Wall pressure fluctuations in hypersonic boundary layer: a strategy to design passive noise control systems

Abstract

The state of the boundary layer is of high importance since skin friction drag and heat transfer rates in a turbulent boundary layer can be several times higher than those of a laminar one. A lot of different strategies are used to delay or prevent the transition process. One possibility to manipulate the transition is using porous surfaces to influence the growth of the second mode in a passive way. The 2nd or so called Mack mode is dominant for the transition process at hypersonic Mach numbers. Some studies showed that an ultrasonically absorptive coating (UAC) can suppress the 2nd instability and then delay the transition of hypersonic boundary layer. The acoustic scattering problem affects the design of ultrasonic absorptive coatings for hypersonic laminar flow control. To investigate this phenomenon a finite element method (FEM) was employed to formulate 2-D simple model of UAC. The results provided are in strong agreement with existing results achieved by direct N-S solution (DNS) and theoretical models. DNS requires important computational costs while theoretical modelling is not adaptable to any type of geometry. Conversely, the FEM is extremely flexible and computationally affordable, resulting as the best candidate to perform design optimizations of more efficient UAC. Pressure time histories for coating of different porosities, various forcing frequencies and single or double cavity configurations are presented. Overall, the amplitude reflection by the UAC decreases with higher porosity and, in most cases, by reducing the dimensionless wavelength of the forcing. Hence, on the basis of our parametric study of the geometrical factors, we identified the dimensionless wavelength of the forcing λ∗ and the porosity ϕ as the most important parameters for UAC design. Moreover a comparison between UAC based on single-depth and double-depth rectangular cavity has been performed suggesting an interesting strategy to design a novel generation of UAC.