Session P33: Flow Instability: Boundary Layers

High-speed linear analysis of a blunt cone

Transition to turbulence critically affects heat transfer towards the walls in the flow over high-speed vehicles. We seek to identify the mechanisms which govern the receptivity and amplification of disturbances in the boundary layer on a blunt cone at Mach 6 by means of global linear analysis. The approach directly captures the influence of the bow shock wave as well as the geometry of the blunt nose of the cone. Two families of modes are computed, and their spatial structure is characterized. One group of modes extend beyond the boundary layer and interacts with the vortical post-shock flow near the cone tip. The other describes acoustic emissions and decays in the free-stream. The receptivity of the modes is directly captured in their corresponding adjoint eigensolutions. Receptivity is highest upstream of the bow shock near the cone axis. The computations are performed using a curvilinear framework with shock capturing and continuous, discretely consistent formulations of the linearized and adjoint linearized governing equations.   

Study for Wall-shear Stress of Pulsatile Flows in 3-D Ducts.

Understanding wall shear-stress (WSS) in human tissues and organs such as blood vessels and synovial bursa is critically important in the prevention, pathogenesis, and treatment of varying diseases. Numerical simulation provides a unique tool for a fast and non-invasive quantification of WSS in realistic flows. We use a GPU-accelerated volumetric lattice Boltzmann method (VLBM) to assess WSS of pulsatile flows in 3D ducts with circular and rectangular cross sections. The computational results are validated through the comparisons with analytical solutions of Womersley flows in the two ducts. From the analytical solutions of Womersley flow, driven by pressure gradient $\partial $p/$\partial $l$=$P$_{\mathrm{s}}+$P$_{\mathrm{o}}$e$^{\mathrm{i\omega t}}$, we observed that the WSS is linear to the magnitude of the unsteadiness (P$_{\mathrm{o}}$/P$_{\mathrm{s}})$. Preliminary analysis indicates that the WSS is promoted/suppressed with small/large Womsley number. The effects of pulsation in more realistic pulsatile pipe flows with and without turbulence will be further examined and presented.   

Hypersonic boundary layer transition over curved-walls: A mechanism based on G\”orlter vortices

We investigate amplification of small disturbances in compressible boundary layers on a flat plate with a concave flare. To understand mechanisms that trigger the transition in the boundary layer flow over a curved wall, we utilize input-output analysis to quantify the receptivity of flow fluctuations to exogenous disturbances. Our analysis identifies G\”orlter vortices as the most amplified flow structures and provides insights into mechanisms that select the dominant spanwise wavelength. The effect of wall heat transfer on the growth of boundary layer perturbations is also explored. Furthermore, we complement the input-output analysis with direct numerical simulations to investigate the non-linear stages of the disturbance evolution. Since G\”orlter vortices are often responsible for boundary layer transition on curved walls, methods to attenuate early stages of their amplification are also analyzed and their effectiveness is discussed.   

Growth of nonlinear streaky structures and the associated streamwise vortices in high-speed boundary layers

High-speed boundary layer transition has recently seen a resurgence of interest and reinvigoration, motivated by the need to improve the design and optimization of future hypersonic transport aircraft or reentry vehicles, increase the efficiency of high-speed engines, improve the flow in natural gas pipelines, or to quieten high-speed wind tunnels. In the pre-transitional stage, streamwise vortices and the associated streaks experience transient growth in boundary layer flows over flat or concave surfaces as a result of various disturbances initiated in the upstream region or from the wall. Here, we study the nonlinear progression of streaky structures in supersonic and hypersonic boundary layers via the full nonlinear compressible boundary region equations, which is the high Reynolds number asymptotic extension of the Navier-Stokes equations under the assumption that the streamwise wavenumber of the disturbances is much smaller than both wall-normal and spanwise wavenumbers. The base flow is excited either by freestream disturbances imposed at the upstream boundary or by disturbances from the wall in the form of wall transpiration. An extensive parametric study is performed in different flow conditions to assess the development of these streaky structures.   

The development of spiral instabilities in the boundary layer on a rotating sphere

The unsteady flow generated due to the impulsive motion of a sphere is a paradigm for the study of many temporally developing boundary layers. The boundary layer is known to exhibit a finite-time singularity at the equator, which manifests as the ejection of a radial jet, preceded by a toroidal starting vortex pair, which detaches and propagates away from the sphere. The radial jet subsequently develops an absolute instability, which propagates upstream towards the sphere’s surface. This talk will present new results on the existence of vortex instabilities in the boundary layer, considering the global stability of the temporally and spatially developing flow in regimes where separation of temporal and spatial scales prohibits the use of classical techniques from hydrodynamic stability theory.   

Nonlinear spatial marching of high-amplitude perturbations

The physics of bypass transition are closely related to the formation of highly energetic streaks within the boundary layer. Owing to the high amplitudes of the streaks, nonlinear interactions and the generation of harmonics play an important role in their development, as well as in triggering their secondary instability. The high amplitudes attained by the streaks also pose unique challenges for their computational modeling. While the nonlinear parabolized stability equations have been shown to accurately describe the exponential amplification of disturbances in classical transition scenarios, they inadequately capture the formation of streaks and the associated generation of perturbation harmonics. In this talk, we present a novel framework for the nonlinear spatial marching of high-amplitude perturbations. In comparisons with direct numerical simulations, we demonstrate the accuracy of the approach in predicting the growth of high-amplitude streaks. The computational cost of the method is comparable to that of the established nonlinear parabolized stability equations.   

The influence of the wall on the stability and transition to turbulence of a free shear layer at low Reynolds number.

Laminar-to-turbulent transition is necessary to close the separation bubble that forms over airfoils at low Re numbers (typically Re below 50,000). The distance required for flow transition depends on the disturbance growth rate in the unstable shear layer. Using both stability calculations and experiments, we study the effects of wall proximity on the disturbance growth rate and the stability of a separated shear layer at Reynolds number approximately 10 (based on momentum thickness at separation). Viscous linear stability theory shows that, when far from the wall, shear layers are very unstable at Re as low as 5. Wall proximity, however, greatly reduces or eliminates instabilities and the wall stabilizing effect increases as the Re number decreases. Experiments using a thin flat plate with a thick half-cylinder leading edge allow us to control both the separation point and the distance of the shear layer to the wall. The shear layer separation angle, linear and non-linear disturbance growth, and shear layer reattachment are measured using hot wire anemometry for several values of Re and wall distance. We show that shear layer wall proximity can greatly increase the distance required for disturbance growth and laminar-to-turbulent transition.   

Interfacial instability in an azimuthally oscillatory two-layer fluid of oil and water

There are interfacial instabilities occurring in multi-layer flows, which are of practical importance in many industrial processes, such as coating, solvent extraction and oil recovery. Especially, these instabilities could be significantly influenced by the external perturbation, e.g., oscillating forcing. In this study, we present experimental results concerning the stability of oscillatory two-layer fluid in a vertical cylinder vessel, using a high-speed imaging. Two immiscible fluids (oil and water) with a relatively low viscosity contrast ($\sim$100), are superposed in the vessel and the oscillating frequency and angular amplitude are varied by 0.1-7.0 Hz and 45-180 degrees, respectively. We measure the evolution of the oil-water interface during the oscillation and identify different interfacial phenomena such as interfacial vibration (like a vibration of a circular membrane), interfacial waves and initial formation of droplets. By processing the acquired images, we characterize these interfacial phenomena and investigate the effect of imposed conditions theoretically. The effect of viscosity contrast on the onset of the interfacial phenomena will be discussed additionally.