Three-Dimensional Simulations with an Anisotropic Hybrid k-$\omega$ SST/STM Approach

Abstract

In this short closing chapter, three-dimensional simulation results have been presented with the anisotropic hybrid k-$\omega$ Shear-Stress Transport/Stochastic Turbulence Model (SST/STM) [16] to make an attempt and a first step towards more complex real-world engineering applications. Therefore, the objective of this chapter is to shed light on possible research areas where further improvements can be made as a future work on the new anisotropic turbulence modelling approach investigated in this book. Numerical simulations are performed for three-dimensional turbulent flows (a) in a horizontal smooth cylindrical pipe, (b) over a NACA 0013 wing and (c) over the Jetstream 31 aircraft, respectively. All simulation results are compared to the k-$\omega$ SST model [20,21,22] and experimental data. The anisotropic scale factors $\lambda _{11}^{\star }$, $\lambda _{22}^{\star }$ and $\lambda _{33}^{\star }$ in the modified deviatoric similarity tensor $\underline{\underline{H}}^{\star }$ (3.99) have been calibrated and validated for three-dimensional turbulent flows related to the experimental work of Laufer [17] in a straight smooth cylindrical pipe. In that case, the anisotropic hybrid k-$\omega$ SST/STM approach [16] captured the physically correct anisotropic Reynolds stress distributions for $y^{+}\gtrapprox 65$. The simulation results suggest that the values of these scale factors have to be higher in the near wall region $(y^{+}\lessapprox 65)$ than in the inertial sublayer to obtain the accurate order of magnitude of the anisotropic Reynolds stresses. For the NACA 0013 wing and the Jetstream 31 aircraft external flows, the lift coefficient $c_{l}$ (4.60) values were under-predicted with the k-$\omega$ SST [20,21,22] and the anisotropic hybrid k-$\omega$ SST/STM [16] models compared to the experimental data in [8, 28]. The results suggest that further investigations on the mathematical properties of the modified deviatoric similarity tensor $\underline{\underline{H}}^{\star }$ (3.97) related to the anisotropic scale factors $\lambda _{11}^{\star }$, $\lambda _{22}^{\star }$ and $\lambda _{33}^{\star }$ are recommended as a future work.

We must learn to live with contradictions, because they lead to deeper and more effective understanding.

- Edward Teller, 1998