Acoustic Properties of Porous Coatings for Hypersonic Boundary-Layer Control

Numerical simulations are performed to investigate the interaction of acoustic waves with an array of equally spaced two-dimensional microcavities on an otherwise flat plate without external boundary-layer flow. This acoustic scattering problem is important in the design of ultrasonic absorptive coatings for hypersonic laminar flow control. The reflection coefficient, characterizing the ratio of the reflected wave amplitude to the incident wave amplitude, is computed as a function of the acoustic wave frequency and angle of incidence, for coatings of different porosities, at various acoustic Reynolds numbers relevant to hypersonic flight. Overall, the numerical results validate predictions from existing theoretical modeling. In general, the amplitude of the reflection coefficient has local minima at some specific frequencies. A simple model to predict these frequencies is presented. The simulations also highlight the presence of resonant acoustic modes caused by coupling of small-scale scattered waves near the coating surface. Finally, the cavity depth and the porosity are identified as the most important parameters for coating design. Guidelines for the choice of these parameters are suggested

Alternate Designs of Ultrasonic Absorptive Coatings for Hypersonic Boundary Layer Control

Numerical simulations of the linear and nonlinear two-dimensional Navier-Stokes equations are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings consisting of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. Based on our previous work, we employ a temporally evolving approximation appropriate to slowly-growing second-mode instabilities. We consider coatings operating in attenuative regimes where the pores are relatively deep and acoustic waves and second mode instabilities are attenuated by viscous effects inside the pores, as well as cancellation/reinforcement regimes with alternating regions of local minima and maxima of the coating acoustic absorption, depending on the frequency of the acoustic waves. The focus is on reinforcement cases which represent a worst case scenario (minimal second-mode damping). For all but one of the cases considered, the linear simulations confirm the results of linear instability theory that employs an approximate porous-wall boundary condition. A particular case with a relatively shallow cavities and very high porosity showed the existence of a shorter wavelength instability that is not predicted by theory. Finally, nonlinear simulations of the same cases led to the same conclusions as linear analysis; in particular, we did not observe any "tripping" of the boundary layer by small scale disturbances associated with individual pores

Evaluation of PSE as a Model for Supersonic Jet Using Transfer Functions

Parabolized Stability Equations (PSE) have been shown to model wavepackets and, consequently, the near field of turbulent jets with reasonable accuracy. Because of these capabilities, PSE is a promising reduced-order model to derive control laws that could be employed to reduce the sound generation of a jet. The purpose of this work is to apply PSE to obtain time-domain transfer functions that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet. The results of this model were compared to results obtained from a database of a well-validated large-eddy simulation of a supersonic jet. Based on the unsteady pressure data at a input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and an empirical method based on the LES data. The prediction scheme employed is a single-input-single-output (SISO), linear model. The unsteady pressure predicted by PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer. For this region, the prediction capabilities of PSE are comparable to those of empirical transfer functions. The agreement is good even for output points taken in the acoustic field, showing that it is possible to estimate the time-domain behaviour of Mach-wave radiation using transfer functions. This indicates that PSE could not only be used to predict the sound generation, but also to open up new potentialities to attenuate noise by means of closed-loop control of the flow. The exploration of the regions where the method displayed good agreement, presented in this work, can guide the positioning of sensors and actuators for experimental implementation of closed-loop control in a jet

Stability of Temporally Evolving Supersonic Boundary Layers over Micro-Cavities for Ultrasonic Absorptive Coatings

Ultrasonic absorptive coatings, consisting of regularly-spaced arrays of micro-cavities, have previously been shown to effectively damp second-mode instability for the purpose of delaying transition in hypersonic boundary layers. However, previous simulations and stability analysis have used approximate porous-wall boundary conditions. Here we investigate the feasibility of using direct numerical simulation to directly compute the hypersonic boundary layer including the micro-cavities. In order to keep the problem computationally tractable, we restrict our attention to the two-dimensional case (which is relevant since the second-mode is initially two dimensional), and we show that temporally evolving layers display qualitatively similar behavior to spatially developing boundary layer and instabilities. We validate the numerical method by comparing the simulation results to temporal linear stability analysis of the (frozen) velocity and temperature profiles from the direct numerical simulation. Two-dimensional linear simulations of the boundary layer on a flat plate and over a porous coating are performed, and it is shown that the presence of the cavities attenuates the instability waves, as expected from theory

Interaction of Acoustic Disturbances with Micro-Cavities for Ultrasonic Absorptive Coatings

Numerical simulations are performed to investigate the interaction of acoustic waves with an array of equally-spaced two-dimensional micro-cavities on an otherwise flat plate without external boundary-layer flow. This acoustic scattering problem is important in the design of ultrasonic absorptive coatings (UAC) for hypersonic laminar flow control. The reflection coefficient, characterizing the ratio of the reflected wave amplitude to the incident wave amplitude, is computed as a function of the acoustic wave frequency and angle of incidence, for coatings of different porosity, at various acoustic Reynolds numbers relevant to hypersonic flight. Overall, the numerical results validate predictions from existing theoretical modeling. In general, the amplitude of the reflection coefficient has local minima at some specific frequencies. A simple model to predict these frequencies is presented. The simulations also highlight the presence of resonant acoustic modes caused by coupling of small-scale scattered waves near the UAC surface. Finally, the cavity depth and the porosity are identified as the most important parameters for UAC design. Guidelines for the choice of these parameters are suggested

Instability of Hypersonic Boundary Layer on a Wall with Resonating Micro-Cavities

Ultrasonically absorptive coatings (UAC) can stabilize the Mack second mode and thereby increase the laminar run on configurations where laminar-turbulent transition is second-mode dominated. Theory indicates that the stabilization effect can be essentially enhanced by increasing the UAC porosity. However, direct numerical simulations (DNS) showed that coatings having closely spaced grooves can trigger a new instability whose growth rate can be larger than that of Mack' second mode. The nature of the new instability is investigated theoretically and numerically. 2D linear DNS and stability analysis are performed for the temporally evolving boundary layer on a flat wall at the outer-flow Mach number 6. The wall is covered by UAC comprising equally-spaced spanwise grooves. It is shown that the new mode is associated with acoustic resonances in the grooves. Disturbance fields near mouths of resonating cavities are coupled such that the boundary-layer disturbance is decelerated and becomes unstable. To avoid this detrimental effect the coating should have sufficiently small porosity and/or narrow pores of sufficiently small aspect ratio. Restrictions on these parameters can be estimated using the linear stability theory with the impedance boundary conditions

Stability of Temporally Evolving Supersonic Boundary Layers over Micro-Cavities for Ultrasonic Absorptive Coatings

Ultrasonic absorptive coatings, consisting of regularly-spaced arrays of micro-cavities, have previously been shown to effectively damp second-mode instability for the purpose of delaying transition in hypersonic boundary layers. However, previous simulations and stability analysis have used approximate porous-wall boundary conditions. Here we investigate the feasibility of using direct numerical simulation to directly compute the hypersonic boundary layer including the micro-cavities. In order to keep the problem computationally tractable, we restrict our attention to the two-dimensional case (which is relevant since the second-mode is initially two dimensional), and we show that temporally evolving layers display qualitatively similar behavior to spatially developing boundary layer and instabilities. We validate the numerical method by comparing the simulation results to temporal linear stability analysis of the (frozen) velocity and temperature profiles from the direct numerical simulation. Two-dimensional linear simulations of the boundary layer on a flat plate and over a porous coating are performed, and it is shown that the presence of the cavities attenuates the instability waves, as expected from theory