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Show turbulence fields (/cand e). This formulation has been shown to recover the standard value of 0.09 for an inertial sublayer in an equilibrium boundary layer. Secondly, a improved transport equation for turbulence dissipation is incorporated. These improvements have been shown to provide substantially better performance than that of the S K E model for a wide variety of flows [10,12]. Reynolds stress model The Boussinesq hypothesis used in the SKE and RKE turbulence models provides a relatively cost effective means of modeling the Reynolds stresses. A disadvantage of this method, though, is that the Boussinesq hypothesis assumes \M to be an isotropic scalar quantity, which is not strictly true. Also, gradient transport models such as the Boussinesq hypothesis neglect turbulent transport via large scale, coherent structures. Unlike the S K E and R K E first order closure models, the Reynolds stress model (RSM) involves calculation of the individual Reynolds stresses using differential transport equations [13,14] given by LocalTimeDerivatn-e Cj sConvecnon -g- IW'"X +P(^kiUi+SikUJ)\ dxL Djj sTurbulentDiJJuswn "^titi Dh ^MolecularDiJJusion ( ~P du Ul;«U«.* * ~d x, V U ,U - du.,) dxk P;; eSlressProduction -Wfau'fl + gju'fi) G^s Buoyancy Production fymPressureStmin EH ^Dissipation - 2pQk (u]uZeikm + uymejkm ) F- sProducttonbySystemRotation The individual Reynolds stresses are then used to obtain closure of the Reynolds-averaged momentum equations. Of these terms, Cy, DLjj, Py, and Fjj do not require modeling. Unfortunately, several terms in the exact equations for the Reynolds stresses (D\ Glj( fop and Ey) are unknown, and modeling assumptions and constants are required in order to close the equations. DTij and G(j are modeled by employing gradient-diffusion assumptions. The pressure-strain term is modeled according to the proposals of Gibson & Launder [13] and others. The dissipation tensor is modeled in terms of the scalar dissipation rate, e, whose equation is identical to that used in the standard k-e model. Combustion chemistry Chemical reactions and heat release within the flame were modeled using an adiabatic, equilibrium chemistry model [15]. With this approach, the combustion chemistry is assumed to be mixing limited (chemical time scales « mixing time scales), and the thermodynamic and chemical state within the flame is described solely in terms of an appropriately defined mixture fraction variable, f, given, for example, by / = Z -Z 7 -Z Here ZH denotes the elemental mass fraction of hydrogen atoms, with F,0 specifying the fuel and oxidizer streams, respectively. Fluent's prePDF module, employing the CHEMKIN [16] chemical kinetics database, was used to determine the functional relationships, ${f), between temperature, density and species concentrations and the mixture fraction. Turbulence-chemistry interactions were accounted for via an assumed-shape, beta PDF, (3(r), for mixture fraction. The beta PDF requires the local mixture fraction mean and variance; these are computed via the transport equations TMH 9N4f f tr dX; G, 3 |
