Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session L2: Instability in Boundary Layers II |
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Chair: Helen Reed, Texas A&M University Room: 302 |
Monday, November 21, 2011 3:35PM - 3:48PM |
L2.00001: Transition to Turbulence and Heat-Transfer Overshoot in an Adverse Pressure Gradient High-Speed Boundary Layer Kenneth Franko, Sanjiva Lele Spatial direct numerical simulations (DNS) of transitional high-speed boundary layers with zero and adverse pressure gradients and an isothermal wall are presented for different transition scenarios. The maximum momentum thickness Reynolds numbers vary between 2500 and 5500 and the edge Mach numbers vary between 6 and 4.8 for the different cases presented. Disturbances are introduced into the initially laminar boundary layer through suction and blowing at the wall. Different transition scenarios including first mode oblique breakdown and second mode fundamental resonance are explored. The presence of an adverse pressure gradient accelerates the transition process. Comparisons of the nonlinear modal growth and breakdown for the different initial forcing scenarios will be shown. First mode oblique breakdown is shown to lead to an overshoot in heat transfer and the most rapid development to a turbulent state. [Preview Abstract] |
Monday, November 21, 2011 3:48PM - 4:01PM |
L2.00002: ABSTRACT WITHDRAWN |
Monday, November 21, 2011 4:01PM - 4:14PM |
L2.00003: Effect of Surface Curvature on Crossflow Instability in Swept-Wing Boundary Layers M. Malik, W. Liao, F. Li, M. Choudhari, C. Chang A three-dimensional boundary layer is subject to crossflow instability that manifests itself in the form of stationary or traveling disturbances. Stationary disturbances are induced by surface roughness while free stream turbulence induces traveling disturbances. It is known that convex surface curvature tends to stabilize crossflow instability while the mean flow non-parallel effect is generally destabilizing, with the net effect being mildly stabilizing when compared to the results obtained using quasi-parallel linear stability theory. Here, an analysis is performed for two swept airfoils using parabolized stability equations that account for both the surface curvature and the non-parallel effect. One airfoil has larger convex curvature than the other, where the convex surface curvature is scaled by defining a Gortler number. The net decrease in the stationary crossflow N factor is about 6 for the airfoil with stronger curvature. The analysis suggests that, if transition is induced by stationary crossflow disturbances, then surface curvature could be used as a control parameter for natural laminar flow design. The strong effect of surface curvature on stationary disturbances highlights the importance of investigating the receptivity of stationary and traveling disturbances since the latter are much less influenced by surface curvature resulting in much higher relative N factors for traveling disturbances. [Preview Abstract] |
Monday, November 21, 2011 4:14PM - 4:27PM |
L2.00004: Secondary instability analysis of pre-transitional streaks in boundary layers M.J. Philipp Hack, Tamer Zaki In the presence of free-stream vortical disturbances, laminar boundary layers develop streamwise-elongated perturbations of high amplitude, commonly known as Klebanoff streaks. The regions of shear surrounding these primary structures provide the potential for the growth of secondary instabilities which ultimately initiate bypass transition. By means of linear analysis, we examine the secondary instability which precedes the formation of turbulent spots. The base state is extracted from direct numerical simulations of the bypass process. The simulation setup is similar to the work of Jacobs \& Durbin (2001), where transition is triggered by broadband free-stream vortical forcing. The velocity field therefore includes a spectrum of streaks with different structures and amplitudes. The stability analysis can nevertheless identify the streaks which indeed develop secondary instabilities and break down to turbulence. The predictions of linear theory, in particular the instability wavelength and phase speed, are compared to the streak instabilities recorded in the DNS of the full bypass process. [Preview Abstract] |
Monday, November 21, 2011 4:27PM - 4:40PM |
L2.00005: Conditional Sampling of Bypass Transition in Pressure Gradient Boundary Layers Kevin Nolan, Tamer Zaki Conditional sampling of velocity fields from Direct Numerical Simulations (DNS) of bypass transition is performed with discrimination between laminar and turbulent events. Individual positive and negative streaks are isolated and an extreme value analysis of their amplitudes is performed. A more detailed view of the growth of positive and negative streaks is obtained than is typical by simply measuring the root mean square perturbations. The resulting velocity distributions are compared with the amplitudes of streaks which undergo secondary instability, and breakdown into turbulent spots. A range of pressure gradients is considered and the rates of turbulent spot production and propagation are investigated. While the spot production rate increases significantly with adverse pressure gradient, it is found that the spot propagation rate is unaffected. By considering the spot spreading angle others have shown a pressure gradient dependence of the propagation parameter. The current work eschews the spreading angle, opting instead to directly track the growth of the spot volume. [Preview Abstract] |
Monday, November 21, 2011 4:40PM - 4:53PM |
L2.00006: Attachment-Line Heating in a Compressible Flow Helen Reed, William Saric The attachment-line boundary layer on a swept wing can be subject to either an instability or contamination by wing-root turbulence. A model of the attachment-line boundary layer is first developed including compressibility and wall heating in a Falkner-Skan-Cooke class of 3-D boundary layers with Hartree parameter of 1.0. For cases otherwise subcritical to either contamination or instability, the destabilizing effect of leading-edge heating under a variety of sweep angles and flight conditions is demonstrated. The results correlate with the attachment-line Reynolds number. Because the required heating levels are reasonable and achievable to trip the flow over the wing to turbulent, one possible application of this work is in the establishing of a baseline turbulent flow (on demand) for the calibration of a laminar-flow-control health monitoring system. **Portion based on work under Framework Agreement between Airbus Americas and NIA, and opinions, findings, conclusions do not necessarily reflect views of Airbus or NIA. **Support from AFOSR/NASA National Center for Hypersonic Research in Laminar-Turbulent Transition through Grant FA9550-09-1-0341 gratefully acknowledged. [Preview Abstract] |
Monday, November 21, 2011 4:53PM - 5:06PM |
L2.00007: Transition prediction for oblique breakdown in supersonic boundary layers with uncertain disturbance spectrum Gennaro Serino, Olaf Marxen, Patrick Rambaud, Thierry Magin Prediction of laminar-turbulent transition is important for the design of heat shields for planetary (re)-entry vehicles. The heat load may increase significantly if a previously laminar boundary layer on the vehicle surface becomes turbulent. Transition-prediction methods based on linear stability theory, such as the $e^N$-method, offer an attractive compromise between simplicity and accuracy. However, non-linear stages of disturbance evolution as well as the receptivity stage are neglected, hampering the general use of these methods. Here we perform an investigation of the oblique breakdown scenario. In this scenario, a pair of oblique waves is convectively amplified and quickly leads to turbulence once these waves reach an amplitude of approximately two percent. This knowledge allows us to define a simple breakdown criterion as a model for the non-linear stage. The receptivity process, whose outcome provides the initial disturbance amplitudes, may not be as easily modeled. Flow physics of the receptivity process are neglected here. Instead, we assume an uncertain disturbance spectrum, which depends on the disturbance frequency and spanwise wave number. Using stochastic collocation, linear stability theory is then employed to yield a probabilistic transition prediction. [Preview Abstract] |
Monday, November 21, 2011 5:06PM - 5:19PM |
L2.00008: ABSTRACT WITHDRAWN |
Monday, November 21, 2011 5:19PM - 5:32PM |
L2.00009: The pre-cursor of Kelvin-Helmholtz instabilities in wake-perturbed separated boundary layers Ayse G. Gungor, Mark P. Simens, Javier Jim\'{e}nez The interaction of large-scale wake disturbances with a pressure-induced separation bubble on a flat plate is studied by direct numerical simulation. The space-time development of the separated region shows roll-up vortices in the separated shear layer. Their appearance is closely associated with the receptivity of the upstream attached boundary layer. The wake-passing excites a linear normal mode of the boundary layer. This mode, which is initially very small, appears in the form of two-dimensional wave-trains upstream of the separation point, but becomes unstable and transforms into the Kelvin-Helmholtz mode as the profile separates. Studies based on varying the frequency or modifying the shape of the forcing further support this scenario of the initial development of the rolls in the separated shear layer, and show that the influence of the wakes is not to directly force the Kelvin-Helmholtz instability of the separation bubble, but to induce perturbations upstream in the attached boundary that eventually seed the instability of the separated shear layer. [Preview Abstract] |
Monday, November 21, 2011 5:32PM - 5:45PM |
L2.00010: Stability of unsteady flow in a rotating torus Richard Hewitt, Andrew Hazel, Richard Clarke, James Denier We consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature; a problem first investigated experimentally by Madden and Mullin (1994), herein referred to as MM. The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container's rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, there is a ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of MM. Detailed quantitative comparisons are made between asymptotic predictions and finite (but small) Ekman number Navier-Stokes computations using a finite-element method. [Preview Abstract] |
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