Implementation of the Anisotropic Hybrid k-$$\omega$$ SST/STM Closure Model

Abstract

This chapter focuses on the computer code implementation of the anisotropic hybrid k-\(\omega \) Shear-Stress Transport/Stochastic Turbulence Model (SST/STM) including computer programming aspects. To achieve this goal, the numerical computation of the elements of the symmetrical anisotropic similarity tensor \(\underline{\underline{H}}\) ( 2.4) has been discussed through the stochastic turbulence model (STM) of Czibere [6, 7] in the first part of this chapter. The importance of the anisotropic similarity tensor \(\underline{\underline{H}}\) ( 2.4) and its modified deviatoric part \(\underline{\underline{H}}^{\star }\) ( 2.30) is to provide physically correct model constants to describe the mechanically similar local velocity fluctuations ( 2.1) related to the new anisotropic Reynolds stress tensor ( 2.41) (see Chap. 2). As a practical approach, the computation of the elements of the similarity tensor \(\underline{\underline{H}}\) ( 2.4) is explained by the implementation of an example MATLAB code. The difference between the implemented STM and the original STM of Czibere [6, 7] is that the Bradshaw constant \(a_{1}\) [4, 5, 14] is considered here for the convergence criterion instead of the von Karman constant \(\kappa \). In the second part of this chapter, the implementation of the anisotropic hybrid k-\(\omega \) SST/STM closure model [11] has been described through C programming language based User-Defined Functions (UDFs) in the ANSYS-FLUENT [1, 2, 3] environment. The additional source terms of the anisotropic hybrid k-\(\omega \) SST/STM closure model [11] are added to k-\(\omega \) SST model of Menter [14, 15, 16] in conjunction with the scalar momentum equations and the additional production terms of the turbulent kinetic energy k and specific dissipation rate \(\omega \) transport equations, respectively. Note that there is no practical guide currently available in the literature about how to implement technically an anisotropic turbulence model in the ANSYS-FLUENT environment. Therefore, the objective of this chapter is to fill the knowledge gap in this subject area.