Prediction of separated transonic wing flows with nonequilibrium algebraic turbulence model

A comparison of the predictive capabilities of several turbulence models using upwind and central-difference computer codes

“…Abid et al [13] extended the J-K model to 3-D flows. Their version (termed J-K1990A) uses equation (8) for the inner model, but the velocity scale u T in equation (10) is given by…”

“…The Johnson-King (J-K) turbulence model is a so-called one-half equation turbulence model that requires the solution of an ordinary differential equation (ODE) for the maximum Reynolds shear stress over the body surface. Since its introduction [6], several modifications and enhancements have been made [12], [13], [14], [15]. An attempt will be made to describe the different versions of the model, as well as the effects of each of the individual modifications.…”

“…In equation (13), the subscript eq denotes the equilibrium value of the maximum Reynolds shear stress. In equations (14) and (15), y m denotes the distance from the body to the location where 0u is maximum.…”

“…As discussed in references [6] and [13], the ODE (13) can be linearized and solved for , where is defined as…”

“…The J-K1990A model was used in reference [13] to predict 3-D separated flow over the ONERA M6 wing successfully on a grid size of 28 65 4 .…”