1.

Expand the Reynolds stress term \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\) for the Spalart-Allmaras model.(a) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = \rho \overline{v} f_{v1} (\frac{\partial U_i}{\partial x_i}+\frac{\partial U_j}{\partial x_j})\)(b) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = \rho \overline{v} f_{v1} (\frac{\partial U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i})\)(c) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = 2\rho \overline{v} f_{v1} (\frac{\partial U_i}{\partial x_i}+\frac{\partial U_j}{\partial x_j})\)(d) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = 2\rho \overline{v} f_{v1} (\frac{\partial U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i}) \)The question was posed to me in an online quiz.The query is from Turbulence Modelling topic in chapter Turbulence Modelling of Computational Fluid Dynamics

Answer»

Right choice is (b) \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = \rho \overline{v} f_{v1} (\frac{\PARTIAL U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i})\)

Easy explanation: The Reynolds STRESS TERM is GIVEN as

\(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = \rho_t (\frac{\partial U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i})\)

Converting to Spalart-Allmaras terms,

\(-\rho \overline{u_{i}^{‘} u_{j}^{‘}} = \rho \overline{v} f_{v1} (\frac{\partial U_i}{\partial x_j}+\frac{\partial U_j}{\partial x_i})\) .



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