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Show Lime stone "'\ QJ c: 0 N en c: ....... 10 QJ .r= QJ ~ n. 4.9i)m - 15 0\ QJ r-c: 0 N c: Upper Level ...... 0 Fuel + Air ....... 10 c: U ~ .U Lower Level QJ Fuel + Air c: 0 N en .-c: 0 0 u Coo 1 ing Air ... ;J ,J, Lime \ ombust .on and Coo11ng Air F.ig. 100 o (pU. ¢ + pu .tp )= ~ r¢,13 q; +Scp" (1) oX j J J oX j oX j where x. denotes the three coordinates directi6ns,j=1,2&3, p is the time averaged density and ~ 1 is the laminar exchange coefficient of' the entity ¢. The three time-averaged velocity components are denoted by U . • The velocity fluctuation are denoted Jby u .. The term ~ represents the time averagedJvalue of the general dependent variable. The terms p u~~ represent the fluctuation correlations and are known as the flux of the entity ¢. due to turbulent diffusion. The term S denotes the source/sink of the entity ~. The term ¢ can take the value of U,V,W, k,e,H&fand any other scaler variables, references 1&2. PHYSICAL MODELLING -In order to yield eq.l soluable,several closure forms should be used to model the turbulent diffusion terms u.~ and the source terms S0 . These assump~ions corne under the mathematical models as; • Turbulence Models • Combustion Models • Heat Transfer Models Turbulence characteristics of the flow are commonly and adequately(l) represented by at least two properties or more. The Two-equation k-e turbulence model had been developed, tested and validated for many flow situations,see references 3,4 and 5 • The model was found to yield reasonable predict~ons of the turbulent characteristics of the flow, such as the Reynolds and Shear stresses. The model is based(3),on the solution of two transport equations for k and e,the kinetic energy of turbulence and its dissipation rate respectively. The effective viscosity Peff is then calculated as: Peff = 0.09 P k 2 / e ............ (2) The turbulent diffusion terms are expressed as; - - a Ui o u.u·=P ff(~ + J 1 J e v Xj aG . ~) + Z ..... (3) 1 where the term Z represents the density variation contribution. It should be noted that the effect of density gradient is already being taken care of. Details of the turbulence model and its modifications to handle steep density and pressure gradients can be found in references (1 and 6). The combustion characteristics of the flow and flame are represented here |