Edition 07/2009

AVL List Gmbh 2009. All right reserved

Theory

AVL BOOST VERSION 2009

Theory BOOST v2009

AVL List Gmbh 2009. All right reserved

AVL LIST GmbH Hans-List-Platz 1, A-8020 Graz, Austria http://www.avl.com AST Local Support Contact: www.avl.com/ast_support Revision Date Description Document No. A 17-Jul-2009 BOOST v2009 Theory 01.0114.2009 Copyright 2009, AVL

All rights reserved. No part of this publication may be reproduced, transmitted, transcribed, stored in a retrieval system, or translated into any language, or computer language in any form or by any means, electronic, mechanical, magnetic, optical, chemical, manual or otherwise, without prior written consent of AVL.

This document describes how to run the BOOST software. It does not attempt to discuss all the concepts of 1D gas dynamics required to obtain successful solutions. It is the users responsibility to determine if he/she has sufficient knowledge and understanding of gas dynamics to apply this software appropriately.

This software and document are distributed solely on an "as is" basis. The entire risk as to their quality and performance is with the user. Should either the software or this document prove defective, the user assumes the entire cost of all necessary servicing, repair or correction. AVL and its distributors will not be liable for direct, indirect, incidental or consequential damages resulting from any defect in the software or this document, even if they have been advised of the possibility of such damage.

All mentioned trademarks and registered trademarks are owned by the corresponding owners.

Theory BOOST v2009

AST.01.0114.2009 - 17-Jul-2009 i

Table of Contents

1. Introduction _____________________________________________________1-1 1.1. Scope _______________________________________________________________________1-1 1.2. User Qualifications ___________________________________________________________1-1 1.3. Symbols _____________________________________________________________________1-1 1.4. Documentation_______________________________________________________________1-2

2. Theoretical Basis ________________________________________________2-1 2.1. Species Transport and Gas Properties __________________________________________2-1

2.1.1. Classic Species Transport__________________________________________________2-1 2.1.2. General Species Transport_________________________________________________2-2 2.1.3. Definition of the fuel species _______________________________________________2-4

2.2. Cylinder_____________________________________________________________________2-5 2.2.1. Basic Conservation Equations______________________________________________2-5 2.2.2. Combustion Models ______________________________________________________2-17 2.2.3. Emission Models_________________________________________________________2-34 2.2.4. Knock Model ____________________________________________________________2-38 2.2.5. Dynamic In-Cylinder Swirl _______________________________________________2-39 2.2.6. Dynamic In-Cylinder Tumble _____________________________________________2-40 2.2.7. Wall Temperature _______________________________________________________2-40 2.2.8. Divided Combustion Chamber_____________________________________________2-41

2.3. Plenum and Variable Plenum_________________________________________________2-43 2.4. Pipe _______________________________________________________________________2-45

2.4.1. Conservation Equations __________________________________________________2-45 2.4.2. Variable Wall Temperature _______________________________________________2-51 2.4.3. Forward / Backward Running Waves_______________________________________2-54 2.4.4. Nomenclature (Pipe) _____________________________________________________2-55

2.5. 3D Cell Elements____________________________________________________________2-57 2.5.1. General: Volume Type ___________________________________________________2-57

2.6. Perforated Pipe _____________________________________________________________2-58 2.6.1. Perforated Pipe contained in Pipe _________________________________________2-58 2.6.2. Perforated Pipe contained in Plenum ______________________________________2-59

2.7. System or Internal Boundary (Pipe Attachment)________________________________2-60 2.8. Restriction _________________________________________________________________2-61

2.8.1. Flow Restriction and Rotary Valve_________________________________________2-61 2.8.2. Throttle ________________________________________________________________2-62 2.8.3. Injector / Carburetor _____________________________________________________2-62 2.8.4. Check Valve_____________________________________________________________2-66 2.8.5. Waste Gate _____________________________________________________________2-67

2.9. Junction____________________________________________________________________2-67 2.10. Charging __________________________________________________________________2-68

2.10.1. Turbine _______________________________________________________________2-68 2.10.2. Compressor ____________________________________________________________2-69

BOOST v2009 Theory

ii AST.01.0114.2009 - 17-Jul-2009

2.10.3. Turbocharger __________________________________________________________2-70 2.10.4. Mechanically Driven Supercharger _______________________________________2-71 2.10.5. Pressure Wave Supercharger (PWSC)_____________________________________2-72 2.10.6. Catalyst _______________________________________________________________2-72 2.10.7. Particulate Filter _______________________________________________________2-73

2.11. Engine ____________________________________________________________________2-73 2.11.1. Engine Control Unit ____________________________________________________2-73 2.11.2. Engine Friction ________________________________________________________2-74 2.11.3. Mechanical Network ____________________________________________________2-78 2.11.4. Electrical Device________________________________________________________2-79

2.12. Acoustic___________________________________________________________________2-80 2.12.1. End Corrections ________________________________________________________2-80 2.12.2. Microphone ____________________________________________________________2-82

2.13. BURN Utility ______________________________________________________________2-84 2.14. Abbreviations______________________________________________________________2-85 2.15. Literature _________________________________________________________________2-85

Theory BOOST v2009

AST.01.0114.2009 - 17-Jul-2009 iii

List of Figures Figure 2-1: Considered Mass Fractions................................................................................................................2-2 Figure 2-2: Energy Balance of Cylinder ...............................................................................................................2-5 Figure 2-3: Inner Valve Seat Diameter ................................................................................................................2-8 Figure 2-4: User-Defined Scavenging Model......................................................................................................2-11 Figure 2-5: Standard Crank Train......................................................................................................................2-11 Figure 2-6: Approximation of a Measured Heat Release...................................................................................2-18 Figure 2-7: Influence of Shape Parameter 'm'....................................................................................................2-19 Figure 2-8: Superposition of Two Vibe Functions .............................................................................................2-21 Figure 2-9: Flame Arrival at Cylinder Wall; Beginning of Wall-Combustion Mode ........................................2-28 Figure 2-10: Pipe Bend Parameters ...................................................................................................................2-47 Figure 2-11: Pipe Bend Loss Coefficient ............................................................................................................2-48 Figure 2-12: Finite Volume Concept...................................................................................................................2-50 Figure 2-13: Linear Reconstruction of the Flow Field ......................................................................................2-50 Figure 2-14: Pressure Waves from Discontinuities at Cell Borders .................................................................2-51 Figure 2-15: Main transport effects in a pipe consisting of different wall layers ............................................2-52 Figure 2-16: Forward / Backward Running Waves............................................................................................2-54 Figure 2-17: Perforated Pipes contained in Pipe ...............................................................................................2-58 Figure 2-18: Two perforated Pipes contained in Plenum..................................................................................2-59 Figure 2-19: The Pressure Function ...............................................................................................................2-61 Figure 2-20: Full Check Valve Model .................................................................................................................2-66 Figure 2-21: Waste Gate......................................................................................................................................2-67 Figure 2-22: Flow Patterns in a Y-Junction.......................................................................................................2-68 Figure 2-23: Flow Chart of the ECU ..................................................................................................................2-74

Theory BOOST v2009

17-Jul-2009 1-1

1. INTRODUCTION BOOST simulates a wide variety of engines, 4-stroke or 2-stroke, spark or auto-ignited. Applications range from small capacity engines for motorcycles or industrial purposes up to large engines for marine propulsion. BOOST can also be used to simulate the characteristics of pneumatic systems.

1.1. Scope This document describes the basic concepts and methods for using the BOOST program to perform engine cycle simulation.

1.2. User Qualifications Users of this manual:

Must be qualified in basic UNIX and/or Microsoft Windows. Must be qualified in basic engine cycle simulation.

1.3. Symbols The following symbols are used throughout this manual. Safety warnings must be strictly observed during operation and service of the system or its components.

!

Caution: Cautions describe conditions, practices or procedures which could result in damage to, or destruction of data if not strictly observed or remedied.

)

Note: Notes provide important supplementary information.

Convention Meaning

Italics For emphasis, to introduce a new term or for manual titles.

monospace To indicate a command, a program or a file name, messages, input / output on a screen, file contents or object names.

SCREEN-KEYS A SCREEN font is used for the names of windows and keyboard keys, e.g. to indicate that you should type a command and press the ENTER key.

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MenuOpt A MenuOpt font is used for the names of menu options, submenus and screen buttons.

1.4. Documentation BOOST documentation is available in PDF format and consists of the following:

Release Notes

Users Guide

Theory

Primer

Examples

Aftertreatment

Aftertreatment Primer

Linear Acoustics

1D-3D Coupling

Interfaces

Validation

GUI Users Guide

Python Scripting

DoE and Optimization

Installation Guide

Licensing Users Guide

Thermal Network Generator (TNG) Users Guide

Thermal Network Generator (TNG) Primer

Theory BOOST v2009

17-Jul-2009 2-1

2. THEORETICAL BASIS Theoretical background including the basic equations for all available elements is summarized in this chapter to give a better understanding of the AVL BOOST program. This chapter does not intend to be a thermodynamics textbook, nor does it claim to cover all aspects of engine cycle simulation.

2.1. Species Transport and Gas Properties The gas properties like the gas constant or the heat capacities of a gas depend on temperature, pressure and gas composition. BOOST calculates the gas properties in each cell at each time step with the instantaneous composition. There are two different approaches for the description of the gas composition (species transport) and the calculation of the gas properties available.

2.1.1. Classic Species Transport Using the Classic Species Transport option conservation equations for combustion products (together with the air fuel ratio characteristic for them) and fuel vapor are solved.

The mass fraction of air is calculated from

CPFVair www = 1 (2.1.1)

airw mass fraction of air

FVw mass fraction of fuel vapor

CPw mass fraction of combustion products

The air fuel ratio characteristic for the combustion products is calculated from

FB

FBCPCP w

wwAF = (2.1.2)

CPAF air fuel ratio of combustion products

FBw mass fraction of burned fuel

Figure 2-1 shows the relations of the mass fractions to each other.

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Figure 2-1: Considered Mass Fractions

For the calculation of the gas properties of exhaust gases the air fuel ratio is used as a measure for the gas composition. Air fuel ratio in this context means the air fuel ratio at which the combustion took place from which the exhaust gases under consideration originate. The composition of the combustion gases is obtained from the chemical equilibrium considering dissociation at the high temperatures in the cylinder.

2.1.2. General Species Transport In case of General Species Transport the composition of the gas can be described based on an arbitrary number of species that is defined directly by the user.

The minimum number of species is 7: Fuel, O2, N2, CO2, H2O, CO, H2. For each species a conservation equation (mass fraction) is solved in each of the elements of the model.

2.1.2.1. Single Species Properties The single species standard state (ideal gas assumption) thermodynamic properties are calculated using polynomial fits to the specific heats at constant pressure (NASA polynomials):

=

=M

1m

)1m(mk

p TaR

ck (1)

The standard state enthalpy is given by

dTcHT

0 pk k= (2) so that

T

amTa

RTH k,1MM

1m

)1m(mkk +

=

+= (3)

The standard state entropy is given by

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17-Jul-2009 2-3

dTT

cS

T

0

pk

k= (4) so that

k,2mM

2m

)1m(mk

k1k a

1mTaTlna

RS

+=

++= (5)

2.1.2.2. Mixture Properties The thermochemical properties of the gas mixture are calculated by mass-weighting the single species properties.

2.1.2.3. Definition of Properties Seven coefficients are needed for each of two temperature ranges in order to evaluate the above polynomials in the following form:

4k53

k42

k3k2k1p TaTaTaTaaR

ck ++++= (6)

T

aT5

aT4

aT3

aT2

aaRTH

k64k53k42k3k2k1

k +++++= (7)

k74k53k42k3

k2k1 aT4aT

3aT

2aTaTlna

RS

k +++++= (8)

All other thermodynamic quantities can be derived from cp, H and S.

For convenience BOOST offers the following species in an internal database:

O HCl

O2 HCNO

OH GASOLINE

CO HYDROGEN

CO2 METHANE

N METHANOL

N2 ETHANOL

NO DIESEL

NO2 BUTANE

NO3 PENTANE

N2O PROPANE

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NH3 CH4

H C2H2

H2 C2H4

H2O C2H6

SO C3H4

SO2 C3H6

SO3 C3H8

For all cases where the above list is not sufficient (i.e. for HCCI auto-ignition) the User Database enables the user to specify properties for and arbitrary number of additional species (or to overrule the properties for the species in the internal database.

2.1.3. Definition of the fuel species For classic species transport calculations only single component fuels are available. However, by manipulating the stoichiometric A/F ratio and lower heating value one can control the main parameters related to the fuel. Additional fuel species can be added upon request.

For general species transport calculations the treatment for the fuel was generalized. This means that the fuel can consist of an arbitrary number of components. In principal all species that are defined in the species list can be a component of the fuel. For each fuel component the user specifies a ratio that defines the mass or volume of this component relative to the total fuel mass or volume.

The definition of the fuel composition affects the following elements in the BOOST model:

Injector: the injected mass is distributed to all species defined as fuel components using the specified ratio (unless modified locally in the injector).

Cylinder (Injection and Evaporation): the injected/evaporated mass is distributed to all species defined as fuel components using the specified ratio.

Results: For all results referring to a Fuel (traces, transients, summary) all species defined as fuel components are summed up. This means that the specified ratio is NOT considered.

Theory BOOST v2009

17-Jul-2009 2-5

2.2. Cylinder

2.2.1. Basic Conservation Equations

Figure 2-2: Energy Balance of Cylinder

The calculation of the thermodynamic state of the cylinder is based on the first law of thermodynamics:

( )

dtdmfqh

ddmh

ddm

ddmh

ddQ

ddQ

ddVp

dumd

evev

ei

iBBBB

wFc

c

+

+=

(2.2.1)

The variation of the mass in the cylinder can be calculated from the sum of the in-flowing and out-flowing masses:

dt

dmd

dmddm

ddm

ddm evBBeic += (2.2.2)

where:

( )d

umd c change of the internal energy in the cylinder

ddVpc piston work

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ddQF fuel heat input

ddQw wall heat losses

ddmh BBBB enthalpy flow due to blow-by

cm mass in the cylinder

u specific internal energy

cp cylinder pressure

V cylinder volume

FQ fuel energy

wQ wall heat loss

crank angle BBh enthalpy of blow-by

ddmBB blow-by mass flow

idm mass element flowing into the cylinder

edm mass element flowing out of the cylinder

ih enthalpy of the in-flowing mass

eh enthalpy of the mass leaving the cylinder

evq evaporation heat of the fuel f fraction of evaporation heat from the cylinder charge

evm evaporating fuel

The first law of thermodynamics for high pressure cycle states that the change of the internal energy in the cylinder is equal to the sum of piston work, fuel heat input, wall heat losses and the enthalpy flow due to blow-by.

Internal/External Mixture Preparation:

Equation 2.2.1 is valid for engines with internal and external mixture preparation. However, the terms, which take into account the change of the gas composition due to combustion, are treated differently for internal and external mixture preparation.

For internal mixture preparation it is assumed that

the fuel added to the cylinder charge is immediately combusted

Theory BOOST v2009

17-Jul-2009 2-7

the combustion products mix instantaneously with the rest of the cylinder charge and form a uniform mixture

as a consequence, the A/F ratio of the charge diminishes continuously from a high value at the start of combustion to the final value at the end of combustion.

For external mixture preparation it is assumed that

the mixture is homogenous at the start of combustion as a consequence, the A/F ratio is constant during the combustion burned and unburned charge have the same pressure and temperature although

the composition is different.

Together with the gas equation

cocc TRmVp = 1 (2.2.3)

establishing the relation between pressure, temperature and density, equation 2.2.1 for the in-cylinder temperature can be solved using a Runge-Kutta method. Once the cylinder temperature is known, the cylinder pressure can be obtained from the gas equation.

2.2.1.1. Port Massflow The mass flow rates at the intake and exhaust ports are calculated from the Equations for isentropic orifice flow under consideration of the flow efficiencies of the ports determined on the steady state flow test rig.

From the energy Equation for steady state orifice flow, the Equation for the mass flow rates can be obtained:

= 112

oooeff TR

pAdtdm

(2.2.4)

dtdm

mass flow rate

effA effective flow area

1op upstream stagnation pressure

1oT upstream stagnation temperature

oR gas constant

For subsonic flow,

=

+

1

1

2

2

1

2

1 oo pp

pp

, (2.2.5)

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2p downstream static pressure

ratio of specific heats and for sonic flow,

11

2 11

max +

+==

. (2.2.6)

The actual effective flow area can be determined from measured flow coefficients :

4

2 = vieff dA (2.2.7) flow coefficient of the port

vid inner valve seat diameter (reference diameter)

The flow coefficient varies with valve lift and is determined on a steady-state flow test rig. The flow coefficient, , represents the ratio between the actual measured mass flow rate at a certain pressure difference and the theoretical isentropic mass flow rate for the same boundary conditions. The flow coefficient is related to the cross section area. of the attached pipe. The inner valve seat diameter used for the definition of the normalized valve lift can be seen in the following figure:

Figure 2-3: Inner Valve Seat Diameter

The composition of the gases leaving the cylinder via the exhaust port is determined by the scavenging model.

Theory BOOST v2009

17-Jul-2009 2-9

2.2.1.2. Scavenging A perfect mixing model is usually used for four-stroke engines. This means that the composition of the exhaust gases is the mean composition of the gases in the cylinder, and also that the energy content of the exhaust gases is equivalent to the mean energy content of the gases in the cylinder. In this case the change of the air purity over crank angle can be calculated from the following formula:

( ) ddmR

mddR i

c

= 11 (2.2.8)

R air purity In the case of a two-stroke engine, the perfect mixing model is not sufficient for accurate simulations. For this reason BOOST also offers a perfect displacement scavenging model and a user-defined scavenging model.

In the perfect displacement model no mixing between intake and residual gases takes place and pure residual gases leave the cylinder (so long as they are available).

The User-defined scavenging model used in the BOOST code divides the cylinder into the displacement zone and the mixing zone.

The mass balance is based on the following scavenging types:

SCAVENGING TYPE A

According to the (positive) Scavenging Quality SCQ the incoming gas delivers both the displacement and the mixing zone while pure mixing zone gas is leaving the cylinder

0>=IZ

IDSC m

mQ &&

IDm& massflow into the displacement zone

IZm& massflow into the cylinder

SCAVENGING TYPE B

According to the (negative) Scavenging Quality SCQ the incoming gas is flowing into the mixing zone and partially short-circuited to the exhaust port, while shortcut and mixing zone gas is leaving the cylinder.

0

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Taking these two scavenging types into account, the Scavenging Quality Function )(SEQSC is calculated from the user defined Scavenging Efficiency Function SE(SR).

( ) ( ) ( )Z

ASconstV

const

SREF

AS

VtV

mtmtSR

CY ==

==

ASm aspirated mass

SREFm reference mass of cylinder charge

ASV volume of aspirated charge

ZV cylinder reference volume

( ) ( ) ( )Z

TASconstV

const

ZEVC

TAS

VtV

mtmtSE

CY ==

==

TASm aspirated mass trapped

ZEVCm total mass of cylinder charge at EVC (Exhaust Valve Closing)

TASV volume of aspirated charge trapped

ZV cylinder reference volume

To consider the different zone temperatures (and densities) during the scavenging process, the scavenging efficiency SE(t) (used for calculating the scavenging quality SCQ (t)=

))(( tSEQSC ) is determined as follows:

( )( )( )

( )( )

( )( )ttm

dmm

tSE

Z

Z

t

t EF

EF

IZ

IZ

= 0&&

IZm& mass flow into the cylinder

EFm& fresh charge mass flow out of the cylinder

Zm total mass of cylinder charge

IZ density of mass flow into the cylinder EF density of fresh charge mass flow out of the cylinder Z density of cylinder charge

0t intake valve opening time

Theory BOOST v2009

17-Jul-2009 2-11

In order to specify the quality of the scavenging system of a two-stroke engine, scavenging efficiency is required as a function of scavenge ratio SE(SR). This can be obtained from scavenging tests.

Figure 2-4: User-Defined Scavenging Model

2.2.1.3. Piston Motion For a standard crank train the piston motion as a function of the crank angle can be derived from Figure 2-5:

Figure 2-5: Standard Crank Train

BOOST v2009 Theory

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( ) ( ) ( ) 2sin1coscos

+++=le

lrlrlrs (2.2.9)

+= lrearcsin (2.2.10)

s piston distance from TDC r crank radius l con-rod length crank angle between vertical crank position and piston TDC position e piston pin offset a crank angle relative to TDC

2.2.1.4. Heat Transfer

2.2.1.4.1. In Cylinder Heat Transfer The heat transfer to the walls of the combustion chamber, i.e. the cylinder head, the piston, and the cylinder liner, is calculated from:

( )wicwiwi TTAQ = (2.2.11) wiQ wall heat flow (cylinder head, piston, liner)

iA surface area (cylinder head, piston, liner)

w heat transfer coefficient cT gas temperature in the cylinder

wiT wall temperature (cylinder head, piston, liner)

In the case of the liner wall temperature, the axial temperature variation between the piston TDC and BDC position is taken into account:

cx

eTTxc

TDCLL =

1, (2.2.12)

=

BDCL

TDCL

TT

c,

,ln (2.2.13)

LT liner temperature

TDCLT , liner temperature at TDC position

BDCLT , liner temperature at BDC position

x relative stroke (actual piston position related to full stroke)

Theory BOOST v2009

17-Jul-2009 2-13

For the calculation of the heat transfer coefficient, BOOST provides the following heat transfer models:

Woschni 1978 Woschni 1990 Hohenberg Lorenz (for engines with divided combustion chamber only) AVL 2000 Model WOSCHNI Model

The Woschni model published in 1978 [38C5] for the high pressure cycle is summarized as follows:

( ) 8.0,1,1,

1,21

53.08.02.0130

+= occcc

cDmccw ppVp

TVCcCTpD (2.2.14)

1C = 2.28 + 0.308 uc / mc 2C = 0.00324 for DI engines

2C = 0.00622 for IDI engines

D cylinder bore

mc mean piston speed

uc circumferential velocity

DV displacement per cylinder

ocp , cylinder pressure of the motored engine [bar]

1,cT temperature in the cylinder at intake valve closing (IVC)

1,cp pressure in the cylinder at IVC [bar]

The modified Woschni heat transfer model published in 1990 [38C6] aimed at a more accurate prediction of the heat transfer at part load operation:

8.0

2.02

153.08.02.0 21130

+= IMEP

VVccTpD TDCmccw (2.2.15)

TDCV TDC volume in the cylinder

V actual cylinder volume IMEP indicated mean effective pressure In the case that

( ) 2.021,1,

1,2 2

IMEP

VVcCpp

VpTV

C TDCmoccc

cD ,

BOOST v2009 Theory

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the heat transfer coefficient is calculated according to the formula published in 1978.

For the gas exchange process, both Woschni models use the same Equation for the heat transfer coefficient:

( ) 8.0353.08.02.0130 mccw cCTpD = (2.2.16) mu ccC /417.018.63 +=

w heat transfer coefficient D cylinder bore

mc mean piston speed

uc circumferential velocity

HOHENBERG Model

In the Hohenberg heat transfer model [C7] the following equation is used for the calculation of the heat transfer coefficient:

( ) 8.04.08.006.0 4.1130 += mccw cTpV (2.2.17) LORENZ Model

The Lorenz Heat Transfer Equation is valid for a cylinder with an attached combustion chamber. In Equation 2.2.14 and 2.2.15 the characteristic speed is:

mC cCw = 1

Cw characteristic speed in the cylinder

For the Lorenz equation the term Cw is modified:

m

CP

C CCxDdt

dV

w 1..

4+

= (2.2.18)

dtdVCP volume flow from the connecting pipe to the cylinder

x clearance between the cylinder head and the piston

Theory BOOST v2009

17-Jul-2009 2-15

AVL 2000 Heat Transfer Model

The heat transfer during gas exchange strongly influences the volumetric efficiencies of the engine, especially for low engine speeds. Based on AVL experience and measurements conducted at Graz Technical University, the Woschni heat transfer has been modified to take this effect into account [C25], [C26]. During the gas exchange the heat transfer coefficient is calculated from the following equation:

=

8.02

453.08.02.0013.0, ininWoschni vd

dcTpdMax (2.2.19)

heat transfer coefficients [J/K/M2] 4C = 14.0

d bore [m]

p pressure [Pa]

T temperature [K]

ind pipe diameter connected to intake port [m]

inv intake port velocity [m/s]

The diameter of the intake port directly at the valve is of special significance for this model, therefore these diameters of the intake ports should be accurately specified over the whole port length.

2.2.1.4.2. Port Heat Transfer During the gas exchange process it is essential also to consider the heat transfer in the intake and exhaust ports. This may be much higher than for a simple pipe flow because of the high heat transfer coefficients and temperatures in the region of the valves and valve seats. In the BOOST code, a modified Zapf heat transfer model is used:

( ) wcmAwud TeTTT pp

w +=

&

(2.2.20)

The heat transfer coefficient, p , depends on the direction of the flow (in or out of the cylinder): The formula

[ ]

+= vi

vviuuup d

hdmTTCTCC 797.015.15.044.02654 & (2.2.21)

is used for outflow and the formula

[ ]

+= vi

vviuup d

hdmTTCTCC 765.0168.168.033.02987 & (2.2.22)

is used for inflow.

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p heat transfer coefficient in the port dT downstream temperature

uT upstream temperature

Tw port wall temperature

Aw port surface area

&m mass flow rate cp specific heat at constant pressure

hv valve lift

dvi inner valve seat diameter

The following table contains the constants used in the formulas above.

Exhaust Valve Intake Valve

4C 1.2809 7C 1.5132

5C -4100451.7 8C -4107.1625 6C -7104.8035 9C -7103719.5

2.2.1.5. Blow-By BOOST considers blow-by losses in the cylinder using the specified effective blow-by gap and the mean crankcase pressure. The blow-by mass flow rates are calculated at any time step from the orifice flow Equations (2.2.4 - 2.2.6).

The effective flow area is obtained from the cylinder bore and from the effective blow-by gap:

= DAeff (2.2.23) effA effective flow area

D cylinder bore blow-by gap If the cylinder pressure exceeds the mean crankcase pressure, the cylinder pressure and temperature are used as upstream stagnation pressure and temperature. The mean crankcase pressure represents the downstream static pressure. The gas properties are taken from the cylinder.

The blow-by gas has the same energy content as the gases in the cylinder.

If the cylinder pressure is lower than the mean crankcase pressure, the pressure in the crankcase is used as upstream stagnation pressure, and the cylinder pressure as the downstream static pressure. The upstream stagnation temperature is set equal to the piston wall temperature, and the gas composition is set equal to the composition of the gas which left the cylinder just before the reverse flow into the cylinder started.

Theory BOOST v2009

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2.2.1.6. Evaporation The model for direct gasoline injection in BOOST relies on the specification of the rate of evaporation. It is assumed that the density of the liquid fuel is much higher compared to the fuel vapor density. Hence the presence of liquid fuel can be neglected.

2.2.2. Combustion Models

2.2.2.1. Pre-Defined Heat Release

2.2.2.1.1. Vibe and Table The simplest approach to model the combustion process is the direct specification of the rate of heat release. The rate of heat release of an engine at a specific operating point is determined from the measured cylinder pressure history. By means of a reversed high

pressure cycle calculation, i.e. by solving equation 2.2.1 for ddQF instead for d

dTc , the heat

release versus crank angle is obtained.

To simplify this approach, only the dimensionless heat input characteristic must be specified over crank angle. From the total heat supplied to the cycle, which is determined by the amount of fuel in the cylinder and by the A/F ratio, BOOST calculates the actual heat input per degree crank angle.

For the direct input of the rate of heat release curve the following options are available:

1. Table

The heat release curve is approximated by specifying reference points versus crank angle. The y-values are scaled to obtain an area of one beneath the curve. Values between the points specified are obtained by linear interpolation.

2. Vibe Function

The Vibe function [C9] is often used to approximate the actual heat release characteristics of an engine:

( ) ( )11 ++=myam

c

eymaddx

(2.2.24)

QdQdx = (2.2.25)

c

oy

= (2.2.26)

Q total fuel heat input

crank angle o start of combustion

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c combustion duration m shape parameter

a Vibe parameter a = 6.9 for complete combustion

The integral of the vibe function gives the fraction of the fuel mass which was burned since the start of combustion:

( ) +== 11 myaedddxx (2.2.27)

x mass fraction burned

Figure 2-6 shows the approximation of an actual heat release diagram of a DI Diesel engine by a vibe function. The start of combustion, combustion duration and shape parameter were obtained by a least square fit of the measured heat release curve.

Figure 2-6: Approximation of a Measured Heat Release

In Figure 2-7 the influence of the vibe shape parameter 'm' on the shape of the vibe function is shown.

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Figure 2-7: Influence of Shape Parameter 'm'

3. Vibe Two Zone

Again the rate of heat release, and thus the mass fraction burned, is specified by a vibe function. However the assumption that burned and unburned charges have the same temperature is dropped. Instead the first law of thermodynamics is applied to the burned charge and unburned charge respectively [C8].

ddm

hddmh

ddQ

ddQ

ddVp

dudm bBB

bBBb

uWbFb

cbb ,

,++= (2.2.28)

= ddmhddmhddQddVpd udm uBBuBBBuWuucuu ,, (2.2.29) index b burned zone

index u unburned zone

The term ddmh Bu covers the enthalpy flow from the unburned to the burned zone due

to the conversion of a fresh charge to combustion products. Heat flux between the two zones is neglected.

In addition the sum of the volume changes must be equal to the cylinder volume change and the sum of the zone volumes must be equal to the cylinder volume.

ddV

ddV

ddV ub =+ (2.2.30)

VVV ub =+ (2.2.31)

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The amount of mixture burned at each time step is obtained from the Vibe function specified by the user. For all other terms, like wall heat losses etc., models similar to the single zone models with an appropriate distribution on the two zones are used.

4. Double Vibe Function

The superposition of two vibe functions (Double Vibe) is used to approximate the measured heat release characteristics of a compression ignition (CI) engine more accurately. In this case two vibe functions are specified, the first one is used to model the premixed burning peak and the second one to model the diffusion controlled combustion. If the fuel allotment to each of the vibe functions is known, the heat releases obtained from the two vibe functions can be added, thus giving a double vibe heat release, Figure 2-8.

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Figure 2-8: Superposition of Two Vibe Functions

2.2.2.1.2. Extended Heat Release For the simulation of engine transients, the above mentioned approaches are not sufficient because the heat release characteristics change with engine speed and load. As the speed and load profile for a transient is not known prior to a simulation run, a model predicting the rate of heat release dependent on the operating point is required.

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WOSCHNI / ANISITS Model

For diesel engines the approach used is based on the model by Woschni and Anisits [31C1]. The vibe function and the characteristic parameters of one operating point must be defined. The model predicts the change of the vibe parameters according to the actual operating conditions:

5.06.0

,

=

ref

refrefcc n

nAF

AF (2.2.32)

3.0

,

,

6.0

=

refIVC

refIVC

refIVC

IVCrefref n

nT

Tpp

idid

mm (2.2.33)

c combustion duration AF air fuel ratio n engine speed

m Vibe shape parameter

id ignition delay

IVCp pressure at intake valve closes

IVCT in-cylinder temperature at intake valve closes

Index ref at reference operating point

The ignition delay is calculated with the relations found by Andree and Pachernegg [C3] which assume that the ignition of the injected fuel droplets takes place if the integral of gas temperature versus time exceeds a threshold.

HIRES ET AL Model

For gasoline engines the change of the combustion duration and the ignition delay is calculated from the in-cylinder conditions at ignition timing [C2].

3/23/1

,

=

ss

ff

nn refrefref

refcc (2.2.34)

3/23/1

=

ss

ff

nnidid ref

refrefref (2.2.35)

s laminar flame speed

f piston to head distance at ignition timing

The laminar flame speed itself is a function of the in-cylinder conditions, the A/F ratio and the mole fraction of the residual gases [C4].

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2.2.2.2. Calculated Heat Release: Combustion Models

)

Note: From BOOST v5.0 on the EBCM and PBCM combustion models are replaced by the Fractal Combustion Model.

2.2.2.2.1. Spark Ignition Engines: Fractal Combustion Model The fractal combustion model for SI engines, implemented in BOOST, predicts the rate of heat release in a homogeneous charge engine. Thereby the influence of the following parameters is considered [C8]:

The combustion chamber shape The spark plug location and spark timing The composition of the cylinder charge (residuals, recirculated exhaust gas, air and fuel

vapor)

The macroscopic charge motion and turbulence level The thermodynamics of the two zone combustion model is outlined in section 2.2.2 - Vibe Two Zone. The two zone model is used to calculate the gas conditions of the combustion products (i.e. the burned zone) and the remaining fresh charge (i.e. the unburned zone).

It is well established that the flame front propagating within the turbulent flow field occurring inside the combustion chamber of an internal combustion engine is a very thin and highly wrinkled surface. This flame area TA , due to the above wrinkling, is much higher than the one occurring in a laminar burning process. The latter, i.e. the laminar flame area LA , can be considered a smooth and spherical surface centered in the spark plug location. The increase in the flame surface ( )LT AA / , is then first responsible for the increase in the turbulent burning rate with respect to the laminar one. The mass burning rate can be then expressed as:

LLL

TuLTu

b SAAASA

dtdm

== (2.2.36)

Equation 2.2.36 underlines that the flame propagation speed remains equal to the laminar one also in a turbulent combustion process, nevertheless, the same burning rate can be also expressed as a function of a turbulent burning speed:

LLL

TuTSu

b SAAA

SAdt

dm

==

=

L

T

L

T

AA

SS

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The above expressions, introduced by Damkhler in 1940 C12], basically represent a definition of the turbulent burning speed. Equation 2.2.36 also puts into evidence that the burning rate can be easily computed once the increase in flame area has been established. However the real physical mechanisms that produce the flame wrinkling are still not perfectly clear today:

A variation of the local temperature, exponentially affecting the kinetic reaction rate, can determine different local burning rates inducing a flame deformation.

The expansion process of the burned gases and the flame curvature together produce a deviation in the trajectory of fluid particles passing through it and an hydrodynamic flame deformation can occur.

The turbulent vortices also produce a convective flame wrinkling on different length scales. This wrinkling is then partly compensated by the local laminar burning process yielding a "smoothing" effect of the local deformations.

The competition of the above phenomena moreover varies with engine operating conditions. At very high engine speeds the deformation action can be so intense to produce a multiple connected flame front, with "islands" of unburned mixture trapped within it. However it is accepted that in a relevant portion of the combustion regimes occurring in an ICE, the flame front behaves like a single connected "passive scalar" mainly wrinkled by the convective action of the turbulent flow field.

Under these hypothesis it is possible to develop a quasi-dimensional combustion model, based on the concept of the fractal geometry. In this approach, an initially smooth flame surface of spherical shape - the laminar flame LA - is then wrinkled by the presence of turbulent eddies of different length scales. The interactions between the turbulent flow field and the flame determine the development of a turbulent flame surface TA , which propagates at the laminar flame speed LS . If a self-similar wrinkling is assumed within the length scales interval maxmin L-L , then the flame front presents the characteristics of a fractal object and its flame surface can be then easily computed:

2

min

max3

=

D

L

T

LL

AA

(2.2.37)

The above expression, substituted in the Equation 2.2.36, allows to compute the burning rate once the laminar flame surface LA and speed LS as well as the wrinkling scales

maxmin L-L and fractal dimension 3D has been properly evaluated:

LL

D

ufractals

b SALL

dtdm

2

min

max3

=

(2.2.38)

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Turbulence

Based on the physical hypothesis recalled above, the computation of the wrinkling scales

maxmin L-L as well as the fractal dimension 3D must depend on the characteristics of the turbulent flow field inside the cylinder. Its evaluation within a zero-dimensional model is really challenging. A number of proposals can be found in the current literature and, among these, a two-equation modified kK approach [C13], is recalled here:

u

uexinin Km

mKPumdtdK

&&& ++= 2

21

u

uex km

mkmP

dtdk

&& ++=

mk

LKcP

It3307.0=

(2.2.39)

2

21

fmUK = ,

2

23 umk =

, ILu 3=

In the above balance equations, K is the kinetic energy of the mean flow field ( fU ) - whose production and destruction is mainly related to the intake and exhaust flow rates ( inm& and exm& ) - k is the kinetic energy of the turbulent flow field (assumed isotropic) while is its dissipation rate. P represents a turbulent production term which characterizes the energy transfer between the mean and the turbulent flow field (energy-

cascade mechanism [C13]). An unique tuning constant, tc , is present and a value of order 1 is usually specified [C13]. Differently from [C13], the Equations 2.2.39 are integrated all over the engine cycle and a turbulent production term due to the in-cylinder unburned

density variation during the compression and expansion stroke is included in both K and k balance equations [C14]. The turbulence intensity is finally derived from the k definition. The above model also gives the possibility to estimate the Kolmogorov length scale which, under the hypothesis of isotropic turbulence, assumes the expression:

4/3

t

Ik Re

Ll = with u

It

LuRe =

and HcL lI = (2.2.40) IL being the integral length scale, assumed proportional ( lc = 0.2-0.8) to the

instantaneous clearance height H inside the cylinder, and u is the kinematic viscosity of the unburned mixture.

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In particular, the integral and the Kolmogorov length scales, IL and kl , are chosen as the maximum and minimum wrinkling scales in Equation 2.2.37, while the 3D dimension mainly depends on the ratio between the turbulence intensity u and the laminar flame speed LS [C15]:

L

L

SuSuD +

+= 05.235.23 (2.2.41)

The above described fractal model is indeed really valid for a fully-developed and freely expanding turbulent flame. During both early flame development and combustion completion correction terms (weight factors 1w and 2w described below) are required.

Ignition

The complex phenomena occurring after spark occurrence, plasma formation and subsequent flame kernel evolution are described in detail in [31C16]. Kernel initiation process ends about 200 ms (tunable with the ignition-formation time multiplier ignc ) after spark at a critical flame radius of about 2 mm. During this period burning speed is very high, depending on energy released by the ignition system, then it reaches a minimum to values similar to the laminar flame speed [C16] and subsequently it increases again, as a consequence of the flame surface wrinkling previously described.

Being the above phenomena not included in the present model, it is assumed to start the computation at the end of kernel initiation process with a stable and spherically-shaped smooth flame of about 2 mm radius. Flame wrinkling process then starts at a rate which increases with both the instantaneous flame radius and the turbulence intensity (proportional to the engine speed). The following expression is proposed for the computation of a non-dimensional flame wrinkling rate:

refreff

fwr n

nrr

,

= (2.2.42)

In the above equation, reffr , parameter is a tunable reference radius of order 1cm, while

refn is a reference engine speed fixed to 1000 rpm. Equation 2.2.41 is finally redefined to handle an increase in the fractal dimension related to the gradual increase in flame wrinkling during time.

L

Lminmax

SuSDuD

D ++= ,3,33

05.2,3 =minD

With this formulation, the first phase of the combustion process will be characterized by a fractal dimension very close to its minimum level min,3D , which determines an initial burning speed close to the laminar one. Note that the minimum value of the fractal dimension is in any case greater than 2.

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This should compensate the very high burning speed which occurs during the kernel formation phase, due to the energy supplied with the spark plug. Of course a careful tuning of the parameters lc and reffr , is required to match the experimental pressure cycles at each engine operating condition.

Wall Combustion

When the flame front reaches the combustion chamber walls the described fractal mechanism of flame propagation is no longer valid. The most important characteristics of combustion completion relate to the effects of the wall on the burning process ("wall-combustion" phenomena). The wall limits gas expansion, constrains all flows, and forms a relatively low-temperature solid boundary that cools the gas. All of these factors change the fundamental behavior of the combustion compared with that of a flame propagating freely across the chamber. A great portion (30-40%) of the unburned mixture really burns in this particular combustion mode. Wall-combustion burning rate can be simply described by an exponential decay, as follows [C17]:

b

combustionwall

b mmdt

dm =

(2.2.43)

being the characteristic time scale of the above process. The overall burning rate can be consequently defined as a weighted mean of the two described combustion rates:

( )combustionwall

b

fractals

b

overall

b

dtdm

wdt

dmw

dtdm

+

=

221

(2.2.44)

The switch between the two combustion modes gradually starts when a transition time trt is reached, identifying the first flame plume arrival to the cylinder wall, i.e.:

( )( ) trLTu

trbf SA

mmr

= (2.2.45)

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LI /2

rcylrf

Figure 2-9: Flame Arrival at Cylinder Wall; Beginning of Wall-Combustion Mode

When Equation 2.2.45 is verified, the characteristic time scale in Equation 2.2.43 is computed assuming that wall-combustion burning rate equals the one derived from the fractal model Equation 2.2.38, hence:

( )( ) trLTu

trb

SAmm

=

(2.2.46)

The above value is then kept fixed during the subsequent wall combustion process. The weight factor 2w indeed linearly increases with time, depending on the instantaneous unburned mass ( )bmm , compared to the one occurring at the transition time trt :

( ) trb

b

mmmm

=

(2.2.47)

In this way a smooth transition between the two modes is easily realized.

2.2.2.2.2. Compression Ignition Engines BOOST uses the Mixing Controlled Combustion (MCC) [C10, C11] model for the prediction of the combustion characteristics in direct injection compression ignition engines.

The model considers the effects of the premixed (PMC) and diffusion (MCC) controlled combustion processes according to:

ddQ

ddQ

ddQ PMCMCCtotal += (2.2.48)

Mixing Controlled Combustion:

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In this regime the heat release is a function of the fuel quantity available (f1) and the turbulent kinetic energy density (f2):

( ) ( )VkfQmfCd

dQMCCFComb

MCC ,, 21 = (2.2.49)

with

( ) ( ) EGRCavailableOxygenMCCFF wLCVQmQmf ,1 , = (2.2.50)

( )32

,VkCVkf Rate = (2.2.51)

MCCQ cumulative heat release for the mixture controlled combustion [kJ]

CombC combustion constant [kJ/kg/deg CA]

RateC mixing rate constant [s]

k local density of turbulent kinetic energy [m2/s2]

Fm vapourized fuel mass (actual) [kg]

LCV lower heating value [kJ/kg] V cylinder volume [m3] crank angle [deg CA]

availableOxygenw , mass fraction of available Oxygen (aspirated and in EGR) at SOI [-]

EGRC EGR influence constant [-]

Conservation equation for the kinetic energy of the fuel jet:

Since the distribution of squish and swirl to the kinetic energy are relatively small, only the kinetic energy input from the fuel spray is taken into account. The amount of kinetic energy imparted to the cylinder charge is determined by the injection rate (first term on RHS). The dissipation is considered as proportional to the kinetic energy (second term on RHS) giving:

for Revised TKE calculation:

5.125.0 kinDissFFturbkin ECvmC

dtdE = & (2.2.52)

( )stoichDiffIF kin mmEk += 1, (2.2.53)

for Default TKE calculation (this is an older status of the model):

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kinDissFFkin ECvm

dtdE = 25.0 & (2.2.54)

( )stoichDiffIF kinturb mmECk +

=1,

(2.2.55)

kinE kinetic jet energy [J]

TurbC turbulent energy production constant [-]

DissC dissipation constant; Revised: [J-0.5/s] ; Default: [1/s]

IFm ,& injected fuel mass (actual) [kg]

v injection velocity = A

m

F

F

&

[m/s]

A effective nozzle hole area [m2] F fuel density [kg/m3]

n engine speed [rpm]

stoichm stoichiometric mass of fresh charge [kg/kg]

Diff Air Excess Ratio for diffusion burning [-] t time [s]

Ignition delay model:

The ignition delay is calculated using the Andree and Pachernegg [C3] model by solving the following differential equation:

ref

refUBid

QTT

ddI = (2.2.56)

As soon as the ignition delay integral idI reaches a value of 1.0 (=at id ) at the ignition delay iD is calculated from SOIidid = .

idI ignition delay integral [-]

refT reference temperature = 505.0 [K]

UBT unburned zone temperature [K]

refQ reference activation energy, f(droplet diameter, oxygen content, ) [K]

id ignition delay [s]

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SOI start of injection timing [degCA] id ignition delay timing [degCA]

Premixed combustion model:

A Vibe function is used to describe the actual heat release due to the premixed combustion:

( ) ( )11 ++=

myam

c

PMC

PMC

eymad

QdQ

(2.2.57)

c

idy

= (2.2.58)

PMCQ total fuel heat input for the premixed combustion= PMCidfuel Cm , idfuelm , total amount of fuel injected during the ignition delay phase

PMCC premixed combustion parameter [-]

c premixed combustion duration = DurPMCid C DurPMCC premixed combustion duration factor

m shape parameter m = 2.0 a Vibe parameter a = 6.9

Droplet heat-up and evaporation model:

According to Sitkei [C22] the equilibrium temperature for the droplet evaporation can be calculated iteratively from:

( )( ) ( )( )15.2733.015.27326.00.20

1093.30

0.4150

4

++

=

cd

T

c

d

dcc

TTe

pT

TTd

(2.2.59)

Using the equilibrium temperature the velocity of the evaporation results from:

=

dTc

de

ep

Tv0.4159

70353.0 (2.2.60)

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The value of 0.70353 can be changed through user input (expert parameters). Finally the change in droplet diameter (and the corresponding change in droplet mass) over time can be calculated:

tvdd edd = 2 0, (2.2.61)

c thermal conductivity of the cylinder [W/ms] cT temperature in the cylinder [K]

dT equilibrium temperature of the isothermal droplet evaporation [K]

cp pressure in the cylinder [Pa]

ev evaporation velocity [m2/s]

dd actual droplet diameter [m]

0,dd initial droplet diameter [m]

2.2.2.2.3. HCCI Auto-Ignition The Single-Zone HCCI Auto Ignition model is available in combination with General

Species Transport only. In this case the term ddQF in Equation 2.2.1 is formulated as:

=

=nSpcGas

iiii

F MWud

dQ1

(2.2.62)

The species mass fractions are calculated as:

iii MW

ddw = (2.2.63)

where:

nSpcGas number of species in the gas phase [-]

MW species molecular weight [kg/kmole]

u species inner energy [J/kgK]

w species mass fraction [-] mixture density [kg/m3] species reaction rate [kmole/m3s] The reaction rate of each species is calculated based on a specified set of chemical reactions that describe the auto-ignition process.

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2.2.2.3. Pre-Defined Pressure Curve (Analysis) Usually in BOOST the rate of heat release is specified or calculated. Based on this the pressure, the temperature and the species mass fractions are calculated. The inverse procedure, the determination of the rate of heat release from a specified target pressure curve is called combustion analysis.

BOOST offers this feature for both, single and two zone analysis.

In order to ensure a consistent thermodynamic state at start of high pressure an adaption has to be made to:

the Pressure Curve (Shift), the Cylinder Mass or to the Cylinder Temperature.

2.2.2.4. Ideal Heat Release For theoretical investigations, BOOST allows the specification of the following theoretical combustion models:

1. Constant Volume

The complete charge is burned instantaneously at the specified crankangle.

2. Constant Pressure

Part of the charge is burned instantaneously at top dead center to achieve the desired peak firing pressure. The remaining charge is burned in such a way as to maintain the specified PFP.

This combination of constant volume and constant pressure combustion is also called Seiliger process.

If the pressure at the end of the compression stroke already exceeds the specified PFP, combustion starts when the pressure drops below this pressure during the expansion stroke.

2.2.2.5. User-Defined Heat Release USER MODEL

By linking user supplied subroutines (UDCOMB_CALCULATE_TS(), ..) to BOOST, the user may define heat release characteristics using BOOSTs high pressure cycle simulation (For details please refer to the BOOST Interfaces Manual).

USER DEFINED HIGH PRESSURE CYCLE

The user-defined high pressure cycle (user supplied subroutines UDHPC_CALCULATE_TS(), ..) replaces the entire high pressure cycle simulation of BOOST (For details please refer to the BOOST Interfaces Manual).

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2.2.3. Emission Models

2.2.3.1. NOx Formation Model The NOx formation model implemented in BOOST is based on Pattas and Hfner [31C18].

The following 6 reactions (based on the well known Zeldovich mechanism) are taken into account:

Stoichiometry Rate

= T

TAa

ii

i

eTkk ,0

k0 [cm3,mol,s] a [-] TA [K]

R1 N2 + O = NO + N ON cckr = 211 4.93E13 0.0472 38048.01

R2 O2 +N = NO + O NO cckr = 222 1.48E08 1.5 2859.01

R3 N +OH = NO + H NOH cckr = 33 4.22E13 0.0 0.0

R4 N2O + O = NO + NO OON cckr = 244 4.58E13 0.0 12130.6

R5 O2 + N2 = N2O + O 2255 NO cckr = 2.25E10 0.825 50569.7

R6 OH + N2 = N2O + H 226 NOH cckr = 9.14E07 1.148 36190.66

All reactions rates ri have units [mole/cm3s] the concentrations ci are molar concentrations under equilibrium conditions with units [mole/cm3]. The concentration of N2O is calculated according to:

22

6.94716125.06

2 101802.1 ONT

ON pceTc =

The final rate of NO production/destruction in [mole/cm3s] is calculated as:

( )4

4

2

12

1110.2

AKr

AKrCCr tKineticMulltPostProcMuNO ++= (2.2.64)

with:

ltPostProcMuequNO

actNO

Ccc 1

,

, = 32

12 rr

rAK += 654

4 rrrAK +=

2.2.3.2. CO Formation Model The CO formation model implemented in BOOST is based on Onorati et al. [C20]. The following two reactions are taken into account:

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Stoichiometry Rate

R1 N2 + O = NO + N

OHCO

T

ccer =

0.110210

1 1076.6 R2 O2 +N = NO + O

2

0.2405512

2 1051.2 OCOT ccer =

The final rate of CO production/destruction in [mole/cm3s] is calculated as:

( ) ( )+= 121 rrCr ConstCO (2.2.65) with

equCO

actCO

cc

,

,= .

2.2.3.3. Soot Formation Model The soot formation model implemented in BOOST is based on Schubiger et al. [C19].

2.2.3.4. HC Formation Model In a spark ignition engine the unburned hydrocarbons have different sources. A complete description of their formation process cannot yet be given and definitely the achievement of a reliable predictive model within a thermodynamic approach is prevented by the fundamental assumptions and the requirement of reduced computational times. Nevertheless a phenomenological model which accounts for the main formation mechanisms and is able to capture the HC trends as function of the engine operating parameter may be proposed. The following major sources of unburned hydrocarbons can be identified in spark ignition engines (D'Errico et al. [C24]):

1. A fraction of the charge enters the crevice volumes and is not burned since the flame quenches at the entrance.

2. Fuel vapor is absorbed into the oil layer and deposits on the cylinder wall during intake and compression. The following desorption takes place when the cylinder pressure decreases during the expansion stroke and complete combustion cannot take place any more.

3. Quench layers on the combustion chamber wall which are left as the flame extinguishes prior to reaching the walls.

4. Occasional partial burning or complete misfire occurring when combustion quality is poor.

5. Direct flow of fuel vapour into the exhaust system during valve overlap in PFI engines.

The first two mechanisms and in particular the crevice formation are considered to be the most important and need to be accounted for in a thermodynamic model. Quench layer and partial burn effect cannot be physically described in a quasi dimensional approach, but may be included by adopting tunable semiempirical correlations.

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The effect of through flow is taken into account automatically as all chemical species are transported through all elements.

(a) Crevice mechanism

Crevices are narrow volumes in which the flame cannot propagate due to the heat transferred to the walls. The most important crevice volumes are the formed between the piston ring pack and the cylinder liner, and mainly the top-land crevices.

These crevice volumes cause hydrocarbon formation due to the following process. During compression unburned mixture is forced to enter their volumes, which have a large surface/volume ratio, and cools exchanging heat transfer with the walls. During combustion, the pressure continues to rise and forces other unburned mixture to flow into the crevice volumes. When the flame arrives it quenches, so that the flow through the crevice entrance inverts its motion when the cylinder pressure starts to decrease.

To describe this process, the model assumes that the pressure in the cylinder and in the crevices is the same and that the temperature of the mass in the crevice volumes is equal to the piston temperature. The mass in the crevices at any time is equal to:

piston

crevicecrevice TR

MVpm = (2.2.66)

where:

mcrevice mass of unburned charge in the crevices [kg]

p cylinder pressure [Pa]

Vcrevice total crevice volume [m3]

M unburned molecular weight [kg/kmol]

R gas constant [J/( kmol K)]

Tpiston piston temperature [K]

As we are interested in the evaluation of the HCs going into the exhaust BOOST begins to accumulate the HCs that are released from the crevice volume at end of combustion.

(b) HC absorption/desorption mechanism

A second significant source of hydrocarbon is the presence of lubricating oil in the fuel or on the walls of the combustion chamber. In fact, during compression, the fuel vapor pressure increases so, by Henrys law, absorption occurs even if the oil was saturated during the intake. During combustion the fuel vapor concentration in the burned gases goes to zero so the absorbed fuel vapor will desorb from the liquid oil into the burned gases. Fuel solubility is a positive function of the molecular weight, so the oil layer contributed to HC emissions depending on the different solubility of individual hydrocarbons in the lubricating oil. As a consequence, for usual gaseous fuels as methane and propane, due to the low molecular weight, oil mechanism does not contribute significantly.

The assumptions made in the development of the HC absorption/desorption are the following:

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the oil film is at the same temperature as the cylinder wall; fuel is constituted by a single hydrocarbon species, completely vaporized in the

fresh mixture;

oil is represented by squalane (C30H62), whose characteristics are similar to the SAE5W20 lubricant;

traverse flow across the oil film is negligible; diffusion of the fuel in the oil film is the limiting factor, since the diffusion

constant in the liquid phase is 104 times smaller than the corresponding value in the gas phase.

Under these hypotheses the radial distribution of the fuel mass fraction in the oil film can be determined by solving the diffusion equation:

022

=

rwD

tw FF (2.2.67)

where:

wF mass fraction of the fuel in the oil film, [-]

t time, [s]

r radial position in the oil film (distance from the wall), [m]

D relative (fuel-oil) diffusion coefficient, [m2/s]

In order to solve Equation 2.2.67 the oil layer can be represented as a cylindrical crown adhering to the walls. The resulting calculation domain is then obtained by subdividing the cylindrical crown into a fixed number of elements in both axial and radial directions.

The diffusion coefficient can be computed applying the following relation:

16.05.08104.7 = fvTMD (2.2.68) where:

M oil molecular weight [g/mol]

T oil temperature [K]

vf molar volume of the fuel at normal boiling conditions [cm3/mol]

oil viscosity [centipoise]

At the liner surface (r=0) a zero flux boundary conditions is applied to Equation 2.2.67, at r=Film the fuel concentration at the gas/oil interface is assigned as boundary condition. Here the following four different conditions can occur:

1) the oil layer is in contact with the fresh mixture

2) the oil layer is in contact with the burned gas

3) the oil layer is in contact with the crankcase gas

4) the oil layer is in contact with the piston layer

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BOOST evaluates the position of the flame front at every time-step and accumulates only HCs that are desorbed into the burned gases, since any HC released into the unburned mixture would be burned by the propagating flame front.

(c) Partial burn effects

Quench layer and partial burn effects cannot be physically described in a quasi-dimensional approach. A possible semi-empirical correlation has been proposed by Lavoie et al. [C23], in which the fraction of unburned charge remaining in the cylinder Fprob is calculated applying the following equation which relates Fprob to the global burn rate parameters:

( ) ( )[ ]{ }( )( )( )

35.011.11003.0

12210032.0exp

2

41

1

0902901

=>+=

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( )dttt

o iD 1 (2.2.71)

iD ignition delay at the unburned zones condition is larger than one before the end of combustion is reached.

The ignition delay for the knock model depends on the octane number of the fuel and the gas condition according to

TB

na

iD epONA

=

100 (2.2.72)

iD ignition delay [ms] ON octane number of the fuel p pressure [atm]

T temperature [K] BnaA ,,, model constants

The default values for gasoline are:

A = 17.68 ms a =3.402

n =1.7

B =3800 K

2.2.5. Dynamic In-Cylinder Swirl BOOST allows the user to specify the swirl characteristics of an intake port versus valve lift. During the intake process, the moment of momentum of the mass entering the cylinder is calculated from the instantaneous mass flow rate and the swirl produced at the instantaneous valve lift. The in-cylinder swirl at the end of the time step is calculated from

( ) ( ) ( ) ( )( )swiiswccsw ndmtntmttmttn ++=+1

(2.2.73)

swn in-cylinder swirl

cm in-cylinder mass

idm in-flowing mass

swin swirl of in-flowing mass

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2.2.6. Dynamic In-Cylinder Tumble BOOST allows the user to specify the tumble characteristics of an intake port versus valve lift. During the intake process, the moment of momentum of the mass entering the cylinder is calculated from the instantaneous mass flow rate and the tumble produced at the instantaneous valve lift. The in-cylinder tumble at the end of the time step is calculated from

( ) ( ) ( ) ( )( )tbiitbcctb ndmtntmttmttn ++=+1

(2.2.74)

tbn in-cylinder tumble

cm in-cylinder mass

idm in-flowing mass

tbin tumble of in-flowing mass

2.2.7. Wall Temperature The cycle averaged wall temperatures influence the wall heat losses during the high pressure cycle and thus the efficiency of the engine. During the gas exchange, the heat transfer from the cylinder walls heats the fresh charge and lowers the volumetric efficiency of the engine. The energy balance between the heat flux from the working gas in the cylinder to the cooling medium determines the wall temperatures.

For transient simulations, this energy balance can be calculated for the cylinder head/fire deck, the liner, and the piston. In addition, the energy balance of the port walls may be considered. The 1D heat conduction equation is solved using the average heat flux over one cycle as boundary condition at the combustion chamber side and the heat transfer to the cooling medium on the outside. With these assumptions the heat conduction Equation

2

2

dxTd

cdtdT =

(2.2.75)

T wall temperature conductivity of wall material density of wall material c specific heat capacity of wall material

can be solved. The mathematical formulation of the boundary conditions is:

dxdTqin = (2.2.76)

inq average heat flux to the combustion chamber wall

( )CMWOCMout TTq = (2.2.77)

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outq heat flux to cooling medium

CM outer heat transfer coefficient WOT outer combustion chamber wall temperature

CMT temperature of cooling medium

For the piston, another term for the heat flux to the liner is taken into account.

2.2.8. Divided Combustion Chamber Indirect Injection (IDI)-Diesel engines or lean burn gas engines with ignition in a stoichiometric or even rich mixture in a pre-chamber may be modeled in BOOST with divided combustion chamber.

The combustion chamber is connected to the cylinder. For modeling the fuel or air fuel mixture feed of gas engines to the combustion chamber, pipes may be attached also to the chamber.

The energy Equation of the cylinder (Equation 2.2.1) must be modified by a term considering the energy flow associated with mass flow from the chamber to the cylinder or vice versa.

Thus 2.2.1 becomes:

( )

ddm

hd

dmhddQ

ddQ

ddVp

dumd cp

cpBB

BBwF

Cc ++= (2.2.78)

ddm

h cpcp enthalpy flow from/to the connecting pipe The concentration changes due to the flows from the chamber are:

C

CPCPcc m

dmcidcidci = ++ ,1,,1

1+Ci Concentration at time step 1+ in the Cylinder CPCi /1+ Conc. at time step 1+ in the connecting pipe

Similar extensions must be made in the energy Equation for the gas exchange.

CONNECTING PIPE MASS FLOW

With a modification of the isentropic flow equation the wall heat flow and the inertia of the gas column in a pipe are taken into account. The downstream states are the same as the pipe states, because no storage effects are taken into account.

( ) =++ 212221 21 wwdltwqhh w (2.2.79)

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223601 WA

nddm = (2.2.80)

21, hh specific enthalpies upstream/downstream

21,WW speed upstream/in the pipe

L

dltw

inertia of the gas column

wq specific wall heat

n engine speed [1/s]

2 density in the pipe flow coefficient The mass flow is obtained from:

ltwqw

TTTcpA

ddm

n

++

=

22123601

1

212 (2.2.81)

The wall heat is calculated from Equation 312.4.13.

COMBUSTION CHAMBER

The combustion chamber is treated as a plenum. Heat release, wall heat losses, volume work and mass flows out of or into the plenum are accounted for (refer to Section 2.3).

With the addition of a term for the heat released due to combustion, Equation 2.3.1 becomes:

( ) ++= d hdmed hidmiddQddQwddVpd umd eBPLPl (2.2.82)

QB ..... heat released due to combustion

The Kamel-Watson equation for the wall heat flow is based on the Nuelt-Reynolds Analogon and takes into account the swirl in the chamber.

( ) 2.053.08.0013.0 = PLPLPLPLWK rTwpL (2.2.83) PLw characteristic speed in the plenum

PLT gas temperature

PLr radius of the plenum

2iPL

PL rmTw = (2.2.84)

T torque

ir inertia radius

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( ) = dtMMT FRADD (2.2.85) ADDM added Momentum

FRM friction Momentum

cpcpcp

ADD rwdtdm

M = (2.2.86)

dtdmcp

mass flow from the connecting pipe to the chamber

cpw speed in the connecting pipe

cpr eccentricity of the connecting pipe to the center of the torque

532 PlPlPl

fFR rCM = (2.2.87)

2,01.0

Re01,0 PlPl

Plf r

sC

= (2.2.88)

2Re PlPlPl r= (2.2.89)

fC coefficient of the friction momentum

Pls swirl radius in the chamber

PlRe Reynolds Number in the chamber

Pl angular speed in the chamber

2.3. Plenum and Variable Plenum The calculation of the gas conditions in a plenum is very similar to the simulation of the gas exchange process of a cylinder, as described in Section 2.2.1:

( )

ddQ

hddm

hddm

ddQ

ddVp

dumd reac

ee

iiw

PlPl ++= (2.3.1)

Plm mass in the plenum

u specific internal energy

Plp pressure in the plenum

V plenum volume

wQ wall heat loss

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crank angle idm mass element flowing into the plenum

edm mass element flowing out of the plenum

ih enthalpy of the in-flowing mass

eh enthalpy of the mass leaving the plenum

reacQ enthalpy source due to chemical reactions

In a General Species Transport calculation chemical reactions can occur in the plenum. In

this case the term ddQreac and the species mass fractions in the plenum are calculated as

described for the cylinder (HCCI Auto-Ignition Model) in section 2.2.2.2.3.

In the case of a variable plenum, the change of the plenum volume over crank angle is calculated from the input specified by the user (user-defined), or from the motion of the piston (crankcase or scavenging pump).

Heat Transfer:

BOOST offers two options for the calculation of the gas/wall heat transfer:

(1) direct specification of the heat transfer coefficient

(2) model based specification of the heat transfer coefficient

( )42.08.0 103.1127.02.01

018.0 += TLuR chcho (2.3.2)

3 VLch =

21

ch

pipe

npipech L

Au

nu =

Lch characteristic length

V plenum volume

uch characteristic velocity

n number of pipe attachments

pipeu velocity at the pipe attachment

Apipe cross-section at the pipe attachment

T temperature in the plenum

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density in the plenum oR gas constant

ratio of specific heats

Please refer to section 2.2.7 for details on the plenum variable heat transfer model.

2.4. Pipe

2.4.1. Conservation Equations The set of conservation equations to describe a one-dimensional pipe flow is given by the well known Euler Equation:

S(U)F(U)U =+

xt

(2.4.1)

Where U represents the state vector

+

=

j

V

w

uTc

u

2

21U

(2.4.2)

and F is the flux vector

( )

++

=

jwupEupu

u

2

F (2.4.3)

with

221 uTcE V += (2.4.4)

The source term on the right hand side comprises two different source terms:

(U)S (F(U))S S(U) RA += (2.4.5) These are sources caused by axial changes in the pipe cross section

FdxdA

A= 1(F(U))SA (2.4.6)

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and sources taking into account homogeneous chemical reactions, heat and mass transfer terms between the gas and solid phase and friction sources. The entire source term is given by

=

hom .R

0

(U)S

R

iijij

w

R

rMW

VqVF

&

(2.4.7)

Please refer to the following sub-sections for details on the definition of the different source terms and for details on the solution mechanism.

2.4.1.1. Pipe Friction The wall friction force can be determined from the wall friction factor f :

uuVF fR =

hydd2

(2.4.8)

The factor is called Fanning friction factor and takes into account deviations from round channel cross sections. It has values as summarized in 41Table 21.

Table 21: Fanning Friction Factor

Channel Cross Section Round 1.00

Square 0.89

Equilateral Triangle 0.83

Sinosoidal (duct open height to open width ratio 0.425)

0.69

The friction factor f is typically described as a function of the Reynolds Number

u= hydd Re

(2.4.9)

and changes depending on the flow regime (laminar, transition or turbulent):

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+

=

==

lamturb

lamturbf,

lamturb

lamlamf,fturblam

turbf,fturb

lamf,flam

ReReReRe

ReReReRe

1|ReReRe

| ReRe| ReRe

(2.4.10)

The bounds for the transition region from laminar to turbulent are set by Reynolds numbers of Relam = 2300 and Returb = 5000. In the turbulent region, turbf , is either considered as a constant input value or can be calculated based on a specified value for the surface roughness. In the laminar region lamf , is given by

1b64aRea blamf,=

==, (2.4.11)

where a is an input value. For gas-exchange simulation b=-1 according to the Hagen-Poisseuille-Law for laminar tube flow and cannot be modified by the user.

2.4.1.2. Bended Pipes BOOST features a simple model which considers the influence of the bend of a pipe on the friction losses. The bend model increases the wall friction losses dependent on a loss coefficient, .

2

2vp = (2.4.12)

This loss coefficient is a function of the bend angle and the ratio between the bend radius and the pipe diameter. For this reason the variation of bend radius over pipe length must be specified. The bend radius is defined as the bend radius of the pipe centerline.

r

D

Figure 2-10: Pipe Bend Parameters

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Figure 2-11: Pipe Bend Loss Coefficient

This model is only valid as long as no significant flow separations occur in the pipe. In the case of a distinct flow separation, it is recommended to place a flow restriction at that location and to specify appropriate flow coefficients.

2.4.1.3. Gas-Wall Heat Transfer The convective heat transfer between the exhaust gas and the pipe wall is modeled by a Nusselt approach:

g

hydgw dNu = (2.4.13)

Based on Lienhard and Lienhard [P5] BOOST offers the following approaches for the definition of the Nusselt number:

Re-Analogy:

pg

hyd cud

Nu = 2019.0

(2.4.14)

Colburn:

8.04.0 RePr0243.0 =Nu (2.4.15)

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Pethukov:

( )210

32

64.1Relog82.11

1Pr8

7.1207.1

PrRe8

=

+

=

f

f

f

Nu (2.4.16)

Gnielinski:

( )

+

=

1Pr8

7.121

Pr1000Re8

32f

f

Nu (2.4.17)

Corrections for pulsating flow and bended pipes:

In order to take into account the influence of flow pulsations and/or pipe bends on the gas/wall heat transfer the Nusselt number is augmented by two additional factors:

BP FFNuNu = (2.4.18) PF represents an additional augmentation factor (pulsation factor taken from Wendland

[P6]) in order to consider the effect of gas pulsation given in engine exhausts. The factor

BF takes into account increased heat transfer conditions within bended pipes. Therefore the following correlation (see Liu and Hoffmanner [P7]) is used

Bhydpipe

B ddL

F += 14.0Re2

1 , (2.4.19)

where hydd is the pipe diameter, pipeL is the pipe length and Bd represents the bending radius.

2.4.1.4. Numerical Solution During the course of the numerical integration of the Euler Equation (Equ. 2.4.1) special attention should be focused on the control of the time step. In order to achieve a stable solution, the CFL criterion (stability criterion defined by Courant, Friedrichs and Lewy) must be met:

au

xt + (2.4.20)

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This means that a certain relation between the time step and the lengths of the cells must be met. BOOST determines the time step to cell size relation at the beginning of the calculation on the basis of the specified initial conditions in the pipes. However, the CFL criterion is checked every time step during the calculation.

If the criterion is not met because of significantly changed flow conditions in the pipes, the time step is reduced automatically.

An ENO scheme [41P1, P2] is used for the solution of the set of non-linear differential equations discussed above. The ENO scheme is based on a finite volume approach. This means that the solution at the end of the time step is obtained from the value at the beginning of the time step and from the fluxes over the cell borders:

Figure 2-12: Finite Volume Concept

For the approach shown in Figure 2-12, the calculation of the mass, momentum and energy fluxes over the cell borders at the middle of the time step is required. This can be done using the basic conservation equations, which give a direct relation between a gradient in the x-direction and the gradient over time.

The gradient in the x-direction is obtained by a linear reconstruction of the flow field at the beginning of the time step.

Figure 2-13: Linear Reconstruction of the Flow Field

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From this information, the mass, momentum and energy fluxes at the cell borders of each cell can be calculated. Normally the flux at the right cell border will not be equal to the flux at the left cell border of the adjacent cell, which is a necessary condition to meet continuity requirements. To overcome this problem, a Riemann-Solver is used to calculate the correct mean value from the two different fluxes at the cell border, as shown in the following figure.

Figure 2-14: Pressure Waves from Discontinuities at Cell Borders

The main advantage of an ENO scheme is that it allows the same accuracy to be achieved as can be obtained with second order accurate finite difference schemes, but has the same stability as first order accurate finite difference schemes.

2.4.2. Variable Wall Temperature In a very generic consideration, the wall of a pipe consists of opaque layers such as steel walls or insulation mats and of transparent layers representing air gaps.

Figure 2-15 sketches such a pipe consisting of three wall layers, an insulation mat and an air gap. Although this configuration may not represent real-life pipes, it shall point out the capabilities of the generic model implemented in BOOST. The main effects taking place within the pipe wall are heat transfer from the exhaust gas, heat conduction in axial and radial direction, heat radiation between the surfaces neighboring transparent layers and heat transfer to the ambient due to convection and radiation.

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Figure 2-15: Main transport effects in a pipe consisting of different wall layers

The wall energy balance equation is given by

( ) + += rTrrrxTxcTt wwlwwlwlpwlw ,,,,, 1 , (2.4.21) where wT is the temperature of the catalyst wall. r and x represent the radial and axial coordinates, respectively. Wall density wl , , wall heat capacity wlpc ,, and its thermal conductivity wl , are given within the time and space derivatives in order to consider their dependency of the temperature. All three properties are