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Scrutinizing URANS in Shedding Flows: The Case of Cylinder in Cross-Flow in the Subcritical Regime

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Abstract

To unravel the widespread perception that the RANS (Reynolds-averaged Navier-Stokes) concept is unreliable in predicting the dynamics of separated flows, we assessed the performance of two RANS closure levels, the linear eddy-viscosity (LEVM) and the second-moment (Reynolds stress, RSM) approaches in a massively separated generic flow over a bluff body. Considered is the canonical, zero-turbulence, cross-flow over an infinite cylinder with reference to our LES and the available DNS and experiments at two Reynolds numbers, Re = 3.9 × 103 and 1.4 × 105, both within the sub-critical regime with laminar separation. Both models capture successfully the vortex shedding frequency, but the low frequency modulations are detected only by the RSM. At high Reynolds numbers the RSM is markedly superior to the LEVM showing very good agreement with the LES and experimental data. The RSM, accounting naturally for the stress anisotropy and phase lag between the stress and strain eigenvectors, is especially successful in reproducing the growth rate of the turbulent kinetic energy in the initial shear layer which proved to be crucial for accurate prediction of the separation-induced transition. A scrutiny of the unsteady RANS (URANS) stress terms based on the conditional phase-averaged LES data shows a remarkable similarity of the normalized coherent and stochastic (modeled) stress components for the two Reynolds numbers considered. The mixed (cross) correlations, while non-negligible at the low Re number, diminish fast relative to the stochastic ones with increasing Reynolds number and, in the whole, are not significant to undermine the URANS concept and its applicability to high Re flows of industrial relevance.

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Notes

  1. A question (raised by one of the reviewers) can be posed if such a decomposition could be applicable to flows with periodic semi-deterministic structures, in view of their underlying inviscid (“mean motion”) character. While the issue is debatable, we argue that semi-deterministic periodic vortices shed from a bluff body, as well as convective cells in thermal convection and rotating flows qualify in just about every feature as coherent structures i.e. as “connected turbulent fluid mass with instantaneously phase-correlated vorticity over its spatial extent” [20, 21].

  2. The data can be downloaded from the website http://web.stanford.edu/~cantwell/. The case name is Case 0411 from the 1980-81 AFOSR Conference data library.

  3. Both RANS models here applied account for viscosity. The elliptic LEVM does that by imposing the Kolmogorov scale as the lower scale bound, which is known to be insufficient for treating transitional flows. The RSM used here does that in a more comprehensive, though still semi-empirical way, using some model-adapting functions in terms of the turbulence Re number and the stress and dissipation-rate anisotropy invariants [23].

  4. The term “inadvertent” was coined by one of the Referees.

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Acknowledgements

This work is funded by Russian Science Foundation grant No. 14-29-00203. The computational resources are provided by Siberian Supercomputer Center SB RAS (Novosibirsk), Novosibirsk State University Computing Center (Novosibirsk) and Joint Supercomputer Center RAS (Moscow). The authors thank B. Cantwell, I. Rodríguez, O. Lehmkuhl and E. Lamballais for sharing their numerical and experimental data and the referees for many valuable suggestions.

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Authors and Affiliations

  1. Institute of Thermophysics SB RAS, Lavrentyeva 1, 630090, Novosibirsk, Russia

    E. Palkin & R. Mullyadzhanov

  2. Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia

    E. Palkin, R. Mullyadzhanov & K. Hanjalić

  3. International University of Sarajevo, Hrasnićka cesta 15, 71210, Ilidźa, Sarajevo, Bosnia and Herzegovina

    M. Hadžiabdić

  4. Delft University of Technology, Julianalaan 136, 2628, BL, Delft, The Netherlands

    K. Hanjalić

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  1. E. Palkin
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Palkin, E., Mullyadzhanov, R., Hadžiabdić, M. et al. Scrutinizing URANS in Shedding Flows: The Case of Cylinder in Cross-Flow in the Subcritical Regime. Flow Turbulence Combust 97, 1017–1046 (2016). https://doi.org/10.1007/s10494-016-9772-z

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