High-order delay detached-eddy simulations of cylindrical separated vortex/vortex induced noise based on transition model and acoustic analogy

Abstract

The numerical prediction of transition from laminar to turbulent flow has proven to be an arduous challenge to computational fluid dynamics (CFD). Few approaches can provide routine accurate results within the cost limitations of engineering applications. In the present paper described is the application of a -Re transition model in combination with the delay detached eddy simulation (DDES) and Ffowcs Williams and Hawkings (FW-H) acoustic analogy method to cylinder vortex/vortex induced noise at a subcritical Reynolds number. In the process of numerical simulation, a traditional DDES based on the full-turbulence model SST is carried out for comparison and a 7th-order weighted compact nonlinear scheme (WCNS-E8T7) is adopted to ensure that the physical models are not affected by numerical dissipation or dispersion. In the first case, single cylinder cross-flow at ReD =4.3104 and Ma=0.21, is considered as a benchmarking problem for validating turbulence models and aerodynamic noise prediction methods. Its aerodynamic coefficients, St, CL and CD at root-mean-square (rms) and averaged values are measured by Szepessy and Bearman, while an acoustic measurement was recently made at Ecole Centrale de Lyon. The traditional DDES only based on SST model (SST-DDES) delays the instability of the shear layer on the sides of the cylinder, which leads to the recirculation zone in mean flow to grow and the induced drag to increase. Moreover, the vortex shedding frequency predicted by SST-DDES is larger than the actual value, which makes the whole sound pressure level (SPL) spectrum move toward high frequency region. However, combining the -Re transition model, the DDES (called Tran-DDES in the present article) can give the results in good agreement with the experimental data. In the second case considered is an airfoil in the wake of the cylinder. The flow condition is similar to that in the first case and the experimental results are also obtained at Ecole Centrale de Lyon. The issue of SST-DDES in recirculation zone in mean flow is weakened, which relates to the interaction between the airfoil and cylinder wake, the prediction of mean flow by SST-DDES is similar to that by the Tran-DDES. But in terms of the rms values of turbulent fluctuation components and SPL, the predictions by Tran-DDES are still better than those by SST-DDES.