Supersonic Flat-plate Boundary Layer Research Articles

Direct numerical simulations of supersonic flat-plate turbulent boundary layers with uniform blowing

The effect of uniform blowing on a spatially developing flat-plate turbulent boundary layer at Mach 2.25 is investigated using direct numerical simulations. Two values of the wall blowing ratio are considered, corresponding to low and high blowing rates. Uniform blowing is found to significantly reduce the near-wall turbulence anisotropy, although the turbulent kinetic energy still exhibits near-wall asymptotic behavior and the Reynolds analogy is relatively insensitive to changes in the blowing ratio. The pre-multiplied spectra of turbulent kinetic energy production demonstrate that increasing the blowing ratio significantly energizes the large-scale structures in the outer region, while suppressing the inner small-scale structures. An increase in the blowing ratio also has a strong influence on the behavior of the fluctuating wall pressure, amplifying the fluctuation intensity and reducing the dominant frequencies in the power spectrum. Two-point space–time correlations indicate that the characteristic length scale of the pressure fluctuations increases with increasing blowing ratio, whereas the convection velocity exhibits the opposite trend. Analysis of the reduced mean wall heat flux reveals that it is dominated by the relative balance between the work of the Reynolds stress and the turbulent transport of heat, but is insensitive to uniform blowing. Importantly, bidimensional empirical mode decomposition of the turbulent structures highlights the increasingly dominant contributions related to the significantly energized outer large-scale structures in the blowing region.

Stability analyses of secondary instability and oblique breakdown in a supersonic boundary layer under the influence of pressure gradients

Studied here is how pressure gradients affect nonlinear transition processes in a supersonic flat-plate boundary layer. Linear stability analysis suggests that a favorable pressure gradient stabilizes the first-mode disturbances significantly, whereas an adverse pressure gradient destabilizes them. Nonlinear stability analysis indicates that the three nonlinear mechanisms of fundamental resonance, subharmonic resonance, and oblique breakdown can induce transition. Oblique breakdown causes the earliest transition, and subharmonic resonance is stronger than fundamental resonance. An adverse pressure gradient significantly destabilizes the primary modes and enhances the nonlinear transition mechanisms. However, a favorable pressure gradient affects the different nonlinear transition processes differently. A weak favorable pressure gradient completely suppresses the transition in fundamental resonance but just delays it slightly in subharmonic resonance. For oblique breakdown, a weak favorable pressure gradient delays the transition significantly, with two high-speed streaks observed clearly. In all cases, a strong favorable pressure gradient leads to a fully laminar flow.

Three-dimensional wall heating elements effect on the instability in zero pressure gradient supersonic boundary layers

The streaky boundary layers have very important roles in laminar-turbulent transition. Streaks of appropriate size can influence stabilities in boundary layers. In this paper, the effect of steady streamwise elongated, spanwise periodic wall heating elements on the first mode instability in supersonic flat plate boundary layers was investigated. For the balance of the efficient and accuracy, the linearized Navier–Stokes equations are used to obtain the base flow and compared with compressible Navier–Stokes equations. A bi-global analysis tool is used for the instability analysis because the heating source has a much larger length-scale in the streamwise direction than that in the spanwise direction, and the streamwise velocity is much larger than the normal velocity and the spanwise one. Results indicated that the distortion caused by the three-dimensional surface heating elements could modify the first mode, resulting in a lower frequency but with an uncertain effect on the higher frequency modes. Additionally, the streaks make the lower spanwise wave number components of the even first mode disturbance in a three-dimensional supersonic boundary layer in the freestream. As a result, the spontaneous radiation of an acoustic wave to the far field was found for the even mode. These findings suggest that laminar-turbulence transition can be suppressed or enhanced by the three-dimensional wall heating.

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.

Thermochemical non-equilibrium effects on hypersonic shock wave/turbulent boundary-layer interaction

The research on shock wave/turbulent boundary-layer interactions is mainly limited to calorically perfect gases; little has been reported on the thermochemical non-equilibrium (real gas) effect. This effect is prominent at conditions of high Mach and Reynolds numbers. In this work, a household parallel solver for hypersonic thermochemical non-equilibrium flows with a Reynolds-averaged Navier–Stokes turbulence model is developed in which the coupling of turbulence with vibration and chemistry occurs under a gradient-law assumption. The thermal non-equilibrium is based on Park's two-temperature model, and the chemical non-equilibrium is based on Gupta's 11-species model. The method proposed in this paper is first validated using experimental data, including cases of a laminar cylinder flow at a high-enthalpy condition, a supersonic flat-plate turbulent boundary layer flow, a hypersonic transition flow, and a hypersonic compression corner flow at a low-enthalpy condition. This approach is then applied to assess the hypersonic flow characteristics past the 34° compression corner at a flight height of 30 km. Results show that the joint effects of turbulence and thermochemical non-equilibrium have a significant impact on the flow field organization, wall data, and separation length of the shock wave/boundary-layer interaction. Furthermore, the mechanism of the neck region accompanied by maximum heat flux, wall pressure and skin friction in both laminar and turbulent cases is well-interpreted. This study can be used as a reference tool for the aerodynamic design of future hypersonic vehicles accounting for multi-physics effects.

Constrained large-eddy simulation of a spatially evolving supersonic turbulent boundary layer at M = 2.25

A spatially developing supersonic flat plate boundary layer flow at M∞=2.25 is analyzed using the constrained large-eddy simulation (CLES) method. The Reynolds number based on the momentum thickness of the inlet boundary layer is Reθ=3429. The mean and statistical quantities, including mean velocity, mean temperature, and total temperature, are obtained and compared among the present approach, large eddy simulation (LES) with the dynamic Smagorinsky model, detached eddy simulation (DES), and naturally developed direct numerical simulation (ND-DNS). As a result, CLES can predict these mean quantities and statistics more accurately than LES and DES, and the results are in good agreement with the ND-DNS data. This demonstrates that CLES is an effective method for spatially developing supersonic flat-plate boundary layer flows.

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.

Linear stability analysis on the most unstable frequencies of supersonic flat-plate boundary layers

In current supersonic transition models, the timescale models of the first and second modes are required to reflect the contribution to the transition onset by the development of the unstable modes. However, the existing correlations of the timescales have problems in showing the Mach number effect and temperature effect correctly. In this paper, linear stability analyses are conducted to study the existing correlations of the timescales for the first and second modes, and the Mach number effect and the temperature effect are explicitly involved and discussed in the modeling of the characteristic timescales. It is found that the existing correlation between the timescale of the first mode and the Reynolds number based on the displacement thickness is not suitable for the supersonic situation. The frequency of the most unstable first mode in supersonic cases rises rapidly with the increasing Mach number while the current timescale model fails to predict this tendency, and the step phenomenon appears in the frequency-Reynolds-number curves when the Mach number is high. For the second mode, the Mach number effect on the timescale cannot be reflected entirely in the original correlation. Additionally, the temperature effect is proved to affect the timescales of unstable modes, which is left out by the current model. Considering the Mach number, the wall temperature and the total temperature effects, new correlation models for the characteristic frequency of the first and second mode with the Reynolds number are established, in order to provide guidelines for supersonic transition modeling. Some inconsistencies between the timescale-based transition models and the linear stability theory are also commented in this paper.

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.

Linear Stability of the Boundary Layer of Relaxing Gas on a Plate

The development of inviscid and viscous two-dimensional subsonic disturbances in the supersonic flat-plate boundary layer of a vibrationally excited gas is investigated on the basis of the linear stability theory. The system of two-temperature gas dynamics which includes the Landau-Teller relaxation equation is used as the initial model. Undisturbed flow is described by the self-similar boundary-layer solution for a perfect gas. It is shown that in the inviscid approximation excitation decreases the maximum growth rate of the most unstable second mode by 10–12% as compared with an ideal gas. The neutral stability curves are calculated for the first and second most unstable modes at the Mach numbers M = 2.2, 4.5, and 4.8. For both modes the critical Reynolds numbers at maximum excitation are greater by 12–13% than the corresponding values for the perfect gas.

Experimental and numerical investigation of excitation of artificial disturbances in the supersonic boundary layer

The influence of the parameters of the impulse action on the laminar supersonic flat-plate boundary layer on the excited localized perturbations is investigated at Mach 2. The influence of the duration of a pulsed discharge on the generated disturbances is studied experimentally. Also, a direct numerical simulation of the influence of the parameters of pulse injection on generated perturbations is carried out. It is obtained that as the duration of the action on the supersonic boundary layer increases, the amplitude of the generated disturbance increases. The velocity of the propagation downstream of localized disturbances in Mach 2 supersonic flat-plate boundary layer is estimated.

Assessment of the IDDES method acting as wall-modeled LES in the simulation of spatially developing supersonic flat plate boundary layers

ABSTRACTThe widely used improved delayed detached eddy simulation (IDDES) method is supposed to accurately predict the mean skin friction when it acts as wall-modeled large eddy simulation (WMLES), as claimed by the original authors. This property has been validated in subsonic flows but not in supersonic flows. In this article, IDDES acting as WMLES was assessed in the simulation of supersonic flat plate boundary layers, accompanied by two other hybrid Reynolds averaged Navier Stokes (RANS)/large eddy simulation (LES) methods which were also employed as WMLES, namely zonal detached eddy simulation (ZDES) and a hybrid RANS/LES method with the blending function proposed by Edwards and Choi (HRLMEC), for comparison. The underprediction of mean skin friction is existent in the results of IDDES but negligible in the results of ZDES and HRLMEC when all other settings are identical, presenting a contrast to the original idea of IDDES and some former research in subsonic flows. With the analysis of the shear stress, the underprediction of mean skin friction of IDDES is attributed to the underprediction of total Reynolds stress and turbulent kinetic energy production in the inner layer. Further research shows that, as for the present supersonic flow cases, IDDES can be capable of precisely predicting skin friction, but only if under the same condition the relevant LES, which uses the same subgrid-scale model, can precisely predict skin friction. This suggests that the problems met by IDDES may be essentially due to the intrinsic difficulty of LES to resolve the inner layer of a supersonic boundary layer: when resolving the inner layer of a supersonic boundary layer, LES should be tuned subtly and needs high computational cost, and may be damaged by any faulty factor, including but not limited to numerical resolution.

Influence Of Heavy Gas Blowing Into The Wall Layer Of Supersonic Boundary-Layer On Its Transition

The experimental investigation of the influence of the distributed blowing of heavy gas (sulfur hexafluoride of SF6) into the wall layer of supersonic flat-plate boundary layer (at free-stream Mach number M = 2) on the laminar-turbulent transition have been performed. For the first time experimentally it is shown that in case of such blowing there is a boundary-layer stabilization, and the laminar-turbulent transition is removed from the model leading edge.

Hot-wire visualization of the evolution of localized wave packets in a supersonic flat-plate boundary layer

Hot-wire visualization of the evolution of localized wave packets in a supersonic flat-plate boundary layer

Transition due to streamwise streaks in a supersonic flat plate boundary layer

A possible bypass transition scenario in a Mach 3 flat plate boundary layer is proposed and investigated numerically.

Combined influence of coating permeability and roughness on supersonic boundary layer stability and transition

A joint theoretical and experimental investigation of the influence of the surface permeability and roughness on the stability and laminar–turbulent transition of a supersonic flat-plate boundary layer at a free-stream Mach number of $M_{\infty }=2$ has been performed. Good quantitative agreement of the experimental data obtained with artificially generated disturbances performed on models with various porous inserts and calculations based on linear stability theory has been achieved. An increase of the pore size and porous-coating thickness leads to a boundary layer destabilization that accelerates the laminar–turbulent transition. It is shown that as a certain (critical) roughness value is reached, with an increase in the thickness of the rough and porous coating, the boundary layer stability diminishes and the laminar–turbulent transition is displaced towards the leading edge of the model.

Joint Influence Of Surface Roughness And Permeability On Stability And Transition Of Mach = 2 Boundary Layer

Joint theoretical and experimental investigation of the influence of surface permeability and roughness on stability and laminar-turbulent transition of the supersonic flat-plate boundary layer at free-stream Mach number M = 2 have been performed. Good quantitative agreement of experimental data obtained with artificially generated disturbances performed on models with various porous inserts and calculations based on the linear stability theory has been achieved. At research of the joint effect of the model surface permeability and roughness on the boundary layer stability and transition, it is shown that, as a certain (critical) roughness value is reached, with the rough and porous coating thickness increase, the boundary layer stability diminishes and the laminar-turbulent transition is displaced toward the model leading edge.

On The Influence Of Porous Coating Thickness On Supersonic Boundary Layer Stability

Theoretical and experimental investigation of the influence of porous-coating thickness on the stability of the supersonic flat-plate boundary layer at free-stream Mach number M = 2 have been performed. Good quantitative agreement of experimental data obtained with artificially generated disturbances performed on models with various porous inserts and calculations based on the linear stability theory has been achieved. It is shown that the increase of the porous-coating thickness leads to the boundary layer destabilization.

Numerical Investigation of Wall Cooling and Suction Effects on Supersonic Flat-Plate Boundary Layer Transition Using Large Eddy Simulation

Reducing friction resistance and aerodynamic heating has important engineering significance to improve the performances of super/hypersonic aircraft, so the purpose of transition control and turbulent drag reduction becomes one of the cutting edges in turbulence research. In order to investigate the influences of wall cooling and suction on the transition process and fully developed turbulence, the large eddy simulation of spatially evolving supersonic boundary layer transition over a flat-plate with freestream Mach number 4.5 at different wall temperature and suction intensity is performed in the present work. It is found that the wall cooling and suction are capable of changing the mean velocity profile within the boundary layer and improving the stability of the flow field, thus delaying the onset of the spatial transition process. The transition control will become more effective as the wall temperature decreases, while there is an optimal wall suction intensity under the given conditions. Moreover, the development of large-scale coherent structures can be suppressed effectively via wall cooling, but wall suction has no influence.