LAMINAR BURNING SPEED MEASUREMENT, AUTOIGNITION AND

FLAME STRUCTURE STUDY OF SPHERICALLY EXPANDING FLAMES

A Dissertation Presented

by

Ali Moghaddas

to

The Department of Mechanical and Industrial Engineering

In partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in the field of

Mechanical Engineering

Northeastern University

Boston, Massachusetts

October 2015

ii

ABSTRACT

Laminar burning speed is a thermophysical property of a combustible mixture. It is a

measure of the rate of energy released during combustion in quiescent gas mixtures and

incorporates the effects of overall reaction rates, energy (heat) of combustion and energy

and mass transport rates. There are several experimental techniques to measure laminar

burning speed and they can be broadly categorized into two general categories of

stationary flames methods and those that are based on propagating flames. Investigation

of spherical flame propagation in constant volume vessels is recognized to be one of the

most accurate approaches for laminar burning speed measurement and flame structure

study.

In this thesis flame structure, laminar burning speed and onset of autoignition are studied

for different premixed combustible mixtures including n-decane, jet-fuels, and

Hydrofluorocarbon (HFC) refrigerants in air at high temperatures and pressures over a

wide range of fuel-air equivalence ratios. The experimental facilities consist of two

spherical and cylindrical vessels. The spherical vessel is used to collect pressure data to

measure the burning speed and cylindrical vessel is used to take pictures of flame

propagation with a high speed CMOS camera located in a shadowgraph system.

A thermodynamic model is employed that assumes unburned gases compress

isentropically and that burned gases are in local thermodynamic equilibrium. Burning

speed is derived from the time rate change of mass fraction of burned gases. The major

advantages of this method are that it circumvents the need for any extrapolation due to

having low stretch rates and that many data points can be collected along an isentrope in

a single experiment.

iii

Flame structures are studied to determine the cell formation conditions. Critical pressures

at which the flame becomes cellular are identified and the effects of important parameters

on cell formation are studied. Autoignition experiments are carried out for JP-8 fuels with

high initial pressures in the spherical chamber. Autoignition occurs at specific

temperature and pressure during the compression of unburned gas due to flame

propagation.

iv

ACKNOWLEDGEMENT

I would like to express my sincere appreciation and deep gratitude to my great advisor,

Professor Hameed Metghalchi, for his excellent guidance, constant encouragement, and

valuable advice during the past few years. His personal warmth, caring, patience, and

friendship have made working with him such a valuable experience for me. I could not

have imagined having a better advisor and mentor for my Ph.D study. Besides my

advisor, I am grateful to the members of my doctoral committee, Professor Yiannis

Levendis and Professor Reza Sheikhi for their support and valuable suggestions.

I would like to thank the faculty and staff at the Department of Mechanical and Industrial

Engineering at Northeastern University. I would like to thank my esteemed colleagues at

the Combustion Laboratory of Northeastern University, Dr. Mohammad Janbozorgi, Dr.

Kian Eisazadeh-Far, Mr. Emad Rokni, Mr. Casey Bennett, and Mr. Omid Askari for their

support, technical assistance and the stimulating discussions.

I would like to thank my friends in Boston who helped me through these years. Special

thanks to Nooshin Valibeig for being there when needed and for her great love and

support. Most importantly, none of this would have been possible without the love and

patience of my family. I give all my appreciation and love to my parents for their endless

support and encouragement.

v

TABLE OF CONTENTS

ABSTRACT .................................................................................................................... ii ACKNOWLEDGEMENT ............................................................................................. iv 1.  Introduction ............................................................................................................. 1 

1.1  Introduction ..................................................................................................... 2 1.2  Different techniques of laminar burning speed measurement ........................ 3 1.3  Structure of this thesis ..................................................................................... 6 1.4  Experimental setup.......................................................................................... 8 

2.  Burning speed and entropy production calculation of a transient expanding spherical laminar flame using a thermodynamic model ............................................... 13 

Abstract ..................................................................................................................... 14 2.1  Introduction ................................................................................................... 14 2.2  Theoretical model ......................................................................................... 16 2.3  Particle trajectories ........................................................................................ 27 2.4  Results and discussion .................................................................................. 29 2.5  Summary and conclusions ............................................................................ 32 

3.  Laminar burning speed measurement of premixed n-decane/air mixtures using spherically expanding flames at high temperatures and pressures ............................... 34 

Abstract ..................................................................................................................... 35 3.1  Introduction ................................................................................................... 35 3.2  Experimental setup........................................................................................ 38 3.3  Flame structure .............................................................................................. 40 3.4  Burning model .............................................................................................. 45 3.5  Results ........................................................................................................... 50 3.6  Summary and conclusion .............................................................................. 59 

4.  Measurement of laminar burning speeds and determination of onset of autoignition of Jet-A/air and JP-8/air mixtures in a constant volume spherical chamber 60 

Abstract ..................................................................................................................... 61 4.1  Introduction ................................................................................................... 61 4.2  Experimental facility ..................................................................................... 64 4.3  Burning speed model .................................................................................... 66 4.4  Results and discussion .................................................................................. 69 4.5  Summary ....................................................................................................... 78 

vi

5.  Laminar burning speeds and flame structures of mixtures of Difluoromethane (HFC-32) and 1,1-Difluoroethane (HFC-152a) with air at elevated temperatures and pressures ........................................................................................................................ 80 

Abstract ..................................................................................................................... 81 5.1  Introduction ................................................................................................... 81 5.2  Experimental facilities .................................................................................. 86 5.3  Flame structures of HFC-152a and HFC-32 ................................................. 87 5.4  Burning speed model .................................................................................... 93 5.5  Results and discussion .................................................................................. 97 5.6  Summary and conclusion ............................................................................ 106 

6.  Summary and conclusions .................................................................................. 107 6.1  Burning speed and entropy production calculation of a transient expanding spherical laminar flame using a thermodynamic model ......................................... 108 6.2  Laminar burning speed measurement of premixed n-decane/air mixtures using spherically expanding flames at high temperatures and pressures ................ 108 6.3  Measurement of laminar burning speeds and determination of onset of autoignition of Jet-A/air and JP-8/air mixtures in a constant volume spherical chamber ................................................................................................................... 109 6.4  Laminar burning speeds and flame structures of mixtures of Difluoromethane (HFC-32) and 1,1-Difluoroethane (HFC-152a) with air at elevated temperatures and pressures ..................................................................................... 110 

REFERENCES ........................................................................................................... 111 Appendix 1 .................................................................................................................. 122 Appendix 2 .................................................................................................................. 125 

1

1. Introduction

2

Laminar burning speed measurement, autoignition and flame structure

study of spherically expanding flames

1.1 Introduction

Among the important thermo-physical properties of every fuel is its laminar burning

speed. Laminar burning speed is a thermophysical property of a combustible mixture and

is defined as the speed at which a planar, one-dimensional, adiabatic flame travels

relative to the unburned gas mixture. It is a measure of the rate of energy released during

combustion in quiescent gas mixtures and incorporates the effects of overall reaction

rates, energy (heat) of combustion and energy and mass transport rates. Laminar burning

speed is also used as a primary parameter in many models of turbulent combustion,

validation of chemical kinetic mechanisms and the modeling of wall quenching

(Ferguson and Keck 1977, Keck 1982).

Propagation of spherically expanding flames in closed vessels has been subject of many

theoretical and experimental studies in the past few years. Investigation of spherical

flame propagation either in constant pressure or rising pressure regimes is recognized to

be one of the most accurate approaches for laminar burning speed measurement and

flame structure study.

3

1.2 Different techniques of laminar burning speed measurement

The experimental techniques employed in the measurement of laminar burning speed can

be broadly categorized into two general categories based on the flame type: methods that

are based on stationary flames and those that are using propagating flames. A brief

overview of the methods is given here for convenience and is not intended to be a

complete summary. Reviews of many of the different methodologies are given in the

literature such as those by Andrews and Bradley (Andrews and Bradley 1972) and Rallis

and Garforth (Rallis and Garforth 1980).

Stationary flame methods include those such as flat flame burners, nozzle burners, and

stagnation flames. In a flat flame burner, a stream of premixed gases flows into a

stationary flame and so the unburned gas speed is equal to the laminar burning speed. Flat

flame burners typically suffer from a lack of uniformity in burning speed over the surface

of the flame in addition to energy losses from the flame to the burner which makes the

accurate determination of burning speed difficult. Nozzle burner methods typically

employ Bunsen burner type flames that are conical and suffer from the same issues that

the flat flame burners do. The speed component normal to the flame surface gives the

burning speed. However the assumption of a conical flame is not a good one and the

challenge lies in determining the actual flame geometry. Another approach to measuring

burning speed is the counterflow or stagnation flame method developed by Wu and Law

(Wu and Law 1985) and used by Tsuji (Tsuji 1982) and Egolfopoulos (Egolfopoulos,

Cho et al. 1989). The method involves impinging two identical, nozzle-generated,

combustible flows onto each other. Upon ignition, two flat flames are situated

symmetrically about a stagnation plane. Reference velocities are identified in the

resulting speed profile of the counterflow and the speed gradient is determined

numerically. Laminar burning speed can be calculated by extrapolating to the point of

zero speed gradient (strain rate).

4

Propagating flame methods include flame tube method and outwardly propagating

spherical flame methods, the latter of which can be further classified into either constant

pressure approaches or constant volume approaches. The flame tube method was

pioneered by Mallard and Le Chatelier (Andrews and Bradley 1972) and consists of a

tube filled with a combustible mixture. Visualization of the flame is obtained through

photography and burning velocities are obtained from the images and frame rates. In their

experiment, a combustible mixture fills a vertical tube that is ignited from the bottom. It

assumes the flames cross-sectional geometry remains flat and uses a digital camera to

capture flame propagation. However, this approach typically suffers from wall effects

owing to quenching. At the flame perimeter, the tube walls act as a sink for the removal

of energy and active species slowing the burning speed at these points; this impacts the

assumption that the burning speed is constant across the cross-section of the tube. The

experiment also suffers from gravity effects that produce different burning velocities

depending on whether the mixture is lit from the top or bottom of the tube.

One of the outwardly propagating spherical flame methods of constant-pressure type is

the one developed by Metghalchi and Eisazadeh-Far (Eisazadeh-Far, Parsinejad et al.

2010). This approach uses a Schlieren/Shadowgraph system during the beginning stage of

combustion where the pressure can be assumed constant and assumes all species are in

local thermodynamic equilibrium, the flame kernel is a constant-mass system, and that

the kernel is spherical. The model includes losses due to radiation from plasma to

surroundings, energy loss associated with anode and cathode voltage drops, and

conduction losses to thermal boundary layers around spark electrodes. The input to the

model is the flame radius as a function of time which is captured through a special

software package.

Also in this category are the conventional constant pressure methods such as the

pressure-release vessel technique developed by Qin and Ju (Qin and Ju 2005). The

5

approach consists of a setup involving two concentric cylinders, the inner of which is an

elaborate setup of perforations, O-rings, iron plates and permanent magnets that are used

to trigger pressure-release upon ignition of mixture. A Schlieren/Shadowgraph system is

in place to capture the flame propagation. The major assumptions are that the burned gas

remains quiescent and so the moving speed of the experimentally visualized flame front

is the burned flame speed and that the unburned gas remains constant at the initial

mixture temperature. It is assumed that close to ignition, the flame speed is a function of

stretch alone and the burning speeds are obtained by extrapolating to the zero-stretch

condition (Bradley, Hicks et al. 1998, Qin and Ju 2005, Ji, You et al. 2008, Chen, Burke

et al. 2009, Chong and Hochgreb 2011, Ji, Wang et al. 2011).

In the category of the constant volume methods is the one developed by Metghalchi and

Keck (Metghalchi and Keck 1980, Metghalchi and Keck 1982). The method utilizes a

constant-volume combustion chamber in which the pressure history is recorded. A

thermodynamic model is employed that assumes unburned gases compress isentropically

and that burned gases are in local thermodynamic equilibrium. Burning speed is derived

from the time rate change of mass fraction of burned gases. This model later was

modified to account for the energy losses due to the electrodes and the vessel wall and

radiation from the burned gas to the wall as well as the temperature gradient in the

preheat zone (Parsinejad, Arcari et al. 2006, Rahim, Eisazadeh-Far et al. 2008, Far,

Parsinejad et al. 2010). The major advantages of this method are that it circumvents the

need for any extrapolation and that many data points can be collected along an isentrope

in a single experiment. In this thesis, this method of burning speed measurement has been

employed.

6

1.3 Structure of this thesis

In this thesis flame structure, laminar burning speed and onset of autoignition are studied

for different premixed combustible mixtures including n-decane, jet-fuels, and

Hydrofluorocarbon (HFC) refrigerants in air at high temperatures and pressures over a

wide range of fuel-air equivalence ratios. Experiments are performed on spherically

expanding flames in constant volume cylindrical and spherical vessels. The structure of

this thesis is based on the manuscripts resulted from the PhD research that have been

published in different journals. Each paper is represented in a separate chapter.

1.3.1. Flame structure and cell formation

Flame instability is an important issue in studying the propagating flames. There have

been many theoretical and experimental studies on hydrodynamic and diffusional-thermal

cellular instabilities in premixed flames in the past few years. One of the major

assumptions in the employed burning model in this thesis is that the flame front is

smooth. Therefore, for all of the conditions at which the burning speed experiments are

being performed, flame structures are studied to determine the cell formation conditions.

Critical pressures at which the flame becomes cellular are identified and the effects of

important parameters (flame radius, pressure, equivalence ratio,…) on cell formation are

studied (Groff 1982, Jomaas, Law et al. 2007, Yuan, Ju et al. 2007).

1.3.2. Measurement of laminar burning speed

Laminar burning speeds of different combustible mixtures are measured at high

temperatures and pressures using the thermodynamic model based on the pressure rise in

7

the spherical and cylindrical vessels. These fuels include liquid fuels such as ethanol, n-

decane, and jet-fuels as well as gaseous fuels. Experiments are conducted on HFC

refrigerants and their burning speeds - as a measure of their flammability - are

determined. Power law correlations are developed to determine the temperature and

pressure dependency of laminar burning speeds of these fuels over the range of the

experiments. In all of these studies a set of experiments are arranged with initial

conditions along an isentrope to investigate the stretch effects. Probable effects of flame

stretch on measured burning speed are studied and it is investigated if any extrapolation

to zero stretch flame is necessary.

1.3.3. Autoignition study

Autoignition experiments are carried out for JP-8 fuels with high initial pressures in the

spherical chamber. Autoignition occurs at specific temperature and pressure during the

compression of unburned gas due to flame propagation. The initial conditions are very

important since the autoignition is strongly dependent on equivalence ratio and

temperature. The autoignition process in an unburned gas mixture is a rapid process with

intense pressure fluctuations. Abnormal pressure fluctuations can be considered as a trace

of autoignition in the unburned gas zone (Heywood 1988). An abrupt rise in the pressure

during the flame propagation along with audible noise is an indicator that the charge has

autoignited. In an ideally homogeneous mixture, it can be assumed that autoignition

occurs everywhere instantaneously. In these conditions, it is assumed that the mixture is

perfectly uniform and there is no temperature, pressure or equivalence ratio gradient in

the mixture.

8

1.4 Experimental setup

1.4.1. Spherical Vessel

Burning speed measurement experiments are done in the existing spherical and

cylindrical combustion chambers. The spherical chamber consists of two hemispheric

heads bolted together to make a 15.24 cm inner diameter sphere (Figure 1). The chamber

was designed to withstand pressures up to 425 atm and is fitted with ports for spark

electrodes, diagnostic probes, and ports for filling and evacuating it. A thermocouple

inserted in one of the chamber ports is used to check the initial temperature of the gas

inside the chamber. A Kistler 603B1 piezo-electric pressure transducer with a Kistler

5010B charge amplifier is used to obtain dynamic pressure data from which the laminar

burning speed is determined. Ionization probes mounted flush with the wall located at the

top and bottom of the chambers are used to measure the arrival time of the flame at the

wall and to check for spherical symmetry and buoyant rise.

The spherical chamber is housed in an oven which can be heated up to 500 K. Liquid fuel

is stored in a 115 cc heated chamber and is transferred through a heated line (500 K) to

the spherical chamber in the oven. Several thermocouples are located on the line from the

fuel reservoir to the chamber to monitor temperature of the fuel passageway. A heated

strain gauge (Kulite XTE-190) in the oven is used to measure partial pressure of fuel in

the chamber.

9

Figure 1: the sketch of the spherical vessel

1.4.2. Cylindrical Vessel

The cylindrical vessel is made of SAE4140 steel with an inner diameter and length of

133.35 mm. The two end windows are 35 mm thick Fused-silica with a high durability

against pressure and temperature shocks as well as having very good optical properties.

This vessel is used to measure pressure rise due to combustion process and to permit

optical observation of the flame shape and structure. Two band heaters and a rope heater

wrapped around the cylindrical chamber are used to heat up the chamber to 500 K. This

chamber is equipped with a heated liquid fuel line system, a pressure strain gauge and

thermocouples similar to the spherical chamber. A Z-type Schlieren/Shadowgraph

ensemble has been set up to visualize the flame propagation (Figure 2). The light source

for the optical system is a 10-Watt Halogen lamp with a condensing lens and a small

pinhole of 0.3 mm in diameter, which provides a sharp and intense illumination

10

throughout the whole system. Two aluminized spherical mirrors with 1/8 wavelength

surface accuracy, over-coated with silicon monoxide and mounted in metal-stands with a

diameter of 152.4 mm and focal length of 1524 mm, are placed on two sides of the

chamber. A high speed CMOS camera (1108-0014, Redlake Inc.) with a capture rate of

up to 40,000 frames per second is placed very close to the focal point of the second

mirror. The capture rate and shutter speed of the camera are optimized depending on the

burning speed of the mixture and the brightness of the flame. Figure 3 shows the

configuration of the shadowgraph system.

Figure 2: Z-type Schlieren/Shadowgraph ensemble with a high speed CMOS camera.

11

Figure 3: Configuration of the optical and shadowgraph system

Figure 4 shows a comparison between the pressure rise during the propagation of

ethanol/air flame in cylindrical and spherical vessels. It can be seen that the pressure rise

signals are identical in both vessels before the flame touches the wall in the cylindrical

vessel (Point A). When flame arrives to the wall in the cylindrical vessel, energy losses to

the wall reduce rate of pressure rise in the cylindrical vessel. In this study, laminar

burning speeds are measured only up to point A.

12

Figure 4: Comparison of pressure rise during the propagation of ethanol/air flame in

cylindrical and spherical vessels.

13

2. Burning speed and entropy production calculation of a

transient expanding spherical laminar flame using a

thermodynamic model

Appeared in Entropy 12 (2010) 2485-2496

K. Eisazadeh-Far, A. Moghaddas, F. Rahim, H. Metghalchi

14

Burning speed and entropy production calculation of a transient

expanding spherical laminar flame using a thermodynamic model

Abstract

A thermodynamic model has been developed to calculate burning speed and entropy

production of transient expending spherical laminar flame in an enclosed vessel. The

model also predicts the particle trajectories of both unburned and burned gases in the

vessel. The input to this model is the dynamic pressure rise due to combustion process.

The unburned gases are divided into three regions: The core unburned gases which are

compressed isentropically, the vessel walls and electrodes boundary layer gases, and

gases in the preheat zone of the flames. The burned gases are in many shells having the

same pressure but different temperatures. The model also includes radiation losses from

the burned gases to vessel walls. Entropy production due to irreversibility has been

calculated by applying entropy balance to the gas mixtures. Burning speed of premixed n-

decane air mixture has been reported for temperatures and pressures along an isentrope.

2.1 Introduction

The definition of a flame needs more detailed clarification which is due to the manner of

fuel/oxidizer mixing. In some combustors fuel and oxidizer are initially separated

spatially. This means that the mixing process is slow before chemical reactions and

mixing processes occur in chemical reaction sheet. This mixture and the consequent

flame is non-premixed or diffusion. If fuel and oxidizer are mixed and initiation of

chemical reactions is achieved in a combustible mixture, the consequent flame is

15

premixed. In a premixed flame reactants enter the flame through the preheat zone and in a

thin layer, which is called reaction zone, chemical reactions take place and combustion

products leave the flame. At each zone the balancing factors are different, for example in

preheat zone the convection of reactants are balanced by energy and mass diffusion from

the reaction zone and in reaction zone the reaction source term is balanced with energy

and mass diffusion to preheat zone. In premixed flames, an external energy source is

usually required to initiate the flame. It can be a spark, high energy laser, surface plasma,

hot spots, etc. No matter what the source of ignition is, a self-sustaining wave of an

exothermic reaction propagates throughout the combustible mixture. Propagation speed

of premixed flame is strongly a function of burning rate of the mixture which is called

laminar burning speed in combustion community. The term of laminar emphasizes that

the flame should be absolutely smooth and the propagation of the wave is only derived by

chemical reactions and transport phenomena. Laminar burning speed is a function of

temperature, pressure and composition of the mixture. At a given temperature, pressure

and fixed composition of mixture, there is a unique value of laminar burning speed which

is a property of the mixture. More details about the theory of flame and its formation and

propagation can be found in (Eisazadeh-Far, Parsinejad et al. 2010, Janbozorgi, Far et al.

2010).

Laminar burning speed of fuel/air mixtures are required both in theoretical and practical

studies. It is needed to validate chemical kinetics mechanisms of combustion of fuel air

mixtures. It is also needed in turbulent flame speed correlations in burners and internal

combustion engines. There are several techniques for the measurement of laminar

burning speed which can be found in (Metghalchi and Keck 1982, Tseng, Ismail et al.

1993, Hunter, Wang et al. 1994, Davis, Law et al. 1998, Ma and Chomiak 1998, Dyakov,

Konnov et al. 2001, Konnov and Dyakov 2004, Jerzembeck, Matalon et al. 2009,

Tahtouh, Halter et al. 2009). In this paper we report a thermodynamic model to calculate

16

burning speed of fuel/air mixtures. The model also calculates entropy production due to

chemical reaction and predicts the location of gas particles in the vessel.

2.2 Theoretical model

Figure 1 shows the snapshots of a transient expanding spherical laminar flame in an

enclosed vessel.

p/pi=1.02 p/pi=1.16 p/pi=1.93

Figure 1. Snapshots of a typical propagating spherical flame.

The thermodynamic model which has been developed uses the dynamic pressure rise of

the combustion process to calculate burning speed of the fuel air mixture. The details of

experimental facilities and systems to do the measurements can be found in previous

publications (Parsinejad, Arcari et al. 2006, Rahim, Eisazadeh-Far et al. 2008, Far,

Parsinejad et al. 2010, Eisazadeh-Far, Moghaddas et al. 2011). In this model, it is

assumed that gases in the combustion chamber can be divided into burned and unburned

regions separated by a pre-heat and a reaction zones as shown schematically in Figure 2.

It is further assumed that: the burned and unburned gases are ideal, the burned gas is in

chemical equilibrium, the unburned gas composition is frozen, the pressure throughout

17

the chamber is uniform, compression of both burned and unburned gases is isentropic.

For the conditions of interest in the present work, all these assumptions have been

validated by numerous experiments in constant volume chambers and internal

combustion engines carried out over the past several decades (Janbozorgi, Far et al.

2010).

Figure 2. Schematic of different zones and their corresponding temperatures in the

thermodynamics model.

18

2.2.1. Burned gas mass fraction, temperature and other thermodynamic

properties

For spherical flames, the temperature distribution of the gases in the combustion chamber

and the burned gas mass fraction can be determined from the measured pressure using the

equations for conservation of volume and energy together with the ideal gas equation of

state:

RTpv (1)

where p is the pressure, v is the specific volume, R is the specific gas constant and T is

the temperature.

The mass conservation equation is:

m = mb + mu = pi(Vc − Ve)/RTi (2)

where m is the mass of gas in the combustion chamber, mb is the burned gas mass, mu is

the unburned gas mass, Vc is the volume of the combustion chamber, Ve is the electrode

volume, and the subscript i denotes initial conditions.

The total volume of the gas in the combustion chamber is:

Vc − Ve = Vb + Vu (3)

where:

bb m

ebbs

m

b VdmvvdmV00 (4)

19

Vb is the volume of the burned gas, vbs is the specific volume of isentropically

compressed burned gas:

dmvvVbm

bseb )(0

(5)

Veb is the displacement volume of the electrode boundary layers:

(1 )b

m

u b us wb ph

m

V vdm m x v V V (6)

Vu is the volume of the unburned gas, xb = mb/m is the burned gas mass fraction, vub is the

specific volume of isentropically compressed unburned gas:

dmvvVwb

uswb )( (7)

Vwb is the displacement volume of the wall boundary layer:

dmvvVph

usph )( (8)

Vph is the displacement volume of the preheat zone ahead of the reaction layer.

The energy conservation equation is:

E − Qw − Qe − Qr = Eb + Eu (9)

20

where E is the initial energy of the unburned gas, Qw is the conduction heat loss to the

wall, Qe is the conduction heat loss to the electrodes, Qr is the heat loss due to radiation

from the burned gas:

eb

m

bs

m

b EdmeedmEbb

00 (10)

Eb is the energy of the burned gas, ebs is the specific energy of isentropically compressed

burned gas:

bm

bseb dmeeE0

)( (11)

Eeb is the energy defect of the electrode boundary layer:

phwbusb

m

m

u EEexmedmEb

)1(

(12)

Eu is the energy of the unburned gas, eus is the specific energy of isentropically

compressed unburned gas:

wb

uswb dmeeE )( (13)

Ewb is the energy defect of the wall boundary:

ph

usph dmeeE )(

(14)

21

Eph is the energy defect of the preheat layer.

Using the perfect gas relation:

e − hf = pv/( − 1) (15)

where hf is the specific enthalpy of formation of the gas at zero degrees Kelvin and =

cp/cv is the ratio of the constant pressure and constant volume specific heats, and

assuming constant specific heats for the gases in the boundary layers and the preheat

zone, the integrals in Equations (11), (13) and (14) may be evaluated approximately to

give:

)1/()1/()( bebb

eb

bseb pVdmvvpE (16)

)1/()1/()( uwbu

wb

uswb pVdmvvpE (17)

)1/()1/()( uphu

ph

usph pVdmvvpE (18)

A relationship between the wall heat transfer and the displacement volume for a gas

subject to a time dependent pressure has been derived by Keck (Keck 1981). In the case

of rapidly increasing pressure such as that occurring during constant volume combustion,

the terms representing compression work on the boundary layer may be neglected and

resulting equations are:

Qe = pVeb/(b − 1) = Eeb (19)

Qw = pVwb/(u − 1) = Ewb (20)

22

in which we have used Equations (16) and (17). Note that, to this approximation, the heat

loss to the wall exactly equals the energy defect in the boundary layer. Substituting the

relation dm = dV into Equations (5), (7) and (8) we obtain:

Veb = 2rerbeb (21)

Vwb = 4rc2wb (22)

Vph = 4rb2ph (23)

where re is the radius of the electrodes, rb is the radius of the burned gas, rc is the radius

of the combustion chamber:

br

0 0 bbseb rdrd1r /)/),(( (24)

eb is the displacement thickness of the electrode boundary layer in which is the radial

distance from the electrode:

drrwb

uswb )1/)(( (25)

wb is the displacement thickness of the wall boundary layer, and:

drrph

usph )1/)(( (26)

ph is the displacement thickness of the preheat zone. Using the approximation:

)1/()/)(()1/),(( 2/1 wbbb

eb

bbs TTrrrdr (27)

23

Equation (24) can be integrated over r to give:

)1/()/)(3/2( 2/1 wbbbbeb TTrr (28)

where b is the thermal diffusivity of the burned gas, Tw is the wall temperature, and Tb is

the burned gas temperature.

The wall boundary layer displacement thickness can be calculated using the expression

derived by Keck (Keck 1981):

zdzdzzzzz z

z

uwb

0

2/1/1/12/1 ))(()(

(29)

where u is the thermal diffusivity of the unburned gas, is a characteristic burning time,

y = t/ is the dimensionless time, and z = p/pi is the dimensionless pressure. For

combustion in closed chambers, the dimensionless pressure can be approximated by:

z = 1 + y3 (30)

Substituting this expression in Equation (29) we obtain:

1/ 2 1/ 2 (1 1/ )/ / / 1u

wb u i it p p p p

(31)

The displacement thickness of the preheat zone has been evaluated assuming an

exponential temperature profile:

)(/)/)(exp()1/(1/ rrrrTTTT usbbuubu (32)

Substituting Equation (32) into Equation (26) we obtain:

24

ph

bubbubph drrrrrrTT 211 )/()1)/)exp()1/((

(33)

bu rr / , Equation (33) can be integrated approximately to give:

)/ln()1/)(/( ububbuph TTTTr (34)

Note that the displacement thickness of the preheat zone is negative while those of the

thermal boundary layers are positive.

The radiation heat loss from the burned gas was calculated using:

t

rr dtQQ0

'

(35)

where:

4bbpr TVQ

(36)

is the radiation rate, p is the Planck mean absorption coefficient and is the Stefan-

Boltzman constant. Finally combining Equations (3), (4) and (6) gives:

bx

phwbebusiusbs mVVVvvdxvv0

/)()( (37)

and combining Equations (9), (10), (12) and (18)–(20) gives:

bx

ruwbbebuphusiusbs mQpVpVpVeedxee0

/))1/()1/()1/(()(

(38)

25

where vi = (Vc − Ve)/m and ei = Ei/m are the initial specific volume and energy of the

unburned gas in the chamber.

Equations (37) and (38) contain the three unknowns p, xb(p), and Tb(xb). Given pressure,

p(t), as a function of time, they can be solved numerically using the method of shells to

obtain the burned mass fraction, xb(t), as a function of time and the radial temperature

distribution T(r,t). The mass burning rate, bb xmm , can be obtained by numerical

differentiation of xb(t). The thermodynamic properties of the burned and unburned used

in the calculations were obtained from the JANAF Tables (Chase 1986).

Total entropy production throughout the process is:

t

w

r

e

e

w

wtprod dt

T

Q

T

Q

T

QSSS

00 )(

(39)

prodS is the entropy produced during the combustion process, tS is the total entropy at t,

0S is the initial entropy, Tw is the wall temperature and Te is the electrode temperature.

2.2.2. Burning speed and flame speed

For closed flames, the burning speed may be defined:

bubb AmS / (40)

where Ab is the area of a sphere having a volume equal to that of the burned gas. This

expression is valid for smooth, cracked, or wrinkled flames of any shape. For smooth

spherical flames:

26

bbbbbb rAVm (41)

where b is the average value of the burned gas density.

Differentiating the mass balance equation:

mb = m − uVu = m − (u/b)b(Vc − Ve − Vb) (42)

with respect to time and neglecting the small contribution from the derivative of u/b,

we obtain:

))()(/( bbecbbbbub VVVrAm (43)

where:

Ab = 4rb2 − 2re

2 (44)

is area of the reaction zone, re is the electrode radius and rb is given by the equation:

Vb = (4/3)rb3 − 2re

2rb (45)

Using Equation (41) to eliminate b in Equation (43), gives:

))1/(/( bubbubbf ySrS (46)

where Sf is the flame speed and yb = Vb/(Vc − Ve) is the burned gas volume fraction. Note

that for yb = 0, Sf = (u/b)Sb and for yb = 1, Sf = Sb.

27

2.3 Particle trajectories

Assuming that unburned gas is compressed isentropically, the unburned gas particle

trajectories can be calculated using the following equations:

u

P

P

rr

rr

V

V

gc

ugc

u

ut1

03

03

33

0

(47)

where utV is the volume of the unburned gas at time t, 0uV is the volume of unburned gas

at time zero, ugr is the location of an unburned gas particle at time t, 0gr is the location of

an unburned gas particle at time zero, and P0 is the initial pressure of the mixture.

Equation (47) can be rewritten as:

3

11

0

3

011

u

P

P

r

r

r

r

c

g

c

ug

(48)

After the particles is burned it would be pushed back towards the center, because of the

compression and it will asymptotically go to its original location. The burned gas

particles trajectories can be calculated using the following equations, using the isentropic

compression relation:

bb

bgbb PVVP (49)

3

bt

bg

bt

bg

r

r

V

V

(50)

28

where bgV is the volume of the burned gas at time t, Vbt is the volume of burned gas at the

time the gas particle burned, Pb is the pressure of the mixture at the time the particle

burned, rbg is the location of a burned gas particle at time t and rbt is the location of a

burned gas particle at the time it burned. Figure 3 shows trajectories of unburned gases

throughout the process. It can be seen that unburned gas is pushed toward vessel walls

before flame catches up. It then goes back toward its original location by being

compressed after combustion.

Figure 3. Gas particles and flame front trajectories.

29

2.4 Results and discussion

Figure 4 shows the laminar burning speeds of stoichiometric n-decane-air mixture versus

temperature at atmospheric pressure.

Figure 4. Laminar burning speed (Sb) curves for stoichiometric n-decane/air mixtures as a

function of temperature, P = 1 atm.

It can be observed that increasing the temperature, increases the laminar burning speed.

The reason for this is the activation of chemical reactions by temperature. Figure 5 shows

the comparison of results with other researchers. It can be seen that the data are in good

agreement with other results. This figure also shows the laminar burning speed at higher

temperature (600 K) and again presents that the laminar burning speed is strongly

dependent on temperature.

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

400 450 500 550 600 65060

70

80

90

100

110

120

130

140

150

160

30

Figure 5. Laminar burning speeds of n-decane/air mixture and its comparison with other

researchers (Skjøth-Rasmussen, Braun-Unkhoff et al. 2003, Kumar and Sung 2007).

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

0.6 0.7 0.8 0.9 1 1.140

50

60

70

80

90

100

110

120

130

140

150

Kumar and Sung [18]Rasmussen et al [19]Present study

600 K

473 K

31

Figure 6 presents the entropy produced throughout the combustion process for the

stoichiometric n-decane air mixtures.

Figure 6. Entropy production as a function of time for stoichiometric n-decane/air

mixture at Pi=1 atm, Ti = 420 K.

This figure demonstrates that entropy increases during the combustion process

dramatically. This figure proves that combustion process is extremely irreversible due to

chemical reactions. Another source of irreversibility is the mass transport phenomenon

within the flame which is a major source of entropy generation at premixed flames

(BERETTA and KECK 1983). Figure 7 shows that the rate of entropy production

increases as the flame propagates.

Time (ms)

En

tro

py

Pro

du

ctio

n(k

J/K

)

0 5 10 15 20 250.011

0.012

0.013

0.014

0.015

32

Figure 7. Entropy production rate for stoichiometric n-decane/air mixture

at Pi = 1 atm, Ti=420K.

2.5 Summary and conclusions

A complicated thermodynamic model to calculate laminar burning speeds and entropy

production of a premixed spherical laminar flame is presented. Laminar burning speeds

of n-decane/air mixtures were calculated from the dynamic pressure rise of a combustion

process and it was observed laminar burning speed increases as temperature of the

unburned mixture rises. The results of calculated values were compared with other

published data and were in excellent agreement. Total entropy production and the rate of

entropy production were also calculated. It was observed that combustion process is a

highly irreversible process. Particle trajectories of the gas mixture in the vessel were also

determined.

Time (ms)

En

tro

py

Pro

du

ctio

nR

ate

(kJ/

K.s

)

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

33

Acknowledgement

This research has been done with the support of the Office of Naval Research (ONR)

grant number 369N00010-09-1-0479 under technical monitoring of Gabriel Roy. The

authors are sincerely indebted to the late James C Keck (1924–2010) from MIT for

scientific discussions and his fundamental support over the past years.

34

3. Laminar burning speed measurement of premixed n-

decane/air mixtures using spherically expanding flames at

high temperatures and pressures

Appeared in Combustion and Flame 159 (2012) 1437–1443

A. Moghaddas, K. Eisazadeh-Far, H. Metghalchi

35

Laminar burning speed measurement of premixed n-decane/air

mixtures using spherically expanding flames at high temperatures and

pressures

Abstract

Normal-decane (n-C10H22) is regarded as a major component of possible surrogates for jet

fuels and diesel fuels. The structure of spherically expanding premixed n-decane/air

flames has been studied at high temperatures and pressures. The laminar burning speeds

of n-decane/air mixtures have been measured for the temperatures of 350 K to 610 K and

pressures of 0.5 to 8 atm. The experiments were performed in lean conditions (0.7≤

≤1). Laminar burning speed was measured using a thermodynamic model based on the

pressure rise during the flame propagation in constant volume vessels. A cylindrical

vessel equipped with a high speed CMOS camera was employed to investigate the flame

structure and a spherical vessel was used for the burning speed measurements. The results

are in good agreement with other experimental data available in the published literature.

3.1 Introduction

Developing surrogates for complex fuels such as jet and diesel fuels is one of the most

important steps in developing the chemical kinetic mechanisms for these fuels (Dagaut,

El Bakali et al. 2006, Humer, Frassoldati et al. 2007, Honnet, Seshadri et al. 2009,

Kurman, Natelson et al. 2011, Pitz and Mueller 2011). Jet and diesel fuels are composed

of many chemical components including straight and branched chain alkanes,

36

cycloalkanes, aromatics and alkenes. The most prominent molecules in the category of

alkanes are the ones with large carbon numbers (C9- C

16). n-Decane (n-C10H22) is an

alkane with large carbon number and it is suggested by many researchers as a major

component in the surrogates for jet and diesel fuels (Agosta, Cernansky et al. 2004,

Dagaut and Cathonnet 2006, Smith and Bruno 2007, Won, Sun et al. 2010, Naik,

Puduppakkam et al. 2011, Seiser, Niemann et al. 2011, Jahangirian, Dooley et al. 2012).

Chemical kinetics mechanism validation of n-decane needs accurate and reliable

experimental data. Laminar burning speed is a valuable type of experimental data that can

be used in this regard. It is one of the fundamental thermo-physical properties of each

fuel/air mixture and is defined as the speed relative to the unburned gas at which a planar,

one-dimensional flame front travels along the normal to its surface (Metghalchi and Keck

1980, Chen, Burke et al. 2009, Eisazadeh-Far, Moghaddas et al. 2011). A number of

studies have been done to measure the laminar burning speed of n-decane/air mixtures,

mostly at atmospheric pressure. Zhao et al. (Zhao, Li et al. 2004) in an experimental

study determined the laminar burning speed of atmospheric n-decane/air flames at 500 K

using the stagnation jet-wall flame configuration. Kumar et al. (Kumar and Sung 2007,

Kumar, Sung et al. 2011) measured the laminar flame speeds of n-decane/air mixtures at

unburned gas temperatures of 360 K to 500 K and atmospheric pressure using a counter-

flow twin-flame. Ji et al. (Ji, Dames et al. 2010) reported laminar burning speed of n-

decane/air flames at atmospheric pressure and elevated unburned gas temperature.

Nevertheless, there are no existing experimental data of laminar burning speed of n-

decane/air flames at pressures greater than atmospheric pressure. Therefore, further

experimental laminar burning speed data is needed to improve chemical kinetic modeling

of n-decane at high temperatures and pressures.

37

Some discrepancies exist among the burning speed data of different researchers which are

attributed to the flame stretch effect and experimental errors. Chen et al (Chen, Burke et

al. 2009) comprehensively investigated the inaccuracy caused by different stretch rates on

determination of laminar burning speed in spherically propagating flames. They found

the threshold values of stretch rates beyond which considerable deviation from zero

stretch burning speed would appear. In the current study, the laminar burning speeds have

been measured at radii larger than 4 cm which have very low stretch rates. In addition, a

careful study has been performed to investigate the probable effects of stretch rates on

measured burning speed. Another advantage of current study in comparison to other

spherical expanding flame techniques that use schlieren photography is the modeling of

burned gas compression. Burke et al. (Burke, Chen et al. 2009) investigated the effects of

cylindrical confinement on determination of laminar flame speeds of outwardly

propagating flames. They concluded that burned gas cannot be assumed to be quiescent

especially at large radii. In this study, burned gas compression is inherently embedded in

the thermodynamic model.

In the present work, experiments have been performed in both spherical and cylindrical

chambers. The cylindrical vessel with optical access has been used to study the structure

of the flame including cell formation. Burning speed measurements have only been

reported for smooth and laminar flames. Laminar burning speeds of lean n-decane/air

mixtures (0.7≤ ≤1) have been measured using a modified thermodynamic model based

on the pressure rise during spherical flame propagation in a constant volume spherical

chamber. The important feature of the spherical chamber in the burning speed

measurement is the minimization of chamber confinement effects on spherical symmetry.

A correlation for laminar burning speed has been developed over the temperature range

of 350 K to 610 K and pressures of 0.5 to 8 atm using a nonlinear least square method. A

38

comparison has been made between our results and available experimental data at

atmospheric conditions.

3.2 Experimental setup

Experiments were performed in constant volume spherical and cylindrical vessels. Figure

1 shows the general configuration of the experimental setup. Spherical and cylindrical

vessels have inner diameters of 15.24 cm and 13.5 cm, respectively. Both chambers are

equipped with fast response piezoelectric pressure transducers installed in their walls to

measure the pressure during the flame propagation. The cylindrical vessel is considered

to withstand a maximum pressure of 50 atm due to having two large 3.5 cm thick fused

silica windows, while the spherical vessel could be used for pressures up to 400 atm.

Both vessels are fitted with two extended spark plug electrodes which provide a central

point ignition source for the chambers. The vessels are equipped with the heaters capable

of elevating the initial temperature up to 500 K.

39

Fig. 1: Experimental setup

The cylindrical vessel is installed in a shadowgraph system giving the advantage of

allowing pictures to be taken during the flame propagation. A detailed description of

shadowgraph facility can be found in Parsinejad et al. (Parsinejad, Keck et al. 2007).

Figure 2 shows a schematic of the shadowgraph system. A CMOS camera with the

capability of taking pictures up to 40,000 frames per second is used for these

experiments. Three ionization probes are installed in the spherical chamber wall to

determine flame arrival time to the wall and prove the flame spherical symmetry. A data

acquisition system is used to capture the pressure-time data as well as the signals from

ionization probes. A computer driven system is used to make the mixture with the

required fuel and oxidizer and to initiate the combustion process. n-Decane is stored in a

liquid fuel reservoir which is attached to a liquid fuel manifold. The liquid fuel manifold

is equipped with two cartridge heaters to evaporate the liquid fuel before entering the

40

combustion chamber. The partial pressure of the fuel vapor is measured by a Kulite

pressure transducer. The method of partial pressures is used to set the initial fuel air

equivalence ratio and the accuracy of this method is verified using gas chromatography.

Fig. 2: Sketch of the shadowgraph system

3.3 Flame structure

As it is necessary to verify the flame smoothness for the laminar burning speed

measurement, the experiments were first performed in the cylindrical vessel and then in

the spherical vessel. Figure 3 shows the comparison between pressure rise in cylindrical

and spherical vessels. It can be seen that pressure rise profiles in both vessels are identical

until the flame touches the wall in the cylindrical vessel. Therefore, the flame structure in

the cylindrical vessel could be a correct indication of flame structure in the spherical

vessel.

41

Fig. 3: Comparison of the pressure rise in spherical and cylindrical vessels for n-

decane/air, Ti = 420 K, Pi = 1 atm, =1

Figure 4 shows snapshots of n-decane/air premixed flames for a range of lean

equivalence ratios. For all of these mixtures, initial temperature and pressure were fixed

at 420 K and 1 atm, respectively. It can be seen that in these conditions flame remains

fairly smooth throughout the propagation towards the vessel wall. Previous studies with

similar heavy hydrocarbon fuels (Far, Parsinejad et al. 2010, Eisazadeh-Far, Moghaddas

et al. 2011) showed that increasing the equivalence ratio (enriching the mixture with fuel)

causes the flame instability. A few wrinkles appeared at large radii of flame propagation

in the stoichiometric condition, which are evidence of spiral instability.

Time (ms)

Pre

ssu

re(a

tm)

0 20 40 60 800

2

4

6

8

spherical vesselcylindrical vessel

flame arrival at cylindricalvessel wall

42

Fig. 4: Snapshots of n-decane/air flames at and different equivalence ratios, Ti= 420 K,

Pi= 1 atm

43

Figure 5 shows a comparison of the flame structure of stoichiometric n-decane/air flames

with different initial conditions. Initial temperature and pressure of these mixtures are

selected along an isentrope. Cell formation is strongly a function of pressure, flame

radius, equivalence ratio and fuel type (Eisazadeh-Far, Moghaddas et al. 2011). High

curvature-induced stretch suppresses instabilities at small flame radii. As it is seen in the

pictures, at higher pressures flame cellularity happens at lower radii. Flame thickness

decreases at high pressures, which reduces flame resistance to perturbations (Jomaas,

Law et al. 2007, Yuan, Ju et al. 2007). Different sources impose disturbances into the

flame such as density gradient, stoichiometric gradient, and interaction with electrodes. If

the growth rate of these disturbances is greater than the flame growth rate it would cause

flame instability.

44

Fig. 5: Snapshots of n-decane/air flames at stoichiometric condition and different initial

pressures and temperatures

Laminar premixed flames are subjected to different modes of cellular instability. The

type of instability depends on the mechanism which causes the disturbances. Diffusional-

45

thermal instability occurs as a result of non-equidiffusive properties and arises when

gases have lower heat diffusivity than mass diffusivity (Lewis number less than unity)

(Groff 1982, Jomaas, Law et al. 2007, Yuan, Ju et al. 2007). The Lewis number of lean

heavy hydrocarbon-air mixtures is larger than unity (Eisazadeh-Far, Moghaddas et al.

2011) which suggests that the instabilities observed in our experiments cannot be

diffusional-thermal. Another type of instability is hydrodynamic instability which arises

as a result of disturbances associated with thermal expansion ( ) across the flame.

The latter is recognized to be the source of instabilities in these experiments. Detailed

analysis of instability is beyond the scope of this paper and more information can be

found in other studies (Groff 1982, Bradley and Harper 1994, Larson, Williams et al.

2001, Kwon, Rozenchan et al. 2002, Jomaas, Law et al. 2007, Yuan, Ju et al. 2007).

3.4 Burning model

A thermodynamic model was used to calculate laminar burning speed based on the

pressure rise during spherical propagation of flame inside constant volume chambers.

This model was originally developed by Metghalchi and Keck (Metghalchi and Keck

1980, Metghalchi and Keck 1982) and later was modified to account for the energy losses

due to the electrodes and the vessel wall and radiation from the burned gas to the wall as

well as the temperature gradient in the preheat zone (Eisazadeh-Far, Moghaddas et al.

2010). It is assumed that gases in the combustion chamber can be divided into burned and

unburned gas regions separated by a reaction layer of negligible thickness. Moreover,

burned and unburned gases are ideal, pressure throughout the chamber is uniform, and

compression of both burned and unburned gases is isentropic.

bu /

46

Furthermore, burned gas in the center of chamber is divided into a number of shells

which the number of shells is proportional to the combustion duration. Burned gas

temperature in each shell is different but all burned gases are in chemical equilibrium

with each other. STANJAN is used to find the equilibrium states of the burned gases.

Thermodynamic properties of some species were calculated using the model developed

by Hui et al. (He, Metghalchi et al. 1999, He, Metghalchi et al. 2000). Burned gases are

surrounded by a preheat zone ( ) having variable temperature, which is itself

surrounded by unburned gases. A thermal boundary layer ( ) separates the unburned

gas from the wall. The effect of energy transfer from the burned gas to the spark

electrodes is taken into account by a thermal boundary layer ( ). Figure 6 shows a

schematic of the model used in this work.

47

Fig. 6: Schematic of different zones and their corresponding temperatures in the

thermodynamic model

The equation of state, volume and energy equations will be solved simultaneously:

(1) RTPv

48

where P is the pressure, v is the specific volume, R is the specific gas constant ( )

and T is the temperature. Pressure is an input to this equation which is measured in the

experiments. The mass conservation equation for the burned and unburned gas regions is:

(2)

where m is the total mass inside the chamber, mb is the mass of the burned gas zone; mu is

the mass of the unburned gas zone. Vc is the volume of the chamber and Ve is the volume

of the spark electrodes. In this equation, subscript i denotes the initial conditions, and

subscripts u and b denote the unburned and burned gas conditions, respectively. The total

volume of the gas in the combustion chamber is:

(3)

And the energy conservation equation is:

(4)

where Ei is the initial energy of the gas, Qe is the conductive energy loss to the electrodes,

Qw is the energy loss to the wall, Qr is the radiation energy loss. By using the

thermodynamic assumptions described in Eisazadeh-Far et al. (Eisazadeh-Far,

Moghaddas et al. 2010), volume (mass balance) and energy balance equations will be:

(5)

(6)

MR /

ieciub RTVVPmmm /)(

ubeci VVVVV

ubrwei EEQQQE

bx

phwbebusiusbs mVVVvvdxvv0

/)()(

bx

ruwbbebuphusiusbs mQPVPVPVeedxee0

/))1/()1/()1/(()(

49

where and are the initial specific volume and specific energy

of the unburned gas in the chamber, is the specific volume of isentropically

compressed burned gas, is the specific volume of isentropically compressed unburned

gas. , and are displacement volume of wall boundary layer, displacement

volume of preheat zone ahead of the reaction layer and displacement volume of electrode

boundary layer, respectively. , , and are the specific energy of isentropically

compressed burned gas, specific energy of isentropically compressed unburned gas and

specific heat ratio of unburned gas, respectively. The above equations will be solved for

two unknowns: burned gas mass fraction and the burned gas temperature of the last shell.

Having pressure as a function of time (measured in the experiments), they can be solved

numerically to obtain the burned gas mass fraction and radial temperature

distribution , .

Ultimately, laminar burning speed may be defined as:

(7)

Where is the area of the sphere having a volume equal to that of the burned gas. More

details of the burning model can be found in previous publications (Elia, Ulinski et al.

2001, Rahim, Elia et al. 2002, Parsinejad, Arcari et al. 2006, Rahim, Eisazadeh-Far et al.

2008, Eisazadeh-Far, Moghaddas et al. 2010).

mVVv eci /)( mEe ii /

bubbubu AxmAmS //

bA

50

3.5 Results

3.5.1. Flame stretch considerations

Flame stretch is a phenomenon caused by the variation of flame area over time. The value

of stretched burning speed is different from zero-stretch laminar burning speed. As it is

extremely difficult to achieve zero-stretched laminar flame, zero stretch laminar burning

speed is estimated by extrapolating the stretched burning speeds to zero stretch (Ji,

Dames et al. 2010, Kumar, Sung et al. 2011). The extrapolation process is regarded as

one of the major sources of discrepancies among laminar burning speed data reported

from different researchers. Various linear and nonlinear extrapolations have been

developed to measure zero stretch laminar burning speed (Bradley, Hicks et al. 1998, Qin

and Ju 2005, Ji, You et al. 2008, Chong and Hochgreb 2011, Ji, Wang et al. 2011). In this

study laminar burning speed is measured at very low stretch rates to minimize the effects.

For spherically expanding flames, stretch rate can be defined as:

(8)

Where is the stretch rate, A is the flame area, t is time, and r is the radius of the flame.

This is a measure of variation of flame area versus time. Depending on the conditions,

stretch can affect the laminar burning speed values. Chen et al. (Chen, Burke et al. 2009)

proposed stretch-corrected flame speed for spherically propagating flames in constant

volume chambers. They found that stretch effect is inversely proportional to flame size.

Also, it was shown that if the pressure rise is more than 20% (P/P0 > 1.2), laminar

burning speed values can approximate the zero stretch ones accurately. It is seen from

equation (8) that as the radius of flame increases the stretch rate decreases. Therefore, in

dt

dr

rdt

dA

A

21

51

these experiments burning speed measurements have been done for conditions with Rf /R0

>0.5 (Rf > 4 cm), which results in very small stretch rates.

In order to study the effect of stretch, laminar burning speeds of n-decane/air have been

measured at the same temperature, pressure and equivalence ratio but different stretch

rates. For this purpose, different experiments have been arranged with initial conditions

along an isentrope. Figure 7 shows an arbitrary isentropic compression curve for

equivalence ratio of 0.8. As the unburned gas is compressed isentropiclly, it would

guarantee that all of the tests with different initial conditions of A, B, C, D and E will

pass through point F which will produce different stretch rates (because of different

radii). Figure 8 shows the variation of laminar burning speed versus stretch at an

equivalence ratio of 0.8 for two different unburned gas conditions. Similar procedure has

been done at stoichiometric condition and measured burning speeds are shown in Figure

9.

Fig. 7: Unburned gas initial conditions along an isentrope at =0.8

Pressure (atm)

Te

mp

era

ture

(K)

0 0.5 1 1.5 2 2.5

360

380

400

420

440

460

480

500

520

A

B

C

D

E

F

A: Pi= 0.75 atm Ti=391 KB: Pi= 1 atm Ti= 422 KC: Pi= 1.25 atm Ti= 446 KD: Pi= 1.5 atm Ti= 466 KE: Pi = 1.75 atmTi= 485 KF: P=1.95 atm T= 500 K

= 0.8

52

Figures 8 and 9 show that this experimental technique enables us to measure burning

speeds at very small stretch rates in comparison to other methods available in the

literature such as constant pressure spherical flame or counter-flow techniques. Also,

over the range of stretch rates which exist in these tests, laminar burning speeds are not

considerably affected by flame stretch and measured burning speed values can estimate

the zero stretch ones very well. This observation is in agreement with the prediction of

Chen et al. (Chen, Burke et al. 2009) for low stretch rates.

Fig. 8: Laminar burning speeds versus stretch rates at =0.8

Stretch Rate (1/s)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

0 20 40 60 80 100 1200

20

40

60

80

100

T=570 K P=3.35 atmT=500 K P=1.95 atm

= 0.8

53

Fig. 9: Laminar burning speeds versus stretch rates at =1.0

3.5.2. Laminar burning speed

As a result of isentropic compression of unburned gas during the flame propagation, each

single run provides burning speeds of a wide range of temperatures and pressures along

an isentrope. Figures 10 and 11 show laminar burning speeds of n-decane/air mixtures

initially at temperature of 420 K and pressures of 1 and 2 atm, respectively. Burning

speeds have been plotted for a range of lean mixtures. It is seen that increasing the

equivalence ratio in these conditions elevates the laminar burning speed. It should be

noted that in these figures pressure corresponding to each unburned gas temperature can

be found using the gas isentropic compression relation:

Stretch Rate (1/s)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

0 50 100 150 20020

40

60

80

100

T=520 K P=2.4 atmT=470 K P=1.6 atm

= 1.0

54

(9)

In this equation , where cp is the specific heat at constant pressure and cv is the

specific heat at constant volume.

Fig. 10: Laminar burning speeds of n-decane/air mixtures for Ti= 420 K, Pi= 1 atm and

different equivalence ratios

)1(/)/( ii TTPP

vp cc /

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

400 450 500 550 600 65040

60

80

100

120

= 0.8 = 0.9 = 1.0Power law fit

Ti = 420 K, Pi = 1atm

55

Fig. 11: Laminar burning speeds of n-decane/air mixtures for Ti= 420 K, Pi= 2 atm and

different equivalence ratios

After measuring laminar burning speeds along different isentropes, these data are fitted to

a power law correlation:

(10)

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

400 450 500 550 600 65020

30

40

50

60

70

80

90

= 0.7 = 0.8 = 0.9 = 1.0Power law fit

Ti = 420 K, Pi = 2 atm

00

2210 ))1()1(1(

P

P

T

TaaSS

u

uuu

56

Where Su0 is the burning speed at reference point (P0 = 1 atm, Tu0 = 350 K and

stoichiometric condition) in cm/s, is the mixture fuel-air equivalence ratio, Tu is the

unburned gas temperature in K, P is the mixture pressure in atm. , , α and β are fit

constants. These values are found using a nonlinear least square method and are shown in

Table 1. The power law fits are also shown in figures 10 and 11. As it is seen from

temperature and pressure exponents, burning speeds increase as temperature increases

and decrease as pressure increases. This correlation is valid only for laminar flames of

lean n-decane/air mixtures (0.7≤ ≤1) over the temperature range of 350 K to 610 K.

The upper limit of the pressure range over which this correlation is valid is determined by

the flame cellularity conditions. As the cell formation is strongly a function equivalence

ratio, table 2 provides the applicable pressure range of different equivalence ratios for this

correlation.

Table 1: Power law fit constants for burning speed of n-decane/air mixture

Suo (cm/s) a1 a2 α β

48.53 -0.81 -1.97 1.96 -0.17

57

Table 2: Applicable pressure range of different equivalence ratios in the power law fit

Pressure (atm)

0.7 ≤ ≤ 0.8 0.5 < P < 8

0.8 < ≤ 0.9 0.5 < P < 5.5

0.9 < ≤ 1 0.5 < P < 4.2

The significance of this work was the measurement of laminar burning speeds of n-

decane/air at high temperatures and pressures. There are some data of burning speed of n-

decane/air at atmospheric conditions, but the authors could not find any available data in

the literature for higher pressures. Figure 12 shows the comparison of measured laminar

burning speeds from this study with other researchers’ at atmospheric pressure and

different temperatures. Solid curves represent the current study and the symbols are

results of other researchers. This comparison shows that the agreement is good between

current study and previous studies at atmospheric conditions.

58

Fig. 12: Laminar burning speeds of n-decane/air mixtures at atmospheric pressure and

comparison with other researchers (Zhao, Li et al. 2004, Kumar and Sung 2007, Ji,

Dames et al. 2010, Kumar, Sung et al. 2011)

Equivalence Ratio,

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

0.6 0.7 0.8 0.9 1 1.120

40

60

80

100

120

140current study (power law correlation)Zhao et al. 500 KRasmussen et al. 473 KKumar and Sung 470 KJi et al. 403 KKumar and Sung 360 K

600K

500K

470K

400K

360K

59

3.6 Summary and conclusion

Flame structure and laminar burning speeds of lean n-decane/air premixed mixtures have

been studied at high temperatures and pressures. It was observed that flame is more

vulnerable to onset of instability and cell formation at higher pressures and rich mixtures.

Cell formations in these experiments were recognized to be as a result of hydrodynamic

instabilities. Probable effects of flame stretch on measured laminar burning speeds were

carefully investigated. The experimental method showed a good capability for measuring

laminar burning speeds at very low stretch rates in comparison to other conventional

experimental techniques. It was concluded that burning speeds are fairly unaffected by

the small flame stretch rates which exist in these experiments. Laminar burning speeds

were measured over the temperature range of 350 K < T < 610 K and pressure range of

0.5 atm < P < 8 atm. In the range of lean equivalence ratios in these experiments, it was

observed that burning speeds increase as temperature and equivalence ratio increase and

decrease as pressure increases. A power law correlation was developed based on all the

laminar burning speeds data obtained in the experiments. Results show good agreement

with available experimental data in the literature at atmospheric conditions.

Acknowledgements

This research has been done by the support of Office of Naval Research (ONR), Grant

No. N00010-09-1-0479. The authors are sincerely indebted to the late James C. Keck

(1924–2010) from MIT for the scientific discussions and his support over the past years.

60

4. Measurement of laminar burning speeds and

determination of onset of autoignition of Jet-A/air and JP-

8/air mixtures in a constant volume spherical chamber

Appeared in Journal of Energy Resources Technology 134 (2012) 022205

A. Moghaddas, C. Bennett, K. Eisazadeh-Far, H. Metghalchi

61

Measurement of laminar burning speeds and determination of onset of

autoignition of Jet-A/air and JP-8/air mixtures in a constant volume

spherical chamber

Abstract

The laminar burning speeds of Jet-A/air and three different samples of JP-8/air mixtures

have been measured and the onset of autoignition in JP-8/air premixed mixtures has been

determined. The experiments were made in a constant volume spherical vessel, which can

withstand high pressures up to 400 atmospheres. Burning speed was calculated from

dynamic pressure rise due to the combustion process in the vessel. A thermodynamic

model based on the pressure rise was used to determine burning speed. The burning

speeds were measured in lean mixtures for pressures of 1 atm to 4.5 atm and temperatures

of 493 K to 700 K. The onset of autoignition of JP-8 fuels was evaluated by observing

intense fluctuations of pressure data during the explosion of the unburned gas. It was

revealed that Jet-A and JP-8 have very similar burning speeds, however autoignition

temperatures of various samples of JP-8 were slightly different from each other.

Autoignition of these fuels was much more sensitive to temperature rather than pressure.

4.1 Introduction

Jet propellant 8 (JP-8) is regarded by the United States Army and Air Force as the main

fuel source for military land vehicles and aircraft. The North Atlantic Treaty

Organization (NATO) has decided to use the same fuel across all battlefields under the

62

“single fuel concept” (Kouremenos, Rakopoulos et al. 1997, Maurice, Lander et al. 2001,

Fernandes, Fuschetto et al. 2007). JP-8 is nearly identical in composition to the kerosene

based commercial aviation fuel known as Jet-A, since JP-8 is simply Jet-A with a

military additives package added to it to improve thermal stability characteristics. This

additives package typically contains an ice inhibitor to prevent water in the fuel from

freezing, corrosion inhibitors to protect fuel distribution components, and a static

dissipater to prevent ignition due to static discharge during fuelling (Heneghan,

Zabarnick et al. 1996, Maurice, Lander et al. 2001, Rawson 2001).

As kerosene based fuels, Jet-A and JP-8 have complex chemical compositions that are

comprised of thousands of hydrocarbons which can be divided into three general classes

– aromatics (~20%), n-alkanes and isoalkanes (~60%), and cycloalkanes (~20%)

(Maurice, Lander et al. 2001, Agosta, Cernansky et al. 2004, Dagaut and Cathonnet

2006). In addition to the complex compositions, the relative concentrations of these

hydrocarbons can vary significantly from one batch to another and from one

manufacturer to another, depending on the crude oil and processes used (Maurice, Lander

et al. 2001, Agosta, Cernansky et al. 2004). These compositional variations make the

development of chemical kinetics mechanisms and surrogates of kerosene fuels very

difficult. The fuel samples in this study were obtained from the Wright Patterson Air

Force Base (WPAFB). The four samples are referred in this paper as Jet-A (4658), JP-8

(4658), JP-8 (3773), and JP-8 (4177). The four-digit number appended to each fuel is

used by WPAFB for sample logging purposes and only serves to identify the particular

fuel. The sample designated Jet-A (4658) is a mixture of five Jet-A fuels from five

different manufacturers and is thus an “average Jet-A”. The fuel designated JP-8 (4658)

is the Jet-A (4658) with JP-8 additives package added to it and hence can be thought of as

an “average JP-8”.

63

It is important to study the thermodynamic and thermophysical properties of various

samples of Jet-A and JP-8 to see if there are any remarkable differences between these

kerosene based fuels. Many researchers have attempted to identify surrogates for jet fuels

with similar properties (Agosta, Cernansky et al. 2004, Dagaut and Cathonnet 2006,

Humer, Frassoldati et al. 2007). In order to verify proper surrogates and chemical kinetics

mechanisms there is a need for reliable experimental data. Laminar burning speed is a

fundamental property of a fuel which can be used to make these verifications (Dam,

Ardha et al. 2010, Monteiro and Rouboa 2011). JP-8 is intended to replace diesel fuel

(DF-2) in internal combustion engines; therefore its explosion limits and autoignition

properties should be studied. However, there is not enough experimental study on the

explosion limits and autoignition of JP-8/air mixtures in the conditions which are

identical to internal combustion engines. Investigation of autoignition from an

experimental approach is a challenging issue. It occurs in a very short period of time, and

precise devices are needed to record the details of this phenomenon (Yilmaz and

Donaldson 2007). Poschl and Sattelmayer (Pöschl and Sattelmayer 2008) investigated the

effect of temperature inhomogeneities on autoignition occurrence. They concluded that

inhomogeneous temperature field has remarkable effects on the initiation process of

autoignition. Kumar and Sung (Kumar and Sung 2010) experimentally studied the

autoignition characteristics of conventional jet fuels using a heated rapid compression

machine in the low-to-intermediate temperature range under elevated pressure conditions.

In this paper, we present the laminar burning speeds of Jet-A/air and three different

samples of JP-8/air mixtures. The burning speeds are measured in lean mixtures for

pressures of 1 atm to 4.5 atm and temperatures of 493 K to 700 K. The onset of

autoignition of these fuels is also explored. The experiments have been performed in a

constant volume spherical vessel with specific initial temperature and pressure. The

64

autoignition can be characterized by intense fluctuations in pressure data and audible

noise.

4.2 Experimental facility

The spherical chamber consists of two hemispheric heads bolted together to make a

sphere with an inner diameter of 15.24 cm. The chamber was designed to withstand

pressures up to 400 atm and was fitted with ports for spark electrodes, ionization probes,

and for filling and evacuation purposes. A thermocouple inserted in one of the chamber

ports is used to check the initial temperature of the gas inside the chamber. A Kistler

603B1 piezoelectric pressure transducer with a Kistler 5010B charge amplifier is used to

record the dynamic pressure rise during the experiments. Ionization probes mounted flush

with the wall located at the top and the bottom of the chamber are used to measure the

arrival time of the flame at the wall and to check for spherical symmetry and buoyant

rise. Figure 1 shows the sketch of the vessel with all the elements. The spherical vessel is

housed in an oven which can be heated up to 500 K. A data acquisition system is used to

capture the pressure-time data as well as the signals from ionization probes. A computer

driven system is used to make the mixture with the required fuel and oxidizer and to

initiate the combustion process. Liquid fuel is stored in a reservoir which is attached to a

liquid fuel manifold. The liquid fuel manifold is equipped with two cartridge heaters to

evaporate the liquid fuel before it enters the combustion chamber. The partial pressure of

the fuel vapor is measured by a high temperature strain gauge (Kulite XTE-190). The

method of partial pressures is used to set the initial fuel air equivalence ratio. Figure 2

shows the schematic of the experimental setup.

65

Figure 1: Sketch of the spherical vessel

Figure 2: Schematic diagram of experimental facilities

66

4.3 Burning speed model

A thermodynamic model has been used to calculate the laminar burning speed based on

the pressure rise during the flame propagation inside a constant volume vessel. This

model was developed by Metghalchi and Keck (Metghalchi and Keck 1980, Metghalchi

and Keck 1982) and was modified to account for the energy losses due to electrodes and

vessel wall and radiation from the burned gas to the wall as well as the temperature

gradient in the preheat zone. It is assumed that gases in the combustion chamber can be

divided into burned and unburned gas regions separated by a reaction layer of negligible

thickness. Also, burned and unburned gases are ideal, pressure throughout the chamber is

uniform, and compression of both burned and unburned gases is isentropic. Figure 3

shows the schematic of the model. The burned gas in the center of chamber is divided

into a number of shells which the number of shells is proportional to the combustion

duration. STANJAN is used to find the equilibrium states of the burned gases.

Thermodynamic properties of some species were calculated using the model developed

by Hui et al. (He, Metghalchi et al. 1999, He, Metghalchi et al. 2000). The burned gases

are surrounded by a preheat zone ( ) having variable temperature, which is itself

surrounded by unburned gases. A thermal boundary layer ( ) separates the unburned

gas from the wall. A detailed description of the model is demonstrated in (Elia, Ulinski et

al. 2001, Parsinejad, Arcari et al. 2006, Rahim, Eisazadeh-Far et al. 2008, Eisazadeh-Far,

Moghaddas et al. 2010, Far, Parsinejad et al. 2010, Eisazadeh-Far, Moghaddas et al.

2011, Eisazadeh-Far, Moghaddas et al. 2011).

ph

bl

67

Figure 3: Schematic of different zones and their corresponding temperatures in the

thermodynamic model

The equation of state, volume and energy equations will be solved simultaneously:

(1)

where P is the pressure, v is the specific volume, R is the specific gas constant and T is

the temperature. The mass conservation equation for the burned and unburned gas

regions is:

RTPv

68

(2)

where m is the total mass of the chamber, mb is the mass of the burned gas zone; mu is the

mass of the unburned gas zone. Vc is the volume of the chamber and Ve is the volume of

the spark electrodes. In this equation, subscript i denotes the initial conditions, and

subscripts u and b denote the unburned and burned gas conditions, respectively. The total

volume of the gas in the combustion chamber is:

(3)

And the energy conservation equation is:

(4)

where Ei is the initial energy of the gas, Qe is the conductive energy loss to the electrodes,

Qw is the energy loss to the wall, Qr is the radiation energy loss. Volume (mass balance)

and energy balance equations can be written as:

(5)

(6)

where and are the initial specific volume and energy of the

unburned gas in the chamber, is the specific volume of isentropically compressed

burned gas, is the specific volume of isentropically compressed unburned gas. ,

ieciub RTVVPmmm /)(

ubeci VVVVV

ubrwei EEQQQE

bx

phwbebusiusbs mVVVvvdxvv0

/)()(

bx

ruwbbebuphusiusbs mQPVPVPVeedxee0

/))1/()1/()1/(()(

mVVv eci /)( mEe ii /

bsv

usv wbV

69

and are displacement volume of wall boundary layer, displacement volume of

preheat zone ahead of the reaction layer and displacement volume of electrode boundary

layer respectively. , , and , are the specific energy of isentropically compressed

burned gas, specific energy of isentropically compressed unburned gas and specific heat

ratio of unburned gas, respectively. The above equations must be solved for two

unknowns: burned gas mass fraction and the burned gas temperature of the last shell.

Given pressure as a function of time (measured in the experiments), they can be solved

numerically to find the burned mass fraction and radial temperature distribution

.

Ultimately, laminar burning speed may be defined as:

(7)

Where is the area of the sphere having a volume equal to that of the burned gas.

4.4 Results and discussion

At least three runs at each initial condition were made to provide a good statistical

sample. It was found that three runs are sufficient to achieve a 95% confidence level

(Parsinejad, Arcari et al. 2006). Burning speed measurements have been performed on

Jet-A/air and JP-8/air premixed mixtures with initial pressure and temperature of 1 atm

and 493 K, respectively. The experiments were done at three equivalence ratios of 0.8,

0.9, and 1 and for pressures of 1 atm to 4.5 atm and temperatures of 493 K to 700 K. A

previous study (Far, Parsinejad et al. 2010) on the structure of JP-8/air flames over the

range of lean premixed mixtures with similar initial conditions revealed that the

phV ebV

bse use u

)(txb

),( trT

bubbubu AxmAmS //

bA

70

assumption of smooth and spherical flame is valid throughout the entire flame

propagation. All reported burning speeds are in the regions where r/R > 0.5 (r and R are

the radii of the flame and the chamber, respectively). It was shown that in these

conditions the effect of stretch on the laminar burning speed is negligible (Far, Parsinejad

et al. 2010, Eisazadeh-Far, Moghaddas et al. 2011, Moghaddas, Eisazadeh-Far et al.

2012). Figure 4 shows the measured burning speed of Jet-A (4658) for three different

equivalence ratios along the isentropes. As it is assumed that the unburned gas is

compressed isentropically, the pressures corresponding to the temperatures in this figure

could be found from the isentropic compression relation ( ). It can be

seen that burning speed decreases as the mixture becomes lean. Figure 5 shows the

burning speed of two samples of JP-8 at three equivalence ratios. This figure shows that

burning speeds of these two fuels are very close to each other and the same is true for

other two fuels as well. Figure 6 shows the comparison of the burning speeds of

stoichiometric mixtures of Jet-A and three samples of JP-8. It can be seen that the laminar

burning speeds of these kerosene based fuels are very close to each other.

)1(/)/( ii TTPP

71

Figure 4: Laminar burning speeds of Jet-A (4658) initially at 493 K and 1 atm

Figure 5: Laminar burning speeds of JP-8 (3773) and (4177) initially at 493 K and 1 atm

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

450 500 550 600 650 700 750

40

60

80

100

120

140

160

=0.8 =0.9 =1.0

Ti=493 K, Pi= 1 atm

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

450 500 550 600 650 700 750

40

60

80

100

120

140

160

JP-8 (3773)JP-8 (4177)

Ti = 493 K, Pi = 1 atm

=0.8

=0.9

=1.0

72

Figure 6: Comparison of Laminar burning speeds of different JP-8 and Jet-A initially at

493 K and 1 atm

Autoignition experiments were carried out for JP-8 (3773) and JP-8 (4177) with an initial

pressure of 8 atm in the spherical chamber. Autoignition occurs at specific temperature

and pressure during the compression of unburned gas due to flame propagation. The

initial conditions are very important since the autoignition is strongly dependent on

equivalence ratio and temperature. The autoignition process in an unburned gas mixture

is a rapid process with intense pressure fluctuations. Abnormal pressure fluctuations can

be considered as a trace of autoignition in the unburned gas zone. In an ideally

homogeneous mixture, it can be assumed that autoignition occurs everywhere

instantaneously. In these conditions, it is assumed that the mixture is perfectly uniform

and there is no temperature, pressure or equivalence ratio gradient in the mixture. In

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

450 500 550 600 650 700 75060

80

100

120

140

160

JP-8 (3773)JP-8 (4177)JP-8 (4658+ADD)Jet-A (4658)

Ti = 493K, Pi = 1 atm, = 1

73

practical combustors such as internal combustion engines, it is hard to have homogeneous

mixtures since these gradients do exist.

Figure 7 shows the pressure-time record of a stoichiometric mixture of JP-8 (3773)

initially at pressure and temperature of 8 atm and 479 K, respectively. An abrupt rise in

the pressure can be seen at the point denoted “A” along with audible noise. This is an

indicator that the charge has autoignited. After repeating the experiments and ensuring

the reproducibility, the corresponding autoignition pressure and temperature of unburned

gas were measured at point “A”. The autoignition pressure was determined by finding

the point at which the value of dP/dt becomes discontinuous as seen in Figure 8. The

autoignition trace of Figure 7 is similar to those in internal combustion engines provided

by Heywood (Heywood 1988).

74

Figure 7: Pressure-time record of autoignition of stoichiometric mixture of JP-8 (3773)

initially at 479 K and 8 atm

Time (ms)

Pre

ssu

re(a

tm)

0 20 40 60 800

10

20

30

40

50

Ti = 479 K, Pi = 8 atm, = 1.0

A

75

Figure 8: Rate of pressure rise (dP/dt) for autoignition of stoichiometric mixture of JP-8

(3773) initially at 479 K and 8 atm

Figures 9 and 10 show the pressure-time records of autoignition of JP-8 (3773) and JP-8

(4177) air mixtures at three different equivalence ratios, respectively. These figures show

that increasing the equivalence ratio in these experiments advances the unburned gas

explosion. Figure 11 demonstrates the temperatures and pressures at which autoignition

took place for two samples of JP-8. The explosion temperature in a flame propagating

combustor is the temperature where the ignition delay time of the unburned gas mixture

is smaller than the time scale of flame propagation. It can be seen that there is a specific

range of temperature for the explosion of JP-8/air mixtures. The temperature varies from

680 K to 695 K for JP-8 (3773) and JP-8 (4177), respectively. The difference between

autoignition temperatures of different samples of JP-8 might be due to their respective

Time (ms)

dP

/dt

(atm

/ms)

0 20 40 60 80

-100

-50

0

50

100

Ti = 479 K, Pi = 8 atm, = 1.0

A

76

crude oil source and refinery process. This figure shows that the onset of autoignition is

much more sensitive to temperature rather than pressure.

Fig 9: Comparison of pressure-time record of autoignition of JP-8 (3773) initially at 479

K and 8 atm at three different equivalence ratios

Time (ms)

Pre

ssu

re(a

tm)

0 20 40 60 80 1000

10

20

30

40

50

= 0.8 = 0.9 = 1.0

77

Fig 10: Comparison of pressure-time record of autoignition of JP-8 (4177) initially at 480

K and 8 atm at three different equivalence ratios

Time (ms)

Pre

ssu

re(a

tm)

0 20 40 60 80 1000

10

20

30

40

50

= 0.8 = 0.9 = 1.0

78

Figure 11: Autoignition temperatures vs. pressures for JP-8/air mixtures

4.5 Summary

The burning speeds and the onset of autoignition of Jet-A/air and different samples of JP-

8/air were studied in a set of experiments in a constant volume spherical chamber. The

burning speed measurements were done in lean premixed mixtures and over the pressures

of 1 atm to 4.5 atm and temperatures of 493 K to 700 K. Results showed that these

kerosene type fuels have very similar laminar burning speeds. The diagnosis of

autoignition was done by analyzing the pressure and ionization probes data. It was

observed that autoignition is characterized by intense pressure fluctuations and abrupt

change in the rate of pressure rise. The autoignition was very sensitive to temperature and

it was shown that there is a specific explosion temperature for each sample of JP-8 over a

wide range of equivalence ratios.

Pressure (atm)

Te

mp

era

ture

(K)

34 36 38 40640

660

680

700

JP-8 (3773) =0.8JP-8 (3773) =0.9JP-8 (3773) =1JP-8 (4177) =0.8JP-8 (4177) =0.9JP-8 (4177) =1

79

Acknowledgment

This work was supported by the Army Research Office (ARO) corresponding to the

Grant No. W911NF0510051. The authors would like to thank Dr. Tim Edwards from the

Air Force Research Laboratory (AFRL) for providing the fuels.

80

5. Laminar burning speeds and flame structures of mixtures

of Difluoromethane (HFC-32) and 1,1-Difluoroethane (HFC-

152a) with air at elevated temperatures and pressures

Appeared in HVAC&R Research 20 (1), 42-50

A. Moghaddas, C. Bennett, E. Rokni, H. Metghalchi

81

Laminar burning speeds and flame structures of mixtures of

Difluoromethane (HFC-32) and 1,1-Difluoroethane (HFC-152a) with air

at elevated temperatures and pressures

Abstract

Laminar burning speeds and flame structures of difluoromethane (HFC-32)/air and 1,1-

difluoroethane (HFC-152a)/air mixtures have been studied. Experiments have been

carried out in constant volume spherical and cylindrical vessels coupled with a

schlieren/shadowgraph system and high speed CMOS camera. Laminar burning speed

was determined using a thermodynamic model that employs the pressure rise history of

the combustion process. Experiments were conducted for different initial conditions over

a wide range of equivalence ratios. Laminar burning speeds of HFC-152a/air mixtures

have been measured over the temperature range of 298 to 580 K and pressure range of 1

to 8 bar. Laminar burning speeds of HFC-32/air mixtures have been measured for the

temperature range of 350 to 475 K and pressure range of 2 to 6.8 bar. Correlations have

been developed for laminar burning speeds of HFC-32 and HFC-152a to demonstrate the

temperature and pressure dependency of laminar burning speeds of these two refrigerants.

5.1 Introduction

The need to replace high global warming potential (GWP) refrigerants with

environmentally friendly refrigerants has been motivated by concerns regarding climate

change. Since the adoption of the Montreal Protocol in 1989 and the Kyoto Protocol in

82

1997 there has been an ongoing phase-out of chlorofluorocarbons (CFCs) and

hydrochlorofluorocarbons (HCFCs) (Secretariat 2006). Refrigerant companies are

working to develop alternatives to CFC based chemicals such as CCl3F (CFC-11) and

CCl2F2 (CFC-12). Alternatives that are currently in use include hydrofluorocarbons

(HFCs) such as tetrafluoroethane (C2H2F4 or HFC-134a) which replaced CFC-12 used in

automobile air conditioning systems. Generally, HFCs have shorter lifetime in the

atmosphere and so lower global warming potential (Takizawa, Takahashi et al. 2006,

Union 2006). While the environment has been the primary driving force behind the

search for next generation refrigerants, safety considerations require thorough studies of

the combustion characteristics of these potential refrigerants. Some HFCs refrigerants

like HFC-32 and HFC-152a are classified as flammable and so the potential for ignition

must be evaluated very carefully. Table 1 summarizes some of the characteristics of these

two refrigerants at 23°C and 1 bar (Jabbour and Clodic 2004). In considering the

potential combustion hazard of any flammable gases, minimum ignition energy and

flammability limits are used for evaluating the possibility of ignition. The scale of the fire

disaster can be estimated in terms of burning speed and heat of combustion (Takizawa,

Takahashi et al. 2006).

83

Table 1: Refrigerant Characteristics

Refrigerant

Number

Chemical Name Chemical

Formula

Molar

Mass

(g/mol)

Heat of

Formation

(kJ/mol)

Heat of

Combustion

(MJ/kg)

Flammability

Limits (φ)

(ASTM-E681)

HFC-32 difluoromethane CH2F2 52.02 -452.3 9.4 0.83 – 1.7

HFC-152a 1,1-

difluoroethane

CH3CHF2 66.05 -497.0 17.4 0.62 – 2.47

Figure 1 shows the refrigerant safety group classification from the ANSI/ASHRAE

Standard 34-2010. This classification has been made based on the toxicity and the

flammability:

Fig. 1: Refrigerant safety group classification (Std 2007)

84

Class 1: refrigerants exhibit no flame propagation when tested for flammability in air at

60°C and 101.3 kPa.

Class 2 (lower flammability): refrigerants exhibit low flammability (LFL > 0.10 kg/m3)

when tested for flammability in air at 60°C and 101.3 kPa and have a low heat of

combustion (Δhc < 19,000 kJ/kg).

Class 3 (higher flammability): refrigerants exhibit high flammability (LFL ≤ 0.10 kg/m3)

when tested for flammability at 60°C and 101.3 kPa or have a high heat of combustion

(Δhc ≥ 19,000 kJ/kg).

HFC-32 and HFC-152a are rank as A2. Flammability class 2 includes a wide range of

moderately flammable substances and additional criterion based on the burning speed is

required for more precise scaling of flammability within this class. A subclass, Class 2L,

are refrigerants that meet the requirements for Class 2 and also have a burning speed less

than or equal to 10 cm/s, when tested at 23°C and 101.3 kPa. The 2L subclass, considered

“mildly” flammable, is an optional classification designed to better identify the

flammability characteristics of a Class 2 refrigerant. Since burning speed is an important

parameter to characterize refrigerant flammability, it is therefore important to accurately

measure the burning speeds of refrigerants.

Laminar burning speed is a thermo-physical property of a combustible mixture and is

defined as the speed at which a planar, one-dimensional, adiabatic flame travels relative

to the unburned gas mixture. It is a measure of the rate of energy released during

combustion in quiescent gas mixtures and incorporates the effects of overall reaction

rates, energy (heat) of combustion and energy and mass transport rates (Linteris 2006).

Laminar burning speed is also used as a primary parameter in many models of turbulent

85

combustion, validation of chemical kinetic mechanisms and the modeling of wall

quenching (Ferguson and Keck 1977, Keck 1982). Linteris (Linteris 2006) measured

burning speed of 1,1-difluoroethane (HFC-152a) using a nozzle burner setup; however,

the flames suffered from considerable stretch and cellular structure and it was

recommended that an experiment that could take stretch into consideration be used in

future works. More recently, the flame tube method was used to measure burning speeds

of HFC-152a and HFC-32 (Jabbour and Clodic 2004). In their experiment, a combustible

mixture fills a vertical tube that is ignited from the bottom. It is assumed that the flame

cross-sectional geometry remains flat and a digital camera was used to capture flame

propagation. However, this approach typically suffers from wall effects owing to

quenching. The experiment also suffers from gravity effects that produce different

burning speeds depending on whether the mixture is lit from the top or bottom of the

tube. Takizawa et al. (Takizawa, Takahashi et al. 2005) measured burning speeds of four

different hydrofluorocarbons in constant volume spherical vessel with the initial

temperature range of 280 to 330 K and initial pressure range of 78 to 108 kPa. They

found that the spherical vessel method is adequate for determining the burning speed of

weakly flammable HFCs as well as mildly flammable compounds. They concluded that

the burning speed of HFCs is strongly dependent on the ratio of Hydrogen to Fluorine

atoms. As it is seen in the literature, except the works by Takizawa et al. (Takizawa,

Takahashi et al. 2005, Takizawa, Takahashi et al. 2006), previous measurements of

burning speeds of HFCs were mostly performed at relatively low temperatures and

pressures. In practical refrigeration cycles, the working refrigerant can experience high

temperatures and pressures after the compressor and at the condenser. Therefore, there

seems to be a need to investigate the burning speed of refrigerants at temperatures and

pressures higher than the room condition.

86

In the current experiment which is based on the method developed by Metghalchi and

Keck (Metghalchi and Keck 1980), we extend the temperature and pressure range of

burning speed measurement of HFC-152a to 580 K and 8 bar and HFC-32 to 475 K and

6.8 bar, respectively. The major advantages of this method are that it circumvents the

need for any stretch corrections and that many data points can be collected along an

isentrope in a single experiment.

5.2 Experimental facilities

Experiments have been carried out in constant volume spherical and cylindrical vessels.

The spherical vessel is constructed from two hemispheres bolted together to form a

sphere with an inner diameter of 15.24 cm. The cylindrical vessel measures 13.5 cm in

diameter and 13 cm in length. The cylinder is fitted with 3.5 cm thick fused silica

windows at both ends which are sealed to the vessel with o-rings. The windows limit the

vessel’s operation to a maximum pressure of 50 bar. The purpose of the windows is to

provide a clear line of sight through the vessel for a shadowgraph setup which allows real

time recording of the combustion event.

Both the spherical and cylindrical vessels were used to measure the pressure rise during

the combustion process via pressure transducers installed in their walls. The vessels were

fitted with two extended spark plug electrodes which provide a central point ignition

source for the vessels and were equipped with heaters capable of elevating the vessel

initial temperature. The cylindrical vessel was installed in a shadowgraph system giving

advantage of taking pictures during the flame propagation. A CMOS camera with the

capability of taking pictures up to 40,000 frames per second has been used for these

experiments. A data acquisition system was used to capture the pressure-time data as well

as the signals from ionization probes installed in the spherical vessel wall to determine

87

flame arrival time. A computer driven system has been used to make the mixture with

required fuel and oxidizer and to initiate the combustion process. Method of partial

pressures was used to set the initial fuel air equivalence ratio and the correctness of the

method was verified using gas chromatography. More details about the experimental

facilities can be found in previous publications (Parsinejad, Arcari et al. 2006,

Eisazadeh-Far, Moghaddas et al. 2010, Eisazadeh-Far, Moghaddas et al. 2011,

Moghaddas, Eisazadeh-Far et al. 2012). Figure 2 shows a schematic of the cylindrical

vessel installed in the shadowgraph system.

Fig. 2: Z-type Schlieren/Shadowgraph ensemble with a high speed CMOS camera.

5.3 Flame structures of HFC-152a and HFC-32

Images of combustion of HFC-152a/air mixtures were taken using the

schlieren/shadowgraph system for all equivalence ratios to check for spherical symmetry,

buoyant rise and cell formation. As it can be seen in figure 3, HFC-152a flame shape

remains spherical throughout the combustion process with initial pressure of 1 bar and

initial temperature of 298 K before the flame encounters the vessel wall. Also, there is no

88

cell formation during the flame propagation and the flame is fairly smooth and laminar.

Figure 4 shows formation of cells during the final stages of flame propagation of HFC-

152a/air mixtures with initial pressure of 2 bar. This picture demonstrates that as pressure

and flame radii increase, flames become more vulnerable to instability. Due to cellularity,

the area of flame increases comparing to smooth flames and the measurement of burning

speed becomes extremely difficult. The cell formation is strongly a function of pressure,

flame radius, equivalence ratio and refrigerant type (Bradley, Sheppart et al. 2000,

Larson, Williams et al. 2001, Kwon, Rozenchan et al. 2002, Eisazadeh-Far, Moghaddas

et al. 2010, Moghaddas, Bennett et al. 2012). In these experiments as well as other

researchers’ studies, it has been observed that elevation of pressure causes cell formation

and instability. However, the analysis of flame instabilities is beyond the scope of this

paper and laminar burning speeds are reported for only stable and smooth flames.

89

Fig. 3: Snapshots of HFC-152a/air flames at different equivalence ratios, Ti = 298 K and

Pi = 1 bar

90

Fig. 4: Snapshots of HFC-152a/air flames at different equivalence ratios, Ti = 298 K and

Pi = 2 bar

91

Figure 5 shows images of HFC-32/air flame propagation that were taken for a range of

equivalence ratios. As it is seen in this figure, buoyancy has much more of an impact on

the HFC-32 flame shape than in the faster burning HFC-152a. It can be seen that for

richer mixtures, buoyancy starts to dominate the flame shape earlier. The images

corresponding to equivalence ratio of 1.5 start to flatten out on the bottom surface of the

flame and have also risen off center of the vessel. In the last sequence corresponding to

φ=1.7 the flame is not symmetrical at all and has risen off center by an entire flame

radius by the end of the process. As it is seen, flame propagation of HFC-32/air mixtures

with room initial temperature was greatly suffered from buoyancy. In order to avoid the

flame deformation effects on laminar burning speed calculation, a set of experiments

were conducted on HFC-32/air mixtures with initial temperature and pressure of 350 K

and 2 bar. Laminar burning speeds of HFC-32 have been calculated only for the tests

with elevated initial temperature (Ti = 350 K).

92

Fig. 5: Snapshots of HFC-32/air flames at different equivalence ratios, Ti = 298 K

and Pi = 1 bar

There are significant amounts of hydrogen fluoride (HF) in the combustion products of

HFCs. When hydrogen fluoride mixes with water that condenses in the products, a mist

of hydrofluoric acid is formed which is a very corrosive and penetrating. It is highly

93

reactive toward glass and its corrosive effect on the glass is visible in the pictures

(reducing quality of the pictures).

5.4 Burning speed model

A thermodynamic model has been used to calculate the laminar burning speed based on

the pressure rise during the flame propagation inside the constant volume vessels. This

model was developed by Metghalchi and Keck (Metghalchi and Keck 1980) and was

modified to account for the energy losses due to electrode and vessel wall and radiation

from the burned gas to the wall as well as the temperature gradient in the preheat zone. It

is assumed that gases in the combustion chamber can be divided into burned and

unburned gas regions separated by a reaction layer of negligible thickness. Also, burned

and unburned gases are ideal, pressure throughout the chamber is uniform, and

compression of both burned and unburned gases is isentropic. Figure 6 shows the

schematic of the model. The burned gas in the center of chamber is divided into a number

of shells whose number is proportional to the combustion duration. Burned gases were

assumed to be in chemical equilibrium in each shell. STANJAN code (Reynolds 1987)

was used to calculate chemical equilibrium concentration. Some of the most important

species present at the equilibrium with concentrations larger than 10-8 are listed in table 2.

Burned gases are surrounded by a preheat zone ( ) having variable temperature, which

is itself surrounded by unburned gases. A thermal boundary layer ( ) separates the

unburned gas from the wall. The effect of energy transfer from burned gas to the spark

electrodes is considered by a thermal boundary layer ( ).

ph

bl

bl

94

Fig. 6: Schematic of different zones and their corresponding temperatures in the

thermodynamic model

Table 2: List of important species present at the equilibrium

N2 CO CO2 H2O NO

HF O2 H2 OH NO2

N2O HCO HO2 H2O2 H

F O N

95

A detailed description of the model is demonstrated in previous publications (Eisazadeh-

Far, Moghaddas et al. 2010, Eisazadeh-Far, Moghaddas et al. 2011, Moghaddas, Bennett

et al. 2012). The equation of state, volume and energy equations will be solved

simultaneously:

(1)

where P is the pressure, v is the specific volume, R is the specific gas constant and T is

the temperature. The mass conservation equation for the burned and unburned gas

regions is:

(2)

where m is the total mass of the chamber, mb is the mass of the burned gas zone; mu is the

mass of the unburned gas zone. Vc is the volume of the chamber and Ve is the volume of

the spark electrodes. In this equation, subscript i denotes the initial conditions, and

subscripts u and b denote the unburned and burned gas conditions, respectively. The total

volume of the gas in the combustion chamber is:

(3)

And the energy conservation equation is:

(4)

where Ei is the initial energy of the gas, Qe is the conductive energy loss to the electrodes,

Qw is the energy loss to the wall, Qr is the radiation energy loss. Volume (mass balance)

and energy balance equations can be written as:

RTPv

ieciub RTVVPmmm /)(

ubeci VVVVV

ubrwei EEQQQE

96

(5)

(6)

where and are the initial specific volume and energy of the

unburned gas in the chamber, is the specific volume of isentropically compressed

burned gas, is the specific volume of isentropically compressed unburned gas. ,

and are displacement volume of wall boundary layer, displacement volume of

preheat zone ahead of the reaction layer and displacement volume of electrode boundary

layer respectively. , , and , are the specific energy of isentropically compressed

burned gas, specific energy of isentropically compressed unburned gas and specific heat

ratio of unburned gas, respectively. The above equations must be solved for two

unknowns: burned gas mass fraction and the burned gas temperature of the last shell.

Given pressure as a function of time (measured in the experiments), they can be solved

numerically to find the burned mass fraction and radial temperature distribution

.

Ultimately, laminar burning speed may be defined as:

(7)

Where is the area of the sphere having a volume equal to that of the burned gas.

bx

phwbebusiusbs mVVVvvdxvv0

/)()(

bx

ruwbbebuphusiusbs mQPVPVPVeedxee0

/))1/()1/()1/(()(

mVVv eci /)( mEe ii /

bsv

usv wbV

phV ebV

bse use u

)(txb

),( trT

bu

b

bu

bu A

xm

A

mS

bA

97

5.5 Results and discussion

Burning speed measurements were done for HFC-32 with initial condition of Ti = 350 K

and Pi=2 bar and covered the temperatures and pressures up to 475 K and 6.8 bar,

respectively. HFC-152a burning speed measurements were performed on the mixtures

with initial temperatures of 298 and 400 K and initial pressures of 1 and 2 bar over a

range of equivalence ratios. HFC-152a burning speed measurement covered the

temperatures and pressures up to 580 K and 8 bar, respectively. In this work the

equivalence ratio is defined as the actual refrigerant/air molar ratio divided by

stoichiometric ratio. The stoichiometric reactions for HFC-32 and HFC-152a can be

considered as followings:

CH2F2 + (O2 + 3.76N2) → CO2 + 2HF + 3.76N2 (8)

C2H4F2 + 2.5(O2+3.76N2) → H2O + 2CO2 + 2HF + 9.4N2 (9)

For other refrigerant/air equivalence ratios, the following reactions were used (φ is the

equivalence ratio):

φCH2F2 + (O2+3.76N2) → Products (10)

φC2H4F2 + 2.5 (O2+3.76N2) → Products (11)

Figure 7 shows a sample of pressure rise history due to combustion of HFC-152a in the

spherical vessel for the room initial temperature and pressure at three different

equivalence ratios. It can be seen that among the three plotted curves, the fastest pressure

rise (correlated to burning speed) occurs at equivalence ratio of 1.2 (equivalence ratio of

1.2 has the highest rising slope).

98

Fig.7: Comparison of the pressure rise in the spherical vessel for HFC-152a/air, Ti=298

K and Pi=1 bar at three different equivalence ratios

Depending on the conditions, stretch can affect the laminar burning speed values.

Typically a radius of ~ 4 cm is required for stretch to be considered negligible

(Eisazadeh-Far, Moghaddas et al. 2011, Moghaddas, Eisazadeh-Far et al. 2012) Flame

stretch is a phenomenon caused by the variation of flame area over time. For spherically

expanding flames stretch rate can be defined as:

(12)

Time (ms)

Pre

ssu

re(b

ar)

0 50 100 1500

1

2

3

4

5

6

7

8

9

10

= 0.8 = 1.0 = 1.2

Pi = 1 bar

Ti = 298 K

dt

dr

rdt

dA

A

21

99

Where is the stretch rate, A is the area of flame, t is time, and r is the flame radius. This

is a measure of variation of flame area versus time. In this study laminar burning speed is

measured at very low stretch rates to minimize the effects.

In order to study the effect of stretch, A set of tests have been arranged to measure the

laminar burning speeds of a stoichiometric mixture of HFC-152a at a temperature of 450

K and pressure of 3.8 bar with different stretch rates. For this purpose, different initial

conditions have been selected along an isentrope in such a way that all tests produced an

unburned gas mixture having temperature and pressure of 450 K and 3.8 bar during the

combustion process. This allowed us to measure the laminar burning speed with different

stretch rates due to different radii. Figure 8 shows variation of laminar burning speed

versus stretch rates. As it is seen, this experimental technique enables us to measure

burning speed at very small stretch rates in comparison to other conventional methods of

burning speed measurement such as constant pressure spherical flame, counter-flow or

nozzle burner. As it can be seen, laminar burning speed is practically constant for the

range of stretch rates from 20 to 80 and there is no need to any correction to get zero

stretch burning speed. This observation is in agreement with prediction of Chen et al.

(Chen, Burke et al. 2009) for low stretch rate flames.

100

Fig. 8: Laminar burning speed versus stretch rate for HFC-152a

With faster burning speeds, flame remains spherical up until it touches the vessel wall.

Burning speeds are not measured for the flames which deviate from a spherical shape.

HFC-32 measured burning speeds are shown in figure 9. These plots depict burning

speed along isentropes for different equivalence ratios with the initial conditions of Ti =

350 K and Pi = 2 bar. It is seen that the maximum burning speed of HFC-32 (in the range

over which the experiments were performed) is achieved at about an equivalence ratio of

1. Figures 10 and 11 show the laminar burning speeds of HFC-152a along the isentropes

with initial pressure of 1 bar and initial temperatures of 298 K and 400 K, respectively. In

all of these figures the pressure corresponding to each temperature can be estimated from

the isentropic compression relation:

Stretch Rate (1/s)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

0 20 40 60 80 100 1200

20

40

60

T = 450 K

P = 3.8 bar

= 1.0

101

(13)

In this equation , where cp is the specific heat at constant pressure and cv is the

specific heat at constant volume for the mixture.

Fig. 9: Laminar burning speeds of HFC-32/air mixture for Ti = 350 K, Pi = 2 bar and

different equivalence ratios

)1(/)/( uuii TTPP

vpu cc /

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

360 380 400 420 440 460 480 5000

2

4

6

8

10

12

14

16

18

20

= 1.0 = 1.1 = 1.2 = 1.3 = 1.4 = 1.5

Ti = 350 K

Pi = 2 bar

102

Fig. 10: Laminar burning speeds of HFC-152a/air mixture for Ti = 298 K, Pi = 1 bar and

different equivalence ratios

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

300 350 400 450 500 550 6000

10

20

30

40

50

= 0.8 = 1.0 = 1.2

Ti = 298 K

Pi = 1 bar

103

Fig. 11: Laminar burning speeds of HFC-152a/air mixture for Ti = 400 K, Pi = 1 bar and

different equivalence ratios

One of the important properties of a combustible mixture is recognized as mass burning

flux. Mass burning flux is calculated using the assumptions that laminar burning speed

was calculated in Equation 7, except it is multiplied by the unburned gas density (

). Mass burning fluxes of stoichiometric HFC-152a with two different initial

pressures of 1 and 2 bar have been shown in figure 12. It shows that mass burning flux of

HFC-152a mixtures increases with increasing the pressure and temperature.

Temperature (K)

La

min

ar

Bu

rnin

gS

pe

ed

(cm

/s)

400 450 500 550 6000

10

20

30

40

50

60

70

80

= 0.8 = 1.0 = 1.2

Ti = 400 K

Pi = 1 bar

bb Axm /

104

Fig. 12: Comparison of stoichiometric HFC-152a/air mixture mass burning fluxes for two

different initial pressures

Correlations have been developed for laminar burning speeds of HFC-32 and HFC-152a.

The following power law correlation has been used to fit to the data over all the

equivalence ratios and isentropes. For HFC-32, Tu0 and P0 are 350 K and 2 bar and for

HFC-152a, Tu0 and P0 are 298 K and 1 bar, respectively. Su0 is burning speed at the

reference condition:

Temperature (K)

Ma

ssB

urn

ing

Flu

x(g

r.se

c-1cm

-2)

300 350 400 450 500 550 6000

0.05

0.1

0.15

0.2

0.25

Pi = 1 barPi = 2 bar

Ti = 298 K

= 1.0

105

(14)

The least square fitted parameters for HFC-32 and HFC-152a are shown in table 3. For

HFC-32, these parameters were fitted over the temperature range of 350 to 475 K,

pressure range from 2 to 6.8 bar, and equivalence ratios from 1 to 1.5. For HFC-152a,

these parameters were fitted over the temperature range of 298 to 580 K, pressure range

from 1 to 8 bar, and equivalence ratios from 0.8 to 1.2.

Table 3: Fitted parameters for HFC-32 and HFC-152a burning speed correlations

Refrigerant Suo (cm/s) a b α β

HFC-32 10.34 -0.781 -0.835 2.4 -0.141

HFC-152a 20.27 1.22 -3.32 1.678 -0.097

A few values of burning speed for the refrigerants have appeared in the literature at the

reference condition of T0 = 298 K and P0 = 1 bar. Jabbour and Clodic (Jabbour and

Clodic 2004) reported a maximum burning speed of about 23 cm/s and 6.7 cm/s for HFC-

152a and HFC-32, respectively. Takizawa et al. (Takizawa, Takahashi et al. 2005)

measured a maximum burning speed of 23.6 cm/s for HFC-152 and 6.7 cm/s for HFC-32.

Linteris (Linteris 2006) obtained a maximum value of 29.6 cm/s as the stretched burning

speed for HFC-152a. Also, he numerically calculated a value of 27.6 cm/s for the

00

20 ))1()1(1(

P

P

T

TbaSS

u

uuu

106

maximum burning speed. The maximum burning speed of HFC-152a in this study was

found to be 22 cm/s which occurred at an equivalence ratio of 1.2 (shown in figure 10).

The maximum burning speed of HFC-32 at 350 K and 2 bar was found at an equivalence

ratio of 1 (about 10 cm/s).

5.6 Summary and conclusion

Laminar burning speeds of HFC-32 and HFC-152a have been measured for a range of

temperatures and pressures. Flame structures have been studied to determine buoyancy

effects and cell formation during the flame propagation. It was observed that

hydrodynamic effects are negligible throughout the combustion of HFC-152a. It was also

seen that the flame instability increases with increasing the pressure, flame radius and

equivalence ratio. The slow burning speed of HFC-32 caused the buoyancy to distort the

flame shape and have a substantial impact on the quality of burning speed measurement

for this refrigerant, especially at low temperatures. Power law correlations have been

developed for laminar burning speed of HFC-32 over the temperature range of 350 to 475

K and pressure range of 2 to 6.8 bar and for laminar burning speed of HFC-152a over the

temperature range of 298 to 580 K and pressure range of 1 to 8 bar to demonstrate the

temperature and pressure dependency of laminar burning speeds of these refrigerants.

Acknowledgments

This research has been supported by ASHRAE (1584-TRP). The authors are thankful to

Dr. Debra Kennoy of Arkema Inc. and Dr. Barbara Minor of DuPont for technical

monitoring and providing the refrigerants.

107

6. Summary and conclusions

108

Summary and conclusions

The summary of this thesis is described in the following sections. Each chapter (paper)

has its individual conclusions which will be explained here.

6.1 Burning speed and entropy production calculation of a transient expanding

spherical laminar flame using a thermodynamic model

A complicated thermodynamic model to calculate laminar burning speeds and entropy

production of a premixed spherical laminar flame is presented. Laminar burning speeds

of n-decane/air mixtures were calculated from the dynamic pressure rise of a combustion

process and it was observed laminar burning speed increases as temperature of the

unburned mixture rises. The results of calculated values were compared with other

published data and were in excellent agreement. Total entropy production and the rate of

entropy production were also calculated. It was observed that combustion process is a

highly irreversible process. Particle trajectories of the gas mixture in the vessel were also

determined.

6.2 Laminar burning speed measurement of premixed n-decane/air mixtures

using spherically expanding flames at high temperatures and pressures

Flame structure and laminar burning speeds of lean n-decane/air premixed mixtures have

been studied at high temperatures and pressures. It was observed that flame is more

vulnerable to onset of instability and cell formation at higher pressures and rich mixtures.

Cell formations in these experiments were recognized to be as a result of hydrodynamic

109

instabilities. Probable effects of flame stretch on measured laminar burning speeds were

carefully investigated. The experimental method showed a good capability for measuring

laminar burning speeds at very low stretch rates in comparison to other conventional

experimental techniques. It was concluded that burning speeds are fairly unaffected by

the small flame stretch rates which exist in these experiments. Laminar burning speeds

were measured over the temperature range of 350 K < T < 610 K and pressure range of

0.5 atm < P < 8 atm. In the range of lean equivalence ratios in these experiments, it was

observed that burning speeds increase as temperature and equivalence ratio increase and

decrease as pressure increases. A power law correlation was developed based on all the

laminar burning speeds data obtained in the experiments. Results show good agreement

with available experimental data in the literature at atmospheric conditions.

6.3 Measurement of laminar burning speeds and determination of onset of

autoignition of Jet-A/air and JP-8/air mixtures in a constant volume spherical

chamber

The burning speeds and the onset of autoignition of Jet-A/air and different samples of JP-

8/air were studied in a set of experiments in a constant volume spherical chamber. The

burning speed measurements were done in lean premixed mixtures and over the pressures

of 1 atm to 4.5 atm and temperatures of 493 K to 700 K. Results showed that these

kerosene type fuels have very similar laminar burning speeds. The diagnosis of

autoignition was done by analyzing the pressure and ionization probes data. It was

observed that autoignition is characterized by intense pressure fluctuations and abrupt

change in the rate of pressure rise. The autoignition was very sensitive to temperature and

it was shown that there is a specific explosion temperature for each sample of JP-8 over a

wide range of equivalence ratios.

110

6.4 Laminar burning speeds and flame structures of mixtures of

Difluoromethane (HFC-32) and 1,1-Difluoroethane (HFC-152a) with air at elevated

temperatures and pressures

Laminar burning speeds of HFC-32 and HFC-152a have been measured for a range of

temperatures and pressures. Flame structures have been studied to determine buoyancy

effects and cell formation during the flame propagation. It was observed that

hydrodynamic effects are negligible throughout the combustion of HFC-152a. It was also

seen that the flame instability increases with increasing the pressure, flame radius and

equivalence ratio. The slow burning speed of HFC-32 caused the buoyancy to distort the

flame shape and have a substantial impact on the quality of burning speed measurement

for this refrigerant, especially at low temperatures. Power law correlations have been

developed for laminar burning speed of HFC-32 over the temperature range of 350 to 475

K and pressure range of 2 to 6.8 bar and for laminar burning speed of HFC-152a over the

temperature range of 298 to 580 K and pressure range of 1 to 8 bar to demonstrate the

temperature and pressure dependency of laminar burning speeds of these refrigerants.

111

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122

Appendix 1

Method of partial pressures to fill the combustion vessel

1- Fill the partial pressure Excel file (see Figure 1) for the fuel that is being

tested to find out the partial pressures and pressure gauge values at the specific

test condition.

2- When the vacuum gauge (VG) shows pressure less than or equal 100

mTorr, close vacuum valves (both vacuum pressure transducer valve (VPTV) and

vacuum pump valve (VPV)).

3- Open PTV to start filling the vessel with the gas that has the lowest partial

pressure until reaching the appropriate partial pressure.

4- Close PTV and the chamber valve (CV). Open the vacuum valves (both

VPTV and VPV) and wait until the vacuum gauge (VG) reach 100 mTorr or less.

Close vacuum valves (both VPTV and VPV).

5- Start to fill the chamber with the second gas (the chamber valve (CV) is

still closed). When it gets higher than previous partial pressure then open the

chamber valve (CV). When reaching the appropriate partial pressure close

chamber valve (CV) and PTV.

6- Open VPV and VPTV and repeat steps 2 to 5 if there are more than two

components in the gas mixture.

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Figure 1: Sample of partial pressure Excel file

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Figure 2: Picture of the valves and pressure gauges system for filling the vessels

125

Appendix 2

FORTRAN code to calculate laminar burning speed

The following section includes the main code and its related subroutines that

calculate the laminar burning speed. The input to this code is the pressure-time

data from the combustion vessel. This code has been written in FORTRAN.

C MAIN PROGRAM THAT READS THE PRESSURE-TIME DATA AND CALCULATES THE BURNING VELOCITY. C========================================================================= IMPLICIT REAL*8 (A-H,O-Z), INTEGER (I-N) C character (len = 30) inputfile C---------------------------------------------------------------------------- C *** Decalre The Variable Arrays *** C REAL*8 TU(1000),TUSUB(1000),TNOT,PNOT,PRES(2000), T(2000),VU(1000),U(1000),H(1000),GAMMA(1000),GAMM, Z(10),PP,XF(1000),CP(10),THERM_COND, QOUT(1000),VOUT(1000), DISPL_THICK(2000),DENSITY_NOT,T_INF,P_INF,AMIX(50),A(10,10), PPA,PPD,PTOT,PPF,RMIX,W_MIX,VISC,WTOT,XXF(1000),POWER,PANSWER, X(2),XB(2000),FVEC1(1000),FVEC2(1000),UTOT,VTOT,TIN, PIN,XG,VOL_B,DXDT(2000),VELOCITY(1000),A_F(1000),R_F(1000), TOLF,TOLX,PRES_INTEG(2000),TB(1000),GAMM_PREV(1000),UB(1000),

VB(1000),vvb(1000),TT(7500),PPRES(7500),PRES_SM(2000),T_SM(2000),9RED_PRES_SM(7500),RED_T_SM(7500),BURNING_RATE(2000), $FLAME_THICKNESS(2000),CPMIX(1000),STR(1000),DRDT(1000),QRAD(1000),$V_B(1000),TB_DUM(1000),q_ratio(1000),rad_ratio(1000),Qe(1000),

cond_ratio(1000), enthalpy(1000), Alpha(1000), CVMIX(1000) C COMMON BLOCK FOR THE BURNED GAS VOLUME THAT IS BEEN CALCULATED IN USRFUN SUBROUTINE common /vol of burned gas/VOL_B

126

ccccccccccccccccccccccccccccc CHARACTER CONA*4, CONB*4, DIL*4, ATOM*6, TIME*4, CH1*4, CH2*4, CH3*4, CH7*4 CCCCCCCCCCCC THE VARIABLES ARE: C TNOT=INITIAL TEMPERATURE, PNOT=INITIAL PRESSURE C TU=UNBURNED GAS TEMPERATURE, TUDUM=DUMMY UNBURNED GAS TEMPERATURE C TUSUB=UNBURNED GAS TEMPERATURE PASSED TO SUBROUTINE C PRES=PRESSURE AT ANY TIME C NPT=NUMBER OF POINTS, C S=ENTROPY OF MIXTURE, DS=DERIVATIVE OF ENTROPY C T=TIME, PHI=STOCHIOMETRIC RATIO C A=JANAF COEFFICIENTS, AMIX=SUM OF PRODUCT OF MOLE FRACTIONS C AND A'S C XF=MOLE FRACTION OF SPECIES, W_MIX=MOLECULAR WEIGHT OF C MIXTURE C PPA=PARTIAL PRESSURE OF AIR, PPD=PARTIAL PRESSURE OF DILUENT C PPF=PARTIAL PRESSURE OF FUEL, PTOT=TOTAL PRESSURE C RMIX=GAS CONSTANT FOR MIXTURE, GAMMA=CP/CV(RATIO OF SPECIFIC HEATS) C GAMM=DUMMY SPECIFIC HEAT RATIO TO PASS TO SUBROUTINE C TB=DUMMY TEMPERTURE TO CHECK THE CKINTP SUBROUTINES C VU=SPECIFIC VOLUME OF UNBURNED GAS C U=SPECIFIC ENERGY OF UNBURNED GAS C THERM_COND=THERMAL CONDUCTIVITY OF THE MIXTURE C VISC=VISCOSITY, A_F=AREA OF THE FLAME, R_F=FLAME RADIUS C UB=SPECIFIC ENERGY OF BURNED GAS, VB=SPECIFIC VOLUME FO THE BURNED GAS C VOL_B=BURNED GAS VOLUME, XB=MASS FRACTION OF BURNED GAS CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C ASKING FOR INITIAL TEMPERATURE AND PRESSURE TNOT = 453 ! TNOT is in KELVIN PNOT = 14.6998

127

PHI = 0.85 WRITE(*,*)TNOT,PNOT,PHI ccccccccc CyyHzz FUEL_AIR_MOLES= 1.0+(4.76*(YY+(ZZ/4.0)))/PHI DIL_MOLES=(DIL_PERC*FUEL_AIR_MOLES)/(1.0-DIL_PERC) PPA=PNOT*(4.76*(YY+(ZZ/4.0))/PHI)/(FUEL_AIR_MOLES+DIL_MOLES) cccccc ETHANOL c FUEL_AIR_MOLES=(1.0+(4.76*(YY+((ZZ-1)/4.0)))/PHI) c DIL_MOLES=(DIL_PERC*FUEL_AIR_MOLES)/(1.0-DIL_PERC) c PPA=PNOT*(4.76*(YY+((ZZ-1)/4.0))/PHI)/(FUEL_AIR_MOLES+DIL_MOLES) PPD=PNOT*DIL_MOLES/(FUEL_AIR_MOLES+DIL_MOLES) PPF=PNOT-(PPA+PPD) goto 103 end if 103 WRITE(*,*)'PPA,PPD,PPF,PNOT' WRITE(*,*)PPA,PPD,PPF,PNOT READ(*,*) C READING THE PRESSURE-TIME DATA c TNOT=((TNOT-32.0)/1.8)+273.15 WRITE(*,*)TNOT C INITIALIZING SOME VARIABLES PTOT=PNOT XG=0.0 C READING THE JANAF COEFFICIENTS,A, FROM THE FILE "DATA2.DAT" C IF THE DILUENT IN AIR IS He OR IF IT IS OXYGEN ONLY YOU HAVE TO

CHANGE THIS C DATA FILE c OPEN(3, FILE='DATA_THERM-for-CH3OH.DAT') c OPEN(3, FILE='DATA_THERM-for-C2H5OH.DAT') c OPEN(3, FILE='DATA_THERM-for-C12H23.DAT') OPEN(3, FILE='DATA_THERM-for-C10H16.DAT') c OPEN(3, FILE='DATA_THERM-for-C7H16.DAT') c OPEN(3, FILE='DATA_THERM-for-CH4.DAT') c OPEN(3, FILE='DATA_THERM-for-reformed.DAT') c OPEN(3, FILE='DATA_THERM-for-C2H6.DAT') c OPEN(3, FILE='DATA_THERM-for-C3H8.DAT') c OPEN(3, FILE='DATA_THERM-for-C4H10.DAT') DO 1 I=1,6 READ(3,*,END=200)ATOM WRITE(*,*)ATOM

128

READ(3,*)(A(I,J),J=1,7) AMIX(J)=0.0 WRITE(*,*) (A(I,J),J=1,7) 1 CONTINUE C CALCULATING MOLE FRACTION, MOLFR, AND THE AMIX USING THE A(I,J) C MOLFR(1)=OXYGEN 200 XF(1)=0.21*PPA/PTOT C MOLFR(2)=NITROGEN IN DILUENT XF(2)=(0.86*PPD/PTOT)+(0.79*PPA/PTOT) XF(3)=0.0 XF(4)=0.0 C MOLFR(3)=ARGON OR ANY OTHER DILUENT REPLACING N2 IN AIR IF(DIL.EQ.'AR')THEN C N2 IN EXTRA DILUENT ONLY XF(2)=0.86*PPD/PTOT XF(3)=0.79*PPA/PTOT XF(4)=0.0 ELSEIF(DIL.EQ.'HE')THEN XF(2)=0.86*PPD/PTOT XF(3)=0.0 XF(4)=0.79*PPA/PTOT ENDIF C MOLFR(5)=FUEL XF(5)=PPF/PTOT C MOLFR(6)=CO2 IN EXTRA DILUENT IF(DIL_PERC.NE.0.0)THEN XF(6)=0.14*PPD/PTOT ELSE XF(6)=0.0 ENDIF WRITE(*,*)'MOLFRACTIONS:' WRITE(*,*)XF(1),XF(2),XF(3),XF(4),XF(5),XF(6) READ(*,*) DO 10 J=1,7 c CALCULATING EACH COEFFICIENT FOR MIXTURE DO 2 I=1,6 AMIX(J)=XF(I)*A(I,J)+AMIX(J) 2 CONTINUE WRITE(*,500) 500 FORMAT('AMIX=') WRITE (*,*) AMIX(J) c READ(*,*) 10 CONTINUE

129

C MOLECULAR WIEGHT OF THE MIXTURE KG/KMOLE OR G/MOLE

W_MIX=(XF(1)*2*15.9994)+(XF(2)*2*14.0067)+(XF(6) 1*(12.011+(2*15.9994)))+(XF(5)*(12.011+(4*1.0079))) 2+(xf(4)*4.0026)+(xf(3)*39.948) WRITE(*,*)'W_MIX' WRITE(*,*)W_MIX READ(*,*) C CALCULATING MIXTURE'S R (KJ/KG.K) RMIX=8.314/W_MIX WRITE(*,*)'RMIX' WRITE(*,*)RMIX READ(*,*) CLOSE(3) I=0 NPT=0 C READING THE INPUT FILE (PRESSURE VS. TIME INPUT FILE) UNITS HAS TO BE C MSEC FOR TIME AND PSI FOR PRESSURE OPEN(1,FILE='pressure.dat') READ(1,*)TIME,CH7 DO WHILE (.NOT.EOF(1)) I=I+1 NPT=I TUSUB(I)=TNOT READ(1,*, END=300) TT(I),PPRES(I) WRITE(*,*)TT(I),PPRES(I),I END DO 300 CLOSE(1) NPT=I C DATA REDUCTION C********************************************** 1111 J = 0 OPEN(6,FILE='PSMOOTH.DAT') OPEN(9,FILE='Preduced.DAT') READ(6,*)TIME,CH7 DO I = 1,NPT READ(6,*) RED_T_SM(I),RED_PRES_SM(I) END DO

130

DO I = 1,NPT,5 J = J + 1 pres_sm(J) = RED_PRES_SM(I) pres(J) = RED_PRES_SM(I) t_sm(J) = RED_T_SM(I) t(J) = RED_T_SM(I) write(9,*) pres_sm(j), t_sm(j), t(j) END DO NPT = J CLOSE(6) write(*,*) npt WRITE(*,*)'WHAT IS THE INFLECTION POINT' READ(*,*)INF c READ(*,*) WRITE(*,*)'T(INF),PRES(INF)' WRITE(*,*)T_SM(INF),PRES_SM(INF) T(INF)=t_sm(inf) PRES(INF)=pres_sm(inf) READ(*,*) P_INF=PRES_SM(INF) T_INF=T_SM(INF) SUMTIME=0.0 SUMPRES=0.0 DO 320 I=2,NPT SUMTIME=SUMTIME+(LOG(T_SM(I)/T_SM(INF))*LOG(T_SM(I)/ 2 T_SM(INF))) WRITE(*,*)'SUMTIME' WRITE(*,*)SUMTIME C READ(*,*) WRITE(*,*)PPRES(I) SUMPRES=SUMPRES+(LOG((PRES_SM(I)-PRES_SM(1))/ 1 (PRES_SM(INF)-PRES_SM(1)))*LOG(T_SM(I)/T_SM(INF))) WRITE(*,*)'SUMPRES' WRITE(*,*)SUMPRES C READ(*,*) 320 CONTINUE C N (CALLED POWER IN THE PROGRAM)IS THE POWER OF THE PRESSURE FIT, C THIS HAS TO BE PASSED TO DISPLACEMNT THICKNESS SUBROUTINE POWER=SUMPRES/SUMTIME 911 WRITE(*,*)'POWER OF THE FIT' WRITE(*,*)POWER READ(*,*) C CALLING THE SUBROUTINE TO CALCULATE THE UNBURNED GAS TEMPERATURE CALL TUN(NPT,TNOT,PNOT,PRES,TUSUB,AMIX,RMIX) C WRITE(*,*)NPT DO 3 K=1,NPT TU(K)=TUSUB(K) WRITE(*,400)

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400 FORMAT('UNBURNED GAS TEMP') c READ(*,*) WRITE(*,*)TU(K),PRES(K),K c READ(*,*) 3 CONTINUE C CALLING THE SUBROUTINES TO CALCULATE SPECIFIC VOLUME AND C ENERGY OF THE UNBURNED GAS CALL VUN(NPT,TU,PRES,RMIX,VU) CALL EUN(NPT,RMIX,AMIX,TU,U) VTOT=VU(1) WRITE(*,*)'VTOT' WRITE(*,*)VTOT c READ(*,*) UTOT=U(1) WRITE(*,*)'UTOT' WRITE(*,*)UTOT c READ(*,*) WRITE(*,*)'VOLUME AND ENERGY UNBURNED' WRITE(*,*) VU(1),U(1) c READ(*,*) WTOT=1.8533E-03/VU(1) DENSITY_NOT=1/VU(1) write(*,*)'wtot,density_not' write(*,*)wtot,density_not C read(*,*) C CALCULATING GAMMA FOR THE MIXTURE AT ANY POINT C SO THE PROGRAM CALLS SUBROUTINE TO CALCULATE CP OF C THE MIXTURE AND THEN THE GAMMA'S OF THE MIXTURE C INITIALIZING THE VARIABLE DO 100 K=1,NPT GAMM=0.0 WRITE(*,*)'K,TU(K)' WRITE(*,*)K,TU(K) C CALLING THE SUBROUTINE TO CALCULATE THE GAMMA AT C EACH POINT FOR THE MIXTURE CALL CPUN(K,TU,CP,A,XF,GAMM,CP_MIX) GAMMA(K)=GAMM CPMIX(K) = CP_MIX c WRITE(*,*) CP_MIX WRITE(*,600) 600 FORMAT('GAMMA UNBURNED GAS AT EACH POINT') WRITE(*,*) GAMMA(K),k c READ(*,*)

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100 CONTINUE C CALCULATING THE VISCOSITY AND THERMAL CONDUCTIVITY OF THE MIXTURE CALL TRANSPORT(TNOT,CP,XF,VISC,THERM_COND) c WRITE(*,*)'VISC,K' WRITE(*,*)VISC,THERM_COND C CALLING THE SUBROUTINE TO CALCULATE THE DISPLACEMENT THICKNESS write(*,*)npt c read(*,*) CALL DISPLACEMENT_THICKNESS (NPT,T_SM,PRES_SM, 1P_INF,T_INF,PNOT,POWER,GAMMA,VISC,DENSITY_NOT,DISPL_THICK) WRITE(*,*)'GOT AFTER DISPLACEMENT' c READ(*,*) qout(1)=0.0 vout(1)=0.0 DO 110 I=2,NPT PRES_INTEG(I)=PRES_SM(I)/14.7 C INTEGRATING THE PRESSURE RESPECT TO DISPLACEMENT THICKNESS CALL INTEG(I,DISPL_THICK,PRES_INTEG,PANSWER) WRITE(*,*)PANSWER,WTOT C READ(*,*) C HEAT AND VOLUME OF THE DISPLACEMENT THICKNESS (BOUNDARY LAYER) QOUT(I)=0.072966*PANSWER*101.325/WTOT VOUT(I)=0.072966*DISPL_THICK(I)/WTOT WRITE(*,*)'I,DIPLACE,QOUT,VOUT' WRITE(*,*)I,DISPL_THICK(I),QOUT(I),VOUT(I) C READ(*,*) 110 CONTINUE cccccccccccccccccccccccccccccccc C INITIALIZING XP=0.0 EP=0.0 VP=0.0 C CALLING THE STANJAN AND CALCULATING THE BURNED C GAS PROPERTIES AND RETURNING THE VALUES 213 DO 350 I=2,NPT PP_PREV=PRES(I-1)/14.7 PP=PRES(i)/14.7 CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C CALCULATING THE TOTAL VOLUME AND TOTAL ENERGY CONSIDERING THE DISPLACEMENT THICKNESS

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UTOT=U(1)- QOUT(I) - qrad(i) - Qe(i) VTOT=VU(1)+VOUT(I) C INITIALIZING THE TOLERANCE AND NUMBER OF TRIALS AND THE NUMBER OF C UNKNOWN VARIABLES (BURNED GAS TEMPERATURE AND MASS FRACTION BURNED) NTRIAL=1000 N=2 TOLX=0.0001 TOLF=0.0001 TB_AVE=0.0 IF (I.EQ.2) THEN X(1)=0.011 X(2)=2000.0 ENDIF C CALL THE SOLVER TO SOLVE THE TWO EQUATIONS AND TWO UNKNOWNS C THIS SUBROUTINE 'MNEWT' IS FROM NUMERICAL RECIPES IN FORTRAN C IT USES THE NEWTON-RAPHSON METHOD TO SOLVE THE EQUATIONS C PLEASE REFER TO THE BOOK FOR THE METHOD CALL MNEWT(I,U,VU,UTOT,VTOT,EP,VP,PP,GAMM_PREV,TB,NTRIAL,X,XP, 1 XB,N,TOLX,TOLF,enthalp) c WRITE(*,*)'MASS FRACTION BURNED LAST SHELL, TOTAL, c 1 TEMPEATURE IN MAIN PROGRAM, and the VOL_B' C MASS FRACTION BURNED AND BURNED GAS TEMPERATURE ARE RETURNED XB(I)=X(1) TB(I)=X(2) enthalpy(i) = enthalp c write(*,*) tb(i) c XP=XB(I)+XP C TOTAL VOLUME OF THE BURNED GAS VOL_B=VOL_B*WTOT C FLAME RADIUS AND AREA OF THE FLAME, SI UNITS c THE R_F(I)=(3*VOLUME OF BURNED GAS/4*PI)^1/3 C VOLUME OF BURNED GAS=WTOT*X(B)*SPECIFIC VOLUME OF BURNED GAS R_F(I)=(3.0*VOL_B*XB(I)/(4.0*3.14159))**(1.0/3.0) A_F(I)=4*3.14159*(R_F(I)**2.0) c WRITE(*,*)'I,R_F(I),A_F(I)' c WRITE(*,*)I,R_F(I),A_F(I) pp = PNOT/14.7 QRAD(I) = pp * 8.2E-8 * VOL_B * XB(I) * (TB(I)**4 - TNOT**4)/ $ WTOT c Converting QRAD to KJ by multiplying the time for each step (0.1 ms or 1e-4)

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c and 1e-3 for J to KJ QRAD(I) = QRAD(I) * 1E-7 V_B(I) = VOL_B * XB(I) Qe(i) = 1e9*(PRES(i)/14.7) * 2.54E-3 * ( R_F(i) - 0.1E-3) * $ (tt(i) * THERM_COND * VU(K) / CPMIX(K)) ** 0.5 350 CONTINUE write(*,*) error = 0. iter = 0 m = 0 do i = 2,npt error = error + (tb(i) - tb_dum(i))**2. end do err_norm = sqrt(error) if (err_norm.ge.1) then iter = iter + 1 write(*,*) 'Number of iterations is' write(*,*) iter do i = 1,npt tb_dum(i) = tb(i) end do goto 213 end if write(*,*) 'error is' write(*,*) err_norm C DERIVATIVE OF MASS FRACTION BURNED RESPECT TO TIME c NPT=K CALL XDOT(NPT,T,XB,DXDT) C DXDT(1)=0.0 CALL STRETCH(NPT,T,R_F,DRDT,STR) OPEN(4,FILE='OUTPUT_VELOCITY.DAT') OPEN(5,FILE='OUTPUT.DAT') OPEN(6,FILE='OUTPUT2.DAT') c write(4,*)"T_Burned, Q_Cond, Q_Rad" DO 360 K=2,NPT C CALCULATING THE VELOCITY (M/SEC) VELOCITY(K)=WTOT*(DXDT(K)*1.0E3)*VU(K)/A_F(K) BURNING_RATE(K) = WTOT * DXDT(K) C WRITE(*,*)'I,VELOCITY' C CALCULATING THE FLAME THICKNESS USING RALLIS & GARFORTH

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FLAME_THICKNESS(K) = ( 4.6 * THERM_COND * VU(K) ) / & ( CPMIX(K) * VELOCITY (K) ) do 919 i = 1,npt q_ratio(i) = qrad(i) / qout(i) rad_ratio(i) = -qrad(i) / u(1) cond_ratio(i) = -qout(i) / u(1) 919 continue c *********************************************************** c WRITE(5,*)R_F(k),CPMIX(K),VU(K) c WRITE(5,*)v_b(k),gamma(k),alpha(k) c WRITE(5,*)t(k),VELOCITY(K),dxdt(k) write(4,*)tu(k),VELOCITY(K),pres(k) c WRITE(4,*)tb(k),tu(k),R_F(K) c write(5,*)FLAME_THICKNESS(K),R_F(K),pres(k) c write(5,*)STR(k),V_B(K),TU(k) c write(5,*)TT(K),qe(K),v_b(k) c write(6,*)cpmix(k),therm_cond,gamma(k) c write(4,*)VU(k),VELOCITY(K),pres(k) c write(5,*)R_F(k),tb(k),enthalpy(k) c write(4,*)v_b(K),rad_ratio(k),cond_ratio(k) c write(4,*)q_ratio(K),qrad(k),qout(k) c write(4,*)tu(k),velocity(K),k 360 continue END

C THIS SUBROUTINE CALCULATES THE UNBURNED GAS TEMPERATURE USING C THE NEWTON-RAPHSON METHOD. SUBROUTINE TUN(NPT,TNOT,PNOT,PRES,TUSUB,AMIX,RMIX) REAL*8 AMIX(50),RMIX REAL*8 TUSUB(1000),PRES(1000),TNOT,PNOT,S,DS,PI,TUDUM, TOL DO 1 I=1,NPT C INITIALIZING VARIABLES S=2.0 DS=1.0 IF (I.EQ.1) THEN C GUESSING THE UNBURNED GAS TEMPERATURE USING INITIAL TEMPERATURE TUDUM=TNOT+0.1 ELSE C FOR OTHER POINTS THE GUESS WILL BE THE PREVIOUS POINT'S TEMPER C -TURE PLUS 0.1 TUDUM=TUSUB(I-1)+0.1 ENDIF PI=PRES(I) C CALLING THE ENTROPY SUBROUTINE TO CALCULATE ENTROPY AND THE

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C DERIVATIVE OF ENTROPY, S AND DS. DO WHILE(ABS(S).GT.0.001) C CALLING THE SUBROUTINES THAT CALCULTES THE ENTROPY AND C IT'S DERIVATIVE CALL ENTROPY(TNOT,PNOT,PI,TUDUM,S,DS,AMIX,RMIX) IF (DS.EQ.0.0) THEN WRITE (*,*) 'INVALID DERIVETIVE' STOP ELSE C USING NEWTON-RAPHSON METHOD TO CALCULATE THE UNBURNED GAS C TEMPERATURE TUDUM=TUDUM-(S/DS) WRITE(*,*)'TUDUM IN TUN_SUB=' WRITE(*,*)TUDUM WRITE(*,*)'PRESS(I),TUDUM' WRITE(*,*)PRES(I), TUDUM C READ(*,*) ENDIF ENDDO C PUTTING THE VALUES IN TUSUB AND INITIAL TEMPERATURE FOR THE C FIRST POINT TUSUB(I)=TUDUM TUSUB(1)=TNOT 1 CONTINUE RETURN END

SUBROUTINE USRFUN(L,U,VU,UTOT,VTOT,EP,VP,PP,GAMM_PREV,TB,x, XP,XB,n,NP,fvec,fjac,enthal) IMPLICIT REAL*8 (A-H,O-Z) REAL*8 X(N),FVEC(NP),FJAC(NP,NP),PP,U(1000),VU(1000),XX real*8 XXF(1000),UUB(1000),VVB(1000),TB(1000),XB(1000), 1GAMM_PREV(1000), enthal CHARACTER CONA*4, CONB*4 XX=X(2) WRITE(*,*)XX,X(1),PP,NP,N FJAC(1,1)=0.0 FJAC(1,2)=0.0 FJAC(2,1)=0.0 FJAC(2,2)=0.0

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EP=0.0 VP=0.0 XP=0.0 read(*,*) IF(L.GT.2)THEN CONA = 'CONT' CONB = 'CONP' DO 1 I=2,L-1 TB(I)=TB(I)*((PP/PP_PREV)**((GAMM_PREV(I)-1.0)/GAMM_PREV(I))) TB_PREV=TB(I) IF(I.EQ.L-1)THEN X(2)=TB(L-1) ENDIF CALL StanjanF(CONA, CONB, TB_PREV,PP,CPP,CVV,TF,PF,VF,HF,UF,SF,WF,XXF,NA) UB(I)=(UF*1.0E-7)*XB(I) VB(I)=(VF*1.0E-3)*XB(I) TB(I)=TF EP=UB(I)*XB(I)+EP VP=VB(I)*XB(I)+VP XP=XB(I)+XP write(*,*)'I PREVIOUS SHELLS,UB(I),VB(I),EP,VP,XP,TB(I)' WRITE(*,*)I,UB(I),VB(I),EP,VP,XP,TB(I) READ(*,*) 1 CONTINUE ELSE UB(L-1)=0.0 VB(L-1)=0.0 ENDIF XX=X(2) CONA = 'CONT' CONB = 'CONP' CALL eqdriv_stanjan(CONA, CONB,XX,PP,CPP,CVV,TF,PF,VF 1 ,HF,UF,SF,WF,XXF,NA) CALL StanjanF(CONA, CONB, XX, PP, 1 CPP,CVV,TF,PF,VF,HF,UF,SF,WF,XXF,NA) PRINT*,'NA',NA print*,'L',L print*,'Tb',TF print*,'P',PF print*,'Vb',VF print*,'Hb',HF print*,'Ub',UF print*,'S',SF PRINT*,'Cp',CPP PRINT*,'Cv',CVV print*,'W',WF print*,'xx',x(1) GAMM_PREV(L)=CPP/CVV

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R=8.314/WF TB(L)=TF VVB(L)=VF*1.0E-3 vol_B=vvb(L) UUB(L)=UF*1.0E-7 C X(1) IS THE BURNED MASS FRACTION AT EACH STEP (L) AND X(2) IS THE BURNED GAS TEMPERATURE AT EACH STEP (L) FVEC(1)= UTOT - ((1-X(1))*U(L))-(X(1)*UUB(L)) FVEC(2)= VTOT - ((1-X(1))*VU(L))-(X(1)*VVB(L)) FJAC(1,2)= -X(1)*CVV*1.0E-7 FJAC(1,1)= U(L) - (UUB(L)) FJAC(2,2)= -X(1)*R/(PP*101.325) FJAC(2,1)= VU(L) - (VVB(L)) enthal = HF 2 CONTINUE RETURN END SUBROUTINE XDOT(NPT,T,XB,DXDT) REAL*8 DXDT(1000),T(1000),XB(1000) DO 1 I=2,NPT-1 123 DXDT(I) = (XB(I+1)-XB(I-1))/(2*(T(I+1)-T(I-1))) 1 CONTINUE DXDT(1)=(XB(2)-XB(1))/(T(2)-T(1)) DXDT(NPT)=(XB(NPT)-XB(NPT-1))/(T(NPT)-T(NPT-1)) RETURN END C THIS SUBROUTINE CALCULATES THE SPECIFIC VOLUME USING THE IDEAL C GAS LAW SUBROUTINE VUN(NPT,TU,PRES,RMIX,VUSUB) REAL*8 TU(1000),PRES(1000),VUSUB(1000),RMIX DO 1 I=1,NPT VUSUB(I)=RMIX*TU(I)/(PRES(I)*101.325/14.7) WRITE(*,*)'VUSUB IN THE SUBROUTINE' WRITE(*,*)VUSUB(I) C READ(*,*) 1 CONTINUE RETURN

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END SUBROUTINE TRANSPORT(Tin,CP,NN,VISC,THERMAL_COND) REAL*8 COEF_SIG(10,10),COEF_EPS(10,10),M(10),SIGMA(10), LAMDA1(10),LAMDA2(10),LAMDA(10),ETA(10),EPS(10), OMEGA1(10),OMEGA2(10) REAL*8 LAMDAMIX,THERMAL_COND,TIN,CP(10),VISC, NN(10) OPEN(2, FILE='COEFF_TRANSP.DAT') DO 10 I=1,2 DO 10 J=1,4 READ(2,*,END=200) COEF_SIG(I,J),COEF_EPS(I,J) 10 CONTINUE DO 20 J=1,4 READ(2,*,END=200)M(J) 20 CONTINUE 200 CONTINUE IF(TIN>300.0) K=2 DO 30 I=1,4 SIGMA(I)=COEF_SIG(K,I) EPS(I)=COEF_EPS(K,I) TSTAR=TIN/EPS(I) DUMMY=1.22*(TSTAR**-0.16) OMEGA2(I)=1.61*(TSTAR**-0.45) IF(DUMMY>OMEGA2(I))OMEGA2(I)=DUMMY ETA(I)=0.000026693*((M(I)*TIN)**0.5) 1/((SIGMA(I)**2)*OMEGA2(I)) ETA(I)=ETA(I)/10.0 LAMDA1(I)=(15.0/4.0)*(8.314/M(I))*ETA(I) LAMDA2(I)=0.88*((2*CP(I)/(5*8.314))-1) 2*LAMDA1(I) LAMDA(I)=LAMDA1(I)+LAMDA2(I) 30 CONTINUE c CALCULATING VISCOSITY OF THE MIXTURE ETAMIX=0.0 LAMDAMIX=0.0

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DO 50 I=1,4 IF(NN(I).EQ.0.0)GOTO 50 DO 40 J=1,4 IF(J.EQ.I) GOTO 40 IF(NN(J).EQ.0.0) GOTO 40 C VARIABLES FOR CALCULATING ETAMIX NUM=1+(((ETA(I)/ETA(J))**0.5)*((M(J)/M(I)) 1**0.25)) DEN=2*(2**0.5)*((1+(M(I)/M(J))**0.5)) PHE=(NUM**2)/DEN PHE_SUM=PHE*NN(J)/NN(I) C VARIABLES FOR CALCULATING LAMBDAMIX NUM=2.41*((M(I)-M(J))*(M(I)-0.142*M(J))) DEN=(M(I)+M(J))**2 CHI=PHE*(1+(NUM/DEN)) CHI_SUM=CHI*NN(J)/NN(I) 40 CONTINUE LAMDAMIX=LAMDAMIX+(LAMDA1(I)/(1+CHI_SUM))+ 2(LAMDA2(I)/(1+PHE_SUM)) ETAMIX=ETAMIX+(ETA(I)/(1+PHE_SUM)) 50 CONTINUE VISC=ETAMIX THERMAL_COND=LAMDAMIX RETURN END SUBROUTINE STRETCH(NPT,T,R_F,DRDT,STR) REAL*8 DRDT(1000),T(1000),R_F(1000),STR(1000) DO 1 I=2,NPT-1 DRDT(I) = (R_F(I+1)-R_F(I-1))/(2*(T(I+1)-T(I-1))) 1 CONTINUE DRDT(1)=(R_F(2)-R_F(1))/(T(2)-T(1)) DRDT(NPT)=(R_F(NPT)-R_F(NPT-1))/(T(NPT)-T(NPT-1)) DO I = 1,NPT STR(I) = (2/R_F(I)) * DRDT(I) END DO RETURN END

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SUBROUTINE mnewt(L,U,VU,UTOT,VTOT,EP,VP,PP,GAMM_PREV,TB,ntrial, 1x,XP,XB,n,tolx,tolf,enthalp) IMPLICIT DOUBLE PRECISION (A-H,O-Z), INTEGER (I-N) DOUBLE PRECISION tolf,tolx,x(n),PP,U(1000),VU(1000),TB(1000), 1 XB(1000),GAMM_PREV(1000), enthalp PARAMETER (NP=10) CU USES lubksb,ludcmp,usrfun INTEGER i,k,indx(NP) REAL*8 d,errf,errx,fjac(NP,NP),fvec(NP),p(NP) do 14 k=1,ntrial C CALLING THE USERFUN SUBROUTINE THAT CALCULATES THE EQUATIONS AND C JACOBIAN'S MATRIX call usrfun(L,U,VU,UTOT,VTOT,EP,VP,PP,GAMM_PREV, 1 TB,x,XP,XB,n,NP,fvec,fjac,enthalp) errf=0. do 11 i=1,n errf=errf+abs(fvec(i)) 11 continue if(errf.le.tolf)return do 12 i=1,n p(i)=-fvec(i) 12 continue call ludcmp(fjac,n,NP,indx,d) call lubksb(fjac,n,NP,indx,p) errx=0. do 13 i=1,n errx=errx+abs(p(i)) x(i)=x(i)+p(i) TB_PREV=X(2) 13 continue if(errx.le.tolx)return 14 continue return END SUBROUTINE ludcmp(a,n,np,indx,d) IMPLICIT REAL*8 (A-H,O-Z), INTEGER (I-N) INTEGER n,np,indx(np),NMAX REAL*8 d,a(np,np),TINY PARAMETER (NMAX=500,TINY=1.0e-20) INTEGER i,imax,j,k REAL*8 aamax,dum,sum,vv(NMAX)

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d=1. do 12 i=1,N aamax=0. do 11 j=1,N if (abs(a(i,j)).gt.aamax) aamax=abs(a(i,j)) 11 continue if (aamax.eq.0.) pause 'singular matrix in ludcmp' vv(i)=1./aamax 12 continue do 19 j=1,n do 14 i=1,j-1 sum=a(i,j) do 13 k=1,i-1 sum=sum-a(i,k)*a(k,j) 13 continue a(i,j)=sum 14 continue aamax=0. do 16 i=j,n sum=a(i,j) do 15 k=1,j-1 sum=sum-a(i,k)*a(k,j) 15 continue a(i,j)=sum dum=vv(i)*abs(sum) if (dum.ge.aamax) then imax=i aamax=dum endif 16 continue if (j.ne.imax)then do 17 k=1,n dum=a(imax,k) a(imax,k)=a(j,k) a(j,k)=dum 17 continue d=-d vv(imax)=vv(j) endif indx(j)=imax if(a(j,j).eq.0.)a(j,j)=TINY if(j.ne.n)then dum=1./a(j,j) do 18 i=j+1,n a(i,j)=a(i,j)*dum 18 continue endif 19 continue return END SUBROUTINE lubksb(a,n,np,indx,b)

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IMPLICIT REAL*8 (A-H,O-Z), INTEGER (I-N) INTEGER n,np,indx(np) REAL*8 a(np,np),b(np) INTEGER i,ii,j,ll REAL*8 sum ii=0 do 12 i=1,n ll=indx(i) sum=b(ll) b(ll)=b(i) if (ii.ne.0)then do 11 j=ii,i-1 sum=sum-a(i,j)*b(j) 11 continue else if (sum.ne.0.) then ii=i endif b(i)=sum 12 continue do 14 i=n,1,-1 sum=b(i) do 13 j=i+1,n sum=sum-a(i,j)*b(j) 13 continue b(i)=sum/a(i,i) 14 continue return END SUBROUTINE INTEG(J,TT,INTEGVAR,ANSWER) REAL*8 ANSWER REAL*8 INTEGVAR(1000),DELTAT,TT(1000) ANSWER=0.0 DO 1 I=1, J IF(I.EQ.1)THEN DELTAT=0.0 ELSE DELTAT=TT(I)-TT(I-1) WRITE(*,*)'DELTAT IN SUBROUTINE,INTEGVAR(I),INTEGVAR(I-1)' WRITE(*,*)DELTAT,INTEGVAR(I),INTEGVAR(I-1) ANSWER = ANSWER+ (0.5*DELTAT*(INTEGVAR(I)+INTEGVAR(I-1))) WRITE(*,*)'ANSWER IN INTEGRAL' WRITE(*,*)ANSWER ENDIF 1 CONTINUE RETURN END C THIS SUBROUTINE CALCULATES THE GAMMA FOR UNBURNED C GAS MIXTURE AT ANY POINT SUBROUTINE CPUN(K,TU,CP,A,XF,GAMM,CP_MIX)

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REAL*8 CP(10),TU(1000),GAMM,GAM_DUM(100),XF(1000),CP_MIX REAL*8 A(10,10),CV(10) DO 1 I=1,6 CP(I)=0.0 DO 2 J=1,5 C CALCULATING THE SPECIFIC HEAT (COSTANT P) FOR EACH SPECIES USING C JANAF COEFF CP(I)=CP(I)+((A(I,J)*(TU(K)**(J-1)))*8.314) 2 CONTINUE C CALCULATING THE CONSTANT VOLUME SPECIFIC HEAT AND THE RATIO GAM_DUM(I)=CP(I)/CV(I) 1 CONTINUE CP_MIX = 0 CV_MIX = 0. GAMM = 0. DO 3 I=1,6 C CALCULATING GAMMA AND CP FOR THE MIXTURE CP_MIX = CP_MIX + CP(I) * XF(I) CV_MIX = CP_MIX -8.314 GAMM = CP_MIX/CV_MIX 3 CONTINUE RETURN END C THIS SUBROUTINE CALCULATES THE ENTROPY AND ITS DERIVATIVE AT C ANY POINT OF PRESSURE AND TU C SUBROUTINE ENTROPY(TNOT,PNOT,PI,TUDUM,S,DS,AMIX,RMIX) REAL*8 AMIX(50),RMIX REAL*8 TNOT,PNOT,S,DS,PI,TUDUM,SUMS,SUMDS WRITE (*,*)TUDUM C CALCULATING THE ENTROPY AND IT'S DERIVATIVE USING IDEAL GAS C RELATIONS SUMS=AMIX(1)*LOG(TUDUM/TNOT) SUMDS=AMIX(1)/TUDUM WRITE(*,*)'SUMS,SUMDS' WRITE(*,*)SUMS,SUMDS DO 10 I=2,5

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SUMS=SUMS+(AMIX(I)*((TUDUM**(I-1))-(TNOT**(I-1)))/(I-1)) SUMDS=SUMDS+(AMIX(I)*(TUDUM**(I-2))) WRITE(*,*)'SUMS2,SUMDS2' WRITE(*,*)SUMS,SUMDS 10 CONTINUE S=RMIX*(SUMS-LOG(PI/PNOT)) DS=RMIX*SUMDS FORMAT('S,DS,PI') WRITE (*,*)S,DS,PI RETURN END C THIS SUBROUTINE CALCULATES THE SPECIFIC ENERGY SUBROUTINE EUN(NPT,RMIX,AMIX,TU,USUB) REAL*8 TU(1000),USUB(1000) REAL*8 AMIX(50),RMIX C CALCULATING THE SPECIFIC ENERGY USING IDEAL GAS REALTIONS DO 1 J=1,NPT USUB(J)=(AMIX(1)+(AMIX(2)*TU(J)/2)+ 1 ((AMIX(3)/3)*(TU(J)**2))+ 2 ((AMIX(4)/4)*(TU(J)**3))+ 3 ((AMIX(5)/5)*(TU(J)**4))+ 4 (AMIX(6)/TU(J)))*(RMIX * TU(J)) - (RMIX*TU(J)) 1 CONTINUE RETURN END