Smoothed particle hydrodynamics with & kappa;-& epsilon; closure for simulating wall-bounded turbulent flows at medium and high Reynolds numbers

In this study, an improved SPH (smoothed particle hydrodynamics) method coupling the ?-e turbulence model and the wall function is proposed to simulate wall-bounded turbulent flows at medium and high Reynolds numbers. The second-order partial derivative term of the composite function containing the turbulent viscosity coefficient is decomposed into the sum of two terms, which helps SPH to avoid numerical errors and difficulties in dealing with boundary conditions in the nested approximation of first-order partial derivatives. Particle shifting technique, d-SPH method, and graphics processing unit parallel technology are used in the simulations to ensure uniform particles, smooth pressure field, and high computational efficiency, respectively. The SPH method with the ?-e turbulence model and the wall function is tested and validated by simulating four classical wall-bounded turbulent flows at medium and high Reynolds numbers, which are the turbulent flat plate boundary layer at Re = 4.2 x 10(6) and Re = 10(7), backward step separation flow at Re-H = 3025, the flow around the airfoil at Re = 3 x 10(6), and the flow around the pitching airfoil at Re = 1.35 x 10(5), respectively. The simulation results are consistent with the references, validating the suitability of the current SPH method for simulating wall-bounded turbulent flows at medium and high Reynolds numbers. Finally, the airfoil motion combining the pitching and deforming at Re = 3 x 10(6) is investigated by the current SPH method. The results show that the deformation of the airfoil's relative thickness affects the lift coefficients of the pitching airfoil. Furthermore, the increase in the relative thickness increment reduces the amplitude of the lift coefficient, while the increase in the deformation period has little effect on the amplitude of the lift coefficient.