Question

Expand the Reynolds stress term (- ho overline{u_{i}^{‘} u_{j}^{‘}}) for the Spalart-Allmaras model.

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

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

(c) (- ho overline{u_{i}^{‘} u_{j}^{‘}} = 2 ho overline{v} f_{v1} (frac{partial U_i}{partial x_i}+frac{partial U_j}{partial x_j}))

(d) (- ho overline{u_{i}^{‘} u_{j}^{‘}} = 2 ho overline{v} f_{v1} (frac{partial U_i}{partial x_j}+frac{partial U_j}{partial x_i}) )

Answer 1

Right choice is (b) (- ho overline{u_{i}^{‘} u_{j}^{‘}} = ho 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

(- ho overline{u_{i}^{‘} u_{j}^{‘}} = ho_t (frac{partial U_i}{partial x_j}+frac{partial U_j}{partial x_i}))

Converting to Spalart-Allmaras terms,

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