Extension of Boussinesq turbulence constitutive relation for bridging methods

Abstract

Bridging methods for turbulence simulation are adaptive eddy-viscosity schemes based on the accuracy-on-demand paradigm, much like hybrid approaches. The object is to resolve more scales of motion than Reynolds-averaged Navier-Stokes (RANS) by suitably reducing the eddy viscosity as a function of grid spacing. Currently, there are two proposals for extending the RANS two-equation model with Boussinesq constitutive relation to bridging methods. In the first approach, it is suggested that the coefficient in the Boussinesq relation be reduced and the transport equations for the length and velocity scales left unaltered for achieving the desired level of viscosity reduction. The second approach suggests that the viscosity reduction is better achieved by suitably modifying the transport equations rather than altering the Boussinesq coefficient. In this paper, we compare the merits of the two methods in two important benchmark cases: flows past circular cylinder and backward facing step. Three types of evaluations are performed. First, we verify if the requisite viscosity reduction is indeed achieved in the calculations. Then, we compare some crucial qualitative aspects of the solutions from the two methods. Finally, we evaluate the two solutions against experimental data for the same level of intended viscosity reduction.

Characterizing velocity fluctuations in partially resolved turbulence simulations

“…[3][4][5] In addition, the fixed point analysis of Girimaji et al 1 demonstrated that the PANS bridging approach recovers the correct energetics in homogeneous turbulence. Furthermore, the computational study of Lakshmipathy and Girimaji 6 demonstrated that PANS a posteriori results are consistent with a priori length-scale cut-off and viscosity reduction specifications. Since its initial formulation, the PANS method has been enhanced to include near-wall effects 7 and added fidelity in regions of resolution variation to address commutation error.…”

Towards a Unified Turbulence Simulation Approach for Wall-Bounded Flows

“…It is important to note that (16) only provides an estimate for the smallest value of F R that a given computational grid can support. A constraint for F R that is similar to (16) has also been proposed by Lakshmipathy and Girimaji [17]. However, rather than using the integral length scale l RANS for turbulence in the constraint for F R , Lakshmipathy and Girimaji argued alternatively for the use of the Taylor microscale as the characteristic length scale.…”

“…In consequence, the k and ε quantities used in our current PRNS approach should be interpreted as (estimates of) "RANS" quantities, which are subsequently used to determine the integral length scale l i required in our F R formulation [cf. (17), (18), and (21)]. From this perspective, the use of conventional RANS values for the turbulence closure coefficients in the k-ε model is justifiable.…”

“…In the PANS approach, no explicit F R was needed to modify the eddy-viscosity owing to the fact that the k and ε quantities here are subscale (or unresolved) turbulent kinetic energy and its dissipation rate. Furthermore, Lakshmipathy and Girimaji [17] re-calibrated the values for the turbulence closure coefficients in their transport equation for the subscale k and ε by incorporating a viscosity reduction factor R (or, equivalently, F R , in our current parlance). Lakshmipathy and Girimaji advocated using a constant value for R in order to minimize the influence of commutation errors.…”

Partially Averaged Navier Stokes simulation of turbulent heat transfer from a square cylinder

“…But, still these values need to be justified by a post simulation check, to know whether the desired physical resolution is achieved or not. Lakshmipathy and Girimaji [25] suggested the eddy viscosity recovery as the parameter to check the credentials of the calculated f k . They contended that, as the extent of the resolution is increased the value of the eddy viscosity should decrease.…”