A dynamic nonlinear subgrid-scale stress model

Abstract

In this paper, a dynamic subgrid scale (SGS) stress model based on Speziale’s quadratic nonlinear constitutive relation [C. G. Speziale, J. Fluid Mech. 178, 459 (1987); T. B. Gatski and C. G. Speziale, J. Fluid Mech. 254, 59 (1993)] is proposed, which includes the conventional dynamic SGS model as its first-order approximation. The closure method utilizes both the symmetric and antisymmetric parts of the resolved velocity gradient, and allows for a nonlinear anisotropic representation of the SGS stress tensor. Unlike the conventional Smagorinsky type modeling approaches, the proposed model does not require an alignment between the SGS stress tensor and the resolved strain rate tensor. It exhibits significant flexibility in self-calibration of the model coefficients, and local stability without the need for plane averaging to avoid excessive backscatter of SGS turbulence kinetic energy and potential modeling singularity problems. It also allows for variable tensorial geometric relations between the SGS stress and its constituent terms, and reflects both forward and backward scatters of SGS turbulence kinetic energy between the filtered and subgrid scales of motions. Turbulent Couette flow for Reynolds numbers (based on channel height and one half the velocity difference between the two plates) of 2600 and 4762 was used in numerical simulations to validate the proposed approach.

Large-eddy simulation of turbulent flows in a heated streamwise rotating channel

“…The DNM is based on an explicit nonlinear quadratic tensorial polynomial constitutive relation of Speziale [12], which includes the conventional DM as its first-order approximation as well as two higher-order tensorial constituent components for nonlinear anisotropic representation of the SGS stress tensor. As a result, it can exhibit local stability without the need for plane-averaging, and reflect the physical mechanisms of both forward and backward scatter of SGS KE between the filtered and subgrid scale motions [11,13,14]. In comparison with the DM, the DNM overcomes several major drawbacks of the DM and admits more degrees of freedom for geometrical representation of the SGS stress tensor.…”

“…For example, it can lead to an unrealistic SGS dissipation effect if the model coefficient is restricted to be positive; on the other hand, a potential numerical instability arises due to the excessive backscatter of the SGS if the model coefficient is allowed to be negative. Furthermore, the DM can be potentially ill-conditioned because the model coefficient is not bounded and admits a possible singularity when the denominator of the formulation (M ij M ij ) becomes very small [11]. Finally, this model requires the principal axes of the SGS stress tensor to be aligned with those of the resolved strain rate tensor, which leads to insufficient representation of the SGS stress components [13].…”

“…Bergstrom [11]. The following section briefly describes the formulations of these two dynamic linear and nonlinear models.…”

“…To overcome the difficulties related to the DM, Wang and Bergstrom [11] proposed an advanced dynamic nonlinear subgrid-scale stress model (DNM). The DNM is based on an explicit nonlinear quadratic tensorial polynomial constitutive relation of Speziale [12], which includes the conventional DM as its first-order approximation as well as two higher-order tensorial constituent components for nonlinear anisotropic representation of the SGS stress tensor.…”

“…ii) To date, the advanced DNM of Wang and Bergstrom [11] for modelling the SGS stress tensor and the DFLTDM of Wang et al [9] for modelling the SGS HF vector, have only been tested using a few canonical test cases such as Couette and Poiseuille flows, mixed natural and forced convection flows in horizontal and vertical channels [9,21], and physiological pulsatile transition-to-turbulent flows in vessels with idealized arterial stenosis [52]. Xun et al [14] thoroughly examined the performance of these advanced modelling approaches in the context of a heated rotating channel flow subjected to spanwise rotations.…”