Publication Date:
2015-06-03
Description:
Direct simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, G = ∇ u ¯ . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants P GG T , Q GG T , and R GG T of the tensor GG T , and imposing the proper cubic near-wall behavior, i.e., ν e = O ( y 3 ) , we deduce that the eddy-viscosity is given by ν e = ( C s 3 p q r Δ ) 2 P G G T p Q G G T − ( p + 1 ) R G G T ( p + 5 / 2 ) / 3 . Moreover, only R GG T -dependent models, i.e., p 〉 − 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman’s model constant via C s 3 p q r = 3 C V r ≈ 0 . 458 ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman’s model, i.e., 0 ≤ ν e ≤ ν e V r . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, C s 3 pqr , should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., C s 3 pq = 0.572 ( p = − 5/2), C s 3 pr = 0.709 ( p = − 1), and C s 3 qr = 0.762 ( p = 0).
Print ISSN:
1070-6631
Electronic ISSN:
1089-7666
Topics:
Physics
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