“…The values of the magnitudes of the streamfunction for Approaches II (Figure 7) and III decrease as the Rayleigh number increases, which facilitates convergence and obtains the numerical solution for high Ra values. Note that the orders of magnitude of the maximum values of the streamfunction for Ra = 10 7 obtained with Approach I are almost 3 × 10 3 times greater than those obtained with Approach II, 3,35–39 and 1 × 10 6 greater than those obtained with Approach III, which clearly influences the stability and numerical solution 40–43 . This can be seen in Table 5, where the computation times in minutes are reported for different Ra values and different mesh sizes.…”
Section: Resultsmentioning
confidence: 90%
“…) , respectively. Three different nondimensionalization approaches were employed and designated as Approach I, 2,14,16,31,34 Approach II, 3,[35][36][37][38][39] and Approach III. [40][41][42][43] 2.1.…”
Section: Ta B L Ementioning
confidence: 99%
“…The system of elliptical PDEs formed by Equations ( 6)-(18d) was solved by orthogonal collocation method [33][34][35][36][37][38][39][40][41][42][43][44][45] (using Legendre polynomials and the computational code NEWCOL2L, as described in Jiménez-Islas. 46 The discretized equations were solved using the modified Newton's method (Equation 20) with LU factorization, and finite differences were employed to approximate the partial derivatives of the Jacobian matrix.…”
Section: Numerical Solutionmentioning
confidence: 99%
“…The governing equations for both cases can be rewritten using the streamfunction‐vorticity forms ( ψ ‐ ω ) ψ and ω , respectively. Three different nondimensionalization approaches were employed and designated as Approach I , 2,14,16,31,34 Approach II , 3,35–39 and Approach III 40–43 …”
This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2‐D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 103 and 108, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.
“…The values of the magnitudes of the streamfunction for Approaches II (Figure 7) and III decrease as the Rayleigh number increases, which facilitates convergence and obtains the numerical solution for high Ra values. Note that the orders of magnitude of the maximum values of the streamfunction for Ra = 10 7 obtained with Approach I are almost 3 × 10 3 times greater than those obtained with Approach II, 3,35–39 and 1 × 10 6 greater than those obtained with Approach III, which clearly influences the stability and numerical solution 40–43 . This can be seen in Table 5, where the computation times in minutes are reported for different Ra values and different mesh sizes.…”
Section: Resultsmentioning
confidence: 90%
“…) , respectively. Three different nondimensionalization approaches were employed and designated as Approach I, 2,14,16,31,34 Approach II, 3,[35][36][37][38][39] and Approach III. [40][41][42][43] 2.1.…”
Section: Ta B L Ementioning
confidence: 99%
“…The system of elliptical PDEs formed by Equations ( 6)-(18d) was solved by orthogonal collocation method [33][34][35][36][37][38][39][40][41][42][43][44][45] (using Legendre polynomials and the computational code NEWCOL2L, as described in Jiménez-Islas. 46 The discretized equations were solved using the modified Newton's method (Equation 20) with LU factorization, and finite differences were employed to approximate the partial derivatives of the Jacobian matrix.…”
Section: Numerical Solutionmentioning
confidence: 99%
“…The governing equations for both cases can be rewritten using the streamfunction‐vorticity forms ( ψ ‐ ω ) ψ and ω , respectively. Three different nondimensionalization approaches were employed and designated as Approach I , 2,14,16,31,34 Approach II , 3,35–39 and Approach III 40–43 …”
This work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2‐D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 103 and 108, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.
“…Esta sección describe en profundidad los resultados obtenidos bajo las condiciones nominales. Se comparan tres modelos, el modelo 3D-0D, el modelo RELAP5 y un modelo CFD 3D completo anterior [20]. El último incluía la geometría completa del separador, secador, bajante y precalentador.…”
Section: Funcionamiento Del Gv En Condiciones Nominalesunclassified
Se aplicó un procedimiento computacional multidominio para modelar el generador de vapor RD-14M. Se utilizó el enfoque Euleriano de dos-fluidos para modelar el flujo de agua y vapor, el método de blending para los términos de fuerzas interfaciales, el modelo de partición de calor de pared (RPI) para la ebullición de pared y el método de transferencia de calor conjugado (CHT) para acoplamiento térmico entre los circuitos primario y secundario. El modelo computacional de todo el generador de vapor se modeló mediante la combinación de una simulación 3D completa del riser y el modelado 0D con condiciones de borde dinámica ad hoc de las regiones del separador/secador, downcomer y precalentador. La implementación se realizó en la plataforma OpenFOAM(R). Se estudió inicialmente la sensibilidad de malla sobre las condiciones nominales de estado estacionario y luego se estudió el evento transitorio parada del reactor. Los resultados se compararon con los modelos RELAP5 y full-3D anteriores y se obtuvo buen acuerdo. El modelo completo demostró ser una herramienta adecuada para comprender el comportamiento termo-hidráulico general de los generadores de vapor, pero también los fenómenos locales alrededor de los tubos y baffles dentro del riser.
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