Numerical Investigation of Porous Coatings Stabilizing Capabilities on Hypersonic Boundary-Layer Transition

Hammachi^1,2, J. Cardesa¹, E. Piot¹, M. Montagnac², H.Deniau¹

¹ONERA/DMPE, Université de Toulouse, F-31055 Toulouse, France

²Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS), 42 avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France

Corresponding author : riwan.hammachi@onera.fr

 

Keywords : Transition, hypersonic, boundary-layer

 

Abstract

This study explores the use of ultrasonically absorptive coatings (UACs) for passive control of laminarturbulent transition in hypersonic boundary layers. Their potential to reduce wall heat flux and skin friction is of particular interest.

The transition process in a low-disturbance environment is driven by the amplification and degeneracy of Mack modes, a family of linearly unstable modes inherent to high-speed wall-bounded flows. At higher Mach numbers, high-frequency trapped acoustic waves in the form of second mode disturbances initiate the transition process. Nonlinear interactions and secondary instabilities follow, ultimately leading to turbulence.

Smooth micro-porous surfaces have been identified as a promising solution for delaying transition in flight, as they effectively dissipate acoustic energy from the second Mack mode during its linear stage with minimal impact on the mean flow.

To capture and quantify the multiscale linear dynamics of these primary instabilities, Direct Numerical Simulations (DNS) of a spatially developing hypersonic boundary layer transition over a blunt cone with a nose radius of R_N = 2.5 mm at M_∞ = 7.4 and at Reynolds numbers Re_m = 6.4 · 10⁶ m⁻¹ are carried out. A high-order spectral difference flow solver previously used for a similar configuration [1].

Unsteady disturbances are generated within the laminar boundary layer by means of a local blowing-suction source term on the plate surface. The broadband acoustic response of UACs is modeled by a time-domain impedance boundary condition (TDIBC) that mimicks the acoustic properties of random porous microstructure coatings.

More precisely, the carbon–carbon ceramic material developed by the German Aerospace Laboratory [2] is chosen to numerically impose the TDIBC by fitting model parameters to experimental acoustic measurements. Once the base flow is computed, Linear Stability

Theory (LST) is applied to it to predict the growth region of the Mack second-mode for specific disturbances and their temporal scales. The LST results are then also used to assess the accuracy of the DNS when a harmonic excitation is chosen.

In the next step, a spatially evolving broadband pulse is introduced within the boundary layer, and its development over a solid wall and the UAC is examined and compared against a set of experimental results.

Our findings shed light on the physics underlying passive control of hypersonic boundary layer transition and the potential benefits of UACs in delaying the onset of turbulence.

 

References

[1] Fiévet, R., Deniau, H., Brazier, J. P., Piot, E. (2021). Numerical analysis of porous coatings stabilizing capabilities on hypersonic boundary-layer transition. AIAA Journal, 59(10), 3845-3858.

[2]Wagner, A., Hannemann, K., Kuhn, M. (2014). Ultrasonic absorption characteristics of porous carbon–carbon ceramics with random microstructure for passive hypersonic boundary layer transition control. Experiments in fluids, 55(6), 1-9.