The study of the phenomenon of compressibility for modeling to second order has been made by several authors, and they concluded that models of the pressure-strain are not able to predict the structural evolution of the Reynolds stress. In particular studies and Simone Sarkar et al., a wide range of initial values of the parameters of the problem are covered. The observation of Sarkar was confirmed by the study of Simone et al. (1997,“The Effect of Compressibility on Turbulent Shear Flow: A Rapid Distortion Theory and Direct Numerical Simulation Study,” J. Fluid Mech., 330, p. 307;“Etude Théorique et Simulation Numérique de la Turbulence Compressible en Présence de Cisaillement où de Variation de Volume à Grande Échelle” thése, École Centrale de Lyon, France). We will then use the data provided by the direct simulations of Simone to discuss the implications for modeling to second order. The performance of different variants of the modeling results will be compared with DNS results.

Pressure field upstream of a transonic rotor with attached shock waves is determined using the rotational method of characteristic. In addition to the theoretical case of rotors with identical blades, the analysis includus the practical case of rotors with blade-to-blade variations due to manufacturing tolerances. The variations are produced in the analysis by assuming perturbations in the blade stagger angle and radius of curvature at the leading edge. Perturbation at one blade is shown to significantly modify the pressure field only at the following two blade channels. Investigations of static pressure waves upstream of the rotor with errors in neighboring blades indicate that the effects of manufacturing errors in the blades are linearly additive. Influence functions for errors in blade stagger angle have been deduced and the pressure pattern due to variety of error configurations has been obtained. Rotation of these pressure patterns results in noise spectra at blade passage frequency and multiples of the shaft rotation frequency, with the manufacturing errors inducing frequency and amplitude modulation effects. The relative intensity of the various harmonics is shown to be dependent on error configurations and the axial location upstream of the rotor. Correlated and uncorrelated error distributions are considered. Comparison with available experimental data, however, indicates that blade errors in actual rotors are essentially uncorrelated.

This paper is devoted to the second-order closure for compressible turbulent flows with special attention paid to modeling the pressure-strain correlation appearing in the Reynolds stress equation. This term appears as the main one responsible for the changes of the turbulence structures that arise from structural compressibility effects. The structure of the gradient Mach number is similar to that of turbulence, therefore this parameter may be appropriate to study the changes in turbulence structures that arise from structural compressibility effects. Thus, the incompressible model (LRR) of the pressure-strain correlation and its corrected form by using the turbulent Mach number, fail to correctly evaluate the compressibility effects at high shear flow. An extension of the widely used incompressible model (LRR) on compressible homogeneous shear flow is the major aim of the present work. From this extension the standard coefficients Ci became a function of the compressibility parameters (the turbulent Mach number and the gradient Mach number). Application of the model on compressible homogeneous shear flow by considering various initial conditions shows reasonable agreement with the DNS results of Sarkar. The ability of the models to predict the equilibrium states for the flow in cases A1 and A4 from DNS results of Sarkar is examined, the results appear to be very encouraging. Thus, both parameters Mt and Mg should be used to model significant structural compressibility effects at high-speed shear flow.