Numerical Investigation Of Transitional Flows Based On Turbulence Model

Laminar-to-turbulence transition of boundary layer is a crucial factor for the performance of gas turbine. In computational fluid dynamics lacking of the transition modeling is one of the main error sources in RANS method. In this paper a transition sensitized three-equation turbulence model is proposed, and it is used for the numerical simulation of transitional flows in gas turbine.In order to get the numerical solution accurately for the complex flows, and for the validating of turbulence models effectively, a solver for the compressible N-S equation based on finite-volume method was developed. For the low-speed simulation of experiment, the preconditioning technique for the time-derivative term of N-S equations is utilized, which make the density based time-marching algorithms can be extended for arbitrary Mach number condition. Multigrid method and local time-stepping algorithm are also implemented to accelerate the convergence rate. The dual time-stepping procedure is introduced for the purpose of unsteady simulations.κ-ωandκ-ωSST models are implemented for the turbulence simulation. Through several typical simulations of flow cases, the reliability of the present solver is confirmed, which ensure this solver can be used for the transition simulation for the next step.Based on the idea of laminar kinetic energy andκ-ωturbulence model, a three-equation turbulence model including transport equations of laminar kinetic energy, turbulent kinetic energy, and specific dissipation rate is developed. New model gives new formulation for the product term and dissipation term of laminar kinetic energy equation, which makes this equation has the general forms of turbulent kinetic energy equation. The turbulent kinetic energy is divided into small and large scale energies. Laminar and turbulent kinetic energies both contribute to the eddy viscosity. Natural and bypass transition are modeled by two transfer terms respectively, which have opposite sign in the laminar and turbulent kinetic energy equations. A Reynolds stress limiter was introduced to the small scale viscosity to modeling the highly-strained flow exactly. And the cross diffusion ofκT andωwas added to theωequation to resolve the unphysical dependence of results on the freestream value of the turbulence variables.The present model has the same form as popular one- and two-equation turbulence model, and the same numerical scheme can be utilized to solve the model equations. In contrast to experiment-correlation transition models, this approach has more advantages in the numerical implementation. Test cases for the flat plate with and without pressure gradient, two and three-dimension low pressure turbine show that this model has the capability to predict natural, bypass and separated-flow transition accurately.