W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. ASME Journal of Heat Transfer, 106:699--706, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of the expansion, correspond to rays that have undergone increasing numbers of reflections. This very natural physical interpretation is often referred to as successive orders of scattering in radiative transfer literature [24, 38] The method of discrete ordinates used in radiative heat tanslet [11, 23], atmospheric scattering [24] and neutron transport [7] works by applying quadrature rules to discretely sampled positions and directions. Thus, it is essentially an application of the Nystr;3m method. A major advantage of the Nystom method is that it can easily accomodate differential operators ....

W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. ASME Joural of Heat Trasfer, 106:699 706, 1984.

....ordinates and proceeds through increasing values of p;q for each p . Zero weight starting directions, satisfying the Cartesian coordinates form of (1) are used to obtain each I p; 1 = 2 . Reflecting wall boundaries and the scattering source can be accounted for by iteration in the manner of [9]. Since our primary focus in this paper is the treatment of wall boundaries, we will not concern ourselves here with the details of the scattering solution. The equation to be satisfied at the outer (r) wall of the domain is I p;q = fflI w b ae X p 0 ;q 0 0 w p 0 ;q 0 p 0 ....

Fiveland, W. A., "Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures," Journal of Heat Transfer, Vol. 106, No. 4, 1984, pp. 699--706.

....with flux limiting. The temperature field T n 1;p ij is used. The system is solved by successive sweeps through the mesh for each ordinate direction. In the computations for this paper we set both reflection and scattering to zero. The ordinate values are taken from the S 6 set listed in [15]. 4.3 Corrector In this step, we perform an approximate projection [2] in order to enforce the divergence constraint (4.2) and find n 1=2 . In the following, D a and G a are standard discretizations of the divergence and the gradient operators. We solve the difference equations (Lffi) ....

W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. J. Heat Transfer, 106:699--706, November 1984.

....of the expansion, correspond to rays that have undergone increasing numbers of reflections. This very natural physical interpretation is often referred to as successive orders of scattering in radiative transfer literature [24, 38] The method of discrete ordinates used in radiative heat ransfer [11, 23], atmospheric scattering [24] and neutron transport [7] works by applying quadrature rules to discretely sampled positions and directions. Thus, it is essentially an application of the Nystrom Linear Operators and Integral Equations 2 17 method. A major advantage of the Nystom method is that it ....

W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. ASME Journal of Heat Transfer, 106:699--706, 1984.

....is not a limitation. A k Gamma ffl model is used for turbulent transport[16] Chemical kinetics is modeled using a a two step scheme for natural gas combustion [30] coupled with a simplified turbulent kinetics model [6, 23] Radiative transport is modeled using the discrete ordinates method [9, 12, 22]. Viscosity and thermal conductivity are modeled with simple polynomial correlations [17] while GRI Mech thermochemical data [13] is used to compute enthalpies, heat capacities, and heats of formation. The equation of state is the perfect gas law. The wall of the furnace is represented as a ....

....with flux limiting. The temperature field T n 1;p ij is used. The system is solved by successive sweeps through the mesh for each ordinate direction. In the computations for this paper we set both reflection and scattering to zero. The ordinate values are taken from the S 6 set listed in [12]. 4.3 Corrector An approximate projection [3] is now used to enforce the divergence constraint (4.2) and determine n 1 = 2 . In the predictor, we use a time lagged pressure gradient to compute a velocity that does not necessarily satisfy the divergence constraint (4.2) ae n 1 = 2 ij ....

W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. J. Heat Transfer, 106:699--706, November 1984.

....is restricted solely by an advective CFL condition. The methodology is applicable only in the low Mach number regime (M :3) typically met in industrial burners. Our method is based on an approximate projection formulation [3] Radiative transport is modeled using the discrete ordinates method [4, 5]. The main goal of this work is to introduce and investigate the simulation of burners using a higher order projection method for low Mach number combustion. As such, we only treat the case of axisymmetric flow in gas fired burners for which the boundaries can be aligned with a rectangular grid, ....

....formulae with flux limiting. The temperature field T n 1;p ij is used. The system is solved by successive sweeps through the mesh for each ordinate direction. In the computations for this paper we set both reflection and scattering to zero. The ordinate values are taken from the S 6 set listed in [4]. Corrector In this step, we perform an approximate projection [3] in order to enforce the divergence constraint (14) and find n 1=2 . In the following, D a and G a are standard discretizations of the divergence and the gradient operators. We solve the difference equations (Lffi) ....

W. A. Fiveland, "Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures", J. Heat Transfer, vol. 106, pp. 699--706, 1984.

....l ; w; k; ffl and (U Delta r ) n 1 = 2 ij for = u; v: II) Compute ae n 1 ij = ae n ij Gamma Deltat P l (r Delta aeUm l ) n 1 = 2 ij . III) Predict values of k; ffl; m l ; h; u ; v ; and w at t n 1 using the Crank Nicholson method. IV) Use a discrete ordinates method [16, 17, 18] to compute (r Delta q rad ) n 1 using values of T computed from the values of h and m l found in (III) V) Correct the values of all the flow quantities to provide the solution at time t n 1 , again using Crank Nicholson differencing. In steps (III) and (V) the evolution equations for the ....

....form of the first two rows of equation (3) The update for species is itself performed sequentially in two steps, one accounting for convection and diffusion and the other for kinetics. In step (III) we use a diamond difference discrete ordinates model similar to those presented in [16, 17, 18], modified to include the appropriate emitting, reflecting, and absorbing boundary conditions along the embedded boundary. In the corrector, an approximate projection [12, 15] is used to enforce the divergence constraint (1) and determine n 1 = 2 . The equation r Delta 0 1 ae n 1 ....

W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. J. Heat Transfer, 106:699--706, November 1984.

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W. A. Fiveland. Discrete-ordinates solutions of the radiative transport equation for rectangular enclosures. ASME Journal of Heat Transfer, 106:699--706, 1984.

No context found.

Fiveland, W. A., "Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures," Journal of Heat Transfer, Vol. 106, No. 4, 1984, pp. 699--706.

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