Global Instability Analysis of Laminar Boundary Layer Flow Over a Bump at Transonic Conditions (original) (raw)
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The aim of this thesis is to describe the linear and non-linear dynamics of both attached and separated boundary-layer flows over a flat plate at low Reynolds numbers. The linear dynamics, driven by the interactions among the non-orthogonal eigenvectors, is studied using two global instability approaches: the global eigenvalue analysis and the direct-adjoint optimization. In these global instability analysis no spatial structure is assumed a-priori for the perturbation, and the convective effects due to the high non-parallelism of the flow are taken into account. In the case of the separated boundary-layer flows, it has been clarified the role of the following features in the onset of unsteadiness: i) the strong two-dimensional convective amplification; ii) the non-normality effects such as the 'flapping' phenomenon; iii) the high sensitivity to external forcing; iv) the globally unstable three-dimensional mode. Concerning the attached boundary layer, the aim has been to identify localized perturbations characterized by more than one frequency in the streamwise and/or spanwise direction, inducing a strong energy amplification. In order to assess the effects of non-linearity on the instability mechanisms identified by the global linear stability analysis, direct numerical simulations have been performed in a two- and three-dimensional framework for both the attached and separated boundary-layer flows. The dynamics of the perturbations which most easily brings the flows on the verge of turbulence have been studied. Different scenarios of transition have been observed, and the mechanisms leading the flow to turbulence have been analyzed in detail.
Linear instability of orthogonal compressible leading-edge boundary layer flow
6th AIAA Theoretical Fluid Mechanics Conference, 2011
Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ M a ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.
A transonic interaction between a shock wave and a turbulent boundary layer is experimentally and theoretically investigated. The configuration is a transonic channel flow over a bump, where a shock wave causes the separation of the boundary layer in the form of a recirculating bubble downstream of the shock foot. Different experimental techniques allow for the identification of the main unsteadiness features. As recognised in similar shock-wave/boundary-layer interactions, the flow field exhibits two distinct characteristic frequencies, whose origins are still controversial: a low-frequency motion which primarily affects the shock wave; and medium-frequency perturbations localised in the shear layer. A Fourier analysis of a series of Schlieren snapshots is performed to precisely characterise the structure of the perturbations at low-and medium-frequencies. Then, the Reynolds-averaged Navier-Stokes (RANS) equations closed with a Spalart-Allmaras turbulence model are solved to obtain a mean flow, which favourably compares with the experimental results. A global stability analysis based on the linearization of the full RANS equations is then performed. The eigenvalues of the Jacobian operator are all damped, indicating that the interaction dynamic cannot be explained by the existence of unstable global modes. The input/output behaviour of the flow is then analysed by performing a singular-value decomposition of the Resolvent operator; pseudo-resonances of the flow may be identified and optimal forcings/responses determined as a function of frequency. It is found that the flow strongly amplifies both medium-frequency perturbations, generating fluctuations in the mixing layer, and low-frequency perturbations, affecting the shock wave. The structure of the optimal perturbations and the preferred frequencies agree with the experimental observations.
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2013
A collection of illustrations of swept-wing boundary layer secondary instability at low subsonic flow velocities is presented in this paper. The experimental results, obtained by hot-wire "visualization," provide detailed insight into the spatio-temporal structure and evolution of oscillations in the three-dimensional laminar boundary layer disturbed by longitudinal vortices and streaky structures. MOVIE 2: Perturbations of the streaky structure at the initial stage of its breakdown FIG. 5: Streaky structure instability at the late stage of the transition to turbulence: isosurfaces u = ±4.0% U 0 (a) and u f = ±1.0% U 0 (b) INSTABILITY OF A SWEPT-WING BOUNDARY LAYER MODULATED BY STATIONARY FLOW PERTURBATIONS 7/30/13 9:25 PM Стр. 8 из 13 INSTABILITY OF A SWEPT-WING BOUNDARY LAYER MODULATED BY STATIONARY FLOW PERTURBATIONS 7/30/13 9:25 PM Стр. 9 из 13
Linear Instability of Shock-Dominated Laminar Hypersonic Separated Flows
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The self-excited spanwise homogeneous perturbations arising in shockwave/boundary-layer interaction (SWBLI) system formed in a hypersonic flow of molecular nitrogen over a double wedge are investigated using the kinetic Direct Simulation Monte Carlo (DSMC) method. The flow has transitional Knudsen and unit Reynolds numbers of 3.4 × 10 −3 and 5.2 × 10 4 m −1 , respectively. Strong thermal nonequilibrium exists downstream of the Mach 7 detached (bow) shock generated due to the upper wedge surface. A linear instability mechanism is expected to make the pre-computed 2-D base flow potentially unstable under spanwise perturbations. The specific intent is to assess the growth rates of unstable modes, the wavelength, location, and origin of spanwise periodic flow structures, and the characteristic frequencies present in this interaction.
Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach
2007
Abstract The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar boundary layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer.
Le Centre pour la Communication Scientifique Directe - HAL - Inria, 2022
Experiments were conducted to study the transition and flow development in a laminar separation bubble (LSB) formed on an aerofoil. The effects of a wide range of freestream turbulence intensity (0.15% < Tu < 6.26%) and streamwise integral length scale (4.6mm < Λ u < 17.2mm) are considered. The coexistence of a modal instability due to the LSB and a non-modal instability caused by streaks generated by freestream turbulence is observed. The presence of streaks in the boundary layer modifies the mean flow topology of the bubble. These changes in the mean flow field result in the modification of the convective disturbance growth, where an increase in turbulence intensity is found to dampen the growth of the modal instability. For a relatively fixed level of Tu, the variation of Λ u has modest effects, however a slight advancement of the non-linear growth of disturbances and eventual breakdown with the decrease in Λ u is observed. The data shows that the streamwise growth of the disturbance energy is exponential for the lowest levels of freestream turbulence and gradually becomes algebraic as the level of freestream turbulence increases. Once a critical turbulence intensity is reached, there is enough energy in the boundary layer to suppress the LSB, which in turn, results in the non-modal instability to take over the transition process. Linear stability analysis is conducted in the fore position of the LSB, and accurately models unstable frequencies and eigenfunctions for configurations subjected to levels of turbulence intensity levels up to 3%. Increasing the Tu resulted in the Reynolds number dependence to increase, suggesting that a viscous, rather than an invicid formulation of the stability equations is appropriate for modeling modal instabilities in the fore portion of the studied LSB.
Linear stability analysis in compressible, flat-plate boundary-layers
2008
The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory. The stability equations obtained from three-dimensional compressible Navier–Stokes equations are solved simultaneously with two-dimensional mean flow equations, using an efficient shoot-search technique for adiabatic wall condition. In the analysis, a wide range of Mach numbers extending well into the hypersonic range are considered for the mean flow, whereas both two- and three-dimensional disturbances are taken into account for the perturbation flow. All fluid properties, including the Prandtl number, are taken as temperature-dependent. The results of the analysis ascertain the presence of the second mode of instability (Mack mode), in addition to the first mode related to the Tollmien–Schlichting mode present in incompressible flows. The effect of reference temperature on stability characteristics is also studied. The results of the analysis reveal that t...
Instability-wave propagation in boundary-layer flows at subsonic through hypersonic Mach numbers
Mathematics and Computers in Simulation, 2004
Direct numerical simulations (DNS) form an important ingredient to physics-based prediction of laminar-turbulent transition in boundary-layer flows, particularly in applications where it is desirable or even essential to model the various stages of transition process in an integrated manner. This paper addresses two building-block issues towards such capability: application to instability-wave propagation in boundary layers over curvilinear surfaces and robust outflow boundary conditions across the speed regime. In particular, detailed comparisons of linear and nonlinear development of instability waves in a range of boundary-layer flows are used to cross-validate a high-order direct numerical simulation algorithm against the approximate but computationally more efficient technique of parabolized stability equations (PSE). Three separate flow configurations are investigated in this study: (i) development of a Tollmien-Schlichting (TS) instability wave over a two-dimensional (2D), symmetric, low-speed airfoil, (ii) both first and second-mode development in a self-similar, flat plate boundary layer at Mach 4.5, and (iii) amplification of first and second modes of Rayleigh instability and a stationary Gortler vortex in the hypersonic, axisymmetric boundary layer over a flared cone. The satisfactory agreement between the DNS and PSE predictions for both amplitudes and mode shapes of the instability waves confirms the overall efficacy of the DNS algorithm, while underscoring the accuracy of predictions based on the PSE approximation. Published by Elsevier B.V. on behalf of IMACS.