A Two-Equation Turbulence Model Combining Eddy Viscosity and Turbulent Kinetic Energy

A new two-equation turbulence model, designed to track the decay of turbulent kinetic energy and be compatible with finite element solvers, is calibrated and evaluated. The proposed model is governed by turbulent kinetic energy and scaled by eddy viscosity. The scaling equation is the same as the governing equation for the Spalart-Allmaras (SA) model, with the addition of a destruction term. Two-equation turbulence models exhibit numerical stiffness in finite element solvers, particularly in free-stream flow. Coupling the numerical robustness of the SA model with a two-equation turbulence model aims to improve performance in these regions. The model is calibrated in a hierarchal fashion, similar to the SA model. The time constant rate of turbulent decay of the k-e model is preserved. Free coefficients are calibrated to optimize performance in the planar mixing layer and planar wake. The behavior of the turbulent kinetic energy is evaluated in a self-similar round jet The performance of the model is evaluated in SANS, a finite element solver developed at MIT. The proposed model is evaluated in the uniform free-stream, which revealed the model required negative branches. The negative branches are derived in the same manner as the SA model. A stability analysis is performed, which reveals marginal stability. The model is further evaluated in planar wake to reveal the proposed model increases diffusion of eddy viscosity in the planar wake. Two test cases from the NASA Turbulence Modeling Resource are used. The first case used is the two-dimensional zero pressure gradient flat plate with a Mach number of 0.15 and Reynolds number of five million. The second case is the NACA 0012 airfoil, with a Mach number of 0.20 and Reynolds number of six million. The proposed model is slower to converge in SANS than the SA model, which could potentially be improved by continuing to improve the negative branch of the kinetic energy equation.