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Published in:
2010 | OriginalPaper | Chapter
Reynolds Stress Model Based on the RDT Equations and Turbulence Dynamics in the Aerodynamic Nozzle
Authors : V. L. Zimont, V. A. Sabelnikov
Published in: Progress in Turbulence III
Publisher: Springer Berlin Heidelberg
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The well known challenge of turbulence modeling is the inclusion of the effects of the large-scale structure in the one-point model equations. We proposed an approach [1,2] to the Reynolds stresses modeling that is based on an unclosed equation in terms of the spectral tensorr
$\Phi_{i,j}(\vec{k})$
deduced in [3]:
$ \frac{d\Phi_{ij}}{dt} - E_{\alpha \beta} \frac{\partial k_{\alpha} \Phi_{ij}}{\partial k_{\beta}} + E_{i \alpha} \Phi_{\alpha j } + E_{j \alpha} \Phi_{i \alpha} - E_{j \alpha} \overline{u_{i} u_{\alpha}} $
$-2E_{\alpha \beta} \frac{k_\alpha}{k^2} (k_i \Phi_{\beta j} + k_j \Phi_{i \beta}) + \dots = 0 \,, (1)$
where
$E_{i j}(t) = \partial U_i / \partial x_j$
and dots denote missed nonlinear and dissipation terms approximated in our model.