Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session HD: Transient Growth and Receptivity of Boundary Layers |
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Chair: Bruno Eckhardt, Philipps Universitaet Marburg Room: 002B |
Monday, November 24, 2008 10:30AM - 10:43AM |
HD.00001: Continuous Spectrum Analysis of Suboptimal Roughness-Induced Growth in Experiments and DNS Nicholas Denissen, Edward White Transient growth theory provides a framework for addressing stability and transition in the absence of unstable eigenmodes. To make use of the theory for stationary, roughness-induced disturbances, the wake flow behind roughness elements must be decomposed into a sum of the continuous spectrum modes of the Orr-Sommerfeld equation. The amplitude of the continuous spectrum modes provides a quantitative measure of the receptivity process. This presentation briefly covers the background of the biorthogonal decomposition procedure and its application to flow behind an array of discrete, periodic, roughness elements in a flat-plate boundary layer. The decomposition of the results into the continuous spectrum modes is given for a test case where both experimental and DNS data is available. These results are compared to solutions for optimal disturbances and linear receptivity models, providing a basis for characterizing flow response in terms of excitation of continuous spectrum wavenumbers. [Preview Abstract] |
Monday, November 24, 2008 10:43AM - 10:56AM |
HD.00002: DNS Study of Transient Disturbance Growth and Bypass Transition Kelly Stephani, David Goldstein Direct numerical simulation was used to investigate the detailed flow past a periodic array of cylindrical roughness elements. The problem was constructed as channel flow over a flat plate surface with roughness elements formed using an immersed boundary technique with a spectral method approach. Solutions were obtained for two roughness heights corresponding to Reynolds numbers (Re$_{k})$ of 189 and 350, and results are presented for both cases. Cylindrical roughness elements with Re$_{k}$=189 produced minimal disturbances and the flow remained laminar in the wake downstream of the roughness elements. Flow past cylindrical roughness elements corresponding to Re$_{k}$=350 was found to transition as soon as 2-3 cylinder diameters downstream and had developed into fully turbulent flow by the end of the domain. Results were found to compare reasonably well with a similar set of DNS computations by Rizzetta and Visbal using a sixth-order-accurate centered compact finite difference scheme as well as experimental results obtained by Ergin and White using time-averaged hotwire measurements of the velocity components. [Preview Abstract] |
Monday, November 24, 2008 10:56AM - 11:09AM |
HD.00003: Experimental Study of Transient Growth of Instabilities in a Laminar Boundary Layer Philippe Lavoie, Ahmed Naguib, Jonathan Morrison Transient growth of instabilities in laminar boundary layers has attracted significant attention in recent years, both theoretically and experimentally. The present work stems from an interest in model reduction for flow control, using the transient growth mechanism as a linear physical model representation of a turbulent boundary layer. As a stepping stone towards this goal, the aim of this study is to investigate the receptivity of laminar boundary layers to transient-growth modes in order to develop a wall-based estimator. Inspired by the work of White (2002) and Fransson et al. (2004), an extensive parametric study was undertaken to study the transient growth of instabilities introduced by a spanwise periodic array of roughness elements in a wind tunnel. A distinctive aspect of the present experiment is that the effects of Reynolds number, and the roughness heigh, diameter and spacing relative to the boundary layer thickness are investigated independently of each other. Physiological-based scaling of the disturbance energy growth and decay is demonstrated over a wide range of perturbation input and flow parameters. Dynamical implications of this scaling are discussed from the point of view of developing a reduced order model for flow control. [Preview Abstract] |
Monday, November 24, 2008 11:09AM - 11:22AM |
HD.00004: Optimal linear growth in MHD duct flow Thomas Boeck, Dmitry Krasnov, Maurice Rossi, Oleg Zikanov We consider the flow of an electrically conducting fluid in a rectangular duct under a homogeneous magnetic field. The field is perpendicular to the flow direction and parallel to one set of the non-conducting walls. Our focus is on the transient growth of linear perturbations as a prerequisite for subsequent numerical studies of subcritical transition in the MHD duct flow. The perturbations with strongest transient growth are obtained by an iterative method based on linearized perturbation equations and their adjoint equations. We study the effect of the magnetic induction and of the aspect ratio of the duct on the maximum energy amplification and on the corresponding spatial structure of the linear perturbations. For wide ducts with magnetic field perpendicular to the long walls we find considerable differences to the periodic channel with wall-normal magnetic field. For narrow ducts the agreement with the periodic channel with spanwise magnetic field is considerably better. [Preview Abstract] |
Monday, November 24, 2008 11:22AM - 11:35AM |
HD.00005: Receptivity to molecular agitation in boundary-layer transition Paolo Luchini Convectively unstable flows behave as amplifiers, and their laminar region can be extended by lowering the level of external disturbances. At first sight, complete laminarization appears possible in principle. However, it was sometimes pointed out in the past (e.g. Betchov 1961) that the velocity fluctuations associated with molecular agitation (those responsible of thermal noise and Brownian motion) in a fluid are 80 to 100 dB below the level of turbulent fluctuations, and thus of the order of magnitude required to provoke transition. Nevertheless, quantitative receptivity calculations have only ever been applied to external disturbances of acoustic or vortical origin or due to surface roughness, omitting thermal noise. Here the amplification of thermal noise by a boundary layer is explicitly computed, confirming that transition can be induced in this way. Therefore, even in a perfect environment with zero disturbances the extent of laminar flow is bounded. In addition, this computed upper bound is not far from practically observed transition lengths, implying that in some environments external disturbances may actually be negligible, and knowledge of their level unneeded to predict transition. [Preview Abstract] |
Monday, November 24, 2008 11:35AM - 11:48AM |
HD.00006: Roughness receptivity in swept-wing boundary layers - Experiments Andrew Carpenter, William Saric, Helen Reed Data are presented on boundary-layer transition to turbulence in low-disturbance environments. The measurements include infra-red thermography to study roughness related issues of boundary-layer transition in flight. A swept-wing model is mounted on the wing of a Cessna O-2 aircraft where nonlinear parabolized stability equations (NPSE) correlate the stability measurements and transition locations. The laminarization scheme of spanwise-periodic discrete roughness elements (DRE) is investigated at chord Reynolds numbers of 7.5 million. Flight experiments were conducted where the surface roughness amplitude was varied from 6 to 50 microns while the disturbance shear-stress was measured with calibrated hotfilm gauges. In this way, the disturbance velocity amplitude was calculated as a function of roughness Reynolds number. These data were then used as initial conditions for the NPSE calculations to determine the efficacy of the DREs. [Preview Abstract] |
Monday, November 24, 2008 11:48AM - 12:01PM |
HD.00007: Roughness receptivity in swept-wing boundary layers - Computations Helen Reed, Richard Rhodes, William Saric The laminarization of a swept-wing boundary layer by the introduction of passive spanwise-periodic roughness elements (DREs) near the leading edge is investigated at chord Reynolds numbers of approximately 7.5 million. The Texas A+M Flight Research Lab (FRL) is currently conducting flight tests of a 30-degree swept-wing model (SWIFT) mounted vertically below the port wing of a Cessna O-2A Skymaster. As a companion to the flight experiments, the current study is concerned with modeling the flowfield over the O-2 aircraft with the SWIFT model. The full-aircraft computational model was used to validate the flight-test configuration, as well as provide the basic state for the nonlinear parabolized stability equation (NPSE) formulation used to correlate shear-stress measurements, disturbance velocity amplitude, and roughness Reynolds number, and determine the efficacy of the DREs. [Preview Abstract] |
Monday, November 24, 2008 12:01PM - 12:14PM |
HD.00008: DNS and theoretical study of perturbations in a hypersonic boundary layer over a flat plate Xiaowen Wang, Anatoli Tumin, Xiaolin Zhong Direct numerical simulation of receptivity in a boundary layer over a flat plate was carried out with perturbations introduced into the flow by periodic-in-time blowing-suction through a slot. The free stream Mach number is equal to 5.92. The perturbation flow field was decomposed into normal modes with the help of the multimode decomposition technique based on the spatial biorthogonal eigenfunction system. The decomposition allows filtering out the unstable mode hidden behind perturbations having another physical nature. The development of the filtered-out unstable mode is compared with a theoretical prediction based on the method of multiple scales that includes the nonparallel flow effects. The results illustrate how the multimode decomposition technique may serve as an efficient tool for gaining insight into the flow dynamics in the presence of perturbations belonging to different modes. [Preview Abstract] |
Monday, November 24, 2008 12:14PM - 12:27PM |
HD.00009: Structure of Streaks Near the Leading Edge Singularity in a Blasius Boundary Layer Jose Manuel Vega, Maria Higuera Streaky (S) perturbations (also called Klebanoff modes) in a Blasius boundary layer are examined in the vicinity of the leading edge singularity. Understanding the mathematical structure of S-perturbations in this limit requires to consider two eigenvalue problems, whose eigenfunctions exhibit two well separated scales in the normal direction: (i) $\zeta=y/\sqrt(x)\sim 1$ and (ii) $y=\zeta \sqrt(x)\sim1$, where $\zeta$ is the usual self similar variable in the boundary layer and $x$ is the streamwise coordinate. These eigenvalue problems were considered by Luchini (JFM 1996), who calculated some of their solutions. The remaining solutions are calculated and used to obtain approximations of the relevant solutions of streamwise evolving parabolic problem that provides S-perturbaions in this limit. Some of the results are also relevant in the restricted 2D problem. [Preview Abstract] |
Monday, November 24, 2008 12:27PM - 12:40PM |
HD.00010: Low-Dimensional Modal Description of Optimal Streaks Maria Higuera, Jose Manuel Vega Streaky perturbations play an essential role in the destabilization of boundary layers, especially in the presence of free-stream turbulence. These perturbations are calculated in terms of a streamwise evolving parabolic problem. Using the asymptotic behaviour of the solutions near the leading edge singularity, we obtain a low-dimensional modal description of the streaks in the case of a boundary layer attached to a flat plate. Comparison with optimal streaks obtained via the adjoint gradient (Luchini, JFM 2000), seems to indicate that the development of the instability may be understood on the basis of appropriate amplitude equations giving the streamwise evolution of the amplitudes of the relevant modes. [Preview Abstract] |
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