Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.
The presence of intense fluctuating pressure is a significant concern for life-prediction of thin-gauge hot-structures operating in high-speed flow. Sources include self-induced components, from panel vibrations, and boundary layer induced from turbulence. While the former has received considerable attention, primarily due to the amenability of the problem for academic study using simple models, the latter is not well-understood due to the complexity of boundary layer turbulence. Important open questions are how strongly coupled fluctuating loads induced by the turbulent boundary layer are to the thermo-structural response, and also if interactions between a turbulent boundary layer and structural response can lead to structural instabilities. This study seeks to examine these questions by incorporating a phenomenological model for turbulent boundary layer loads into an aerothermoelastic framework. The enhanced aerothermoelastic model is then used to study the combined effect of self and boundary layer induced fluctuating pressures on responses of simple panels, and to characterize features in the turbulent boundary layer loads that can lead to large amplitude structural vibrations. The developed phenomenological model predicts that the magnitude of the boundary layer induced fluctuating pressure increases with increasing panel inclination, and decreases with increasing temperature. Furthermore, it is found that both RMS magnitude and phase angle of the boundary layer induced pressure loads play key roles in panel response. Certain combinations of these features, coupled with the self-induced pressure fluctuations, are found to cause onset of fluid-structural instabilities earlier than observed when pressure fluctuations from the turbulent boundary layer are neglected. NomenclatureF c = compressible flow transformation function h = panel thickness H = enthalpy k = thermal conductivity k = parameter representing compressibility and heat transfer effects L = length of the panel M = Mach number m = viscosity power law exponent, η/η e = (T /T e ) m N = number of time instant values for time variant TBL fluctuating pressure load n = velocity power law exponent, U/U e = (y/δ) p = pressure P r = Prandtl number p = RMS fluctuating pressure q = ρU 2 /2, dynamic pressure Q aero = aerodynamic heat flux Q rad = radiation heat flux r = P r 1/3 , turbulent flow recovery factor t = time T = temperature t max = duration of time domain signal U = velocity, air w = transverse panel displacement x = chordwise coordinate Y = Fourier domain signal y = normal distance into boundary layer from wall y t = time domain signal z = coordinate in the direction perpendicular to the panel surface α = thermal expansion coefficient β = parameter to evaluate spatial phase angle γ = ratio of specific heats ∆ = incremental change δ = boundary layer thickness δ 1 = boundary layer displacement thickness ζ = separation distance of two points on the panel η = viscosity θ = overall phase angle λ = viscous/velocity power law exponent ν = Poissons ratio ρ...
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