Session T03: Flow Instability: Boundary Layers and Transition to Turbulence

Global receptivity of instability waves in the boundary layer on a high-speed blunt cone

Unstable waves in parallel and near-parallel compressible boundary layers are well studied and can be important to boundary layer transition on flight vehicles in low disturbance environments. What is less well understood are the processes that occur near leading edges or in complex regions of the flow where these waves are incepted. Understanding the early stages in the development of instabilities is key to enabling accurate transition models that do not require calibration with flight test data. In this work the global direct and adjoint eigenvalue problems for the linearized compressible Navier-Stokes equations are solved on a spherically blunted cone. The results provide insight into the evolution of waves which later become unstable and are reminiscent of Mack’s second mode as the boundary layer approaches a nearly parallel state. In addition to visualizing the 2D structure of these waves, their receptivity can be inferred from the adjoint eigenvectors which provide insight into important mechanisms governing their excitation due to disturbances in the freestream.   

Predicting the nonlinear amplification of disturbances using the Spatial Perturbation Equations in a viscous boundary layer

The Spatial Perturbation Equations (SPE) are a well-posed streamwise marching formulation that utilizes a series of downstream traveling solutions to stabilize the marching procedure. This technique avoids the inconsistencies of the Parabolized Stability Equations (PSE) which require ad-hoc remedies to stabilize the inherently ill-posed marching procedure.  

A consistent use of streamwise non-parallel terms, viscous terms, and nonlinear terms are introduced and used to march the disturbances and remove undesirable upstream-traveling solutions that arise due to numerical error.

Our novel framework does not rely on 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 linear and nonlinear disturbances in a boundary-layer flow show excellent agreement with direct numerical simulations (DNS) for both incompressible and compressible flow at a fraction of the computational cost.   

Asymptotic analysis of wavepackets in high speed boundary layers.

Analyzing the propagation of wavepackets in a boundary layer is useful in understanding laminar-turbulent transition phenomenon. In this work, a small amplitude coherent perturbation generates a wavepacket that is analyzed within the framework of Linear Stability Theory and the wavepacket comprised of coherent three dimensional disturbances is expressed as a double integral that is evaluated using asymptotic techniques. We demonstrate the application of the steepest descent method for wavepacket analysis valid at large downstream distances, while differing from currently published literature by accounting for a compressible, weakly non-parallel boundary layer. The steepest descent method identifies the wave frequency and wavenumber corresponding to the maximum amplitude of the wavepacket at an observation location and a Gaussian approximation around this maximum is used to construct the fine structures of the wavepacket. Details of wavepacket evolution in two high speed boundary layer perfect gas flows (edge Mach number, $M_e$=2 and $M_e$=7) over a flat plate at zero angle of attack are presented. Each case represents either Mack's first mode or second mode dominated flow instability.   

Interaction of Ultrasonic Acoustic Waves and Metasurface Structures for Hypersonic Boundary-Layer Stability Applications

Hypersonic aircraft design is still a challenging problem because of the complex flow physics involved. Prediction and control of the boundary-layer transition from a laminar to a turbulent state is vital to hypersonic vehicles. The boundary-layer transition has a first-order impact on aerodynamic heating, drag force, engine performance, and vehicle operation. Mack’s second mode is an acoustic wave reflecting between the aircraft’s exterior surface and the sonic line in the boundary layer, which acts as an acoustic waveguide. The trapped instability waves gain amplitude, break down, and cause a transition to a turbulent state. This talk will present the interaction between the acoustic waves and several metasurfaces with various geometric shapes. In the numerical simulations, we considered a disturbance wave with a 30-degree incident angle and two frequencies 100 kHz and 400 kHz. We simulate the interactions using the ultrasound module of the COMSOL Multiphysics solver. In the simulations, the background flow is neglected. The reflection ratios are computed in the time and frequency domains. We will present the reflection ratios and the performance of the metasurface designs for future direct numerical simulations (DNS) and experimental studies.   

Matched DNS and experiments of roughness induced transition over realistic airfoil

Experiments and direct numerical simulations (DNS) have suggested shielding as a mitigation strategy for roughness induced boundary layer transition (RIT) by examining its various stages. Recent DNS (Suryanarayanan et al., Int. J. Heat Fluid Flow 86, 108688, 2020) explored the effect of pressure gradients (PGs) on specific RIT mechanisms by applying PGs over specified streamwise extents. To apply this fundamental understanding of RIT shielding, matched DNS and experiments of RIT over a 63(3)-418 airfoil are performed. The PG and boundary layer profiles over the leading edge of the airfoil are determined using wind tunnel measurements and XFOIL simulations which serve as an input to the DNS code. The PG is achieved in DNS through a contouring of an upper wall that is updated until the PG matches XFOIL measurements in 2D laminar DNS. Additionally, various boundary layer metrics are compared between XFOIL and DNS for consistency in boundary layer evolution. A geometrically identical 3D discrete roughness element is then introduced in experiments and DNS, and RIT processes are studied for a variety of shielding configurations at a matched chord Reynolds number. DNS and experimental results are compared to demonstrate shielding over airfoils.   

Recurrent Neural Network Model for Laminar-Turbulent Transition

A physics-based model has been proposed for end-to-end prediction of laminar-turbulent transition in boundary layer flows. Traditional methods lack generalizability to multiple instability mechanisms and different flow configurations, especially where transition is dependent on a large set of parameters. Neural network methods allow for higher dimensional input features, however previously proposed neural network models follow an involved methodology of predicting instability growth rates over a broad range of frequencies, which are then integrated to obtain N-factor curves for each frequency, and, then transition location is determined via empirical correlation of the envelope N-factor. We propose a recurrent neural network (RNN) with a simplified workflow, by directly predicting the N-factor envelope and, hence, the transition location. The model processes the flow information in a physically consistent manner, providing a direct link with the physics of the underlying transition mechanism. Furthermore, the simplified workflow requires minimal user expertise, allowing non-expert users to apply the RNN model to multiple instability mechanisms. The proposed model has been analyzed for an extensive dataset of two-dimensional boundary-layer flows over a diverse set of airfoils.   

Influence of step height on the secondary instability in a boundary layer over backward-facing step

The development of secondary instabilities is investigated numerically for a zero pressure-gradient transitional boundary layer over a backward-facing step at Re_δ*o = 1000. Two step heights are considered in this work, namely, h/δ*_o = 0.5 and 1.0 (δ*_o denotes the displacement thickness evaluated at the step location). Small disturbances are introduced by periodic blowing and suction through the wall within a narrow ribbon. A well-resolved direct numerical simulation (DNS) is carried out for the two cases to characterize the laminar-turbulent transition. The results for the h/δ*_o = 1.0 case show a rapid transition due to the Kelvin-Helmholtz (K–H) instability downstream of step such that the non-linear interactions already occur within the recirculation region, and the flow pattern loses its mirror-symmetry in the middle stage of transition.  In contrast, case h/δ*_o = 0.5 presents a  transition road map in which transition occurs far downstream of the step and the coefficient of skin-friction, C_f, demonstrates different slopes before the `over-shoot' is reached. Mirror-symmetry holds till close to the late stage of transition.    

On the Physics and Control of Laminar Separation Bubbles Using Experiments, Theory and DNS

A laminar separation bubble on a flat plate is investigated using a combined approach of wind tunnel experiments and high-fidelity direct numerical simulations. The favorable to adverse pressure gradient under a displacement body, an inverted modified NACA 64(3)-618 airfoil at a chord Reynolds number of Re=90k, generates a separation bubble on the plate. In the experiment, flow control on the displacement body ensures laminar flow and the time-averaged flow field is matched with the boundary conditions in the simulations. Without free-stream turbulence in the DNS, the mean separated region on the flat plate exceeds the experiment, where disturbances in the free-stream facilitate an earlier onset of transition. Introduction of low-levels of isotropic, vortical FST in the DNS accelerates transition, and decreases the mean separated region, matching remarkably well with the experiments. Dominant coherent structures in the separated shear layer are identified using proper orthogonal decomposition, Fourier analysis and instantaneous flow visualization from DNS. Linear stability theory based on the time averaged flow field identifies the most dominant structures to be the inviscid shear-layer instability.   

Direct numerical simulation of supersonic boundary layer transition induced by tunnel acoustic radiation

The prediction of the laminar-to-turbulent transition location is vital in the design of hypersonic vehicles, since it affects the heat transfer and drag on the vehicle. The freestream disturbance composition is a crucial input to the problem but is difficult to characterize experimentally. In this work, numerically generated, spatially developing wall turbulent boundary layer data in a supersonic channel at Mach 2.5 are employed with a data-driven technique to extract the spectral makeup of the acoustic radiation. These modeled disturbances are then used to study the transition from receptivity to breakdown stages on a canonical adiabatic flat plate configuration. The freestream slow acoustic waves induce multiple oblique first mode waves in the boundary layer which amplify according to the linear theory. This is followed by the distortion of spanwise vorticity by the growth of secondary instabilities via oblique and asymmetric sub-harmonic resonance mechanisms. Positive and negative streaks are generated, with hairpin vortices developing predominantly on the latter. Turbulent spots are generated intermittently due to the interaction of multiple instability waves, which merge leading to turbulence onset.    

Transition to turbulence over oriented superhydrophobic riblets.

Superhydrophobic surfaces exhibit numerous interesting properties such as reduced friction or a delay in the transition to turbulence. This work aims to investigate the underlying mechanisms leading to these properties for 45°-oriented super-hydrophobic riblet roughnesses coated on the walls of a channel flow. The surface is modelled with a homogenization technique yielding a set of effective boundary conditions. Modal and non-modal stability analysis is obtained. A strong asymmetry of the neutral curve can be observed with the presence of two unstable branches in the β<0 region. Transient growth is also affected: maximum gain is obtained for a small but non-zero α and for β<0, thus inducing oblique optimal initial perturbations. Transition to turbulence is studied through direct numerical simulation (DNS) for both unstable branches. Two different transition scenarii are identified: the upper branch is governed by modal primary and secondary instability while the lower branch relies on non-modal mechanisms such as transient growth.   

Counter-gradient vorticity transport mechanisms in boundary layer transition: Insights from conditional statistics

The mechanisms in the late stages of boundary layer transition caused by four vastly different disturbances are analyzed using direct numerical simulations.  The cases considered are (1) roughness-induced bypass transition behind a single discrete roughness element, (2) bypass transition downstream of a distributed roughness patch, (3) bypass transition triggered by strongly three-dimensional free stream forcing, and (4) a classical route involving the interaction of a large amplitude Tollmien–Schlichting wave with noise.  The present analyses follow the recent results (Goldstein et al. DFD2018, Suryanarayanan et al. IUTAM2019) that suggested universal features in the mechanisms of the amplification of near-wall streamwise vorticity, and focus on the connection between the streamwise vorticity and the increase in wall shear stress through the vorticity flux term wω_y.  Conditional statistics over regions with a specific range of instantaneous or mean shear stress, including the correlation between ω_x² and wω_y are presented.  Flow structures characteristic of different ranges of wall shear stress values are extracted and compared. The results point to common features across the widely different transition routes.  Implications for transition modeling and control will be discussed.