This contribution presents a stability analysis for compressible boundary layer flows over indented surfaces. Specifically, the effects of increasing depth D /δ * and Ma ∞ number on perturbation time-decay rates and spatial amplification factors are quantified and compared with those of an unindented configuration. The indented surfaces represent aeronautical lifting surfaces endowed with the smooth gap resulting when a filler material applied at the junction of leadingedge and wing-box components retracts upon its curing process. Since the configuration considered is such that the parallel/weakly-parallel assumptions are necessarily compromised, a global temporal stability analysis is considered in this study. Our analysis does not require a parallel flow constrain, and hence it is believed to be valid when two dimensional effects are relevant. We find that small surface modifications enhance certain flow instabilities. An increase in Ma ∞ enhances further this behaviour: for the D /δ * = 1.5, Ma ∞ = 0.5 case, amplification factors at a given location can be up to 20 times larger than those corresponding to the unindented case.
Stability analysis in the framework of fluid dynamics is often expressed in terms of a complex eigenvalue problem (EVP). The solution of this EVP describes underlying flow features and their stability characteristics. The main shortcoming of this approach is the high computational cost necessary to solve the EVP, limiting the applicability of this analysis to simple two-dimensional configurations. Many efforts have been focused on overcoming this limitation. Reducing the computational domain to encompass only those regions of physical interest may help alleviate the computational cost. However, the accuracy of the eigenmodes recovered from a reduced region needs to be carefully assessed. In this work, an in-depth analysis of the domain reduction (DR) strategy is presented, and an error estimation tool is provided. The applicability and limitations of this methodology are studied on the open-cavity problem. Next, the error estimation tool is exploited in the transonic buffet phenomenon on a NACA 0012 profile, giving valuable recommendations for the best use of this methodology. Finally, the DR strategy has been applied to investigate the asymmetries induced by jet cooling of turbine blades. K E Y W O R D S complex flows, domain reduction, eigenvalue problems, fluid dynamics, stability analysis 1 Int J Numer Meth Fluids. 2020;92:727-743. wileyonlinelibrary.com/journal/fld
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