We report the characteristics of wall shear stress (WSS) and wall heat flux (WHF) from direct numerical simulation (DNS) of a spatially developing zero-pressure-gradient supersonic turbulent boundary layer at a free-stream Mach number M∞ = 2.25 and a Reynolds number Reτ = 769 with a cold-wall thermal condition (a ratio of wall temperature to recovery temperature Tw/Tr = 0.75). A comparative analysis is performed on statistical data, including fluctuation intensity, probability density function, frequency spectra, and space–time correlation. The root mean square fluctuations of the WHF exhibit a logarithmic dependence on Reτ similar to that for the WSS, the main difference being a larger constant. Unlike the WSS, the probability density function of the WHF does not follow a lognormal distribution. The results suggest that the WHF contains more energy in the higher frequencies and propagates downstream faster than the WSS. A detailed conditional analysis comparing the flow structures responsible for extreme positive and negative fluctuation events of the WSS and WHF is performed for the first time, to the best of our knowledge. The conditioned results for the WSS exhibit closer structural similarities with the incompressible DNS analysis documented by Pan and Kwon [“Extremely high wall-shear stress events in a turbulent boundary layer,” J. Phys.: Conf. Ser. 1001, 012004 (2018)] and Guerrero et al. [“Extreme wall shear stress events in turbulent pipe flows: Spatial characteristics of coherent motions,” J. Fluid Mech. 904, A18 (2020)]. Importantly, the conditionally averaged flow fields of the WHF exhibit a different mechanism, where the extreme positive and negative events are generated by a characteristic two-layer structure of temperature fluctuations under the action of a strong Q4 event or a pair of strong oblique vortices. Nevertheless, we use the bi-dimensional empirical decomposition method to split the fluctuating velocity and temperature structures into four different modes with specific spanwise length scales, and we quantify their influence on the mean WSS and WHF generation. It is shown that the mean WSS is mainly related to small-scale structures in the near-wall region, whereas the mean WHF is associated with the combined action of near-wall small-scale structures and large-scale structures in the logarithmic and outer regions.

The effect of wall temperature on the size of the separation bubble in the shock wave/turbulent boundary-layer interaction of a 24 deg compression ramp with Mach 2.9 is numerically investigated. The ratios of wall temperature to recovery temperature T w ∕T r are 0.6, 1.14, 1.4, and 2.0, respectively. To validate the simulation, the statistical results with T w ∕T r 1.14 are tested and the results show a good agreement with theoretical and experimental results. It is shown that wall temperature has a remarkable effect on the size of the separation bubble and the size increases significantly with the increase of wall temperature. Through theoretical analysis, combined with numerical results, we get a semitheoretical formula L∕δ ∝ T w ∕T r 0.85 , in which L and δ are the length of the separation bubble and the thickness of upstream boundary layer, respectively. The turbulent kinetic energy budgets are also analyzed based on the numerical data, and results show that turbulence kinetic energy is chiefly produced both in the buffer layer and near the shock wave, and turbulent dissipation is mainly in the center of the separation bubble as well as in the nearwall region. It is also shown that the intrinsic compressibility effect is not significant in all these cases. = separation point δ = upstream boundary-layer thickness μ = viscosity coefficient ρ = density

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Large eddy simulation and FW-H acoustic analogy method are performed to investigate the effect of serrated leading edge on rod-airfoil interaction (RAI) noise. A NACA 0012 airfoil with straight and serrated leading edge at zero angle of attack is located one chord length behind a cylinder rod. The leading edge serrations are in the form of sinusoidal profiles .The free stream Mach number is 0.2 and the Reynolds number based on the rod diameter is 48,000. Firstly, the numerical results of straight leading edge airfoil are compared with experimental data, both the flow field predictions and the acoustic results are in good agreement with experiment. Secondly, the numerical results are compared between straight and serrated airfoils. The wake of the serrated airfoil is a little bit narrower and weaker and the leading edge serrations efficiently reduce the span-wise correlation coefficient. There is almost no noise reduction effect below the Karman vortex shedding frequency. The reduction of SPL at the Karman vortex shedding frequency is about 2.4 dB. A significant noise reduction is achieved by the serrations over a quite wide frequency range between 2 KHz and 6.5 KHz. It can be noted that the OASPL directivities at different azimuth angles all reduced 2-5.5 dB due to the serrations, which means than the leading serrations are an effective passive flow control method to reduce RAI noise. NomenclatureA = amplitude of the leading edge serration W = wavelength of the leading edge serration c = baseline airfoil chord lenght c(z) = serrated airfoil chord length c = serrated airfoil mean chord length d = cylinder rod diameter L span = span-wise length of the experiment L sim = span-wise length of the simulation R = radius of the observer points around the airfoil a 0 = free stream speed of sound 0  = free stream dendity U 0 = free stream velocity 2 u mean = stream-wise mean velocity RMS = root mean square rms u = root mean square of stream-wise velocity fluctuation rms p = root mean square of pressure fluctuation f 0 = Karman vortex shedding frequency St = Strouhal number C L = lift coefficient of the airfoil C D = drag coefficient of the airfoil C P = pressure coefficient SPL = sound pressure level PWL = sound power level PSD = power spectral density OASPL = overall sound pressure level FFT = fast Fourier transform