Stabilization of Hypersonic Boundary-Layer: Acoustic Metasurfaces

Hypersonic vehicles have the benefit of rapid global arrival, high detection difficulty, strong penetration ability, and high combat effectiveness, and therefore become one of the main focuses of international competition. A number of hypersonic flight verification projects have been successfully carried out, but there are still many unknown areas. Boundary layer (BL) transition is one of the most important and inevitable uncertainties (Bertin and Cummings in Prog Aerosp Sci 39:511–536, 2003; An Fuxing, Li Lei, SU Wei, Liu Wenling and Dong Chao. Key issues in hypersonic vehicle aerodynamic design. SCIENTIA SINICA Physica, Mechanica & Astronomica, 2021, 51(10):6–25. (in Chinese);). Within the flight altitude, speed, and Reynolds number range of hypersonic vehicles, the BL transition has a high probability of occurrence (Bertin and Cummings in Annu Rev Fluid Mech 38:129–157, 2006). As shown in, vehicles powered by air-breathing propulsion systems spend most of their atmospheric hypersonic flight in conditions where the flow will be transitional. In a higher attitude with faster speed, the BL transition becomes more complex because of the interaction with real-gas effects. Particularly, it might occure under other flight conditions where the flow around the vehicles is normally thought to be laminar unless roughnesses or defects exist.

Various instability modes can exist in the hypersonic boundary layer depending on the flow condition. Mack (Mack L. M., Special course on stability and transition of laminar flow, AGARD report, No. 709, 1984) first categorized the flow disturbances into the first mode and the second mode. In hypersonic boundary layers, the second mode plays an important role, and it behaves like a trapped acoustic wave propagating in a waveguide between the wall and the sonic line, but has a phase velocity larger than the speed of sound.

The stabilization effect of acoustic metasurfaces on hypersonic BL flow is caused by the interaction between their acoustic characteristics and instability waves. In addition to the use of direct numerical simulations of the flow field within microstructures, an acoustic impedance boundary condition of the vertical velocity at the wall (\(v_{{\text{w}}}^{\prime } = p_{{\text{w}}}^{\prime } /Z\)) is adopted to model the metasurface. Here, \(v_{{\text{w}}}^{\prime }\) and \(p_{{\text{w}}}^{\prime }\) denote the vertical velocity and pressure perturbations, respectively. Z denotes the surface impedance, which is a complex quantity that depends on the properties of the wall material, porosity parameters, mean flow characteristics on the wall surface, and flow perturbation parameters such as wave frequencies and wavelengths. This treatment saves computational resources for numerical simulations and assists in the LST analysis. The influence of the microstructure geometry parameters such as depth, diameter, and porosity can be systematically investigated using the impedance model.

As mentioned above, acoustic metasurfaces are planar metamaterial structures constructed with monolayer or multilayer stacks of subwavelength building blocks, which have significantly broadened the horizon of acoustic wave manipulation from wave-front modulation, to sound insulation, and absorption.

The theoretical study by LST shows the existence of unstable modes in the hypersonic boundary layer by mathematically giving the growth rate of these modes. However, it is still a mystery how these unstable modes are amplified downstream from a physical perspective. There have been attempts to provide a physical interpretation of the growth of small disturbances in the flow field based on energy approaches.