Numerical study of stability of flows from low to high Mach number

Interest in the study of stability lies in the strong link with the laminar-to-turbulent transition with several implications in the design of new vehicles in the aerospace community. If on one side aeronautics would like to predict and control transition to limit drag, boost efficiency and reduce the fuel consumption on the other hand, space design faces reentry problem where an accurate transition prediction could lead to a better sizing of the thermal protection system, thus enhancing the overall performance of the spacecraft. Nevertheless one has to keep in mind that transition can occur because of several causes, which make the link between stability and transition not as direct as one would it like to be. On an engineering point of view the use of the eN method has been selected as our preferred way of estimating the onset of transition. Despite the great amount of software available to study stability of incompressible flows and, to a lesser extent, low supersonic flows, there is a restricted number of codes dealing specifically with hypersonic flows. The objective of this work is then to write a consistent toolkit to be able to study stability of flows at different regimes, from low to high Mach numbers. The VESTA toolkit (VKI Extensible Stability and Transition Analysis toolkit) gathers a number of codes for different regimes which are based on Chebyshev pseudo-spectral methods. It compares well against literature for the incompressible and compressible flows while hypersonic cases are more difficult to test, because of the narrower body of literature treating them. Nevertheless some comparisons allow us to estimate a reasonable good matching with existing results. The incompressible study was not limited to the reproduction of standard cases and techniques but included also an original expansion of the $\tau$-method capable of treating boundary layer flows. Results have been verified against the ones obtained by other methods even if its complexity makes the $\tau$-method an unideal candidate for the development of the compressible solver. The compressible linear stability solver is able to cope with both subsonic and supersonic regime and it has been used to verify and expand the current database of neutral stability curves at different Mach, by plotting results for adiabatic flows with different free stream static temperatures. The compressible solver served as a base for the implementation of the specialized hypersonic code. For this case, when temperature is high enough, air molecules start dissociating and chemical reactions happen between the different species. For this reason air should be considered as a mixture of gases. In the present work this effect is taken into account by means of the Local Thermodynamic Equilibrium (LTE) assumption. A deep investigation has been carried on the effect of free stream temperature and pressure. It turned out that in the investigated range, pressure plays a minor role, while temperature results to be the driving parameter, even more at lower Reynolds numbers. It has been observed that the critical Reynolds number decreases when temperature increases. As the free stream temperature increase the neutral stability curves show also a larger instability area. Another important aspect of hypersonic flows is the strong shock in front of the body. Its influence on the boundary layer has been modeled as a boundary condition for the calorically perfect gas (CPG) and LTE solver. Nevertheless the latter implementations is new and only simple verifications against a calorically perfect gas was possible. It is already known in literature that the shock stabilizes the flow at low wave numbers. Our computations on chemically reacting flows found out that LTE tends to stabilize it even more, with growth rates as low as three times the respective one for CPG. Future works will take advantage of the modularity of the VESTA toolkit to add other stability feature like Parabolized Stability Equations and BiGlobal stability. On the numerical side some work will be devoted to the implementation of more general and faster algorithm retaining the same level of accuracy of the present solvers. On a different level the results found in this work could be readily used together with an eN code for the prediction of transition for flight condition and ground testing while the software will be used as the founding brick of an Uncertainty Quantification for transition prediction.