Comparison of Turbulence Modeling Approaches to the Simulation of a Dimpled Sphere

Abstract

Use of computational fluid dynamics (CFD) in the aerodynamic simulation of sports projectiles has always been a challenge. The majority of these are spherical, classic bluff bodies, which typically experience flow transition during flight, and large flow separations. Current research of such flows is predominantly concentrated on the use of computationally intensive large eddy scale (LES) simulation methods, and even direct numerical simulation (DNS). Use of such approaches requires careful application of the models, and significant computational resource. The alternative is the use of unsteady Reynolds-averaged Navier Stokes (URANS) turbulence models, which are typically known to struggle in such flow scenarios. URANS however are, in comparison to LES, computationally economical and as such these models find significant use amongst both industry and academia alike, and their development still continues. In recent years transitional URANS models based on the calculation of intermittency, and hybrid scale resolving simulation approaches (SRS), have started to appear in proprietary CFD codes. Hybrid SRS models such as scale adaptive simulation (SAS) and detached eddy simulation (DES), combine LES with the use of economical well tuned URANS in the simulation of near wall flows. However to date the use of such models in the simulation of sports projectiles has been extremely limited. This paper provides a CFD comparison of these turbulence modelling approaches, with application to the simulation of a dimpled sphere, a golf ball. The study investigates and compares the suitability of URANS, transitional URANS, and SRS models. Simulations are run between 10,000 < Re < 115,000, from sub-critical through transition to supercritical. Comparisons are drawn between predictions of drag coefficient, dimple shear layers and surface shear stress, with URANS being shown to be in reasonable agreement with SRS. However as may be expected although URANS predicted a comparable size of wake to SRS, no small scale structure was observed. Indeed it is shown how URANS failed to demonstrate any large scale time periodic shedding phenomena, instead becoming essentially steady state.