Space-time Characteristics And Noise Of Compressible Turbulent Shear Flow

Compressible shear turbulence is prevalent in nature and in engineering applications.The study of the spatio-temporal evolution of compressible turbulence and its radiation of noise is important for solving practical problems in engineering applications,improving the understanding of turbulence as well as contributing to the development of turbulence models.In this work,large eddy simulations and direct numerical simulations are carried out for two typical types of shear turbulence,namely,compressible turbulent jets and turbulent boundary layers,respectively.This thesis focuses on investigating characteristics of the spatio-temporal correlation in compressible jets,nonlinear noise modelling and pressure fluctuation characteristics in turbulent boundary layers.The specific work and findings are as follows:(1)A turbulent round jet with a Mach number of 0.9 is simulated with an integrated large eddy simulation(LES)of internal and external flow including the nozzle configuration.The improved accuracy of the jet simulation is obtained by triggering the development of a turbulent boundary layer on the inner wall of the nozzle.The near-field flow characteristics and far-field noise radiation compare well with the experimental measurements.The spatio-temporal correlation properties of velocities within the shear layer are investigated based on the LES data of turbulent jets.The Taylor freeze flow model and the elliptical approximation model are quantitatively assessed in the near nozzle region,the jet development region and the turbulent mixing region.It is found that the contours of the spatiotemporal correlation function behave as self-similar closed elliptic curves.The results show that the Taylor freeze flow model does not hold and the elliptical approximation model can predict the spatio-temporal correlation properties of the current compressible free shear turbulent system more reasonably.Comparing the theoretical and actual values of the two characteristic velocities(convective velocity and sweep velocity)of the elliptical approximation model,it is found that the theoretical and actual values of convective velocity in the region where except the near nozzle are in good agreement,and the theoretical and actual values of sweep velocity have the same variation trend as well.(2)Based on the current LES database of the turbulent jet,the spectral proper orthogonal decomposition(SPOD)modes in the jet field are extracted,and the evolution of instability waves in the jet is predicted using the parabolic stability equation(PSE).It is found the most energetic SPOD modes exhibit a clear growthsaturation-decay wavepacket signature,moreover the PSE and SPOD modes conform well in the near field,with deviations occurring mainly in the downstream region after the decay of the coherent structure.However,the far-field noise amplitude extrapolated by the PSE mode is much lower than the result of the LES mode,indicating that considering only the nonlinearity involved in the mean flow is not sufficient to construct a wavepacket model which can reasonably predict the far-field noise.In order to examine the role of non-linear effects,firstly the nonlinear effects of incoherent fluctuations are modelled in the form of external forcing.Combined with the adjoint PSE method,the overall energy of the wavepacket is used as the objective function.Sensitivity analysis is conducted to determine the form of the distribution of the external forcing.Although the external forcing can increase the amplitude of the wavepacket perturbation,the enhancement of the far-field noise is very limited.The nonlinearity near the critical layer is not the main missing mechanism for constructing the wavepacket with high acoustic radiation efficiency.Secondly,coherence decay due to nonlinear effects is also a missing factor in the linear model.Based on the coherence distribution calculated from the LES results,a coherent matching PSE wavepacket model is proposed.The model significantly improves the far-field noise level,suggesting that coherent matching is an effective modification of the linear wavepacket model.(3)The effect of wall cooling on the pressure fluctuations in the turbulent boundary layers with a friction Reynolds number of 650 is investigated by direct numerical simulations,and three sets of cases with Mach numbers ranging from subsonic to hypersonic are examined.Wall cooling enhances the coherence of streak structures and suppresses vorticity fluctuations.It also boost the turbulent Mach number and compressibility effects.Moreover,the generation of wave-like alternating positive and negative structures(APNS)near the wall is excited in the hypersonic boundary layer.Wall cooling overall suppresses pressure fluctuations in the subsonic and supersonic boundary layers,but substantially enhances pressure fluctuations near the wall in the hypersonic boundary layer.Based on the current data,the Laganelli wall pressure fluctuation model is modified and an approximately linear relationship between far-field pressure fluctuations and Mach number is found.The pressure decomposition method is extended to the compressible boundary layer to investigate the pressure fluctuations from the perspective of their generation mechanism.The reduction of pressure fluctuations in the subsonic and supersonic boundary layers is found to be due to the suppression of rapid and slow pressures by wall cooling,and the enhancement of pressure fluctuations in the hypersonic boundary layer is due to the excitation of compressible pressures by wall cooling.Furthermore,the APNS are found to be responsible for the peak wavelength in the wave number spectrum of pressure fluctuation,and the compressible pressure responds well to the APNS due to the dilatation motion.Essentially,the main effects of wall cooling can be interpreted by the suppression of the vorticity mode and the enhancement of the acoustic mode.