Winter Jordanian German Academy Feb 2006

Governing Equations for Combustion Processes Prepared By: Rasha Odetallah & Fatima Abbadi

Combustion Combustion 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. CO 2 is the only oxidation product. 3. Spherical Particle

1. Diffusion of gaseous reactant O 2 through the film surrounding the coal particle to the surface of the solid. 2. Diffusion of O 2 through the ash to the surface of unreacted coal particle core which should be adsorbed by the surface. 3. Reaction of gaseous O 2 with solid carbon at the reaction surface to form adsorbed CO Adsorbed products have to be desorbed from the inner solid surface.

5) Diffusion of CO 2 through the ash back to the exterior surface of the solid. 6) Mass transfer of CO 2 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.

 The expected profiles of C CO2,C O2 and T are shown in fig(2): Fig (2): Variations of temperature and concentrations of O 2 and CO 2 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

Where: K 0 : 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 r A: rate of reaction s: subscript for solid phase

Mathematical Modeling of Combustion  Governing Equations : Conservation Equations Assumptions: 1. Solid particle 2. Complete Combustion 3. CO 2 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 O 2 gas entering the CV through the faces a, c and e and leaving through the faces b, d and f.

Governing Equations LHS: The first term represents the accumulation of O 2 in the control volume. The second, third and fourth terms represent the mass flow of O 2 in x, y and z directions where: u: velocity of O 2 in x-direction v: velocity of O 2 in y-direction w: velocity of O 2 in z-direction : mass density of O 2

Governing Equations RHS: The right hand side term describes the gas production due to the evaporation of coal during combustion. Where: : particle mass change n coal : local particle numeric density (no. of particles per unit volume) X O2 : mass stoichiometric ratio (amount of O 2 per 1Kg of fuel) for the combustion reaction.

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.

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 :

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.

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/m 2.k 4 A : Area

Governing Equations  Conservation of Species: Where: r A: is the species reaction rate (mol/cm 3 /sec) D: is the species diffusion coefficient Y: is the mole fraction of O 2

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 A. Kanury, Introduction to Combustion Phenomena, India, R. Bird, W. Stewart, E. Lightfoot, Transport Phenomena, USA, O. Levenspiel, Chemical reaction engineering, 3 rd edition, India, J. Holman, Heat transfer, 8 th edition,USA, L. Jelemensky, R. Zajdlik, J. Markos, B. Remiarova, Modeling of coal particle combustion, Acta Montanistica Slovaca, vol 3,1998, pp

THANKS FOR ALL