Stability of compressible boundary layers in presence of smooth roughness and wall temperature effects
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In natural laminar flow design, aircraft manufacturers aim to delay the laminar-to-turbulent transition by modifying the geometric features of the aircraft to stabilize the boundary layer. Yet, the transitional process is highly sensitive to surface imperfections; the presence of grooves, rivets or dimples, for instance, greatly affects the transitional properties of the flow and need to be considered for accurate predictive modelling. To this end, the nonlinear parabolized stability equations (NPSE) have shown promising predictive capabilities over a wide range of operating conditions. The NPSE are less dependent on experimental data, which is a step towards a generalizable transition model. Here, we first present a novel NPSE-based numerical framework, developed in-house but made open-source, to investigate transition in compressible flows. The code can handle complex geometries and only requires the coordinates of the wall to generate an orthonormal computational grid. The mesh spacing is refined based on the curvature of the wall. The model is formulated in dimensionless variables, and the disturbances are discretized using a finite-bandwidth approach. Written in Python and leveraging well-established libraries, the framework includes a laminar flow solver using the same numerical formulation as the modal stability solver to remain consistent. The code is validated against published cases and large-scale Direct Numerical Simulations (DNS). It can serve as the basis for the future development of modal stability-based problems in aerospace engineering, geophysical, and multiphase flows. The computational framework is used in combination with large-scale DNS to study the effect of smooth two-dimensional surface roughness on the stability characteristics of a canonical boundary layer flow under transonic conditions (M=0.714). In particular, the influence of two-dimensional smooth roughness on the stability of 2D Tollmien-Schlichting (T-S) waves is investigated with a particular emphasis on frequency content generation. The DNS reveals a stronger destabilizing effect of the disturbance higher frequencies for the case featuring the highest roughness amplitude. This causes a rapid growth of secondary instabilities which skips the standard T-S mechanism and give rise to a cyclical transitional pattern in which both late K-type structures and premature bypass transition are observable. The modal stability analysis also shows that, in the presence of two-dimensional smooth roughness, the mode experiencing the highest linear growth is three-dimensional. Finally, the coupling effect between roughness and wall temperature inhomogeneities is investigated at transonic condition using the nonlinear parabolized stability equations (NPSE). To this end, the effect of localized heating and cooling strips on the stability of a flat plate boundary layer with zero pressure gradient at M=0.714 is first investigated and confirms the stabilizing (destabilizing) effect of cooling (heating) strips. Then, the coupling effect between the wall roughness and heating strips is addressed by superimposing the effect of a smooth roughness patch, consisting of five sinusoidal, two-dimensional humps, to the numerical setup. The NPSE study reveals a catalytic coupling effect between the temperature strips and roughness. In other words, compared with the flat plate case, the stability of the flow is decreased in the presence of heating strips and roughness, and, inversely, increased in the presence of cooling strips and roughness.
Cite this version of the work
Francis Lacombe (2023). Stability of compressible boundary layers in presence of smooth roughness and wall temperature effects. UWSpace. http://hdl.handle.net/10012/19127