments are still needed to verify the simulation results in some cases in order to ensure that the simulation tool predicts correctly the results in other cases

1.2 Diesel process modelling

A diesel process research and development (spray combustion, emissions formation and heat transfer) is at least partially possible to do now by a numerical simulation tool, because the knowledge of different physical/chemical phenomena in the cylinder has currently been increased greatly (Pedersen et al., 1995, Reitz et al, 1995, Taskinen, 2002) Especially nowadays the computing resources have been largely increased thus enabling the simulation of more complicated cases In a complete diesel process modelling the following phenomena have to be modelled: fuel spray atomisation, drops vaporisation, vapour ignition, vapour combustion by chemical kinetics/turbulent mixing, NOx formation, soot formation and its oxidation, heat transfer by convection and radiation This is a very complex phenomena set and many of them are coupled together, e.g spray dynamics, drops vaporisation and combustion, soot formation, soot oxidation and radiation rendering the solving process In Fig 1.1 is shown a general view of the KIVA-II simulation code and its main sub-models related to the diesel process modelling (Pedersen et al., 1995)

Fig 1.1 KIVA-II sub-models and solver structure

The basic idea in the diesel process modelling which is also valid for other this kinds of processes (SI engine, gas turbine, etc) is to solve numerically the governing equations (partial differential equations) of the field quantities such as temperature or internal energy, species concentration, gas velocities, gas pressure, gas turbulence kinetic energy and its dissipation rate in every computational cells (control volumes) of the physical space considered The governing equations are basic physical laws such as conservation of mass, balance of linear momentum and conservation

of energy The heart of the modelling process is often related to the source terms of the governing equations The source terms related to the sub-models of different physical/chemical phenomena of the cylinder gas The sub-models should naturally describe phenomena as near correct as possible

in order to obtain reasonable results and their behaviour correctly, when input data are varied One special feature in diesel process modelling is that the control volume moves, which requires special treatment for the computational mesh

The special features of large medium speed diesel engines compared to the high speed diesel engines are that they are operated on a heavy fuel oil and the flow in the cylinder after an intake stroke is nearly quiescent (non-swirl) The flow in cylinder is therefore caused merely by the spray This causes high demands in the fuel spray model in order to able to correctly predict fuel drops and the vapour spreading and further the mixing with air in the combustion chamber The dynamic behaviour of the fuel drops is also influenced by the drag force, which depends directly on the drop drag coefficient The drop drag coefficient during the vaporisation process should be able to describe as correct as possible The standard model of Putnam used in KIVA-II (Amsden et al., 1989) tends to over-estimate the drag and in the model does not take into account the reduction of drag in drop boundary layer during the drop vaporisation According to Cliffe and Lever (1986) this effect should be taken into consideration

The ideal gas law is widely used model to describe the equation of state in engine CFD codes It is a quite well valid, when the pressure of the gas is moderate and temperature of gas is high The conditions in medium speed diesel engine cylinder are some extended different during the combustion process than in the high speed (small) light fuel oil used diesel engine cylinder, i.e high pressure of the gas all the time and a great amount of fuel vapour before early phase of the combustion (low temperature), that the real gas effects have to take into consideration in the

equation of state According to the literature (Leborgne et al, 1998, Reid et al., 1987) and author’s

experience the formulation of Redlich-Kwong (RK) or Peng-Robinson equation of state is the most

suitable and accurate enough to use and implement into the engine CFD code

Due to low a vapour pressure of heavy fuel oil a high pressure drop vaporisation model should be used instead of the widely used low pressure model in order to avoid too long ignition delay and a weak early phase of combustion (Taskinen, 2000) In a high pressure formulation of drops vaporisation the mass fraction of fuel vapour in the surface of drop is calculated based on the equality of vapour and liquid phase fugacity in the drop and gas interface (Reid et al, 1987) Especially with the heavy fuel oil the low mass fraction of fuel vapour causes too long an ignition delay

Due to a large fraction of such hydrocarbon components of the heavy fuel oil, which easily form soot, the flame is therefore luminous and the effect of soot radiation on flame temperature in the soot region and heat transfer to walls will be a considerable, as Abraham et al., (1999) and Kaplan

et al., (1999) have discovered Therefore the soot radiation should be taken into consideration in order to obtain more realistic results with the simulation code For optically thin flames the absorption of gas can be ignored and this leads to the pure emission model of the soot radiation It tends to over-predict heat fluxes to walls, if the radiation medium includes a lot of soot as in medium speed diesel engines with the heavy fuel oil In the diesel process modelling the emission model of radiation is some extended used due to its simplicity and the computationally cheap approach In strong radiation flame cases the absorption of radiation medium has to be taken into account and therefore a directional dependence has to be taken into account in the radiation transfer equation (RTE) The RTE has then to solve numerically using, e.g DOM or DTM method (Modest, 1993) A few modelling of diesel process cases have published where the DOM method has been used in the solution of the RTE Author has implemented and used the DOM and the emission methods in the soot radiation modelling

The convective heat transfer from the gas to the walls is still a dominant component of the total heat transfer The radiation dominates in the later phase of combustion, when the amount of soot is high and the flow in cylinder is weak due to end of injection Normally in the engine CFD codes standard wall functions (velocity and temperature profiles) are used to calculate a shear stress and convective heat transfer coefficient They are usually based on the Reynolds analogy between the velocity and thermal boundary layer A great under prediction of wall heat fluxes has been found using the traditional wall functions (Han et al., 1997) Han et al., (1997) and Kays et al (2004) have

derived new equations for the heat fluxes to walls based on the one-dimensional energy equation in the boundary layer and correlations for the turbulent Prandtl number and dimensionless temperature

of the gas The author has used these equations in slightly modified form and also obtained better predictions of the heat fluxes than with the standard wall functions used in KIVA-II

The basic engine simulation codes like KIVA-II and Star-CD have typically a two-equation model for the gas turbulence, merely the standard k-epsilon (later e) and/or the basic form RNG k-e models It is well known that the standard k-e model over-predicts the turbulence diffusivity of the gas and therefore causes the over-spreading of spray (Rodi, 1996, Han et al., 1997) The basic form RNG k-e model under-predicts the turbulence diffusivity in the high strain rate region, while in the low strain rate region, it over-predicts and therefore causes un-realistic fuel vapour transfers This can be avoided by modifying suitably the additional term of the k-e equation of the basic RNG model and the model constants (Taskinen, 2003, 2004) The spray spreading and vapour combustion proceeds then on a more realistic way yielding almost correctly the cylinder pressure and rate of heat release than using the basic form standard or RNG k-e model

1.3 Goal and outline of this thesis

The goal of this work was to develop a simulation tool for a medium speed diesel process analysis based on the MARINTEK Company version of KIVA-II code In the developing process of the code attention has been focused to the vaporisation of drops in high-pressure environment, gas turbulence, soot emissions and convective/radiation heat transfer Typically in the engine simulation codes the drops vaporisation model based a low-pressure formulation The soot radiation modelling in diesel process analysis have been done a quite little and especially in medium speed

diesel analysis where this effect is more important practically nothing In order to get more realistic

total heat fluxes into walls the effect of soot radiation has to be included into the modelling The convection heat transfer model of KIVA-II code was based on the standard temperature law of the wall equations and these were improved Turbulence models of KIVA-II yield unsatisfactory results and the modified RNG k-e model therefore was developed based on the behaviour of the basic

RNG and STD k-e models

The Introduction discussed the general things and background related to the medium speed diesel process modelling The main shortages of current engine CFD codes have been presented and how

they can be avoided

In Chapter 2, the basic theory of diesel process modelling and the most important sub-models related to the gas turbulence, fuel spray, drops vaporisation, combustion, emissions formation, convection and radiation heat transfer are presented

In Chapter 3, the author’s implemented/developed sub-models and their contribution to the modelling tool for diesel process are presented

In Chapter 4, the essential numerical simulation results with the different sub-models and their formulations are presented and how they verified Discussion of the simulation results and their comparison with the available experimental values

In Chapter 5, conclusions of the work and the estimation of their capability to predict medium speed diesel process realistically were done Also the improvements of the code to get better results are presented

2 THEORY OF DIESEL PROCESS MODELLING

2.1 Governing field equations

A turbulent reacting flow can be described by the continuity, Navier-Stokes or momentum, energy conservation, species concentration and equation of state equations These governing equations describe the velocity, pressure, temperature and species concentration fields They can be written in three-dimensional case for a Newtonian fluid using Reynolds and Favre averages in the form:

Continuity

Sray m i

i j

i i

j l j

i

j i j

j i

S g u

u x

U x

U x

x

p x

U U t

U

++

v i i

i i

i c u T S S S

x

I k x x

U p x

I U t

Y l i i

l Y i

l i

x

Y D x x

Y U t

By using the well known the Boussinesq eddy-viscosity concept the Reynolds stresses and the turbulence scalar fluxes can be expressed as follows:

−

k k i

j j

i t ij j

i

x

U x

U x

U k

2

(6)

i t

t i

v

x

I Pr T

u

c

∂

∂µ

i t

t l

i

x

Y Sc Y

u

∂

∂µ

−

=

Spray m

S ~ S ~ I Htr S ~ Y l

(8)

described in chapters 2.2.5.2, 2.2.5.3 and 2.2.7

The boundary conditions are needed for the velocity and temperature in this context For velocities the standard law of the wall equations of the KIVA-II are used (Amsden et al., 1989), where the critical Reynolds number when the velocity profile changes from the laminar to turbulent type is

122, corresponding the dimensionless distance from the wall 11.0 The temperature boundary conditions (temperature wall functions) are presented in Section 2.2.71 in the context of the heat transfer Turbulence quantities boundary conditions are presented in the next Section 2.2.1

2.2 Main sub-models in diesel process modelling

During the diesel process cycle several the chemical/physical phenomena occur in a cylinder, such

as fuel spray atomisation in a nozzle, drops vaporisation, vapour ignition, vapour combustion controlled by chemical kinetics/turbulent mixing, nitrogen oxide and soot emissions formation and soot oxidation, heat transfer to walls by convection and radiation Mathematically formulated sub-models are needed to describe the above phenomena The following chapters will present briefly the most important sub-models related to the diesel process modelling

2.2.1 Turbulence modelling

The modelling of the turbulent viscosity (sometimes called the eddy-viscosity) is very essential and challenging task The gas turbulence plays an important role in the fuel vapour mixing and combustion and further the emission formations From literature can be found many types of turbulence models, but it seems that the k-epsilon (later e) model and its variant RNG (Re-Normalization-Group) k-e model are the most popular especially in the combustion modelling cases (Han et al., 1995, Abraham et al., 1997a) They both belong to the so-called 2-equation models framework They are robust and computationally much cheaper models compared to more complicated RSM (Reynolds Stress Models) or the LES (Large Eddy Simulation) models They yield quite reasonable turbulence quantity results, if the situations are avoided, where they are not able to predict correct results The situations where their results fail can be mentioned e.g the flow separation/re-attachment, streamline curvature and swirl (Younis, 1997) The k-e models are not able to predict correctly the separation and/or reattachment of the flow The standard k-e model can only be used for a high Reynolds number flow Near a wall when the turbulence Reynolds number decreases, it can be modified by additional source terms to the so-called low Reynolds number k-e model The source terms are activated near a wall and therefore the flow is possible to compute to the wall without to use the law of the wall functions Especially the heat transfer is then computed more reliably than in the case of using the standard wall functions

All these standard, RNG and low turbulence Reynolds number k-e models are quite similar types and can be then presented in the same form The turbulence kinetic energy equations are identical, but the epsilon equations are different In the epsilon equation of the RNG-model there is an additional term, which changes dynamically with the rate of strain of the turbulence, providing more accurate predictions for flows with rapid distortion and an-isotropic large-scale eddies (Han et al., 1995) Models can be expressed with the same equations as described in below

Turbulent kinetic energy is defined through the turbulence velocities (fluctuations from the mean flow) as follows:

' i

'

i u u

k

2

1

The transport equation of the kinetic energy

spray j

i i

j j

i t

i

i i

l k

t i

i

W x

U x

U x

U

x

U k x

k x

x

k U t

=+

ερ

∂

∂µσ

−+

=+

spray s j

i i

j j

i t i

i

i

i i

l t i

i

W C C

x

U x

U x

U C

C k x

U

x

U k C C C

C x

x x

U t

i

&

ερ

∂

∂εµσ

2 1

1 3

23

2

~

(11) The turbulent viscosity is calculated

ερρν

η

(Yakhot et al., 1992; Han et al., 1995; Abraham et al., 1997a; Taskinen, 2003):

3 2

0 1

1

ηβη

ηη

η η

∂

∂

=

i j j

i ij

x

U x

U S

~

~

21

η

(14)

The term C changes dynamically with the mean-strain rate, η In regions of largeη , the sign of was changed and the turbulent viscosity was decreased accordingly Hence, they concluded that this feature of the RNG k-epsilon model was responsible for the improvement of their modelling of separated flows (Choudhury et al., 1993 and Han et al., 1995) According to Taskinen (2003, 2004)

η

C

the term control purely the largeness of the additional term and the term C prevents an unphysical diffusion with the low

η

1

η values, e.g with the basic RNG model Cη ≈0.9 whenη≈1.2

The constants used in different cases of the additional term of RNG k-epsilon turbulence model are given in Table 2.1 In the Table 2.1 symbol A=STD, B=basic RNG and C= one of the modified RNG k-epsilon model cases More the modified RNG model cases are discussed in the context of the modelling results in Chapter 4

Table 2.1 Turbulence models constants

5 0 5 0 1

σ

Where von Karman constant

The boundary condition for k is:

2.2.2 Fuel spray modelling

2.2.2.1 General aspects

Fuel spray plays an important role in a diesel combustion process Especially in medium speed diesel engines, where the initial flow field in a cylinder when the fuel injection starts is weak due to low running speed and large cylinder dimensions The gas motion and its turbulence in a cylinder are mainly caused by fuel spray Therefore it influences the vapour combustion, drops hitting the piston top, nitrogen oxide and soot formation etc greatly

Fuel spray models describe mechanisms as to how a fuel jet and/or a drop break-up take place at the nozzle exit or later in the combustion chamber A part of the spray characteristics are obtained as a result of break-up modelling, such as a drop size distribution of the product drops and the spray angle The very important spray quantity, spray tip penetration is calculated later, when the drops size, gas velocities (drag) and direction are known

In literature (Reitz et al., 1982; Corcione, Pelloni and Luppino et al., 1999; Bianchi et al., 1999) have presented several theories for the controlling of the break-up phenomena such as an aerodynamic, liquid turbulence or cavitation-induced mechanisms In reality, some of them can also appear simultaneously such as the cavitation and turbulence or aerodynamic mechanism In spite of the large number of studies the liquid jet break-up and atomisation are still not well understood The theoretical understanding of the controlling process for the break-up of low-speed jets has been developed well, but for the high-speed atomisation jets the theories describing the jet break-up and drops formation have been inadequate (Ramos, 1989) Several more or less complicated fuel jet break-up/atomisation models have been introduced Some of them able to predict quite well the fuel spray characteristics in certain situations When a jet velocity, nozzle diameter, liquid viscosity etc change a little the correctness of model results deteriorates considerably This indicates that the break-up/atomisation model does not pose a universal character The break-up process is very sensitive phenomena and it depends on many factors such as nozzle diameter, fuel viscosity, fuel flow velocity in the nozzle (Weber number), ambient gas density, etc In certain cases where using very high injection pressures and therefore high fuel flow velocities the nozzle flow break-up is very fast and the break-up can be assumed to have already happened Under these conditions the droplet size distribution method in the nozzle exit can be applied

2.2.2.2 Fuel jet break-up/atomisation regimes

When considering a liquid fuel jet so it can be identified as two different lengths of the liquid, namely the intact core length and the break-up length as shown in Fig 2.1 Both lengths mentioned above depend on the jet velocity

regimes are well understood In the Rayleigh regime the break-up is due to the unstable growth of surface waves caused by surface tension and results in drops larger than the jet diameter (Ducroq,

1998) When the jet velocity increases from the value of Rayleigh regime, the first wind-induced

break-up mode becomes the main control mechanism of the break-up In this case the force due to the relative motion of the jet and the surrounding gas augment the surface tension force, and lead to drop sizes of the order of the jet diameter The break-up and intact core lengths are same in the Rayleigh and the first wind-induced break-up regimes Typically in diesel engines the jet velocity is much greater than the velocities appear in Rayleigh and the first wind-induced break-up modes Normally the second wind-induced or using very high injection pressure the pure atomisation regime appears in a real diesel spray Behaviour of the break-up length is still some extended controversy in the in second wind-induced regime as shown by dashed line in Fig 2.2 (Ramos, 1989) The second wind-induced break-up mechanism is mainly due to aerodynamic forces that generate instabilities into the shear layer between the jet flow and ambient gas as shown in Fig 2.3

Nozzle

Fig 2.3 Instability grows in liquid/gas interface as it moves downstream

These Kelvin-Helmholz (KH) instabilities tend to grow going into the downstream forming vortexes (Ishikawa et al., 1996) When the instabilities in the shear layer of jet flow grow into the critical value the jet flow break-up into smaller drops whose sizes are much smaller than the jet diameter In the second wind-induced break-up mode the jet surface break-ups before the jet axis and therefore the break-up length is shorter than the intact core length both the wind induced break-up mechanisms belong in the laminar regime, where the liquid properties and the ambient gas conditions are factors determining the aerodynamic-induced atomisation (Bianchi et al, 1999)

In the cases where using high jet velocities and low viscosity of fuels the jet flow changes from the laminar to turbulent mode Thus the break-up is induced by jet internal turbulence The break-up

begins in the nozzle passage from small disturbances of flow caused by turbulence and they grow bigger going in downstream according to KH theory (Ishikawa et al 1996) The break-up could take place before the nozzle exit unlike in the aerodynamic model, but normally the break-up length

is greater than zero (Ramos, 1989)

When using very high injection velocities (very high injection pressure) the jet break-ups immediately at the nozzle exit This atomisation regime (Region 5 in Fig 2.3) is defined as the regime where the break-up length is zero (Ramos, 1989, Tanner et al (1998)) The break-up process at nozzle exit is not considered anymore, only a secondary break-up of drops is possible to consider as Tanner et al (1998) has done The SMR of drops formed has to determine in some way, e.g by experimentally

The break-up process is the so called cascade process where the drop break-up can take place many times during the injection period until they reach a stable form (Tanner et al., 1998) Normally only the primary and secondary break-up modes are considered Actually some spray models (Wave, TAB) do not distinguish the primary and secondary phase The primary break-up take place in the region close to the nozzle exit at high Weber number (>1000) while the secondary break-up take place later on the combustion chamber at lower Weber number range (<1000) The main primary break-up mechanism(s) can be in the laminar, turbulent, cavitation or in some unknown regimes (Reitz et al., 1982; Bianchi et al., 1999) The secondary break-up is typically the aerodynamically induced and therefore belongs into the laminar regime (Bianchi et al., 1999) Cavitation is a mechanism, which augments the break-up process, but according to literature (Su, 1980; Reitz et al., 1982) it cannot be the sole agency of break-up

2.2.2.3 Short review of the fuel spray drop break-up models

There exist several break-up models that have been used, such as HUH&GOSMAN (HG), TAB or WAVE Despite the fact that several models have been developed to simulate the diesel fuel spray drop break-up, the complexity of this process still does not allow one to provide accurate predictions in the case of high injection pressure (Bianchi et al., 1999) Due to this reason the hybrid models have been developed in order to able to predict more correctly all break-up processes, the primary and secondary break-up events In the next present sections will be discussed

briefly the most general and widely used the spray models

HG MODEL

Huh and Gosman (1991) have been presented the HG model and it is a turbulence-induced spray break-up model The basic idea is that the turbulence fluctuations in the jet are mainly responsible for the initial perturbations on the jet surface These surface waves then grow according to KH instabilities until they detach as atomised droplets (Corcione, Pelloni and Bertoni et al., 1999; Bianchi et al 1999) The time scale of atomisation is assumed to be a linear function of the turbulent and the KH surface wave time scales as follows:

W T

Substituting from Eq (19) into Eq (18) C = ⋅

The constant C is a correction factor that accounts for the liquid viscosity (Bianchi et al., 1999) 4

The time scale of waves derived from the KH instability theory on an infinite plane for an in-viscid liquid is:

( ) ( )

5 0 3

2 2

⋅

=

W g d

d W

rel d

g d W

L L

V t

σρ

ρ

ρρ

The average turbulent kinetic energy and its dissipation rate in the injector can be obtained by computing using appropriate turbulence model, by experimentally or by using a simple force balance equation based on the pressure drop along the nozzle downstream length (Bianchi et al., 1999)

CFD-The turbulent length and time scales are expressed with the equations as:

AVE

/ AVE T

k C

L

ε

µ

2 3

=

AVE

AVE T

k C t

The spray angle is calculated as:

rel

A A

TAB (Taylor Analogy Break-up) MODEL

In the TAB model (Taylor, 1963) droplet oscillation and distortion are modelled by using a simple forced harmonic oscillator, based on the analogy suggested by Taylor between an oscillating and distorting droplet and a spring-mass system The aerodynamic force is analogous to the external force and the surface tension is analogous to the spring restoring force while the damping force is related to the liquid viscosity force The governing equation of such a system is the following (O’ Rourke et al 1987; Assanis et al 1993; Taskinen et al., 1996; Taskinen, 1998; Bianchi et al., 1999):

(25)

x d x k F x

m⋅ &&= − ⋅ − ⋅&

According to the forced harmonic oscillator analogy it can be written:

r

U C

m

F

l g

k

l

l k

d

l

l d

x y

t t

We C C

C y y

t C

C

C y e

We C C

C t

y

d

b k F

b k F

t t b

k

ωω

ω

sin21

µ

2 3

d d

d k

t r

Where

The break-up take place wheny>1

The size of the product drops after break-up is randomly selected from a chi-squared distribution function around the SMR SMR is calculated through the energy conservation before and after break-up as follows (Taskinen, 1998):

2 3 2

46

C

r SMR

−

⋅

⋅

⋅++

C

ρ

ρθ

22

The original TAB model constants have obtained based on the shock wave experiments and by

Some researchers have been modified the model constants in order to avoid shortages mentioned above (Assanis et al., 1993, Taskinen et al., 1996, Taskinen, 1998; Bianchi et al., 1999) After modifying the spray tip penetration and the SMR of the drop size become more realistic, but the

spray angle still remains too narrow compared to the experimental values

WAVE MODEL

In the WAVE model the droplet break-up is due to aerodynamic interaction between the liquid and gas leading to unstable KH wave growth on the surface of a cylindrical jet “blob” of liquid (Castleman, 1932) The flow is assumed to be incompressible and a cylindrical coordinate system is chosen which moves with the jet (Reitz et al., 1982) The linearised Navier-Stokes equations for the surrounding gas and liquid fuel velocities and pressure perturbations can be written and solved by introducing a velocity potential and stream functions as described in the (Reitz et al., 1982 and Levich, 1962) Solution of the analysis leads to a dispersion equation The dispersion equation relates wave growth rate to its wavelength and its solution is very complicated Only in the limiting cases the solutions can be found (Reitz et al., 1982) The maximum growth rate and the corresponding wavelength are related to the liquid and gas physical properties via the equations (Beatrice et al., 1995):

( 1.67)0 6

7 0 5

0

87.01

4.0145

.0102

9

gas

We

Ta Oh

⋅+

⋅+

0 3

4.111

38.034.0

Ta Oh

We

liq

⋅++

⋅+

liq liq

⋅Λ

⋅

=

a B

a V

a min

a B

B

r

33 0 2

33 0 2

0 0

,4/3

,2

/3

,

π

Where, the characteristics numbers above equations are defined as: Ohnesorge number,