Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session BP: Instability: Boundary Layers II |
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Chair: Anatoli Tumin, University of Arizona Room: 200D |
Sunday, November 22, 2009 10:30AM - 10:43AM |
BP.00001: Modal description of optimal internal streaks in a Falkner-Skan Boundary Layer Jose Sanchez-Alvarez, Maria Higuera, Jose Manuel Vega Understanding the growing disturbances in boundary layers is of crucial interest for numerous engineering applications. Here we examine the optimal streaky perturbations (which maximize energy growth) in a wedge flow boundary layer. These 3D perturbations are governed by a system of equations obtained by linearizing the 3D Navier-Stokes equations around the base flow given by the Falkner-Skan similarity solution. Based on an asymptotic analysis of this system near the free stream and the leading edge singularity, we show that optimal streaks can be described in terms of a single streamwise-growing solution of the linearized equations, which is associated with an eigenvalue problem first formulated in this context by Tumin (Phys. Fluids 13, 5, (2001)). Such a solution may be regarded as an internal spatially-unstable mode, in analogy with the usual eigenmodes of standard linear stability theory. An important consequence of this result is that the optimization procedure heretofore used to define optimal streaks is not necessary. Comparison with previous results in A.Tumin and D.E. Ashpis AIAA (2003) show excellent agreement. [Preview Abstract] |
Sunday, November 22, 2009 10:43AM - 10:56AM |
BP.00002: RNS streak description Carlos Martel, Juan Angel Martin We use the Reduced Navier-Stokes (RNS) equations for the simulation of the nonlinear evolution of streaks in a flat plate boundary layer. The RNS are asymptotically derived from the Navier Stokes equations for $Re \gg 1$, and they are appropriated for flow configurations with one slow scale and two short scales. We derive the RNS with the appropriate boundary conditions for the simulation of the spatially growing streaks, comment the details of the numerical method used, and compare our 3D streak simulations with the results present in the literature. The presented RNS scheme for computing nonlinear streaks is much faster than full 3D DNS computations, and does not exhibit the numerical instabilities present in previous nonlinear PSE calculations. [Preview Abstract] |
Sunday, November 22, 2009 10:56AM - 11:09AM |
BP.00003: Optimal Disturbances and Receptivity of 3D Boundary Layers David Tempelmann, Ardeshir Hanifi, Dan Henningson We will present spatial optimal disturbances in a Falkner-Skan-Cooke boundary layer and illuminate how these can be used to determine the receptivity of crossflow vortices to freestream disturbances. Optimal disturbances, which are obtained by solving a parabolized set of equations, initially take the form of vortices tilted against the direction of the mean crossflow shear. Further downstream they evolve into bended streaks and finally into crossflow disturbances. A large potential for initial non-modal growth becomes apparent where both the lift-up effect and the Orr-mechanism are identified as responsible physical mechanisms. We inquire if non-modal growth is related to a receptivity mechanism for modal instabilities in 3D boundary layers. We therefore use continuous modes from the Orr-Sommerfeld/Squire spectrum as a model for freestream turbulence and project them onto initial optimal disturbances in order to obtain receptivity coefficients. A parametric study concerning optimal growth and receptivity will be presented as well as a comparison to existing DNS and experimental data. [Preview Abstract] |
Sunday, November 22, 2009 11:09AM - 11:22AM |
BP.00004: Scaling of Transient Growth of Instability Induced by a Periodic Array of Roughness Elements in a Blasius Boundary Layer Philippe Lavoie, Ahmed Naguib, Jonathan Morrison The receptivity of laminar boundary layers to three-dimensional perturbations and the ensuing evolution of the transient growth of disturbances have attracted much attention in recent years. The motivation for the present study is related to the development of a reduced-order model and estimator for the closed-loop control of transient growth instabilities in a laminar boundary layer. We focus here on the scaling characteristics of the streamwise component of the disturbance energy. Starting from the linearized boundary layer equations and given assumptions with respect to the boundary layer receptivity to perturbations, we derive scaling arguments for the evolution of the disturbance energy. These are examined against experimental data, which were obtained by inducing transient growth in a Blasius boundary layer in the wind tunnel using spanwise-periodic arrays of cylindrical roughness elements with different geometrical parameters. It is found that the growth and decay region of the energy evolution scale differently. The dynamical implications of the scaling presented here are discussed from the point of view of model reduction for flow control. [Preview Abstract] |
Sunday, November 22, 2009 11:22AM - 11:35AM |
BP.00005: Toward the foundation of a global modes concept Anatoli Tumin Recent progress in using global modes for the analysis of a variety of complex (and ``simple'') flows led to their applications in flow control. The progress in computational capabilities brings this advanced technique to common practice in studies of flow perturbations. However, the formulation of global eigenvalue problems is accompanied by uncertainties in the choice of boundary conditions. Today, the choice of boundary conditions has a heuristic nature, and this provokes questions regarding the suitable formulation of the eigenvalue problems. A simple model can help us to understand the effect of the upstream and downstream boundary conditions on the eigenvalues and eigenfunctions. I consider the ``box formulation'' in a uniform flow. In the limit of an infinite domain in the $y$-direction, the problem is reduced to a system of ODEs with constant coefficients using the Fourier transform in $y$. There are boundary layers in the vicinity of the upstream and downstream boundaries. The pressure wave penetrates upstream at a distance about the characteristic scale of the perturbation in the $y$ direction. Discussion of Dirichlet and Neumann boundary conditions for the model problem is accompanied by comparisons with available publications for boundary layer flows. The model helps to understand the spectrum features in published results. [Preview Abstract] |
Sunday, November 22, 2009 11:35AM - 11:48AM |
BP.00006: How many unstable modes are in high-speed boundary layers? Alexander Fedorov, Anatoli Tumin L. Mack (1969) carried out the inviscid stability analysis of high-speed boundary layers, and he found that in addition to the unstable mode having a viscous nature, there are other unstable discrete modes associated with acoustic perturbations ``trapped'' inside the boundary layer. In contemporary stability analysis of high-speed boundary layers at finite Reynolds numbers, two discrete modes are identified: the 1st and 2nd modes. However, at high Mach numbers and finite Reynolds numbers, the discrete spectrum of normal modes has only one eigenvalue that is meandering in the complex plane (the wave number or the frequency, depending on the stability framework) that corresponds to an unstable perturbation. In the present work, we illustrate how the synchronism and branching of discrete modes can lead to a spectrum with one or two unstable discrete normal modes. One has to be aware of this phenomenon and to keep in mind the ambiguity associated with the terminology of the ``1st mode'' and ``2nd mode.'' [Preview Abstract] |
Sunday, November 22, 2009 11:48AM - 12:01PM |
BP.00007: Large Eddy Simulation of Transitional Boundary Layer Taraneh Sayadi, Parviz Moin A sixth order compact finite difference code is employed to investigate compressible Large Eddy Simulation (LES) of subharmonic transition of a spatially developing zero pressure gradient boundary layer, at $Ma = 0.2$. The computational domain extends from $Re_x = 10^5$, where laminar blowing and suction excites the most unstable fundamental and sub-harmonic modes, to fully turbulent stage at $Re_x = 10.1\times10^5$. Numerical sponges are used in the neighborhood of external boundaries to provide non-reflective conditions. Our interest lies in the performance of the dynamic subgrid scale (SGS) model [1] in the transition process. It is observed that in early stages of transition the eddy viscosity is much smaller than the physical viscosity. As a result the amplitudes of selected harmonics are in very good agreement with the experimental data [2]. The model's contribution gradually increases during the last stages of transition process and the dynamic eddy viscosity becomes fully active and dominant in the turbulent region. Consistent with this trend the skin friction coefficient versus $Re_x$ diverges from its laminar profile and converges to the turbulent profile after an overshoot. 1. Moin P. \textit{et. al.} Phys Fluids A, \textbf{3}(11), 2746-2757, 1991. 2. Kachanov Yu. S. \textit{et. al.} JFM, \textbf{138}, 209-247, 1983. [Preview Abstract] |
Sunday, November 22, 2009 12:01PM - 12:14PM |
BP.00008: Effects of passive porous walls on hypersonic boundary layers Sharon Stephen, Vipin Michael We consider the effect of a passive porous wall on the first mode of a hypersonic boundary layer on a sharp slender cone. A theoretical stability analysis is used for large Mach number and large Reynolds number which includes the effect of curvature and of the attached shock. The formulation considers the scales appropriate to the first mode which is associated with Tollmien- Schlichting waves and this results in a triple-deck structure. The flow in the hypersonic boundary layer is coupled to the flow in the porous layer. We consider the porous layer on the cone surface to be a sheet perforated with cylindrical blind holes of equal spacing\footnote{Fedorov, A. V., Malmuth, N. D., Rasheed, A. and Hornung, H. G. {\it AIAA J.} {\bf 39}, 605 (2001).}. The linear stability analysis results in an eigenrelation, relating the streamwise wavenumber and the frequency of the disturbances. Neutral solutions will be presented, indicating a destabilizing efect of the porous wall. Spatial growth rates obtained will demonstrate that the porous wall leads to a significant increase in disturbance growth rates. In addition, the effect of nonlinearity is considered. [Preview Abstract] |
Sunday, November 22, 2009 12:14PM - 12:27PM |
BP.00009: Investigation of Transition Initiated by a Wave Packet in a Hypersonic Cone Boundary Layer Jayahar Sivasubramanian, Hermann Fasel Direct Numerical Simulations (DNS) are performed to investigate the linear and nonlinear transition regime of a hypersonic boundary layer on a sharp circular cone at zero angle of attack. In a natural transition scenario a broad disturbance spectrum is excited by freestream disturbances leading to complex wave interactions. Therefore, in order to understand the natural transition process in hypersonic cone boundary layers, the flow was pulsed through a hole on the cone surface to generate a wave packet with a wide range of disturbance waves. First, DNS of a linear three-dimensional wave packet was performed and results are compared to linear stability theory (LST). A good agreement was found to exist between DNS and LST results. Then to study the nonlinear regime, DNS of a nonlinear wave packet was performed. The wall pressure disturbance spectrum of the nonlinear wave packet indicated the presence of fundamental and subharmonic resonance mechanisms. [Preview Abstract] |
Sunday, November 22, 2009 12:27PM - 12:40PM |
BP.00010: Hypersonic Boundary Layer Stabilization Through Chemical Energy Absorption Heath Johnson, Graham Candler A number of studies have been performed looking at the effects of surface blowing or suction on boundary layer stability. This situation can arise in the case of forced mass flow through a porous surface or in the case of an ablative surface material which absorbs energy and releases gas into the boundary layer. Here we investigate the effects of blowing or suction in high-enthalpy, hypersonic flows where the injected gas will not only mix with the free-steam gas, but may also become vibrationally excited and chemically react both in the steady mean flow and in the unsteady disturbances. The effect of chemical and vibrational energy exchange on boundary layer stability is investigated in numerical simulations through application of the parabolized stability equations. [Preview Abstract] |
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