Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session R34: Instability: Boundary Layers II - Geometry and Flow Conditions |
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Chair: Jose Eduardo Wesfreid, PMMH Room: 405 |
Tuesday, November 26, 2013 1:05PM - 1:18PM |
R34.00001: Experimental Investigation of Effect of Wall Suction on Cross-Flow Absolute Instability in a Rotating Disk Boundary Layer Joanna Ho, Thomas Corke, Eric Matlis The research is intended to investigate the effect of uniform suction on the absolute instability of Type I cross-flow modes on a rotating disk. Specifically it is designed to investigate if wall suction will transform the absolute instability into a global mode as postulated in the numerical simulations of Davies and Carpenter (2003). The disk is designed so that with a suction parameter of $a=w/(\nu\omega)^{1/2}=0.4$, the radial location of the absolute instability critical Reynolds number, $R_{C_{a}}=803$, occurs on the disk. Uniform wall suction is applied from $R=449$ to 919. The design for wall suction follows that of Gregory and Walker (1950), where an array of holes through the disk communicate between the measurement side of the disk and the underside of the disk in an enclosure that is maintained at a slight vacuum. The holes in the measurement surface are covered by a stretched silk cloth that provides a smooth, finely porous surface. A companion numerical simulation was performed to investigate the effect of the size and vacuum pressure of the underside enclosure on the uniformity of the measurement surface suction. Temporal disturbances are introduced using the method of Othman and Corke (2006), and the evolution of the resulting wave packets is documented. [Preview Abstract] |
Tuesday, November 26, 2013 1:18PM - 1:31PM |
R34.00002: The flow along an external corner revisited Jim Denier, Nathaniel Jewell We revisit the problem of the flow of an almost inviscid fluid along an external corner made from the junction of two quarter infinite plates joined at an angle $0 < \alpha < \pi/2$. The structure of the boundary layer which develops along the corner is explored using a computational approach based upon a spectral element discretisation of the steady two-dimensional boundary-layer equations. We pay particular attention to the case when the angle $\alpha$ is small, thus approximating the semi-infinte quarter plate problem considered by Stewartson (1961) and recently revisited by Duck \& Hewitt (2012). Our results, which demonstrate a thickening of the boundary-layer near the sharp corner, will be discussed in the context of the asymptotic theory developed in the aforementioned papers. [Preview Abstract] |
Tuesday, November 26, 2013 1:31PM - 1:44PM |
R34.00003: Stabilization by shape optimization Christophe Hennekinne, Matthew P. Juniper In a wide range of flows called oscillator flows, the transition to turbulence starts with a modal instability. This first instability can be accurately predicted by performing a linear stability analysis. With the aim of preventing this instability, we examine one of the simplest passive control strategies : the modification of the shape of the boundary. We present a gradient-based algorithm to recover a locally optimal shape of our problem. This algorithm is similar to existing shape optimization algorithms in that it requires computation of the shape gradient, which is the gradient of the objective function with respect to a modification of the boundary. However it differs from existing shape optimization algorithms in the sense that the objective to minimize is not a functional of the flow field but the growth of the most unstable mode of the linearized operator. Consequently two adjoint equations need to be solved sequentially to recover the shape gradient: one associated with the eigenproblem and the other with the steady Navier--Stokes equation. The algorithm is tested on the flow over a backward facing slope. By changing the shape of the slope, the three-dimensional instability that grows on top of the two-dimensional flow is delayed. [Preview Abstract] |
Tuesday, November 26, 2013 1:44PM - 1:57PM |
R34.00004: Instability of the 2-D bottom boundary layer under a solitary wave Mahmoud Sadek, Philip Liu, Luis Parras, Peter Diamessis Fully nonlinear 2-D simulations are used to investigate the temporal instability of the bottom boundary layer (BBL) driven by a soliton-like pressure gradient in an oscillating water tunnel (an approximation of the BBL under a solitary wave). As a function of the associated Reynolds number ({\it {Re}}), the base flow (BF) can be classified as unconditionally stable, conditionally unstable or unconditionally unstable. In the third regime, the BBL flow is unstable, regardless of perturbation amplitude. Two distinct unstable modes emerge in this last regime depending on the value of {\it {Re}}. In the unconditionally unstable regime, we identify the limiting {\it {Re}} value above which instability is observed in the acceleration phase of the BF. The BF profile in this phase lacks a deflection point, suggesting that the above instability is of viscous origin. A sensitivity analysis has been carried out to assess the effect of the different initial perturbation characteristics (i.e. amplitude, spectral shape, time of insertion, e.t.c.) and a variety of wave shapes on the BBL's instability properties for different {\it {Re}} values. In parallel with the fully non-linear simulations, the applicability of both modal and non-modal instability analysis is also examined. [Preview Abstract] |
Tuesday, November 26, 2013 1:57PM - 2:10PM |
R34.00005: New boundary layer structures due to wall slippage Hsien-Hung Wei We demonstrate that wall slip can significantly modify temporal and spatial structures of boundary layer flows. Two benchmark problems for flow generated by a moving plate are re-investigated to reveal how the boundary layer thickness $\delta $ and the slip length $\lambda $ determine flow characteristics: (i) Stokes's first problem, and (ii) Blasius's problem. In (i), the solution is found to combine the features of two problems: (a) simple vorticity diffusion driven by a constant wall stress created by strong wall slippage, and (b) the classical Stokes first problem driven by a no-slip moving plate, characterizing short time and long time solution behaviors, respectively. A similar slip-to-no-slip transition can occur \textit{spatially} to (ii), leading the friction law to change from the well-known Blasius law $C_{\mathrm{f}} \sim $ \textit{Re}$^{-1/2}$ to the free-surface-like result $C_{\mathrm{f}} \sim $ ($L$/$\lambda )$\textit{Re}$^{-1}$ when the Reynolds number \textit{Re} (based on the plate length $L)$ is greater than ($L$/$\lambda )^{2}$. [Preview Abstract] |
Tuesday, November 26, 2013 2:10PM - 2:23PM |
R34.00006: Global stability analysis of axisymmetric boundary layers Rameshkumar Bhoraniya, Vinod Narayanan Global stability analysis of the axisymmetric boundary layer flow explores the stability features of a nonparallel flow. Consider an incompressible flow past a cylinder, where flow direction is parallel to the axis of cylinder. The ensuing boundary layer is axisymmetric but non-similar. Due to the boundary layer growth, the velocity profile is two dimensional. This work aims to understand the nonparallel effects of an axisymmetric boundary layer using a biglobal stability analysis. The linearized biglobal stability equations are derived in polar cylindrical coordinates. The resulting stability equations along with boundary conditions form an eigenvalue problem, which is solved using Chebyshev spectral collocation method. Arnoldi's algorithm is used to compute selective eigenvalues and eigenfunctions. The results show that the nonparallel effects are considerable at very moderate Reynolds numbers. More detailed results will be presented at the time of conference. [Preview Abstract] |
Tuesday, November 26, 2013 2:23PM - 2:36PM |
R34.00007: Stability of high-speed boundary layers in oxygen including chemical non-equilibrium effects Jill Klentzman, Anatoli Tumin The stability of high-speed boundary layers in chemical non-equilibrium is examined. A parametric study varying the edge temperature and the wall conditions is conducted for boundary layers in oxygen. The edge Mach number and enthalpy ranges considered are relevant to the flight conditions of reusable hypersonic cruise vehicles. Both viscous and inviscid stability formulations are used and the results compared to gain insight into the effects of viscosity and thermal conductivity on the stability. It is found that viscous effects have a strong impact on the temperature and mass fraction perturbations in the critical layer and in the viscous sublayer near the wall. Outside of these areas, the perturbations closely match in the viscous and inviscid models. The impact of chemical non-equilibrium on the stability is investigated by analyzing the effects of the chemical source term in the stability equations. The chemical source term is found to influence the growth rate of the second Mack mode instability but not have much of an effect on the mass fraction eigenfunction for the flow parameters considered. [Preview Abstract] |
Tuesday, November 26, 2013 2:36PM - 2:49PM |
R34.00008: The influence of the pressure gradient on the development of G\"{o}rtler vortices Josuel Rogenski, Leandro F. de Souza, Jerzy M. Floryan The optimization in the process of turbomachinary design demands the ability to predict the transition region. The flow over the concave part of a turbine blade is subjected to centrifugal instability and pressure gradient where streamwise vortices can be formed. These vortices cause strong distortions in the streamwise velocity profile. In this sense, a study of the pressure gradient effect focused on the G\"{o}rtler vortices development is necessary. The Navier-Stokes equations in the vorticity-velocity formulation are used. It is assumed periodicity in the spanwise direction. A mesh stretching in the normal direction is adopted. The use of Direct Numerical Simulation is necessary to ensure that all relevant scales are correctly be represented. Compact high-order finite difference approximations are adopted in the streamwise and wall normal directions. The temporal advance is done by the classical 4th order Runge-Kutta method. The elliptic problem is solved by the use of a multigrid method. The code is parallelized using a domain decomposition technique. The results indicate that the numerical code is able to simulate the physical phenomena under investigation. The presence of a favorable pressure gradient tends to stabilize the flow. [Preview Abstract] |
Tuesday, November 26, 2013 2:49PM - 3:02PM |
R34.00009: Heat transfer enhancement by the Goertler vortices developed on a wall with a finite thermal conductivity Innocent Mutabazi, Harunori Yoshikawa, Jorge Peixinho, Lyes Kahouadji G\"ortler vortices appear in a flow over a concave wall as a result of centrifugal instability [Saric, Annu. Rev. Fluid Mech. 26, 379 (1994)]. They may have a strong influence on heat transfer [Momayez et al., Int. J. heat Mass transfer 47, 3783(2004)]. The purpose of this work is to model heat transfer by G\"ortler vortices using a weakly nonlinear analysis of Smith \&-Haj- Hariri [Phys. Fluids A5, 2815(1993)]. We have investigated the coupling of the convective heat transfer by the stationary vortices with the heat conduction inside the solid wall. The finite thickness and thermal conductivity of the wall enter into the boundary conditions of the problem through the ratio $\delta$ of the wall thickness to the boundary layer thickness and through the ratio $K$ of the thermal conductivities of the fluid and the wall. The parametric dependence $Nu(\delta, K)$ of the Nusselt number is performed and it is shown that found the heat transfer is quite well modified by these two parameters. The local thermal stress can be estimated in order to analyze the effects on ageing of the wall material. [Preview Abstract] |
Tuesday, November 26, 2013 3:02PM - 3:15PM |
R34.00010: Optimal divergence-free inflow perturbations in flow over an airfoil Sean Loh, Hugh Blackburn, Xuerui Mao Linear transient growth analysis has identified various key mechanisms in transition due to free-stream turbulence in canonical flow open flow configurations (Durbin \& Wu 2007). In the present work, the role of inflow disturbances in promoting transition for flow over airfoil type geometries is examined. Using an optimal control based methodology, optimal divergence-free inflow perturbations for linear transient energy growth are computed for a NACA 0012 airfoil at $4^\circ$ angle of attack. At various low-to-moderate Reynolds numbers, the flow response to optimal two-dimensional inflow perturbations with varying streamwise length scale is analysed. The relationship between the flow physics induced by optimal inflow perturbations, optimal initial perturbations and leading linear instability modes is then examined. Durbin P \& Wu X (2007), Transition beneath vortical disturbances, \emph{Annu. Rev. Fluid Mech.} \textbf{39}:~107. [Preview Abstract] |
Tuesday, November 26, 2013 3:15PM - 3:28PM |
R34.00011: A 2D pendulum submitted to an incoming flow: drag acting like gravity and new instabilities Andrea Fani, Francois Gallaire Flow induced oscillations of slender bodies facing an incoming flow are relevant in a large number of engineering applications, such as the design of tubular structures of offshore platforms, heat exchangers and energy harvesting. Numerical simulations and experiments available in literature often consider a circular cylinder in an uniform flow which can move only transversally with respect to the flow direction. In a recent work Semin \textit{et al.} (\textit{JFM}, 2011) studied a tethered 2D cylinder strongly confined between two parallel plane walls. It is shown that confinement alters significantly the flow dynamics, with a new instability, denoted confinement induced vibration (CIV), which occur at a Reynolds number much lower than the vortex induced vibration (VIV) critical one. In the present work we characterize the instability scenario of a confined tethered cylinder by means of a global stability analysis of the fluid-structure problem. In strongly confined channels, a periodic unstable mode, related to CIV vibrations, is observed, while for moderated confinement a new steady diverging instability is founded. [Preview Abstract] |
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