Broadband shock-associated noise is an important component of the overall noise generated by modern airplanes. In this study, sound generated by the weakly nonlinear interaction between linear instability waves and the shock-cell structure in supersonic jets is investigated numerically in order to gain insight into the broadband shock-noise problem. The model formulation decomposes the overall flow into a mean flow, linear instability waves, the shock-cell structure and shock-noise. The mean flow is obtained by solving RANSequations with a k-ε model. Locally parallel stability equations are solved for the shock structure, and linear parabolized stability equations are solved for the instability waves. Then, source terms representing the instability wave/shock-cell interaction are assembled and the inhomogeneous linearized Euler equations are solved for the shock-noise.Three cases are considered, a cold under-expanded Mj = 1.22 jet, a hot under-expanded Mj = 1.22 jet, and a cold over-expanded Mj = 1.36 jet.Shock-noise computations are used to identify and understand significant trends in peak sound amplitudes and radiation angles. The peak sound radiation angles are explained well with the Mach wave model of Tam & Tanna J. Sound Vib. Vol. 81, 1982, p. 337). The observed reduction of peak sound amplitudes with frequency correlates well with the corresponding reduction of instability wave growth with frequency. However, in order to account for variation of sound amplitude for different azimuthal modes, the radial structure of the instability waves must be considered in additionto streamwise growth. The effect of heating on the Mj = 1.22 jet is shown to enhance the sound radiated due to the axisymmetric instability waves while the other modesare relatively unaffected. Solutions to a Lilley–Goldstein equation show that soundgenerated by ‘thermodynamic’ source terms is small relative to sound from ‘momentum’ sources though heating does increase the relative importance of the thermodynamic source. Furthermore, heating preferentially amplifies sound associated with the axisymmetric modes owing to constructive interference between sound from the momentumand thermodynamic sources. However, higher modes show destructive interference between these two sources and are relatively unaffected by heating.

The spatiotemporal linear stability of viscoelastic planar mixing layers is investigated. A one-parameter family of velocity profiles is used as the base state with the parameter, S, controlling the amount of shear and backflow. The influence of viscoelasticity in dilute polymer solutions is modeled with the Oldroyd-B and FENE-P constitutive equations. Both models require the specification of the ratio of the polymer-relaxation and convective time scales (the Weissenberg number, W e) and the ratio of solvent and solution viscosities (β). The maximum polymer extensibility, L, must also be specified for the FENE-P model. We examine how the variation of these parameters along with the Reynolds number, Re, affects the minimum value of S at which the flow becomes locally absolutely unstable. With the Oldroyd-B model, the influence of viscoelasticity is shown to be almost fully captured by the elasticity, E * ≡ (1−β)W e Re , and S crit decreases as elasticity is increased, i.e., elasticity is destabilizing. A simple approximate dispersion relation obtained via long-wave asymptotic analysis is shown to accurately capture this destabilizing influence. Results obtained with the FENE-P model exhibit a rich variety of behavior. At large values of the extensibility, L, results are similar to those for the Oldroyd-B fluid as expected. However, when the extensibility is reduced to more realistic values (L ≈ 100), one must consider the scaled shear rate, η c ≡ W eS 2L , in addition to the elasticity. When η c is large, the base-state polymer stress obtained by the FENE-P model is reduced, and there is a corresponding reduction in the overall influence of viscoelasticity on stability. Additionally, elasticity exhibits a stabilizing effect which is driven by the streamwise-normal perturbation polymer stress. As η c is reduced, the base-state and perturbation normal polymer stresses predicted by the FENE-P model move towards the Oldroyd-B values, and the destabilizing influence of elasticity observed with the Oldroyd-B model is again present.

The linear instability of compressible axisymmetric unheated jets is investigated numerically. Solutions to the linear parabolized stability equations with Reynolds-averaged Navier-Stokes mean flows are used to describe the streamwise evolution of instability waves. For transonic jets, helical ͑azimuthal mode number m =1͒ instability waves tend to exhibit the largest gain over the jet potential core followed by the m = 2 and axisymmetric modes. At higher frequencies, the disparity in energy growth between the different azimuthal modes decreases, and there is a progressive reduction in energy growth as azimuthal mode number is increased from two to four. The entropic and pressure components of the total energy are compared to the kinetic energy. We find that the pressure term tends to be small, while the importance of the entropic component increases with frequency and decreases with azimuthal mode number. It is shown that the helical mode growth rates exhibit similarity when a local "mixing layer" scaling is adopted. This similarity is then used to concisely illustrate the stabilizing effect of compressibility over a broad range of frequencies and Mach numbers. Computed phase velocities are compared to measured convective velocities for unforced turbulent jets with Mach numbers M j = 0.51 and M j = 1.41. Good agreement is observed provided that the appropriate azimuthal mode number is selected.

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A hybrid Large Eddy Simulation (LES) related technique is used to explore some key turbomachinery relevant flows. Near wall RANS modeling is used to cover over especially small scales, the LES resolution of which is generally intractable with current computational power. Away from walls, large eddy type simulation is used but with no LES model (NLES). Linking of the two model zones through a Hamilton-Jacobi equation is explored. The hybrid strategy is used to predict turbine and compressor endwall flows, flow around a fan blade section, jet flows and a cutback trailing edge. Also, application of NLES to the flow in an idealized high pressure compressor drum cavity is considered. Generally, encouraging results are found. However, challenges remain, especially for flows where transition modeling is important.