Session R25: Flow Instability: Boundary Layers and Transition I

Mixed mode transition in boundary layers: Helical instability

Laminar to turbulence transition in attached subsonic boundary layers underneath free stream turbulence is known to proceed via the orderly or bypass routes. In a previous work (Bose & Durbin, Phys. Rev. Fluids, 1, 073602, 2016), an intermediate mixed mode transition regime was reported at super-critical Reynolds numbers. In this regime, the amplitudes of the Klebanoff streaks and instability waves are similar, and these can potentially interact. Mixed mode transition was reported for both zero- and adverse-pressure-gradient boundary layers beneath moderate levels of free stream turbulence (Tu ≤ 2%). Direct Numerical Simulation (DNS) results revealed a secondary streak instability different from the sinuous and varicose forms seen in pure bypass transition. Three-dimensional visualization of the perturbation fields resembled a helical pattern. In the current work, stability analyses are performed for base flow profiles extracted from DNS of mixed mode transition. A helical breakdown is tracked back in time, and cross-stream planes are extracted for the stability analysis. Instability modes are extracted by Arnoldi iterations: they confirm the helical instability, and show how it is quite distinct from previous analyses of streak instability. The mixed mode precursor is the distinctive cause. The phase speed, growth rate and mode shape of the unstable modes are in good agreement with those extracted from the direct simulations. The three-dimensional view of the eigenfunction indeed reveal a helical pattern that is significantly different from the sinous and varicose modes. Based on its phase speed, the helical mode is an inner instability. The streak configuration leading to the formation of the helical instability is different from those leading to the genesis of sinuous and varicose streak instabilities.   

Direct Numerical Simulation of K-type and H-type transitions in a flat-plate boundary layer with supercritical fluids

Supercritical fluids are often used in industrial processes. Yet, their transition to turbulence has not been elucidated. Therefore, we investigate a transitional flat-plate boundary layer with fluids at supercritical pressures. K-type and H-type breakdowns are simulated by means of Direct Numerical Simulations at a Mach number of 0.2. For each scenario, two different non-ideal regimes with respect to the pseudoboiling temperature are considered at a reduced pressure of p_r=1.1: subcritical (liquid-like) and transcritical (pseudoboiling). The latter is characterised by sharp gradients in thermophysical properties close to the Widom line. To model the non-ideal gas effects, the Peng-Robinson cubic equation of state is used. In the subcritical regime, the formation of aligned (K-type) and staggered (H-type) Λ-vortices, which are followed by hairpin-shaped eddies in the late-transitional stage, is delayed, as the wall temperature approaches the Widom line. Conversely, in the transcritical regime (where the wall temperature is higher than the pseudoboiling temperature), the classical breakdown patterns are highly altered by the non-ideal gas effects. A combination of strong vortical structures, resembling Λ-vortices, and high-low-speed streaks with high-low-density fluid is found. Hence, transition is further delayed.   

Effect of stochastic base flow uncertainty in transitional high speed compressible flows

We analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the compressible linearized Navier-Stokes equations. We extend the input-output framework proposed by Hewawaduge and Zare (PRF, vol. 7, no. 7, 2022) to account for base flow velocity and temperature variations that enter the linearized dynamics of high speed flows as multiplicative sources of uncertainty and can alter their stability and frequency response. This allows us to investigate the stability of laminar flows near leading edges and nose tips that have been shown to undergo early transition to turbulence at supersonic and hypersonic free-stream speeds both in flight and wind tunnel conditions. Our analysis reveals that small amplitude near-wall perturbations of the base flow velocity can compromise the mean-square stability of the laminar flow. We also provide insights into how changes in different physical parameters, such as the temperature of the wall and its curvature, influence the mean-square stability of the fluctuation dynamics. We show that increasing the leading edge radius and decreasing the wall temperature can significantly deteriorate the robustness of laminar flows in the presence of base flow variations. Our approach offers a systematic framework for quantifying the influence of base flow uncertainties that can appear from stochastic sources (e.g., surface roughness and background turbulence) and are unavoidable in experiments in transitional high speed flows.   

Linear stability analysis of discontinuous boundary layer profiles with shock capturing schemes

Modal linear stability analysis is performed on flat plate hypersonic self-similar, zero pressure gradient boundary layer profiles containing strong discontinuities due to the presence of the leading-edge shock wave. For this investigation, a planar wedge with half-angle of 5 degrees is placed in Mach 8 flow at free-stream unit Reynolds number 1.6E7 1/m. Boundary layer edge conditions, and exact location of the shock wave, then follow from oblique shock relations and permit baseflow computation. To capture flow discontinuities in time-asymptotic analyses, we introduce WENO schemes to the discretized generalized complex non-symmetric linear stability eigenvalue problem. The linearized Navier-Stokes equations are discretized with WENO schemes which split the linear fluxes into positive and negative parts and treat them with appropriate WENO differential operator, shown to depend only on the steady-state solution. It is demonstrated that present WENO implementation significantly reduces the amplitude of spurious oscillations introduced to eigenfunctions near strong discontinuities by standard finite-difference or spectral discretization schemes. Presently, the work is being extended to BiGlobal modal analysis aiming to incorporate shock waves present on blunted geometries.   

Injection of a non-Newtonian fluid into an otherwise Newtonian boundary layer

We consider the description and subsequent analysis of a natural phenomenon observed in certain species of fish, which have been observed to secrete complex fluids. This thin fluid layer on the skin has been shown to provide beneficial attributes to the fish, in some instances aiding to reduce skin-friction drag. We provide a modified boundary layer analysis to model this secretion.

 

Firstly, we investigate the relevant flow quantities of a two-phase system, in which a shear-thinning fluid is injected into a larger Newtonian boundary layer. The background fluid is subject to a constant uni-directional flow in the far field, and our non-Newtonian phase is characterised by the Carreau-Yasuda viscosity law. We present the base flow solutions for a variety of parameter space, in which the interfacial location is determined by the flow. These solutions are available both using a self-similar framework, for a specific inclination of flat plate, and in two dimensions, which consider no angle of inclination. Furthermore, we provide a linear perturbation analysis to evaluate the stability of the system to small changes in velocity and pressure.

 

The fundamental aim of our research is to compare the stability of our shear-thinning injection case study against both the Newtonian equivalent and the one-tier system in the absence of injection. It has been shown in previous studies, that for a specific choice of shear-thinning parameter space, one can delay the onset of instability given no injection. Therefore, we investigate our model to evaluate if the same can be observed with a two-tier boundary layer model. Further key variations, including the change in injection velocity, injection angle and viscosity ratio are considered, and their stability characteristics analysed.   

DNS Study of Wall Temperature Effects on the H-type Transition in a Transonic Boundary Layer

Wall temperature influences the stability of a boundary layer. For a compressible boundary layer, the velocity and temperature fluctuations couple nonlinearly, and the coupling affects the dynamics in transitional and turbulent regimes. To investigate such nonlinear physics in detail, a direct numerical simulation (DNS) is desirable. In this study, the wall temperature effects on the laminar-to-turbulent boundary layer transition in a transonic boundary layer (Ma=0.8) over an isothermal flat plate are investigated with the DNSs. Three distinct isothermal wall conditions are considered: quasi-adiabatic, 10% heated, and 10% cooled. In the present DNSs, we provide tiny wall-normal velocity disturbances mimicking blowing and suction on the wall to induce the so-called H-type transition. As a result, the wall heating promotes the H-type transition onset while the wall cooling delays it considerably further downstream, compared to the quasi-adiabatic case. In the transitional regime, in particular, we observe that the wall cooling elongates the staggered lambda vortices and delays their breakdown to turbulence.