ESTIMATION OF FLAME TEMPERATURE AND DROPLET COMBUSTION … · 2017. 4. 28. · liquid boiling point, none of the heat is conducted into the liquid interior and the vaporization rate

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 4, April 2017, pp. 289–308 Article ID: IJMET_08_04_032 Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=4 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed

ESTIMATION OF FLAME TEMPERATURE AND

DROPLET COMBUSTION CHARACTERISTICS

OF HYDROCARBON FUELS FOR SPRAY

APPLICATIONS

Shah Shahood Alam, Arees Qamareen and Rahul Varshney

Pollution and Combustion Engineering Lab, Department of Mechanical Engineering,

Aligarh Muslim University, Aligarh-202002, U.P. India

ABSTRACT

A fundamental and comprehensive work has been carried out in determining, adiabatic

flame temperatures of pure fuels like n-heptane (alkane), ethanol (alcohol), methyl

linoleate (bio diesel ) and commercial fuels: DF2, automobile gasoline and jet propulsion

fuel JP5 through computer programmes as a function of ambient temperature, pressure

and equivalence ratio including the effects of dissociation. Important thermophysical and

transport properties are evaluated next on the basis of adiabatic flame temperature using

appropriate correlations by developing computer codes. These properties are then used in

calculating important droplet combustion parameters like transfer number burning rate,

burning constant and droplet lifetime for three cases of steady state, droplet heating and

droplet heating with convection from the point of view of their incorporation in spray

combustion CFD analysis.

Key words: Pure and commercial hydrocarbon fuels, ambient temperature, pressure and composition effects, adiabatic flame temperature, thermodynamic properties, droplet burning parameters, spray combustion.

Cite this Article: Shah Shahood Alam, Arees Qamareen and Rahul Varshney, Estimation of Flame Temperature and Droplet Combustion Characteristics of Hydrocarbon Fuels For Spray Applications. International Journal of Mechanical Engineering and Technology, 8(4), 2017, pp. 289–308. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=4

Estimation of Flame Temperature and Droplet Combustion Characteristics of Hydrocarbon Fuels For Spray Applications


1. INTRODUCTION AND LITERATURE VIEW

It is estimated that over 90% of the energy used for transportation, power production and heating is produced by the combustion of petroleum based fuels. These applications include gas fired furnaces and gasoline engines; oil fired furnaces, gas turbine and diesel engines; liquid rockets; coal fired furnaces, fluidized beds etc. [1]. The transportation sector utilizes a large chunk of liquid fuels to power aircraft gas turbine engines, diesel and petrol engines.

In all these devices, although spray combustion is the dominant feature, however, understanding of the laws governing isolated liquid droplet combustion is an essential prerequisite for analysis (modelling) of complex liquid fuel sprays [2].

A hydrocarbon liquid fuel spray (made up of discrete droplets) encounters extreme conditions of temperature, pressure, apart from other factors when it enters the combustion chamber of practical devices. For example, the pressure inside the combustion chamber may exceed the injected fuel's critical pressure in case of diesel and gas turbine engines leading to supercritical combustion.

It is a established fact that the accuracy of numerical simulation is heavily dependent on the correct estimation of thermodynamic properties [3]. In the present work, computer codes are developed for estimating the adiabatic flame temperature (an important parameter for combustor design and emissions) as a function of ambient temperature, pressure and composition for different fuels.

Thermodynamic properties are determined next on the basis of flame temperature and finally important droplet combustion variables are calculated which can be used in spray combustion analysis.

1.1. Spherically Symmetric, Steady State Droplet Combustion:

Since the early 1950’s, it has been recognized that spherically symmetric burning of an isolated liquid droplet (achieved through drop towers) [4], represents an ideal situation to study the complex coupling of the chemical reactions and two phase flow and providing a fundamental foundation for developing an accurate description of spray combustion.

The combustion of a single isolated liquid droplet in an oxidizing medium is shown schematically in Figure 1 below.

Figure 1 Droplet Combustion Process



Following important assumptions are invoked for the spherically symmetric, droplet combustion model:

1. The system is spherically symmetric.

2. The fuel is single component liquid with zero solubility for gases. 3. Phase equilibrium prevails at the liquid-vapour interface expressed by the Clausius-Clapeyron relation.

3. Infinitely fast chemical kinetics.

4. The gas phase Lewis number (Leg) is unity.

5. Radiation heat transfer is negligible.

6. The pressure is uniform and constant.

1.2. Advanced Approaches

1.2.1. Droplet Heating Effect

By accounting for transient heating of the liquid droplet (Figure 1), it is possible to explain the experimentally observed initial period during which the droplet burning rate is low, even with the infinitely fast chemistry. An energy balance at the droplet surface shows that heat conducted to the surface from the gas phase balances with heat lost from the surface due to vaporization phase change.

Initially, when the droplet temperature is low, much of the heat supplied to the surface is conducted inward, resulting in a lower rate of vaporization. Once the droplet heats up towards the liquid boiling point, none of the heat is conducted into the liquid interior and the vaporization rate reaches its quasi-steady value ( 2 -d law is followed) [4].

1.2.2. Fuel Droplets in a Convective Stream

Individual droplets forming a liquid hydrocarbon fuel spray face high convection/turbulance when injected in a combustion chamber.

In practical applications, droplets in a spray will be moving at some relative velocity to the surroundings. The Reynolds number

gRe based on relative velocity and gas properties can be of

the order of 100 [5]. Boundary layer present due to convection surrounding the droplet enhances heat and mass transport rates over the values for the spherically symmetric droplet.

Further, shear force on the liquid surface causes an internal circulation that enhances the heating of the liquid. As a result, vaporisation rate increases with increasing Reynolds number.

An effective and simpler way of tackling this situation is to modify the heat and mass transfer rates by employing multiplicative correction for convection in terms of empirical correlations [6, 2].

1.2.3. Variable Thermodynamic Properties

In advanced approaches related to droplet combustion modelling, thermophysical and transport properties are not treated as constant as assumed in simplified theories. In most of these studies, thermophysical properties are strong functions of temperature, pressure and concentration.

Actually 2 -d law assumes a non convective, steady state spherical combustion together with constant properties assumption. In an actual combustion chamber, temperature may vary from a few hundred degrees to a few thousand degrees in the gas surrounding the droplet. Pressure may



vary from atmospheric to many times the critical pressure of the fuel (depending upon the engine). Fuels used may be multicomponent in nature.

These variations are bound to affect the thermophysical properties, which must be evaluated as a function of temperature, pressure and concentration as the situation suggests. Only then the modelling results obtained will be closer to the experimental observations under the same burning conditions.

The spherically symmetric diffusion controlled combustion model is usually broken up into two regions, the inflame zone (between the droplet surface and flame) and the post flame zone (between the flame surface and ambient atmosphere).

Hubbard et al. [7] numerically integrated the governing equations of energy (in both liquid and gas phases) and mass, momentum and species equations in gas phase, for a diffusion controlled droplet combustion model.

These authors used different empirical relations for calculating the thermophysical properties and came to the conclusion that one can use the arithmetic mean or empirical results of Sparrow and Gregg (popularly known as Sparrow’s one third rule).

2. PROBLEM FORMULATION

2.1. Flame Temperature Estimation

One of the most important aspects of spray analysis is the choice of an appropriate droplet vaporization/combustion model which is going to predict the spray characteristics like burning rate, residence time and emission behaviour.

Inclusion of oversimplified models may give approximate results whereas complex models are generally overlooked to avoid costly computations. Hence, droplet combustion model has to be simple, but realistic [5].

When modelling combustion of a droplet, the key parameter is the evaluation of burning constant, which effects the burning rate and droplet lifetime (residence time). Once the burning constant is obtained, it can be used as an input parameter in a spray combustion CFD code like

Open FOAM, an open source code used for simulating spray combustion.

In majority of spray burning applications, liquid sprays are made up of droplets ranging in size from 30-100 . Further, existing air pressure and temperature before combustion can be as high

as 100 bar, 800 K and 40 bar, 1500K respectively in diesel and gas turbine engines.

Also, these engines operate with multicomponent fuels in these conditions in presence of air. Therefore, correct estimation of flame temperature is of high priority since thermodynamic properties are calculated on the basis of flame temperature.

A simplified approach for calculating adiabatic flame temperature (AFT) may be valid for single component fuels burning (without dissociation effects) in atmospheric conditions. However, these methods are not suitable for practical situations.

To overcome this deficiency, present work has developed a detailed computer program for estimating adiabatic flame temperature by incorporating correlations provided by Gülder [8].

The expression for estimating flame temperature, given below was developed by curve fitting of data obtained from a detailed chemical equilibrium code covering the range of pressure/temperature and fuels prevalent in gas turbines and diesel engines.

bk

mµ



This expression is applicable for the given ranges [8]:

[0.3 1.6; 0.1 7.5 ;MPa P MPaφ≤ ≤ ≤ ≤

275 950 ; 0.8 / 2.5]K Tu K H C≤ ≤ ≤ ≤

( )2

.exp . yx zT Aadiabatic

ασ β σ λ π θ ψ

= + (2.1)

where,

21 1 1

22 2 2

23 3 3

x a b c

y a b c

z a b c

σ σ

σ σ

σ σ

= + +

= + +

= + + π is dimensionless pressure = /

oP P (

oP = 0.1013 MPa )

θ is dimensionless initial mixture temperature /u a

T T=

aT = 300 K

ψ is /H C atomic ratio

σ = φ for φ ≤1 (φ is the fuel-air equivalence ratio defined as

( / ) /( / )actual stoichiometric

F A F A ) and

σ = 0.7, for φ φ− >1

Now,

( )

( )

/

/pf l pa a

u

pf pa

C T A F C T LT

C A F C

+ −=

+ (2.2)

pfC is the specific heat of fuel vapour

in kJ/kg K , aircp is the specific heat of air obtained from standard air tables, l

T is the liquid fuel

temperature.

pfC =(0.363+0.000467.

bT )(50.001

foρ ) (2.3)

foρ is density of fuel at 288.6 K , bT is boiling point Temperature ( K ),

[ ]2.40630.2527

0.9479 100mb f

Tψ ρ−

= ⋅ (2.4)

mbT is the fuel mid boiling point ( K )

fρ is the relative liquid density of fuel at 20 C

° .

Once φ and θ are known, other constants can be chosen to be used in equation (2.1).

For getting flame temperature at high pressures, fuel’s boiling pointbT is evaluated using

Redlich-Kwong equation of state, latent heat of vaporizationfg

h by Watson correlation [9] and

liquid density by employing Hankinson-Brobst-Thompson method [3,9].

lρ



2.2 Calculation of Fuel Vapour Specific heat pfv

C , Thermal Conductivity fv

λ and

Absolute Viscosityfv

µ .

Once the flame temperature is determined, reference temperatures are calculated using 1/3 rule [7]. Thermophysical and transport properties are evaluated next through computer programs developed for the present work.

The values obtained for fuel vapour properties likepfv

C , fv

λ and fv

µ are further modified using

1/3 rule for composition i.e. (for air and fuel vapour mixture).

2.3. Correlations for Obtaining pfv

C , fv

λ and fv

µ

We know the reference temperatures for the inner and outer zones are:

1 1/ 3 2 / 3b f

Tr T T= +, 2 1/ 3 2 / 3

fTr T T∞= +

(2.5)

where, f

T , T∞ and b

T are respectively the flame, ambient and boiling point temperatures.

Specific heat and thermal conductivity of fuel vapours are provided by the following equations [10]:

1

1

1

6

2

(0.363 0.000467 )(5.0 0.001 )

10 [13.2 0.0313( 273)]{ / 273}

2.0 0.0372[ / ]

fv r bn

n

fv bn r

r bn

cp T

T T

n T T

ρ

λ −

= + −

= − −

= −

Then, 1/ 3 2 / 3air fv fv air

cp cp cp+ = + (2.6)

2; is at

air rhere cp T

, similarly,

1/ 3 2 / 3air fv fv air

λ λ λ+ = + (2.7)

For determining absolute viscosity of fuel vapourfv

µ , method of Bird et. al [11] was used. For

absolute viscosity of air-fuel vapour mixtureair fv

µ +, relation suggested by Lucas [9] was considered.

2.4. Determination of Droplet Burning Characteristics

Droplet combustion characteristics were determined through the following relations for transfer number, burning rate, burning constant and droplet lifetime (for steady state burning), given respectively as [2]:

( )/T c air fv b fgB h Cp T T hν + ∞= ∆ + − (2.8)

2f l l b

m r kπ ρ= (2.9)

( )8 ln 1 b air fv T l air fvk B cpλ ρ+ += + (2.10)

24d lo b

t r k= (2.11)

ch∆ is the heat of combustion of fuel



(kJ/kg),ν is the ( / )stoichA F on mass basis, fg

h is the latent heat of vaporization (kJ/kg), l

r is the

instantaneous droplet radius. In the case of droplet burning with droplet heating, the relation for

TB is modified as:

( )

( )c air fv b

T

fg pl b

h Cp T TB

h C T T

ν + ∞

∞

∆ + −=

+ − (2.12)

plC is liquid fuel specific heat. with droplet heating and convection is given by equation

(2.13) below

( ) ( )( )

0.5 0.331 0.3c air fv b g g

T

fg pl b

h Cp T T Re PrB

h C T T

ν + ∞

∞

∆ + − +=

+ − The gas phase Reynolds number based on droplet

diameter and Prandtl numbers are respectively: 0 /air fvg air fv

Re D U ρ µ+∞ += , (2.14)

.g air fv air fv air fv

Pr Cp µ λ+ + += , (2.15)

0D is the original droplet diameter, U∞ is the relative velocity between the droplet surface and

the ambient gas and air fv

ρ+

is the mixture density.

The flow diagram (Figure 2) depicts the general methodology adopted for the present work.

Figure 2 Flow Diagram

TB



3. RESULTS AND DISCUSSION

Some important results are plotted and discussed. Figures 3-6 show the behaviour of adiabatic flame temperature (AFT) which is actually the equilibrium flame temperature as a function of ambient pressure, temperature and equivalence ratio for n-heptane (pure fuel) and commercial, multicomponent fuels like diesel fuel DF2, jet propulsion fuel JP5 and automobile gasoline.

Figures 3-6 suggest that at a fixed value of ambient pressure and equivalence ratio , AFT

increases with an increase in ambient temperature .

It is also found to increase with ambient pressure for a particular value of ambient temperature. Also, there is an increase in AFT with an increase in equivalence ratio at a fixed ambient

temperature and pressure.

Trend of present results are in general conformity with those of [8,12].

Figure 3 AFT Variation with ambient pressure at different temperatures and equivalence ratios

Figure 4 AFT Variation with ambient pressure at different temperatures for DF2

Figure 5 AFT versus ambient pressure for JP5

P∞ φ

T∞

φ



Figure 6 Behaviour of AFT with ambient pressure for Gasoline

Droplet sizes usually encountered in combustion systems can be of the order of 20 -100

. Plots of burning constant against for =1 atmosphere are depicted in Figures 7-9 for

a spherically symmetric,100 droplet of n-heptane (C7H16), ethanol (C2H5OH) and methyl

linoleate (C19H34O2) burning (i) without droplet heating (steady state combustion), (ii) with droplet heating and (iii) with droplet heating and convection.

It is observed that increases with an increase in for each fuel. This is because as is

increased, AFT also increases which leads to a higher value of transfer number and

subsequently enhanced .

This variation is true for all the three cases. Further, highest values of are noted for the third

case of droplet heating with convection, followed by steady state combustion case and droplet heating case.

values are highest for the third case because due to convection, more fuel is evaporated

from the droplet surface leading to a higher burning rate and eventually higher burning constant

(since burning constant is directly propotional to burning rate ).

Here convection effect dominates the droplet heating effect. For droplet heating case (ii), relatively less fuel evaporates initially from the droplet surface thereby leading to a lower value.

Figure 7 Variation of burning constant for n-heptane, ethanol and methyl linoliate with ambient temperature at 1 atm without droplet heating

mµ

mµ bk T∞P∞

mµ

bk T∞ T∞

TB

bk

bk

bk

bkf

m



Figure 8 Burning constant behavior with droplet heating

Figure 9 Burning constant variation with droplet heating and convection

Figure 10 Boiling point against ambient pressure

Figure 11 Latent heat of Vaporization versus ambient pressure



Figure 12 Variation of liquid density against ambient pressure

From Figure 10, it is observed that boiling point temperature b

T increases with an increase in

ambient pressure . The values of bT at high pressures were calculated using Redlich-Kwong

equation of state [9] which is more accurate.

It is a fact that an increase in ambient pressure should lead to higher boiling point temperature

and lower latent heat of vaporizationfg

h (Figure11). Variation of fg

h with was determined

through Watson relation [9].

Figure 12 shows that liquid density increases with an increase in . This behaviour was

obtained using Hankinson-Brobst-Thompson relation [3,9].

It is further observed that initially this increases is gradual but becomes quite high as the critical pressure of the fuel (20.89 bar) is approached since thermodynamic properties assume abnormal behaviour in the vicinity of the critical point [3].

Other important properties like specific heat, thermal conductivity, viscosity and density of air+fuel mixture denoted respectively as

pgC ,

gλ ,

gµ and

gρ were calculated for DF2 (C14H3O), a

commercial fuel used in diesel vehicles using the correlations provided by Chin and Lefebvre [10].

A plot ofpg

C against at different (Figure 13), suggests thatpg

C increases with both

ambient pressure and temperature, if any one parameter is held constant. It is also noted that as the ambient pressure approaches the critical pressure of the fuel of about 20.89 bar, there is a decrease in

pgC values at the given ambient temperature.

From Figure 14, it is observed that thermal conductivityg

λ of air-fuel mixture shows a slight

increasing trend at a particular temperature with increasing ambient pressure values while at a fixed pressure,

gλ increases with .

A plot of absolute viscosityg

µ versus ambient pressure and temperature (Figure 15) shows that

there is an appreciable increase in the viscosity of air-fuel mixture with increasing at a fixed

, also it increases with at a given value.

For calculating absolute viscosity of air-fuel vapour mixture, relation suggested by Lucas [9] was considered.

Figure 16 conveys the information that the air-fuel mixture density g

ρ decreases with an

increase in ambient temperature at a given ambient pressure and increases with ambient pressure for a given temperature. The mixture density was determined with the help of a real gas equation of state.

P∞

P∞

lρ P∞

P∞ T∞

T∞

T∞

P∞ P∞ T∞



From Figure 17, it is observed that the transfer number (without droplet heating) or steady state

transfer numberT

B increases with when pressure is held constant, while it increases with

at constant temperature. Equation 2.8 was utilised for calculating T

B .

For the case of droplet heating, the transfer number T

B is got from equation 2.12. The plot of

TB with (Figure 18) tells that at a constant value of ambient temperature,

TB decreases with

ambient pressure and if the pressure is kept constant, then T

B increases with an increase in ambient

temperature .

Variation of transfer number with droplet heating and convection (obtained from equation 2.13) is depicted in Figure 19, which suggests that at a given temperature, transfer number first increases and then decreases with an increase in pressure, while at a fixed pressure, it increases with increasing temperature.

A plot of steady state burning constant b

k with ambient pressure P∞ at different ambient

temperatures T∞ is shown in Figure 20. It can be noted that b

k increases with at different

ambient temperatures. Also, it increases with T∞ at constant P∞ .

The b

k variation is found to follow the same trend as that of T

B (Figure 17), since b

k is directly

propotional to T

B from equation 2.10.

The same qualitative agreement of b

k with transfer number is seen for droplet heating and

droplet heating with convection cases (Figures 21-22).

From Figures (23-25), it is observed that the trend of burning ratef

m variation with ambient

pressure at various temperatures lead to the same conclusions as for the burning constant and transfer number for the three cases.

The variation of droplet lifetime dt with ambient pressure at different ambient temperatures

(Figures 26-28) suggest that dt is varying in just the opposite manner to transfer number, burning

constant and burning rate due the relationship coming out from the 2 -d law (equation 2.11).

Finally, Figures (29-31) are plots of droplet lifetimedt versus ambient pressure P∞ and ambient

temperature T∞ for the three cases of steady state, droplet heating and droplet heating with

convection for the purpose of meaningful comparison.

While Figure 29 is for DF2, Figures 30-31 are respectively for jet propulsion fuel JP5 (C12H24) and automobile gasoline (C7H17). The trend in the variation of droplet lifetime with ambient pressure and temperature for the three caes is similar.

Faeth et al. [13] conducted experiments on the steady state burning of spherically symmetric, 875 micron n-decane liquid droplet under zero gravity at ambient temperature and different reduced anmbiet pressures

rP (Figure 32).

Their results indicate that droplet lifetime decreases with an increase in reduced ambient pressure (defined as /

cP P∞ ) till the reduced pressure

rP is unity, (in the subcritical ambient

pressure range), after that, there is an increase in the droplet lifetime in the supercritical range (reduced pressure

rP greater than one).

The same trend was obtained in Figures 29-31, that is for the steady state combustion case, droplet lifetime is found to decrease with ambient pressure P∞ as the critical pressure

cP is

T∞P∞ P∞

P∞

T∞

P∞



approached or in other words in the subcritical ambient pressure range for DF2 and automobile gasoline, while for the JP5 fuel (Figure 30), it starts to increase slightly at higher pressures.

Quantitative agreement is not possible due to the difference in fuel properties including the critical properties and droplet diameter.

For example Faeth et al [13] have considered a pure fuel like n-decane whereas present work has undertaken commercial multicomponent fuels.The critical properties for these fuels are: (DF2; Pc=20.89 bar, Tc=725.9K), (JP5; Pc=22.75 bar, Tc=684.8K), (Automobile gasoline; Pc=24.9 bar, Tc=568.8K).

Another comparison of dt versus r

P is shown in Figure 33, where results of present model for

a combustion of spherically symmetric, 2000 n-heptane were compared with those of Kadota

and Hiroyasu [14], who conducted an experimental study of combustion of suspended fuel droplets like n-heptane etc. at reduced pressures as large as 1.5 under the influence of natural convection.

It was observed that the two results depict the same trend, apart from small quantitative differences.

Another investigation is required to validate the behaviour of droplet lifetime in the supercritical ambient pressure range (

rP >1)

Figure 13 Specific heat versus ambient pressure at different temperatures

Figure 14 Thermal conductivity against ambient pressure and temprature

mµ



Figure 15 Variation of viscosity with ambient pressure at different temperatures

Figure 16 Density versus ambient pressureand temperature

Figure 17 Variation of transfer number with pressure and temperature

Figure 18 Behaviour of transfe number for droplet heating



Figure 19 Transfer number versus pressure at different temperatures

Figure 20 Plot of burning constant against pressure at various temperatures

Figure 21 Variation of burning constant with pressure

Figure 22 Burning constant versus pressure



Figure 23 Burning rate variation with pressure and temperature

Figure 24 Burning rate versus pressure and temperature

Figure 25 Behaviour of burning rate with pressure at different temperatures

Figure 26 Variation of droplet lifetime



Figure 27 Droplet lifetime variation in case of droplet heating

Figure 28 Droplet lifetime versus pressure and temperature

Figure 29 Plot of droplet lifetime with pressure and temperature for

Figure 30 Droplet lifetime against pressure and temperature



Figure 31 Droplet lifetime versus pressure and temperature

Figure 32 Droplet lifetime versus reduced ambient pressure

4. CONCLUSIONS AND SCOPE FOR FUTURE WORK

[1] There is an increase in adiabatic flame temperature (AFT) with respect to both ambient pressure P∞

and temperature at a fixed equivalence ratio , and also, AFT increases with an increase in , at

constant P∞ and for each fuel checked.

[2] pg

C increases with both ambient pressure and temperature, if any one parameter is held constant.

[3] An increase in ambient pressure leads to a higher boiling point temperature and lower latent heat of vaporization

fgh .

∗

∗

∗

∗

∗

0.0 0.3 0.5 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0∗

t d(

s)

Pr

Present Model

Experiment of Kadotaand Hiroyasu [14]

Figure 33: Ambient pressure effect on droplet lifetime

T∞φ φ

T∞



[4] Liquid density increases with an increase in . The increase becoming steep as the critical

pressure of the fuel is approached.

[5] Gas phase thermal conductivity g

λ and absolute viscosityg

µ increase with both ambient pressure

and temperature, whereas density g

ρ decreases with an increase in ambient temperature at a given

ambient pressure and increases with ambient pressure for a given temperature.

[6] It is observed that the steady state transfer numberT

B increases with when pressure is held

constant, while it increases with at constant temperature.

For the case of droplet heating, at a constant value of ambient temperature, T

B decreases with

ambient pressure and if the pressure is kept constant, then T

B increases with an increase in ambient

temperature .

Variation of transfer number with droplet heating and convection suggests that at a given temperature, transfer number first increases and then decreases with an increase in pressure, while at a fixed pressure, it increases with increasing temperature.

[7] The b

k variation is found to follow the same trend as that ofT

B , since b

k is directly propotional to

TB from equation 2.10.

[8] It is observed that the trend of burning ratef

m variation with ambient pressure at various

temperatures lead to the same conclusions as for the burning constant and transfer number for the three cases.

[9] The variation of droplet lifetime dt with ambient pressure at different ambient temperatures suggest

that dt is varying in just the opposite manner to transfer number, burning constant and burning rate

due the relationship coming out from the 2 -d law (equation 2.11).

[10] A more meaningful comparison is obtained from Figures 29-31, where variation of droplet

lifetime dt is plotted against ambient pressure at different ambient temperatures for the three

cases on a single graph.

Future Work

The present work can be extended to obtain important droplet combustion characteristics related to flame position like dimensionless flame diameter, flame standoff distance, flame to droplet diameter ratio etc which can be determined by solving the unsteady gas phase conservation equations of mass, species and energy.

Apart from burning variables, important emission characteristics can also be estimated with respect to single droplet combustion.

lρ P∞

T∞P∞

P∞

T∞

P∞ T∞



REFERENCES

[1] Ragland, Kenneth W., and Bryden, Kenneth M., Combustion Engineering, Second Edition, CRC Press, Taylor and Francis Group, 2011.

[2] Turns, S. R., An Introduction to Combustion Concepts and Applications, McGraw Hill International Edition, 2011.

[3] Kuo, K. K., Principles of Combustion, Second Edition, John Wiley and Sons, 2005.

[4] Law, C.K., Recent Advances in Droplet Vaporization and Combustion, Progress in Energy and Combustion Science, Vol. 8, pp. 171-201, 1982.

[5] Sirignano W. A., Fluid Dynamics and Transport of Droplets and Sprays, Cambridge University Press, 1999.

[6] Faeth, G. M., Current Status of Droplet and Liquid Combustion, Progress in Energy and Combustion Science, Vol. 3, pp. 191-224, 1977.

[7] Hubbard, G. L., Denny, V. E., and Mills, A. F., Droplet Evaporation: Effects of Transients and Variable Properties”, International Journal of Heat and Mass Transfer, Vol. 18, pp. 1003-1008, 1975.

[8] Gülder, Ö. L., Flame Temperature Estimation of Conventional and Future Jet Fuels, Transactions of the ASME, Vol. 108, pp. 376-380, 1986.

[9] Reid, R.C., Prausnitz, J. M., and Poling, B. E., The Properties of Gases and Liquids, Fourth Edition, McGraw Hill Book Company, 1989.

[10] Chin, J. S. and Lefebvre, A.H., Steady-State Evaporation Characteristics of Hydrocarbon Fuel Drops, AIAA Journal, Vol. 21, No.10, pp.1437-1443, 1983.

[11] Bird, R. B., Stewart, W. E., and Lightfoot, E. N., Transport Phenomena, Second Edition, John Wiley and Sons, Inc, 2004.

[12] Lefebvre, A. H., Gas Turbine Combustion, Taylor and Francis Group, 270 Madison Avenue, New York, 1999.

[13] Faeth et. al., Supercritical Bipropellant Droplet Combustion, Proceedings of the Twelfth Symposium (International) on Combustion, The Combustion Institute, pp.9-17, 1969.

[14] Kadota, T. and Hiroyasu, H., Combustion of a Fuel Droplet in Supercritical Gaseous Environments, Proceedings of the Eighteenth Symposium (International) on Combustion, The Combustion Institute, pp. 275-282, 1981.

Documents

ESTIMATION OF FLAME TEMPERATURE AND DROPLET COMBUSTION … · 2017. 4. 28. · liquid boiling point, none of the heat is conducted into the liquid interior and the vaporization rate