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Velocity gradient tensor scalar invariants

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October 24, 2022, 11:52	Velocity gradient tensor scalar invariants	#1
Boone New Member Join Date: May 2022 Posts: 18 Rep Power: 5	Hello, I am performing RANS simulation with the k-omega SST model. I would like to compute the two following scalar invariants of velocity gradient for a 2D periodical channel flow: $Q_A=-0.5A_{ij}A_{ji}$ and $Q_s=-0.5S_{ij}S_{ji}$ with $A_{ij}=\frac{\partial U_i}{\partial x_j}$ and $S_{ij} = 0.5 (A_{ij}+A_{ji})$ . Could you confirm me that: $Q_A=-0.5A_{ij}A_{ji}=-0.5(A_{11}A_{11}+A_{12}A_{21}+A_{22}A_{22}+A_{21}A_{12})$ ? $Q_S=-0.5S_{ij}S_{ji}=-0.5(S_{11}S_{11}+S_{12}S_{21}+S_{22}S_{22}+S_{21}S_{12})$ ? Moreover, I want to compute the ratio between production and dissipation. The production can be approximated with : $P\nu_t S^2$ . Could you confirm me that the production is linked to the invariant? $P=\nu_t(-2Q_S)$ ? Thanks ! Boone

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dissipation, invariant, k-omega sst model, production, rans

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