STABLE IMPLEMENTATION OF K-KL TURBULENT FLOW MODEL IN UNSTRUCTURED GRID SOLVER

Low-Re turbulent flow model resolves the flow all the way up to the wall thus requiring very fine mesh in the near-wall regime. The use of explicit methods for such models is highly expensive due to the stability restrictions. Whereas, straightway use of an implicit method for lows with strong source terms results in barely stable system. This paper summarizes a highly stable, positivity preserving implicit method to solve the recently proposed length-scale based turbulent flow model; k-kL model. The k-kL model is a RANS-based two-equation model that solves the transport equation of turbulent kinetic energy (TKE) and TKE times the integral length scale to model the effect of turbulence on the mean flow field. It is extremely necessary for an underlying numerical method to maintain the positivity of the turbulent flow variables to avoid unrealistic flow physics, such as negative viscosity, being predicted. The situation gets worst in the case of a k-kL model as it deals with very small values of k and kL are the order of 1e-3 in the free-stream to around 1e-16 in near-wall regimes.

Paper first introduces the newly developed k-kL model, then a stable implicit method is discussed to solve the transport equations of k and kL followed by stability demonstration of the method with respect high CFL number.

Full Paper: Kalkote N., Assam A.,and Eswaran V., Stable implementation of k ? kl turbulent flow model in unstructured grid CFD solver , 25th National and 3nd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2019), Paper No.–,IIT Roorkee, India, December 28-31, 2019.