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Conceptual model to quantify uncertainty in steady-RANS dissipation closure for turbulence behind bluff bodies

Zengrong Hao* and Catherine Gorlé

  • Wind Engineering Laboratory Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, USA

  • *haozr16@stanford.edu
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Phys. Rev. Fluids 7, 014607 – Published 21 January, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.014607

Abstract

In turbulent bluff body flows, the presence of vortex shedding, a form of coherent structures (CS), introduces a new characteristic scale that is distinct from the scale of background stochastic turbulence (ST). This double-scale picture essentially invalidates the conventional single-scale modeling for the turbulence energy dissipation in steady Reynolds-averaged-Navier-Stokes (RANS) simulations. In this paper, we present a conceptual model to quantify the uncertainty in the steady-RANS dissipation closure for flows past bluff bodies with vortex shedding. This model is developed in two steps. First, we formulate a double-scale, double-linear-eddy-viscosity (DSDL) framework for the transport of CS and ST energy, with an undetermined energy transfer rate from CS to ST. In this framework, the dissipation of ST energy follows a conventional transport model; the length scale of CS is determined such that the CS energy is intensely produced in free shear layers. Second, we design a functional form for the energy transfer rate based on a qualitative analysis and an analogy with the “return-to-isotropy” process. This form contains two uncertain parameters that control the CS-ST interaction. Subsequently, the DSDL model is tested on simulations of the flows past circular and square cylinders, and of the flow in a pin-fin array. In all cases, the model provides a significant improvement upon both conventional models and models with Reynolds stress shape perturbations. The sizes of the recirculation zones are accurately predicted, and simulations with varying values for the uncertain parameters predict intervals for the peak turbulence kinetic energy that encompass reference data.

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Outline

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Phys. Rev. Fluids 7, 014607– Published 21 January, 2022
  • Received 18 March 2021
  • Accepted 1 November 2021
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