Boundary Layer In Supersonic Flow Research Articles

Stochastic receptivity of laminar compressible boundary layers: An input-output analysis

In this study, a receptivity analysis of streaks, oblique and two-dimensional flow structures is presented with a stochastic receptivity framework for different inputs for supersonic adiabatic boundary layer flows. In particular, an active role of temperature fluctuation is identified for the amplification of oblique patterns, while a passive role is observed for the onset of streaks and two-dimensional flow structures. From a practical point of view, this study can help to improve the effectiveness of actuators aiming at a particular response in supersonic boundary layer flows.

Explicit series solutions for supersonic flat-plate boundary layer flows

This paper describes explicit series solutions for supersonic flat-plate boundary layer flows that are convergent in the whole spatial domain for Mach numbers of up to 50. These series solutions are achieved by means of the homotopy analysis method (HAM), an analytic technique for highly nonlinear problems. Unlike the analytic approximations given by perturbation methods or other approaches, our explicit series solutions are guaranteed to converge with arbitrary physical parameters because of the so-called “convergence-control parameter” in the HAM framework. Explicit analytic expressions for the local surface skin-friction coefficient and the local heat-transfer coefficient of the supersonic boundary layer flow are also derived. These analytical solutions are found to be in perfect agreement with the corresponding numerical results, allowing the effects of physical parameters on supersonic boundary layer flows to be discussed in detail. The explicit series solutions described in this paper provide a benchmark for supersonic flat-plate boundary layer flows with Mach numbers in the range 0.8≤Ma≤50. To the best of our knowledge, no such explicit series solutions for supersonic flat-plate boundary layer flows have previously been reported. To enable relevant applications, a corresponding Mathematica package is provided to enable convenient access to explicit series solutions for supersonic flat-plate boundary layer flows.

Feasibility Study of Controlling Supersonic Boundary-layer Flows Using Jets Flapping at Several Tens of Kilohertz

Feasibility Study of Controlling Supersonic Boundary-layer Flows Using Jets Flapping at Several Tens of Kilohertz

Spatially developing supersonic turbulent boundary layer subjected to static surface deformations

The effects of static surface deformations on a spatially developing supersonic boundary layer flow at Mach number M=4 and Reynolds number Reδin≈49300, based on inflow boundary layer thickness (δin), are analyzed by performing large eddy simulations. Two low-order structural modes of a rectangular clamped surface panel of dimensions ≈33δin×48δin are prescribed with modal amplitudes of δin. The effects of these surface deformations are examined on the boundary layer, including changes in the mean properties, thermal and compressibility effects and turbulence structure. The results are analyzed in the context of deviations from concepts typically derived and employed for equilibrium turbulence. The surface deflections, to some degree, modify the correlations that govern both Morkovin’s hypothesis and strong Reynolds analogy away from the wall, whereas in the near-wall region both the hypotheses breakdown. Modifications to the turbulence structure due to the surface deformations are elucidated by means of the wall pressure two-point correlations and anisotropy invariant maps. In addition to the amplification of turbulence, such surface deformations lead to local flow separation, instigating low-frequency unsteadiness. One consequence of significance to practical design is the presence of low frequency unsteadiness similar to that encountered in impinging or ramp shock boundary layer interactions.

Cost-effective and high-fidelity method for turbulent transition in compressible boundary layer

An efficient high-fidelity simulation approach is investigated for laminar-to-turbulent transition in compressible boundary layer flow. This approach combines large-eddy simulation (LES) with the parabolized stability equations (PSE) analysis. LES is chosen for high-fidelity simulation of the transitional flow, whereas the PSE analysis is used for an efficient treatment of instability modes in the flow. Instability modes from the PSE analysis are assigned as forcing at the inlet of the LES computational domain. A framework of LES combined with PSE (PSE+LES) for the turbulent transition is demonstrated in supersonic boundary layer flow at Mach 3. Complete transition to turbulence via oblique-mode breakdown is well resolved in the current study. Detailed flow features associated with the turbulent transition are compared well with previous direct-numerical simulation (DNS) studies, including the growth of instability modes in the pre-transition regime, the transition range shown in the evolution of the skin friction, and the turbulent boundary layer. It is shown that the current PSE+LES approach can reduce the computational cost by two orders of magnitude, compared to the relevant DNS cost. The current study for supersonic flow and the authors' previous study for subsonic flow imply that the PSE+LES approach can be used in boundary layer flows at various speeds.

Influence of distributed heavy-gas injection on stability and transition of supersonic boundary-layer flow

This study performed a joint theoretical and experimental investigation of the influence of distributed normal-to-the-surface and inclined heavy-gas injection into the near-wall sublayer of a boundary layer through a permeable wall on the laminar-turbulent transition (LTT). Sulfur hexafluoride (SF6) is used as a foreign gas for injection into the boundary layer. It also assessed stability in relation to both natural and artificial (controlled) disturbances of a supersonic flat-plate boundary layer at a free-stream Mach number (M) of 2. It is established, theoretically, that the action of a large molecular weight gas injection on the boundary layer is similar to the action of wall cooling and leads to an increase in boundary layer stability and LTT delay. The influence of injection on the position of transition is estimated by means of the eN method. Principally, the analysis shows the possibility of increasing the transition Reynolds number by means of SF6 injection. Controlled disturbances are introduced in the model boundary layer by means of a point harmonic glow-discharge disturbance generator and are measured by using a hot-wire anemometer. For the first time, it is shown experimentally that distributed injection of the heavy SF6 gas leads to boundary layer stabilization. This is mostly due to the reduction in growth rates of disturbances at higher frequencies, while the LTT shifted to higher Reynolds number values. Good qualitative agreement is achieved between the experimental data obtained with artificially generated disturbances and computations based on linear stability theory.

Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

Experimental investigation of the shock-induced flow over a wall-mounted cylinder

The unsteady aerodynamic and aerothermal phenomena resulting from the interaction between a shock-induced supersonic boundary-layer flow and a wall-mounted cylinder are investigated. Experiments were conducted in a shock tube at three different post-shock unit Reynolds numbers and a single Mach number to investigate the effects of differing ratios of inviscid and viscous temporal scales on the flow development. Two cylinder heights were studied: ‘large’ and ‘small’ protuberances based on calculated boundary-layer thicknesses. Heat-flux measurements on the shock-tube wall were performed using an ultra-fast-response temperature sensitive paint and verified by independent thermocouple measurements. High-speed schlieren provided visualizations of the inviscid flow phenomena. The unsteady shock-wave/boundary-layer interaction ahead of the cylinder resulted in high transient heat loading on the wall and caused transition to turbulence of the incoming laminar boundary layer. Once this incoming boundary layer had naturally transitioned, the region of enhanced heat flux collapsed back towards the cylinder; during this process, heat transfer in the immediate wake increased significantly. The overall heat flux upstream of the cylinder was higher for the large protuberance, whereas the downstream heat flux was generally higher for the small protuberance. In the case of the large protuberance, the viscous scaling appeared to best collapse the upstream heat-flux development for the three different unit Reynolds numbers, though the agreement downstream was less satisfactory. Neither the viscous nor the inviscid scaling appeared to adequately collapse the development for the small protuberance.

On a Problem of Optimal Control of the Laminar Boundary Layer in Supersonic Flows on Constant-Pressure Surfaces

We consider the variational problem of Newtonian friction minimization that affects surfaces in supersonic flows at the constant velocity on the outer edge of the boundary layer.

Optimization of slot geometry in shock wave boundary layer interaction phenomenon by using CFD–ANN–GA cycle

Slot is one of the measures to control the Shock Wave–Boundary Layer Interaction (SBLI) used to avoid strong interference of shock waves with the boundary layer in supersonic flows. In this control measure, the Height of Triple Point (HTP) of λ shock significantly increases, compared to the one without controller, and cause a decline in shock power and pressure drops rate. In this paper, the main focus is on optimization of slot geometry as an influential parameter on the structure of the shock and flow characteristics by using Genetic Algorithm (GA). The averaged implicit Navier–Stokes equations and two equation standard k–ω turbulence models for the numerical simulation of the flow field have been used. The optimization problem is formulated in term of one objective function, namely, height of triple point maximization. Artificial neural network with two hidden layers has been used to achieve objective function based on the numerical simulation of the flow field data base. Root Mean Square Error (RMSE) was calculated for comparison and selecting the best algorithm in sequential steps. In order to simulate and compare the results with data obtained from experimental tests, the Cambridge University's wind tunnel tests and geometry have been used as the base design. The study demonstrates that, the HTP for optimized slot geometry is about 7.6 percentages more than base design.

A numerical investigation on the effects of slot geometry on shock boundary layer interaction

Slot is one of the features that control Shock wave-boundary layer interaction (SBLI), which is generally used to prevent strong interference from shockwaves to the boundary layer in supersonic flows. With this feature, the height of the triple point of λ shock significantly increases, and this increase causes a decline in shock power and pressure drop rate. In the current paper, the main focus is on the monitoring of the geometrical effect of slot as an influential parameter on the structure of the shock and flow characteristics by using numerical methods. Therefore, the averaged implicit Navier-Stokes equations and two equation standard k-ω turbulence models for the numerical simulation of the flow field have been used. Results indicate that the numerical results are fairly consistent with the experimental data. Because of the increase in the number of slots (n), and the leading leg of the λ shock is located within the slot, the height of the triple point increases. However, because of the increasing drops due to viscosity, the total pressure changes are negligible. In addition, with an increase in this parameter, changes in the static pressure caused by the leading leg of the shock have increased. By increasing the width of the slots, the height of the triple point has had an upward trend up to s = 8 mm and then had nearly constant values. In this mode, the static pressure changes resulting from the leading leg of the shock are negligible. For increasing the number or the width of slots, the re-expansion waves formed within the slot are removed because of the reduction in the severity of the changes in the boundary layer. To simulate and compare the results with the data obtained from the experimental tests, results from the Cambridge University's wind tunnel tests have been used.

On the influence of a single roughness element on the flow in supersonic boundary layer on a blunted cone

The work presents the results of numerical modeling of a supersonic flow around a blunted cone with an isolated cylindrical roughness on the forebody surface in the three-dimensional formulation. The roughness element is shown to distort the mean flow and to give rise to small-amplitude disturbances with distinguished spectral peaks in the boundary layer.

Aerodynamic criterion of weak blowing in optimal control of laminar boundary layer in supersonic flows on permeable surfaces

The purpose of the paper is to obtain a criterion for the optimal blowing intensity on the permeable surface at supersonic flow regime, which makes it possible to use the boundary layer equations for friction and heat flows computation.

Entropy and its application in turbulence modeling

The entropy concept was introduced into the turbulence modeling strategy in the present work. First, the turbulent boundary-layer was described from the point of energy dissipation. Based on the theoretical analysis and direct numerical simulations, the relationship between the entropy increment and viscosity dissipation was systematically investigated. Then, an entropy function f (s) was proposed to distinguish the turbulent boundary-layer from the external flow. This function is universal, independent of the inflow conditions or any specific turbulence model. With this function, a new version of delayed-detached-eddy simulation method SDES was constructed and verified with the supersonic boundary-layer flow and the cavity-ramped flow. Initial results showed that this method could successfully avoid the modeled stress depletion problem inherited from the original DES method.

Control of separated flow in a reflected shock interaction using a magnetically-accelerated surface discharge

A numerical investigation was carried out to explore the effects of a magnetically-accelerated surface discharge on a separated, turbulent boundary layer in supersonic flow. The geometry and test conditions were chosen for comparison to experiments carried out at Princeton University. For those studies, a reflected shock interaction was created using a 14° shock generator acting on an incoming turbulent boundary layer with a Reynolds number based on momentum thickness of 1 × 104 and a freestream Mach number of 2.6. Three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) calculations were carried out to simulate the experiments, using the US3D code developed at the University of Minnesota. The baseline code was modified to include a semi-empirical model of the surface discharge actuator, implemented through source terms in the momentum equation, vibrational energy equation, and total energy equation. The computational results for the baseline flow and several control cases were compared to experimental measurements of mean surface pressure. The level of discrepancy was typical of well-resolved RANS computations of three-dimensional, separated flows: qualitative agreement was obtained, and the general experimental trends were captured by the numerical model. Substantial three-dimensionality was observed even in the baseline flow, and significant changes in the flow topology were observed with the application of the actuator. Because of the highly three-dimensional nature of this shock interaction, the initial interpretation of the experiments may need to be revisited.

Statistical Characteristics of an Isothermal, Supersonic Developing Boundary Layer Flow from DNS Data

Direct numerical simulation results for a developing, supersonic boundary layer flow with either an adiabatic wall temperature condition or a cold wall (relative to adiabatic) temperature condition are evaluated to assess the comparative effect on the mean and turbulent fields. Included in the analysis are two-point turbulent spanwise spatial correlations and the corresponding one-dimensional energy spectra distributions as well as higher-order statistics including skewness and flatness factors. In addition to the mean field velocity and temperature behavior, the turbulent Reynolds stress, temperature variance, and heat and mass flux distributions are discussed. An overall focus of the analysis is to both contrast the velocity and thermal field behavior and to provide some additional insight into the dynamic balance of the various statistical correlations and their impact on model development.

Behavior of Boundary Layer in Supersonic Flow with Applied Lorentz Force

Experimental study on behavior of boundary layer in supersonic flow with applied Lorentz force was carried out. In the experiment, Mach 1.5 supersonic wind tunnel driven by a shock-tube was used. At the test section, the current from the external DC power supply and the magnetic field of 2.4 Tesla were applied to the boundary layer developing on the bottom wall. Argon seeded with cesium was used as an electrically conducting gas. Effect of the direction of the Lorentz force on static pressure distribution was investigated, and the remarkable increase of static pressure at the test section was observed for the decelerating Lorentz force. It is noted that the acceleration of the flow inside the boundary layer was demonstrated for the first time without accelerating the main flow when the accelerating Lorentz force was applied. At the same time, the acceleration efficiency defined by a ratio of work done by the Lorentz force to energy input into the flow was found 54-61%. These results have suggested the possibility of the boundary layer separation control by applying the accelerating Lorentz force. In the case of the decelerating Lorentz force, the significant reduction of Mach number was observed not only inside the boundary layer but also in the main flow. The reduction of Mach number could be ascribed to the growth of the boundary layer due to gas heating inside the boundary layer. When the direction of the current was changed, the difference of light emission from the discharge inside the boundary layer was observed, and this was due to the difference of the electromotive force induced in the supersonic flow.

Lighthill and the triple-deck, separation and transition

In 1953 James Lighthill, conducting an investigation into the potential mechanisms for upstream influence within boundary layers in supersonic flow, published a theoretical approach which explicitly took into account the influence of viscosity on a disturbance to an incident boundary-layer profile. In doing so he was able to predict a length-scale for upstream influence which scales with the global Reynolds number R, assumed large, as R−3/8. The physical process he identified is now referred to as a pressure–displacement (or viscous–inviscid) interaction. This article discusses Lighthill’s original paper and then proceeds to show how an appreciation of this interaction mechanism can help in the solution of many other problems in fluid mechanics and especially those of flow separation and late-stage laminar–turbulent transition. Finally, the article gives a brief description of the similarities between these two processes as seen from the unifying viewpoint of Lighthill’s pressure–displacement interaction.

On the merging of turbulent spots in a supersonic boundary-layer flow

The complex transition flow physics associated with the merging of turbulent spots in a Mach 2 boundary-layer has been studied using direct numerical simulation. Dynamics of an isolated turbulent spot, merging of laterally displaced spots, and merging of two spots in tandem are considered. The coherent structures associated with the wingtip region of the spot are found to play a major role in destabilising the surrounding laminar fluid. In the merging of laterally displaced spots a strong velocity defect, resulting in unstable inflectional velocity profiles, is observed in the interaction zone. These local inflectional instabilities within the interaction region trigger new large scale coherent structures. During the inline merging, the calmed region behind the tail of the downstream spot is found to suppress the growth of the upstream spot. The upstream spot is ultimately engulfed by the downstream spot.

Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M=2.25

A spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞=2.25 and Reθ≈4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consistently, the turbulent Prandtl number is not unity, and it varies between 0.7 and 0.8 in the outer part of the boundary layer. Nonetheless, a modified strong Reynolds analogy is still verified. In agreement with the low Mach number results, the streamwise velocity component and the temperature are only weakly anti-correlated. The turbulent kinetic energy budget also shows similarities with the incompressible case provided all terms of the equation are properly scaled; indeed, the leading compressibility contributions are negligible throughout the boundary layer.