A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient

Abstract

In this paper, we propose an efficient formula for estimating the model coefficient of a Smagorinsky model based subgrid scale eddy viscosity. The method allows vanishing eddy viscosity through a vanishing model coefficient in regions where the eddy viscosity should be zero. The advantage of this method is that the coefficient of the subgrid scale model is a function of the flow solution, including the translational and the rotational velocity field contributions. Furthermore, the value of model coefficient is optimized without using the dynamic procedure thereby saving significantly on computational cost. In addition, the method guarantees the model coefficient to be always positive with low fluctuation in space and time. For validation purposes, three test cases are chosen: (i) a fully developed channel flow at ${\mathop{\rm Re}\nolimits} _\tau = 180,\,395$ Re τ=180,395, (ii) a fully developed flow through a rectangular duct of square cross section at ${\mathop{\rm Re}\nolimits} _\tau = 300$ Re τ=300, and (iii) a smooth subcritical flow past a stationary circular cylinder, at a Reynolds number of ${\mathop{\rm Re}\nolimits} = 3900$ Re =3900, where the wake is fully turbulent but the cylinder boundary layers remain laminar. A main outcome is the good behavior of the proposed model as compared to reference data. We have also applied the proposed method to a CT-based simplified human upper airway model, where the flow is transient.

Turbulent flow around a square cylinder at Reynolds number 22,000: A DNS study

“…The majority of the research on flow around cylindrical objects has been carried out for circular cylinders [1][2][3][4][5][6][7][8][9][10][11][12]. In this regard, since the first experimental results were published in the mid-90s [5], the configuration at Re = 3900 has attracted the attention of many researchers.…”

Response to “Comment on ‘A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient’” [Phys. Fluids 25, 099101 (2013)]

“…As can be seen from the posteriori analysis of C s shown in Ref. 2 test cases, the C s value goes to zero at the walls and the behavior of the model coefficient near the walls is comparable with that of the dynamic Smagorinsky. (2) Coordinate invariance:…”

“…Now, we turn our attention to the model developed in Ref. 2. As already mentioned, in our case a local frame is used and when the coordinate system is rotated the domain will also rotate and then the formulation for C s remains unchanged.…”

“…This reply is in response to the comments raised by Fang et al 1 on the novel formulation of Smagorinsky model coefficient developed in Ghorbaniasl et al 2 In Fang et al 1 comments, some issues regarding the invariance properties of the proposed Smagorinsky model coefficient are pointed out, which will be answered and clarified as follows.…”

“…(10) and (11) of Ghorbaniasl et al 2 ) is evaluated in a frame fixed to the grid cell itself (see Fig. 1).…”