Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session A18: Flow Instability: Boundary Layers |
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Chair: Joseph Kuehl, Baylor University Room: D135 |
Sunday, November 20, 2016 8:00AM - 8:13AM |
A18.00001: Implications of a wavepacket formulation for the nonlinear parabolized stability equations to hypersonic boundary layers. Joseph Kuehl The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new ``wavepacket'' formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a ``nonlinear coupling coefficient.'' It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70\%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. [Preview Abstract] |
Sunday, November 20, 2016 8:13AM - 8:26AM |
A18.00002: Optimal Disturbances in Spatially Developing Turbulent Boundary Layers Timothy Davis, Farrukh Alvi Perturbations leading to optimal energy growth in zero pressure gradient turbulent boundary layers are computed. A spatial formulation is adopted to account for the slow development of the turbulent mean flow. Optimals are computed using both an eddy viscosity and quasi-laminar assumption with initial focus given towards steady, streamwise elongated streaks. Results using the eddy viscosity qualitatively agree well with previous temporal analyses, identifying both inner and outer scaled peaks in the energy amplification. Significant differences, however, are noted in the large scale outer structures with spanwise wavelengths ${\sim}3\delta$. The eddy viscosity is further shown to have a substantial effect on the optimal structures and, in general, better agreement with experimental observation is found using the quasi-laminar approach. In this case, the optimal structures are found to scale with the geometric mean of the logarithmic layer in the mean flow. Propagating modes are also considered, achieving large energy amplifications when the disturbance phase speed approaches the local mean. The most energetic streamwise scales and optimal structures are found to agree well with natural structures observed in turbulent boundary layers. [Preview Abstract] |
Sunday, November 20, 2016 8:26AM - 8:39AM |
A18.00003: Real gas effects on receptivity to kinetic fluctuations Anatoli Tumin, Luke Edwards Receptivity of high-speed boundary layers is considered within the framework of fluctuating hydrodynamics where stochastic forcing is introduced through fluctuating shear stress and heat flux stemming from kinetic fluctuations (thermal noise). The forcing generates unstable modes whose amplification downstream and may lead to transition. An example of high-enthalpy ($16.53\, {\rm MJ/kg}$) boundary layer at relatively low wall temperatures ($T_w = 1000 \, {\rm K} - 3000\, {\rm K}$ ), free stream temperature ($T_e=834\, {\rm K}$), and low pressure ($0.0433 \, {\rm atm}$) is considered. Dissociation at the chosen flow parameters is still insignificant. The stability and receptivity analyses are carried out using a solver for calorically perfect gas with effective Prandtl number and specific heats ratio. The receptivity phenomenon is unchanged by the inclusion of real gas effects in the mean flow profiles. This is attributed to the fact that the mechanism for receptivity to kinetic fluctuations is localized near the upper edge of the boundary layer. Amplitudes of the generated wave packets are larger downstream in the case including real gas effects. It was found that spectra in both cases include supersonic second Mack unstable modes despite the temperature ratio $T_w/T_e >1$. [Preview Abstract] |
Sunday, November 20, 2016 8:39AM - 8:52AM |
A18.00004: Modeling boundary-layer transition in DNS and LES using Parabolized Stability Equations Adrian Lozano-Duran, M. J. Philipp Hack, Parviz Moin The modeling of the laminar region and the prediction of the point of transition remain key challenges in the numerical simulation of boundary layers. The issue is of particular relevance for wall-modeled large eddy simulations which require 10 to 100 times higher grid resolution in the thin laminar region than in the turbulent regime (Slotnick \emph{et al.}, NASA/CR-2014-218178, 2014). Our study examines the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate, yet computationally efficient treatment of the growth of disturbances in the pre-transitional flow regime. The PSE captures the nonlinear interactions that eventually induce breakdown to turbulence, and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the point of transition is the solution of the Navier-Stokes equations, it provides a natural inflow condition for large eddy and direct simulations by avoiding unphysical transients. We show that in a classical H-type transition scenario, a combined PSE/DNS approach can reproduce the skin-friction distribution obtained in reference direct numerical simulations. The computational cost in the laminar region is reduced by several orders of magnitude. [Preview Abstract] |
Sunday, November 20, 2016 8:52AM - 9:05AM |
A18.00005: Convective and global stability analysis of a Mach 5.8 boundary layer grazing a compliant surface Fabian Dettenrieder, Daniel Bodony Boundary layer transition on high-speed vehicles is expected to be affected by unsteady surface compliance. The stability properties of a Mach 5.8 zero-pressure-gradient laminar boundary layer grazing a nominally-flat thermo-mechanically compliant panel is considered. The linearized compressible Navier-Stokes equations describe small amplitude disturbances in the fluid while the panel deformations are described by the Kirchhoff-Love plate equation and its thermal state by the transient heat equation. Compatibility conditions that couple disturbances in the fluid to those in the solid yield simple algebraic and robin boundary conditions for the velocity and thermal states, respectively. A local convective stability analysis shows that the panel can modify both the first and second Mack modes when, for metallic-like panels, the panel thickness exceeds the lengthscale $\delta_{99}Re^{-0.5}_x$. A global stability analysis, which permits finite panel lengths with clamped-clamped boundary conditions, shows a rich eigenvalue spectrum with several branches. Unstable modes are found with streamwise-growing panel deformations leading to Mach wave-type radiation. Stable global modes are also found and have distinctly different panel modes but similar radiation patterns. [Preview Abstract] |
Sunday, November 20, 2016 9:05AM - 9:18AM |
A18.00006: Some Insights on Roughness Induced Transition and Control from DNS and Experiments Saikishan Suryanarayanan, Ifeoluwa Ibitayo, David Goldstein, Garry Brown We study the receptivity and subsequent evolution of an initially laminar flat boundary layer on a flat plate to single and multiple discrete roughness elements (DRE) using a combination of immersed boundary DNS and water channel flow visualization experiments. We examine the transition caused by a single DRE and demonstrate the possibility of suppressing it by an appropriately designed second DRE in both DNS and experiments. The different phases of transition are identified and the roles of Reynolds numbers based on roughness height and boundary layer thickness are investigated. The underlying mechanisms in the observed transition and its control are understood by examining detailed vorticity flux balances. Connections are also made to recent developments in transient growth and streak instability. A unified picture is sought from a parametric study of different DRE dimensions and orientations. The potential applicability of the observations and understanding derived from this study to controlling transition caused by design and environmental roughness over aircraft wings is discussed. [Preview Abstract] |
Sunday, November 20, 2016 9:18AM - 9:31AM |
A18.00007: On The Stability Of Model Flows For Chemical Vapour Deposition Robert Miller The flow in a chemical vapour deposition (CVD) reactor is assessed. The reactor is modelled as a flow over an infinite-radius rotating disk, where the mean flow and convective instability of the disk boundary layer are measured. Temperature-dependent viscosity and enforced axial flow are used to model the steep temperature gradients present in CVD reactors and the pumping of the gas towards the disk, respectively. Increasing the temperature-dependence parameter of the fluid viscosity ($\varepsilon )$ results in an overall narrowing of the fluid boundary layer. Increasing the axial flow strength parameter ($T_{s})$ accelerates the fluid both radially and axially, while also narrowing the thermal boundary layer. It is seen that when both effects are imposed, the effects of axial flow generally dominate those of the viscosity temperature dependence. A local stability analysis is performed and the linearized stability equations are solved using a Galerkin projection in terms of Chebyshev polynomials. The neutral stability curves are then plotted for a range of $\varepsilon $ and $T_{s}$ values. Preliminary results suggest that increasing $T_{s}$ has a stabilising effect on both type I and type II stationary instabilities, while small increases in $\varepsilon $ results in a significant reduction to the critical Reynolds number. [Preview Abstract] |
Sunday, November 20, 2016 9:31AM - 9:44AM |
A18.00008: Exact coherent structures for the turbulent cascade Bruno Eckhardt, Stefan Zammert The exact coherent structures that are connected with the transition to turbulence in interior flows usually extend across the full height of the domain. Using exact coherent states that are localized in the shear direction together with scaling ideas for the Navier-Stokes equation that combine length and Reynolds number, we show how such large scale structures can be morphed into smaller scale coherent structures. As the Reynolds number increases, more of these states with ever smaller scales appear, all the way down to the Kolmogorov scale. We present the structure and dynamical properties of several families of exact coherent solution in plane Couette flow, with different degrees of spatial localization: Some of them remain localized in the center and help to built the turbulence cascade, others are localized near the walls and contribute to shaping the boundary layer profile. [Preview Abstract] |
Sunday, November 20, 2016 9:44AM - 9:57AM |
A18.00009: Helical mode breakdown in transitional boundary layers Rikhi Bose, Paul Durbin Results of direct numerical simulation of transition to turbulence in adverse pressure gradient boundary layers beneath free-stream turbulence will be presented. Instability waves are excited spontaneously and may be identified when intensity of free-stream turbulence ($Tu$) is sufficiently low. At very low $Tu\sim0.1\%$, secondary instability of the TS waves and at high $Tu>2\%$, conventional bypass mechanisms trigger turbulent spot formation. At low $Tu\sim1\%$ transition proceeds through formation of helical modes. Helical structures as in $n = 1$ instability modes of axisymmetric wakes and jets are clearly identifiable in visualizations of isosurfaces of stream-wise perturbation velocity. Helical modes also trigger transition at same level of $Tu$ in zero pressure gradient boundary layers as well, provided that the inlet disturbances include a low amplitude time-periodic unstable TS wave. This indicates that these secondary instability modes might arise due to interaction of Klebanoff streaks and instability waves. Characteristically, the helical modes are inner instability modes. [Preview Abstract] |
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