Anisotropy-invariant Reynolds stress model of turbulence for practically relevant inhomogeneous flows
Final Report Abstract
The objective of the project was to take over important ideas from the Anisotropy–Invariant Reynolds Stress Modeling of Turbulence by Jovanović et al. and to evaluate these concepts in the context of a hybrid LES–URANS method for non–equilibrium turbulent flows. For this purpose, the hybrid LES–URANS method developed by Breuer et al. was extended by an enhanced formulation of the turbulent dissipation rate ε in the highly anisotropic near–wall region. Since in the present hybrid approach the URANS mode is applied close to solid walls, the model for ǫ in the transport equation for the turbulent kinetic energy k is a critical issue. With the aid of the unique assumption of Jovanović et al. the splitting of the total turbulent dissipation rate into two parts was taken into account. In the direct vicinity of the wall the homogeneous part εh and the inhomogeneous dissipation rate εinh were considered separately. The decisive advantage of this splitting is that now both parts can be predicted based on exact formulations and thus are founded on a proper physical background; the inhomogeneous part εinh is based on a relation to the molecular diffusion term D and the homogeneous part εh is predicted as a function of the homogeneous Taylor microscale λh . Thus, by introducing the dissipation model of Jovanović et al. [6–9] an exact formulation is supplied for the important near–wall region. The performance of the New Model was evaluated based on the classical turbulent channel flow (not shown here) and two non–equilibrium turbulent flow configurations, which provide a challenging range of anisotropic vortical structures including separation from curved walls and reattachment. The results of the New Model were compared with previous simulations to determine the possible enhancement. In general, the Previous Model based on a simple empirical model for ǫ delivered a promising level of agreement with the reference data. Nevertheless, the simulations relying on the New Model show a slight improvement of the quality of the predictions of the mean velocities and the second–order moments compared with the reference data. Furthermore, the variation of the dynamically determined interface location between the URANS and LES mode for the periodic hill flow as well as for the diffuser flow delivered results with a similar level of agreement. Hence, the extension of the URANS region did not deteriorate the predictions, despite the observation that previous pure RANS predictions show great discrepancies to the experimental or numerical reference data. Due to the insensitivity of the interface location found for the New Model, a further decrease of the computational costs for hybrid simulations is possible. To sum up, the improved formulation of the dissipation rate in the near–wall region leads to (i) improved results for complex separated turbulent flows and to (ii) a decreasing sensitivity regarding the interface location. Thus a significant improvement of the hybrid LES–URANS method was achieved. To further prove and underline the superiority of the New Model, additional test cases must be carried out. After the intensive evaluation of internal flow situations, an external flow configuration such as the flow around an airfoil (e.g., SD 7003) including flow separation and reattachment will deliver enlightening statements to finish the validation procedure of the hybrid LES–URANS method. This is presently work in progress.
Publications
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Refinement of a Hybrid LES–URANS Approach for Non-Equilibrium Turbulent Flows, 7th Int. Symp. on Turbulence, Heat and Mass Transfer, (THMT-7), Palermo, Sicily, Sept. 24–27, 2012, In: Turbulence, Heat and Mass Transfer 7 (plus CD with long papers), eds. K. Hanjalić et al., ISBN 978–1–56700–301–7, pp. 507–510, Begell House Inc., New York, Wallingford (UK), (2012)
Breuer, M., Schmidt, S.
