An entropy viscosity method for large eddy simulation of turbulent thermal flow in a rotor–stator cavity

Abstract

Turbulent flow and heat transfer in a rotor-stator cavity has fundamental importance in both academia of turbulence research and industry of rotating turbomachinery. The main characteristic of the flow is that there is the centrifugal Ekman layer on the rotor, and the centripetal Bödewadt layer on the stator, which are separated by a central rotating core. In this paper, an entropy-viscosity subgrid model based large-eddy simulation (LES) method is proposed to solve the complex flow with heat transfer in a rotating frame at high Reynolds number. The method is fully validated by the simulation of turbulent thermal flow in a closed stator-rotor cavity up to Re = 10^6. By performing 12 simulations, the sensitivity of the simulation results to mesh resolution and the free parameters of entropy-viscosity is systematically studied and the proper range for the parameters is determined. In particular, it is found that the prediction on the mean flow and fluctuation from the simple turbulent diffusivity model, which scales linearly with the eddy viscosity, is as accurate as that from the alternative model that is more computationally complex model. Despite the comparable accuracy, the entropy-viscosity based LES uses the mesh resolution two-order lower than that of direct numerical simulation (DNS), therefore it is feasible to apply the LES to the flow at the practical Reynolds number in aircraft engine that Re {greater than or equal to} 10^7.

Deep reinforcement transfer learning of active control for bluff body flows at high Reynolds number

“…The numerical simulation of the unsteady incompressible flow past the cylinders of different diameters is achieved by employing the high-order computational fluid dynamics code Nektar that employs spectral element discretization on the (x-y) plane and Fourier expansion along the cylinder axial direction (z) (Karniadakis & Sherwin 2005). In particular, we employ entropy viscosity method based large-eddy simulations (LES), which were originally proposed by Guermond, Pasquetti & Popov (2011a,b) and later developed further for complex flows by Wang et al (2018Wang et al ( , 2019 and Du et al (2023). In the simulations, the computational domain has a size of [−7.5 D, 20…”

“…The computational mesh is similar to the one used in Fan et al (2020). At Re D = 500, the computational domain is partitioned into 2462 quadrilateral elements, while at Re D = 10 4 and Re D = 1.4 × 10 5 , it consists of 2790 quadrilateral elements.…”

“…In our previous study (Fan et al 2020), an efficient DRL algorithm was developed to discover the best strategy to reduce the drag force, by using the DRL to control the rotation of two small cylinders placed symmetrically in the wake of the big cylinder. Specifically, for the flow at Re D = 10 4 , it has been demonstrated that DRL can discover the same control strategy as experiments in learning from data generated by high fidelity numerical simulation.…”

“…Simulated data are noise free, but learning from the simulated data is restricted by the simulation speed. For instance, in Fan et al (2020), in the case of Re D = 10 4 , it took 3.3 h to generate the simulated data for each episode, and one month to finalize the DRL strategy. In contrast, in companion experimental work it only took a few minutes to learn the same control strategy.…”

“…In contrast, in companion experimental work it only took a few minutes to learn the same control strategy. As Re D increases to 1.4 × 10 5 , one can expect that, even for the simplest task in Fan et al (2020), performing DRL from scratch could take months, and hence it might not be practical to apply DRL directly to the more difficult tasks at higher Re D .…”