Direct Numerical Simulation Of Turbulent Pressure Fluctuations Over A Cone At Mach 8

Direct numerical simulations (DNS) were conducted to characterize the pressure fluctuations under the turbulent portion of the boundary layer over a sharp 7◦ half-angle cone at a nominal freestream Mach number of 8 and a unit Reynolds number of Reunit = 13.4 x 106/m. The axisymmetric cone geometry and the flow conditions of the DNS matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8). The DNS-predicted wall pressure statistics, including the root-mean-square (r.m.s.) fluctuations and the power spectral density (PSD), were compared with those measured in the Sandia HWT-8. A good comparison between the DNS and the experiment was shown for the r.m.s. and PSD of wall-pressure fluctuations after spatial averaging was applied to the DNS data over an area similar to the sensing area of the transducer. The finite size of the PCB132 transducer, with a finite sensing area of d+ ≈ 50, caused significant spectral attenuation at high frequencies in the experimentally measured PSD, and the loss in sensor resolution resulted in an approximately 27% reduction in r.m.s. pressure fluctuations. The attenuation due to finite sensor sizes has only a small influence on wall-pressure coherence, as indicated by the good comparisons between the DNS without spatial filtering and the experiment for transducers with either streamwise or spanwise separations. The characteristics of turbulent pressure fluctuations at the cone surface were also compared with those over a flat plate and at the wind-tunnel nozzle wall to assess the effect of flow configurations on the scaling relations of turbulent pressure fluctuations. The inner scale was found to successfully collapse wall-pressure PSD of the cone with those over a nozzle wall and on a flat plate at a similar freestream Mach number. For all the three flow configurations, the Corcos model was found to deliver good predictions of wall pressure coherence over intermediate and high frequencies, and the Corcos parameters for the streamwise and spanwise coherence at Mach 8 were found to be similar to those reported in the literature at lower supersonic Mach numbers

Direct Numerical Simulation of Nozzle-Wall Pressure Fluctuations in a Mach 8 Wind Tunnel

Direct numerical simulations (DNS) of the full-scale axisymmetric nozzle of a Mach 8 wind tunnel are conducted with an emphasis on characterizing the properties of the pressure fluctuations induced by the turbulent boundary layer (TBL) along the nozzle wall. The axisymmetric nozzle geometry and the flow conditions of the DNS match those of the Sandia Hypersonic Wind Tunnel at Mach 8. The mean and turbulence statistics of the nozzle-wall boundary layer show good agreement with those predicted by Pate\u27s correlation and Reynolds Averaged Navier-Stokes (RANS) computations. The wall-pressure intensity, power spectral density, and coherence predicted by DNS show good comparisons with those measured in the same tunnel. The Corcos model is found to deliver good prediction of wall pressure coherence over intermediate and high frequencies. The streamwise and spanwise decay constants at Mach 8 are similar to those predicted by DNS and experiments at lower supersonic Mach numbers