Session H05: Flow Instability: Boundary Layers (5:45pm - 6:30pm CST)

Transport limits on dissolution from a spinning disk -- effects of instabilities in the flow

A rotating disk is the "gold-standard" experiment for measuring surface reactions rates. Von Karman derived an exact solution of the Navier-Stokes equation around an infinite disk and Levich later solved the corresponding mass transport equation; then the connection between surface concentration and bulk concentration could be calculated analytically. Levich's derivation involved a number of assumptions: laminar flow, uniform radial concentration, and dilute solutions. Our simulations of a spinning disk experiment found that the flow is unstable at surprisingly small rotation rates (\textless 10 rpm), well below the rates used in laboratory experiments (100 - 1000 rpm). We aim to determine how these instabilities might affect experimental measurements of surface reaction rates, particularly for more complex solutions where the ion concentrations are not necessarily small. Our simulations are finite volume based, using the OpenFOAM toolkit. I will present preliminary results for the rate of mass transfer from the disk at low rotation speeds. Our results start to deviate from literature predictions at about 30 rpm, where time-dependent oscillations in concentration flux were noticed. Currently we are validating our code for the "rotor-stator" problem, by comparing with spectral solutions.   

Global eigenfunctions of a hypersonic blunt cone

Transition to turbulence in external high-speed flows is sensitive to free-stream disturbances. Current methods for predicting boundary-layer transition are unable to account for the physics of the receptivity process. We address the receptivity of hypersonic flows by solving the global eigenvalue problem in the linearized and adjoint linearized compressible Navier-Stokes equations (CNSE) without a priori assumptions. The effects of shocks and complex geometry are directly captured in the analysis. Eigenfunctions of the linearized CNSE identify the structure of instabilities while eigenfunctions of the adjoint linearized CNSE connect the free-stream disturbances to perturbations within the boundary layer. We present results for a cone with a blunt nose and geometry comparable to experimental studies at hypersonic conditions. The direct eigenfunctions describe short-scale waves that are concentrated within the lower half of the boundary layer and amplify as they travel downstream. The corresponding adjoint eigenfunctions identify the region of highest receptivity as the location immediately upstream of the normal portion of the bow shock.   

On the effect of velocity slip and temperature jump on flat plate boundary layer stability at Mach 4.5

The laminar flat plate boundary layer is revisited using the Direct Simulation Monte Carlo (DSMC) method at Mach 4.5 and rather low pressure of 45Pa. Steady mean flow profiles are extracted from the DSMC results using a novel stack auto-encoder neural network algorithm, the latter trained using ensemble averaged DSMC simulation results at a number of stations on the plate. The laminar profiles obtained from the neural network are of sufficient quality to accurately compute wall-normal derivatives appropriate for the subsequent linear modal instability analysis. The profiles also compare favorably with those obtained from compressible laminar boundary layer theory subject to the standard Maxwell-von Smoluchowski wall-slip and temperature-jump wall boundary conditions. Linear stability characteristics of the DSMC-obtained boundary layer flow, in which velocity slip and temperature jump are naturally included in the base flow are compared with results delivered by classic laminar boundary layer instability analysis based on the Linearised Navier-Stokes Equations. First and second (Mack) modes are identified in the DSMC eigenspectrum and the influence of slip on instability characteristics at these parameters is documented. Work to include the leading-edge shock in the analysis is underway.   

Mitigation of Tollmien Schlichting waves over a laminar airfoil

Mitigation of Tollmien Schlichting (T-S) waves on an unswept natural laminar flow airfoil at a chord-based Reynolds number of 990,000 was explored experimentally. The T-S wave control is facilitated by Piezoelectrically Driven Oscillating Surface actuators located at three streamwise locations on the airfoil. The technique used includes introducing well-defined waves at the upstream location to phase-lock the T-S waves and then mitigating them using the two downstream actuators. Two scenarios were explored: (1) introduction of a disturbance that is a pure sine wave (to introduce a single frequency disturbance into the flow), and (2) introduction of a bandwidth of frequencies to better simulate naturally growing T-S waves. For both scenarios, the active wave cancellation technique was very effective in mitigating the T-S waves. In addition, for the single frequency signal, open-loop flow field measurements were conducted with 2D particle image velocimetry while closed-loop mitigation was tested using a surface-mounted hot film sensor. For the bandwidth of frequencies, only open-loop experiments were conducted, and the feasibility of the mitigation was demonstrated using the same hot film sensor that was used for the single frequency excitation.   

The Mack's amplitude method revisited

Mack (1977) criticized methods referring to a single frequency perturbation for correlation of transition prediction because the external disturbance source should have a broad band spectrum. Delta-correlated perturbations are characterized by the mean square of physical amplitude, which is expressed as a double integral of the spectral density square in frequency and the spanwise wave number. It is suggested to evaluate this integral asymptotically. The results obtained using the asymptotic method and direct numerical integration are compared with ad hoc approaches for high speed and moderate supersonic boundary layers. This allows us to suggest recommendations on rational usage of the amplitude method with avoiding unconfirmed simplifications while reducing the computational effort to the level affordable for engineering practice.   

Structure of hypersonic turbulent spot evolution.

Boundary layer transition subjects hypersonic flight vehicles to strong localized increases in skin friction, wall heat transfer and fatigue due to acoustic loading. These effects are more pronounced in the late stages of transition, which are characterized by turbulent spots. The underlying physics of these spots is different from those in low Mach number regimes due to the existence of acoustic instabilities. To understand the role of these instabilities, high-fidelity simulations are performed with an isolated turbulent spot triggered on a flat plate at Mach 6. Momentum potential theory is used to examine the interplay of vortical, entropic and acoustic components during the spot evolution. The vortical component is found to be predominant in the lift-up structures and in the calmed region. In the turbulent core, the entropic component reveals cell-like structures around the critical layer along with a radiating acoustic component; while closer to the wall, the latter component exhibits roller-like structures, a signature of Mack modes. The role of these additional mechanisms may provide clues on potentially adapting control strategies developed for lower-speed flows.   

Bypass transition in flow over a vibrating flat plate

The development of free-stream disturbances in flow over a vertically vibrating flat plate with a slender leading edge is investigated. The evolution of the optimal inflow perturbation that results in the maximum amplification is computed to remark the impact of the plate vibration on the development of free-stream disturbance, secondary instability of streaks and subsequently the bypass transition to turbulence. It is observed that the plate vibration leads to periodic change of the angle of attack, shifting the free-stream disturbance to the upper or lower side of the plate. Therefore, the development of steady inflow perturbations, which receive the largest amplification, is interrupted by the vibration, and the perturbation amplification via the lift-up mechanism is weakened. The vibration brings a second peak of perturbation growth at the vibration frequency, leading to high-frequency free-stream perturbations penetrating into the base boundary layer, which is not observed in flow over a stationary plate owing to the sheltering mechanism. This resonance of the flow perturbation and the vibrating plate is explained by the staggering effect of the leading edge. Further, the vertical vibration of the plate leads to streamwise periodic vorticity near the edge of the boundary layer. This inhomogeneity of the streamwise vorticity brings about streamwisely localised distortion of the low-speed streaks and thus an intermittent secondary instability. Therefore, before the streaks break down to turbulence, they undergo several rounds of secondary instabilities, resulting in an elongated bypass transition process.   

Modeling the amplification of disturbances using the Spatial Perturbation Equations

We introduce a computational framework for capturing the evolution of nonlinear disturbances in spatially developing viscous shear flows. The Spatial Perturbation Equations (SPE) describe a well-posed streamwise marching formulation that identifies downstream traveling solutions based on their group speed and projects the perturbation state vector onto them. The scheme avoids the inconsistencies of the Parabolized Stability Equations which require ad-hoc remedies such as minimum step sizes or physically unmotivated modifications of the governing equations to stabilize the inherently ill-posed marching procedure. Our novel framework does not rely on spanwise modal wave behavior and enables the use of an explicit advancement scheme. Additionally, it incorporates a robust treatment of nonlinear interactions of harmonics which allows the accurate capturing of high-amplitude perturbations. Comparisons of the evolution of nonlinear disturbances in a boundary-layer flow show excellent agreement with direct numerical simulations.   

On the interaction among different instability modes in a transitional boundary layer under an accelerating/decelerating free stream

Results from a DNS of a flat-plate boundary layer that is subject to an elliptic leading edge and an accelerating followed by a decelerating free stream are presented. The free-stream acceleration is appreciably stronger than the critical levels required for relaminarization: $K=(\nu/U_{\infty}^2)dU_{\infty}/dx=3.7 \times 10^{-6}$. Beneath these free-stream conditions - which are typical of the suction side of a low-pressure turbine blade - the predominant transition process can be classified into three regimes: \textit{(i)} an initial zone where a separated shear layer forms near the leading edge and triggers a rapid growth of disturbances via an inviscid instability mode; \textit{(ii)} a strongly accelerated intervening region where upstream structures are effectively frozen and disturbance amplitudes are depressed well below the levels required for the onset of secondary instability; \textit{(iii)} a final zone where the decelerating free stream causes rapid transition without separation. Visualizations of flow structures inside zone \textit{(iii)} suggest a coupling between viscous and helical instability modes. Identification of the helical modes is noteworthy; it has only been observed previously in boundary layers under elevated free-stream turbulence.   

Roughness induced transition on boundary layers with realistic pressure distributions

Experiments and direct numerical simulations (DNS) have provided a mechanistic understanding of the different stages of roughness induced boundary layer transition (RIT) and have suggested mitigation methods. Recent DNS (Suryanarayanan et al., TSFP11) explored the effect of pressure gradients on specific RIT mechanisms by applying pressure gradients over specified streamwise extents of the domain. To extend this fundamental understanding to technological implementation of RIT mitigation strategies, DNS of RIT on a boundary layer with an inflow and continuously varying free stream corresponding to flow over a 63(3)-418 airfoil is performed. The pressure distribution and boundary layer profiles over an appropriate extent of the airfoil are determined using wind-tunnel measurements and XFOIL simulations which serve as an input to the immersed boundary (IB) pseudo spectral DNS code. Appropriate velocities on the virtual top surface are determined and implemented in the DNS using IB forces. Following validation of the 2D laminar solution, a 3D discrete roughness element is introduced, and RIT processes are studied for a series of realistic pressure distributions obtained by varying angle of attack. The results are interpreted from a vorticity dynamics point of view.