Winter Jordanian German Academy

5 -10 Feb 2006

Governing Equations for Combustion Processes

Prepared By:

Rasha Odetallah

&

Fatima Abbadi

CombustionCombustion is defined as the chemical reaction of fuel and oxidizer involving significant release of energy as heat

About 90% of the world’s energy comes from combustion of fossil fuels. Energy needed for transport, electricity generation, heating and industrial processes.Combustible material can be fluid, solid or gas.

Combustion Phenomena

A Model of Coal Combustion:

Solid material combustion involves the following steps assuming:

1. Complete Combustion 2. CO2 is the only oxidation product. 3. Spherical Particle

22 COOC

1. Diffusion of gaseous reactant O2 through the film surrounding the coal particle to the surface of the solid.

2. Diffusion of O2 through the ash to the surface of unreacted coal particle core which should be adsorbed by the surface.

3. Reaction of gaseous O2 with solid carbon at the reaction surface to form adsorbed CO2.

4. Adsorbed products have to be desorbed from the inner solid surface.

5) Diffusion of CO2 through the ash back to the exterior surface of the solid.

6) Mass transfer of CO2 through the gas film back into the main body of fluid.

7) Heat of combustion is conducted and radiated to the surrounding.

The previous steps occurs in series, the slowest step determines the burning rate which is step no. 3 that includes surface reaction.

Visualization of Combustion Process

Case: spherical particle

Fig(1): representation of reaction for particle of unchanging size.

22 COOC

The expected profiles of CCO2,CO2 and T are shown in fig(2):

Fig (2): Variations of temperature and concentrations of O2 and CO2 of the burning carbon particle.

Reaction Rate:

The burning rate (reaction rate) for combustion is determined by the chemical kinetics and therefore, the process is kinetic controlled. The burning rate depends on the temperature in accordance with a law of Arrhenius type, the local oxygen and carbon concentrations.

Mathematical Modeling of Combustion

Mathematical Modeling of CombustionWhere:

K0: Frequency factor.

T: Surface temperature of the

carbon surface, Kelvin

E: Activation energy

n, m: Solid surface conc. exponent, oxygen, carbon respectively

R: universal gas constant

K: rate constant

C: concentration

rA: rate of reaction

s: subscript for solid phase

mCS

nOSA

mCS

nOSA

CCRT

EKr

RT

EKK

CCKr

,,0

0

,,

.).exp(.

)exp(.

..

2

2

Mathematical Modeling of Combustion Governing Equations : Conservation Equations

Assumptions:1. Solid particle

2. Complete Combustion

3. CO2 is the only product

4. 3 Dimensional Analysis (J. Makovicka et al, 2005)

5. An element of Control Volume (∆x, ∆y, ∆z)

6. Unsteady state

Governing Equations Equation of continuity:

Governing Equations

Equation of continuity:

This continuity equation for O2 gas entering the CV through the faces a, c and e and leaving through the faces b, d and f.

dt

dmnX

z

w

y

v

x

u

tcoal

coalOgasOgasOgasOO .

).().().(2

2222

Governing Equations

LHS:

The first term represents the accumulation of O2 in the control volume.

The second, third and fourth terms represent the mass flow of O2 in x, y and z directions where:

u: velocity of O2 in x-direction

v: velocity of O2 in y-direction

w: velocity of O2 in z-direction

: mass density of O2

Governing Equations

RHS:The right hand side term describes the gas production due

to the evaporation of coal during combustion.

Where:

: particle mass change

ncoal : local particle numeric density (no. of particles per unit

volume)

XO2 : mass stoichiometric ratio (amount of O2 per 1Kg of

fuel) for the combustion reaction.

dt

dmcoal

Governing Equations Conservation of Momentum:

Momentum = mass * velocity

Governing Equations

LHS:The first term represents the momentum accumulation

stored inside the CV.The second term represents the x-momentum entering

into the CV through the faces a to b.The third term represents the x-momentum entering into

the CV through faces c to d.The third term represents the x-momentum entering into

the CV through faces e to f.

zyxx

P

z

wv

y

uv

x

u

t

uzxyxxxgasgasOgasgasOgasOgasO

)..()..().(2222

2

Governing Equations

The fourth term is the pressure force on faces a to b.

RHS:The right hand side term represents the viscous forces in x-

direction on the system.

Where :

2

2

2

2

2

2

,,z

w

y

v

x

uxzxyxx

Governing Equations Conservation of Energy:

Governing Equations

In the energy equation we take into account heat transfer by conduction and radiation.

h: denotes the specific enthalpy of either coal or gas.

crcoalcoal

coal

combcoal

coalgasgasOgasgasOgasgasOgasO

qqhdt

dmn

hdt

dmn

z

hw

y

hv

x

hu

t

h

.

.)..()..()..(

2222

Governing Equations LHS:

The first term represents the energy accumulation

The second, third and fourth terms represent the x ,y and z energy directions into the CV.

RHS:

The right hand side terms are

1. The heat of combustion

2. Enthalpy increase due to phase change

3. Heat transfer by radiation

4. Heat transfer by conduction

Governing Equations

Where:

, K: thermal conductivity

ε : emissivity

σ : Stefan-Boltzman constant = 5.66*10-8 w/m2.k4

A : Area

).(.. 44surfacesgasr TTAq

Ay

TKqc .

Governing Equations

Conservation of Species:

Where:

rA: is the species reaction rate (mol/cm3/sec)

D: is the species diffusion coefficient

Y: is the mole fraction of O2

AO

OOOOOOOOOOOO r

y

YD

yz

Yw

y

Yv

x

Yu

t

Y

2

2

22222222222 .)..()..()..(

Finally ,

To solve the previous partial differential equations we use a numerical method such as Finite Volume Method.

References:

1. J. Makovicka, V. Havlena, M.Benes, On a model of coal combustion, Proceedings of ALGORITMY,2005,pp. 12-21

2. A. Kanury, Introduction to Combustion Phenomena, India, 1996

3. R. Bird, W. Stewart, E. Lightfoot, Transport Phenomena, USA, 1960

4. O. Levenspiel, Chemical reaction engineering, 3rd edition, India, 1999

5. J. Holman, Heat transfer, 8th edition,USA,19976. L. Jelemensky, R. Zajdlik, J. Markos, B. Remiarova,

Modeling of coal particle combustion, Acta Montanistica Slovaca, vol 3,1998, pp. 295-300

THANKS FOR ALL