High-speed Boundary Layer Research Articles

Nonlinear interaction among second mode resonance waves in high-speed boundary layers using the method of multiple scales

Nonlinear interaction among resonance waves prior to transition has been observed in earlier numerical and experimental studies. However, these earlier studies were performed for incompressible or compressible flow with a wave triad composed of either Tollmien–Schlichting mode or oblique and planner first modes or crossflow mode. In the case of high-speed flow, the significance of first mode waves becomes lesser, or in most cases, it is not responsible for instability, and second mode waves mostly dominate the flow. The nonlinear interaction among resonance waves in a high-speed boundary layer where a wave triad is composed of second mode waves is presented. The nonlinear interaction formulation is performed using the method of multiple scales. The nonparallel effect has been taken into account by considering the mean flow to be slightly nonparallel. A detuning parameter is used for the wavenumbers, whereas frequencies are assumed to be perfectly tuned, satisfying the resonance condition. Based on the eigenfunctions' distribution normal to the wall, it is observed that the temperature disturbance is more dominant than the other disturbances. With an increase in Mach number, the disturbances shift toward the boundary layer edge. A significant increase in amplification factor due to wave interaction has been observed. The maximum amplification factor for the second mode wave due to wave interaction has increased by around 20% of its non-interaction value. Although the non-interaction amplification factor for the difference mode is much smaller than the other modes, its interaction amplification factor has increased more significantly. The amplification factor for the difference mode has increased almost by 60% due to wave interaction.

Analytical prediction of low-frequency fluctuations inside a one-dimensional shock

Linear instability of high-speed boundary layers is routinely examined assuming quiescent edge conditions, without reference to the internal structure of shocks or to instabilities potentially generated in them. Our recent work has shown that the kinetically modeled internal nonequilibrium zone of straight shocks away from solid boundaries exhibits low-frequency molecular fluctuations. The presence of the dominant low frequencies observed using the direct simulation Monte Carlo (DSMC) method has been explained as a consequence of the well-known bimodal probability density function (PDF) of the energy of particles inside a shock. Here, PDFs of particle energies are derived in the upstream and downstream equilibrium regions, as well as inside shocks, and it is shown for the first time that they have the form of the noncentral Chi-squared (NCCS) distributions. A linear correlation is proposed to relate the change in the shape of the analytical PDFs at a specified upstream number density and temperature as a function of Mach number, within the range \(3 \le M \le 10\), with the DSMC-derived average characteristic low-frequency of shocks, as computed in our earlier work. At a given Mach number \(M=7.2\) and upstream number density \(n_1=10^{22}\,\hbox {m}^{-3}\), it is shown that the variation in DSMC-derived low frequencies is correlated with the change in most-probable-speed inside shocks at the location of maximum bulk velocity gradient for upstream translational temperature in the range \(\sim 90 \le T_{tr,1}/(K) \le 1420\). Using the proposed linear functions, average low frequencies are estimated within the examined ranges of Mach number and input temperature and a semi-empirical relationship is derived to predict low-frequency oscillations in shocks. Our model can be used to provide realistic physics-based boundary conditions in receptivity and linear stability analysis studies of laminar-turbulent transition in high-speed flows.

Investigation of Görtler vortices in high-speed boundary layers via an efficient numerical solution to the non-linear boundary region equations

Streamwise vortices and the associated streaks evolve in boundary layers over flat or concave surfaces due to disturbances initiated upstream or triggered by the wall surface. Following the transient growth phase, the fully-developed vortex structures become susceptible to inviscid secondary instabilities resulting in early transition to turbulence via `bursting' processes. In high-speed boundary layers, more complications arise due to compressibility and thermal effects, which become more significant for higher Mach numbers. In this paper, we study G\"{o}rtler vortices developing in high-speed boundary layers using the boundary region equations (BRE) formalism, which we solve using an efficient numerical algorithm. Streaks are excited using a small transpiration velocity at the wall. Our BRE-based algorithm is found to be superior to direct numerical simulation (DNS) and ad-hoc nonlinear parabolized stability equation (PSE) models. BRE solutions are less computationally costly than a full DNS and have a more rigorous theoretical foundation than PSE-based models. For example, the full development of a G\"{o}rtler vortex system in high-speed boundary layers can be predicted in a matter of minutes using a single processor via the BRE approach. This substantial reduction in calculation time is one of the major achievements of this work. We show, among other things, that it allows investigation into feedback control in reasonable total computational times. We investigate the development of the G\"{o}rtler vortex system via the BRE solution with feedback control parametrically at various freestream Mach numbers $M_\infty$ and spanwise separations $\lambda$ of the inflow disturbances.

Optimal heat flux for delaying transition to turbulence in a high-speed boundary layer

Abstract

Detection of second-mode instabilities on a flared cone in Mach 6 quiet flow with linear array focused laser differential interferometry

In this work, an enhanced version of the focused laser differential interferometer (FLDI) is used to measure second-mode instabilities in the boundary layer on a flared cone in Mach 6 quiet flow. A diffractive optical element added to the FLDI system provides six beams that pass through a single Wollaston prism, allowing for multiple points of measurements without the need for additional Wollaston prisms. This technique, linear array-FLDI (LA-FLDI), is used for six simultaneous measurements of second-mode instabilities in a hypersonic boundary layer. This is the first time that this variation of FLDI has been used for second-mode instability measurements and demonstrates that the inclusion of a diffractive optical element into the traditional FLDI and splitting of beam power does not preclude such usage. Thus, LA-FLDI appears to have significant potential for increasing the efficiency of measurements of high-speed boundary layers by enabling multiple measurements at different locations within a single facility run. The velocity of the second-mode wavepacket is estimated and a bispectral analysis is presented showing that harmonics are associated with quadratically phased coupled interactions.

Analysis of the instabilities induced by an isolated roughness element in a laminar high-speed boundary layer

Abstract

Numerical Method for Particulate-Induced High-Speed Boundary-Layer Transition Simulations

A new numerical method to efficiently simulate particulate interactions with high-speed transitional boundary-layer flows is presented. A particulate solver, employing Crowe’s correlation, is used to calculate the particulate trajectory. The solver is fully coupled via a particulate–flow interaction source term to a nonlinear disturbance flow solver based on the compressible Navier–Stokes equations. To efficiently simulate the particulate–flow interactions, an adaptive mesh refinement approach is used to capture the wide range of temporal and spatial scales present in the laminar–turbulent transition process. The particulate impingement simulations for a flow over a 14 deg wedge and two different particulate impingement locations employing the newly developed numerical approach are compared against simulations using a conventional static-mesh approach. For the flow conditions considered, oblique first-mode instability waves dominate the early stage of the transition process. In the second part of this paper, the differences between pulse and particulate impingement simulations are investigated in two and three dimensions for a flat-plate boundary-layer flow where two-dimensional second-mode instability waves are most amplified in the primary instability regime.

Stationary cross-flow breakdown in a high-speed swept-wing boundary layer

A new type-II secondary instability mode was recently identified in high-speed cross-flows using stability analysis, but its role in the transition process is not yet clear. Here, the breakdown of stationary cross-flow vortices at high speeds is examined using direct numerical simulation to determine differences from the low-speed case. The transition is achieved by disturbing stationary cross-flow vortices with unsteady blowing/suction in a swept-wing boundary layer with swept angle 45°, free-stream Mach number 6, and unit Reynolds number 8 ×106. The results reveal that, as in low-speed cases, the type-I secondary instability mode (with frequency ≈190 kHz) is crucial to the breakdown, but neither the traditional nor the new type-II secondary instability play a role. The vortical structure induced by the type-I secondary instability mode has two counter-rotating tubes stretched along the spanwise direction and a footprint aligned normal to the mean flow direction. The composite vortex structures are similar to rolls/braids in plane free-shear layers arising from Kelvin–Helmholtz instability and they evolve into hairpins in the late stage of the transition. Some preliminary statistics from a three-dimensional turbulent boundary layer are provided as a comparison to the two-dimensional ones. The fluctuating cross-flow velocity does not contribute to the momentum and heat transfer on average, probably due to the very weak mean cross-flow profile. Thus, the obtained three-dimensional turbulent boundary layer is the same as the two-dimensional one but inclined by a swept angle. To the authors’ knowledge, this is the first in-depth analysis of the high-speed cross-flow transition to full turbulence.

Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone

Properties of wall pressure beneath a transitional hypersonic boundary layer over a 7∘ half-angle blunt cone at angle of attack 6∘ are studied by Direct Numerical Simulation. The wall pressure has two distinct frequency peaks. The low-frequency peak with f≈10−50 kHz is very likely the unsteady crossflow mode based on its convection direction, i.e. along the axial direction and towards the windward symmetry ray. High-frequency peaks are roughly proportional to the local boundary layer thickness. Along the trajectories of stationary crossflow vortices, the location of intense high-frequency wall pressure moves from the bottom of trough where the boundary layer is thin to the bottom of shoulder where the boundary layer is thick. By comparing the pressure field with that inside a high-speed transitional swept-wing boundary layer dominated by the z-type secondary crossflow mode, we found that the high-frequency signal originates from the Mack mode and evolves into the secondary crossflow instability.

On the receptivity of surface plasma actuation in high-speed boundary layers

Significant amounts of work have been conducted in the area of plasma flow control, while the receptivity of plasma actuation in high-speed boundary layers has not had much attention over the last two decades. In the present study, the receptivity of a Mach 4.5 flat-plate boundary layer to plasma heating actuation produced by pulsed-DC surface dielectric barrier discharge (SDBD) has been studied by direct numerical simulation (DNS) and stability analysis. With the help of multimode decomposition technology, the amplitude of normal modes can be obtained. The results show that both fast and slow modes can be excited by plasma actuation, and the receptivity maximum is observed near the lower neutral branch. Because the pulsed-DC SDBD actuation is typical periodic pulse signals, when the total power remains constant, the Fourier components with multiples of actuation frequency have the same energy, regardless of the waveform, period, and width of the actuation signal. Such characteristics benefit the robustness of the pulsed-DC SDBD actuator. A theoretical prediction method by combining the receptivity model and linear parabolized stability equations is considered in the present study, and good agreement with the DNS results is achieved.

An improved local correlation-based intermittency transition model appropriate for high-speed flow heat transfer

An improved local correlation-based intermittency transition model is developed for high-speed flow heat transfer in this paper. Based on the intermittency transition model, two improvements have been proposed. One is introducing a new correlation of the momentum thickness Reynolds number for high-speed boundary layer into the transition onset function. In this new correlation, the free stream Mach number and the free stream Reynolds number are used to reflect the compressible effects. The other improvement is the modification of the intermittency factor transport equation to include physical information regarding the transition processes. Several test cases containing supersonic and hypersonic flat plates, a slender cone at different Reynolds numbers, the X-51A forebody, and the Hypersonic Inflatable Aerodynamic Decelerator are conducted to assess the applicability of the improved intermittency transition model. The numerical results show the ability of the improved model to describe the high-speed boundary layer transition processes. However, further research is needed to reproduce the overshoot phenomena and verify the capacity of the improved model on complex cases.

Transient growth analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92

We study physical mechanisms that trigger transient growth in a high-speed spatially-developing laminar boundary layer that interacts with an oblique shock wave. We utilize an approach based on power-iteration, with the global forward and adjoint linearized equations, to quantify the transient growth in compressible boundary layers with flow separation. For a Mach 5.92 boundary layer with no oblique shock wave, we show that the dominant transient response consists of oblique waves, which arise from the inviscid Orr mechanism, the lift-up effect, and the first-mode instability. We also demonstrate that the presence of the oblique shock wave significantly increases transient growth over short time intervals through a mechanism that is not related to a slowly growing global instability. The resulting response takes the form of spanwise periodic streamwise elongated streaks and our analysis of the linearized inviscid transport equations shows that base flow deceleration near the reattachment location contributes to their amplification. The large transient growth of streamwise streaks demonstrates the importance of non-modal effects in the amplification of flow perturbations and identifies a route for the emergence of similar spatial structures in transitional hypersonic flows with shock wave/boundary-layers interaction.

Numerical Investigation of High-Speed Turbulent Boundary Layers of Dense Gases

High-speed turbulent boundary layers of a dense gas (PP11) and a perfect gas (air) over flat plates are investigated by means of direct numerical simulations and large eddy simulations. The thermodynamic conditions of the incoming flow are chosen to highlight dense gas effects, and laminar-to-turbulent transition is triggered by suction and blowing. In the paper, the behavior of the fully developed turbulent flow region is investigated. Due to the low characteristic Eckert number of dense gas flows ( $$\hbox {Ec}=U_\infty ^2/c_{p,\infty }T_\infty$$ ), the mean velocity profiles are largely insensitive to the Mach number and very close to the incompressible case even at high speeds. Second-order velocity statistics are also weakly affected by the flow Mach number and the velocity spectra are characterized by a secondary peak in the outer region of the boundary layer because of the higher local friction Reynolds number. Despite the incompressible-like velocity and Reynolds-stress profiles, the strongly non-ideal thermodynamic and transport-property behavior of the dense gas results in unconventional distributions of the fluctuating thermo-physical quantities. Specifically, density and viscosity fluctuations reach a peak close to the wall, instead of vanishing as in perfect gas flows. Additionally, dense gas boundary layers exhibit higher values of the fluctuating Mach number and velocity divergence and a larger dilatational-to-solenoidal dissipation ratio in the near-wall region, which represents a major deviation from high-Mach-number perfect gas boundary layers. Other significant deviations are represented by the more symmetric probability distributions of fluctuating quantities such as the density and velocity divergence, due to the more balanced occurrence of strong expansion and compression events.

HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

In this study, the open-source Hypersonics Task-based Research (HTR) solver for hypersonic aerothermodynamics is described. The physical formulation of the code includes thermochemical effects induced by high temperatures (vibrational excitation and chemical dissociation). The HTR solver uses high-order TENO-based spatial discretization on structured grids and efficient time integrators for stiff systems, is highly scalable in GPU-based supercomputers as a result of its implementation in the Regent/Legion stack, and is designed for direct numerical simulations of canonical hypersonic flows at high Reynolds numbers. The performance of the HTR solver is tested with benchmark cases including inviscid vortex advection, low- and high-speed laminar boundary layers, inviscid one-dimensional compressible flows in shock tubes, supersonic turbulent channel flows, and hypersonic transitional boundary layers of both calorically perfect gases and dissociating air. Program summaryProgram Title: Hypersonics Task-based Research solverProgram Files doi:http://dx.doi.org/10.17632/9zsxjtzfr7.1Licensing provisions: BSD 2-clauseProgramming language: RegentNature of problem: This code solves the Navier–Stokes equations at hypersonic Mach numbers including finite-rate chemistry for air dissociation along with multicomponent transport. The solver is designed for direct numerical simulations (DNS) of transitional and turbulent hypersonic turbulent flows at high enthalpies, and accounts for thermochemical effects such as vibrational excitation and chemical dissociation.Solution method: This code uses a low-dissipation sixth-order targeted essentially non-oscillatory (TENO) scheme for the spatial discretization of the conservation equations on Cartesian stretched grids. The time advancement is performed either with an explicit method, when the chemistry is slow and therefore does not introduce additional stiffness in the integration, or with an operator-splitting method that integrates the chemical production rates with an implicit discretization.Additional comments: The HTR solver builds on the runtime Legion [1] and is written in the programming language Regent [2] developed at Stanford University. Instructions for the installation of the components are provided in the README file enclosed with the HTR solver and in the Legion repository [1].

Supersonic boundary layer transition induced by self-sustaining dual jets**Project supported by the National Natural Science Foundation of China (Grant Nos. 11602299, 11872374, and 51809271).

To promote high-speed boundary layer transition, this paper proposes an active self-sustaining dual jets (SDJ) actuator utilizing the energy of supersonic mainflow. Employing the nanoparticle-based planar laser scattering (NPLS), supersonic flat-plate boundary layer transition induced by SDJ is experimentally investigated in an Ma-2.95 low-turbulence wind tunnel. Streamwise and spanwise NPLS images are obtained to analyze fine flow structures of the whole transition process. The results reveal the transition control mechanisms that on the one hand, the jet-induced shear layer produces unstable Kelvin–Helmholtz instabilities in the wake flow, on the other hand, the jets also generates an adverse pressure gradient in the boundary layer and induce unstable streak structures, which gradually break down into turbulence downstream. The paper provides a new method for transition control of high-speed boundary layer, and have prospect both in theory and engineering application.

Mathematical modeling and the study of exchange processes in disperse boundary layer control actions

A significant interest of researchers is attracted to the effective management and forecasting of exchange processes in the boundary layer, which are key for the implementation of effective and reliable equipment. Modeling of exchange processes occurring in a high-speed dispersed boundary layer with external influences is a very difficult task. Mathematical modeling allows us to develop reliable devices and engines for the fields of aircraft, energy, shipbuilding with minimal costs for its creation. Despite the interest of numerous groups of researchers around the scientific projects and a large number of works, the current theory of the boundary layer is imperfect. This may be due to several circumstances: firstly, the theory of single-phase turbulent flows of continuous media is far from being completed, secondly, turbulent flows with dispersed impurities in the form of particles greatly complicate the already intricate flow pattern. Interest in dispersed flows is particularly relevant due to the fact that almost all gas-dynamic flows contain a certain concentration of particles, and their impact can provoke significant changes in the structure of the boundary layer and affect the intensity of exchange processes. The article proposes a two-fluid mathematical model describing the motion of a high-speed dispersed boundary layer on a surface with hemispherical damping cavities. The use of hemispherical damping cavities allows to reduce turbulent exchange in the boundary layer, which makes it possible to control the intensity of metabolic processes. The possibility of a significant reduction of turbulent heat transfer and friction in the dispersed boundary layer is established. The proposed method of impact on the turbulent transport in the boundary layer will improve the equipment and installations, including GTU and GTE used in various industries of our country, such as energy, aircraft, shipbuilding.

Model of Distributed Receptivity to Kinetic Fluctuations in High-Speed Boundary Layers

The receptivity of high-speed compressible boundary layers to kinetic fluctuations is considered within the framework of fluctuating hydrodynamics. The formulation is based on the idea that KF-induced dissipative fluxes may lead to the generation of unstable modes in the boundary layer. Fedorov and Tumin (“Receptivity of High-Speed Boundary Layers to Kinetic Fluctuations,” AIAA Journal, Vol. 55, No. 7, 2017, pp. 2335–2348) solved the receptivity problem using an asymptotic matching approach, which used a resonant inner solution in the vicinity of the neutral point. This study adopts a method of multiple scales approach, which requires fewer assumptions about the locus of primary excitation. The approach is modeled after the one taken by Luchini (“Receptivity to Thermal Noise of the Boundary Layer over a Swept Wing,” AIAA Journal, Vol. 55, No. 1, 2017, pp. 121–130) to study low-speed incompressible boundary layers over a swept wing. The new framework is used to study examples of high-speed flat plate boundary layers whose spectra exhibit nuanced behavior near the generation point, such as first-mode instabilities and near-neutral evolution over moderate length scales.

Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

We investigate the hydrodynamic stability of compressible boundary layers over adiabatic walls with fluids at supercritical pressure in the proximity of the Widom line (also known as the pseudo-critical line). Depending on the free-stream temperature and the Eckert number that determines the viscous heating, the boundary-layer temperature profile can be either sub-, trans- or supercritical with respect to the pseudo-critical temperature, $T_{pc}$. When transitioning from sub- to supercritical temperatures, a seemingly continuous phase change from a compressible liquid to a dense vapour occurs, accompanied by highly non-ideal changes in thermophysical properties. Using linear stability theory (LST) and direct numerical simulations (DNS), several key features are observed. In the sub- and supercritical temperature regimes, the boundary layer is substantially stabilized the closer the free-stream temperature is to $T_{pc}$ and the higher the Eckert number. In the transcritical case, when the temperature profile crosses $T_{pc}$, the flow is significantly destabilized and a co-existence of dual unstable modes (Mode II in addition to Mode I) is found. For high Eckert numbers, the growth rate of Mode II is one order of magnitude larger than Mode I. An inviscid analysis shows that the newly observed Mode II cannot be attributed to Mack’s second mode (trapped acoustic waves), which is characteristic in high-speed boundary-layer flows with ideal gases. Furthermore, the generalized Rayleigh criterion (also applicable for non-ideal gases) unveils that, in contrast to the trans- and supercritical regimes, the subcritical regime does not contain an inviscid instability mechanism.

Reverse Design of Ultrasonic Absorptive Coating for the Stabilization of Mack Modes

The effects of ultrasonic absorptive coating (UAC) admittance on the first and second modes in a high-speed boundary layer are analyzed using linear stability theory. It is shown that the growth rate of the first mode is increased as UAC admittance phase varies from to , whereas the second mode is amplified when tends to and damped if . The frequency range of the first mode is broadened when is in the vicinity of , and the second mode shifts to low frequencies when . Moreover, the stabilization or destabilization effects on Mack modes, frequency band broadening, and frequency shifting are promoted by large UAC admittance magnitudes. Based on the requirements of the admittance phase and magnitude for the stabilization of Mack modes, a design strategy for UAC is proposed to stabilize the second mode in a wide frequency range with the first mode little amplified.

Effect of Wall Transpiration and Heat Transfer on Görtler Vortices in High-Speed Flows

Görtler vortices in boundary-layer flows over concave surfaces are caused by the imbalance between centrifugal effects and radial pressure gradients. Depending on various geometrical and/or freestream flow conditions, vortex breakdown via secondary instabilities leads to early transition to turbulence. It is desirable, therefore, to reduce vortex energy in an attempt to delay the transition from laminar to turbulent flow, and thereby achieve a reduced frictional drag. To this end, a proportional control algorithm was applied, aimed at reducing the wall shear stress and the energy of Görtler vortices evolving in high-speed boundary layers. The active control scheme is based on wall transpiration with sensors placed either in the flow or at the wall. In addition, the effect of wall cooling and heating on Görtler vortices evolving in high-speed boundary layers was evaluated, by reducing or increasing the upstream wall temperature. The numerical results are obtained by solving the full Navier–Stokes equations in generalized curvilinear coordinates, using a high-order numerical algorithm. The results show that the active control based on wall transpiration reduces both the wall shear stress and the energy of the Görtler vortices; the passive control based on wall cooling or heating reduces the wall shear stress, but slightly increases the energy of the vortices in both supersonic and hypersonic regimes.