Supersonic Boundary Layer Research Articles

Parameter Influence on Porous Bleed Performance for Supersonic Turbulent Flows

Porous bleed systems are a common technique to control shock-/boundary-layer interactions and/or supersonic boundary layers. However, the influence of various design parameters is still unknown. Even though porous bleed models are required to minimize the costs of the design process, they often do not include parameter effects. In the present study, the effect of the plate length, the hole diameter, the porosity level, the thickness-to-diameter ratio, and the stagger angle are investigated by means of three-dimensional Reynolds-averaged Navier–Stokes simulations. The bleed efficiency and the effectiveness in thinning a Mach M=1.6 turbulent boundary layer are determined. The findings show a crucial influence of the hole diameter on both the efficiency and effectiveness of the porous bleed. Similar findings are made for the porosity and stagger angle but with a smaller significance. The thickness-to-diameter ratio and plate length are shown to mainly affect the bleed efficiency.

Effect of cone rotation on the nonlinear evolution of Mack modes in supersonic boundary layers

In this paper, we present a systematic study of the nonlinear evolution of the travelling Mack modes in a Mach 3 supersonic boundary layer over a rotating cone with a $7^{\circ }$ half-apex angle using the nonlinear parabolic stability equation (NPSE). To quantify the effect of cone rotation, six cases with different rotation rates are considered, and from the same streamwise position, a pair of oblique Mack modes with the same frequency but opposite circumferential wavenumbers are introduced as the initial perturbations for NPSE calculations. As the angular rotation rate $\varOmega$ increases such that $\bar \varOmega$ (defined as the ratio of the rotation speed of the cone to the streamwise velocity at the boundary-layer edge) varies from 0 to $O(1)$ , three distinguished nonlinear regimes appear, namely the oblique-mode breakdown, the generalised fundamental resonance and the centrifugal-instability-induced transition. For each regime, the mechanisms for the amplifications of the streak mode and the harmonic travelling waves are explained in detail, and the dominant role of the streak mode in triggering the breakdown of the laminar flow is particularly highlighted. Additionally, from the linear stability theory, the dominant travelling mode undergoes the greatest amplification for a moderate $\varOmega$ , which, according to the $e^N$ transition-prediction method, indicates premature transition to turbulence. However, this is in contrast to the NPSE results, in which a delay of the transition onset is observed for a moderate $\varOmega$ . Such a disagreement is attributed to the different nonlinear regimes appearing for different rotation rates. Therefore, the traditional transition-prediction method based on the linear instability should be carefully employed if multiple nonlinear regimes may appear.

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.

Coexistence of stationary Görtler and crossflow instabilities in boundary layers

The coexistence of stationary Görtler and crossflow instabilities in boundary layers covering incompressible to hypersonic regimes is investigated by varying the local sweep angle, pressure gradient, wall curvature, and wall temperature using linear stability analysis. The results show that increasing the local sweep angle under a fixed concave curvature in incompressible boundary layers leads to the appearance of two unstable modes at certain sweep angles, which is conventionally known as the “changeover” regime between the crossflow and Görtler modes. This study identifies a synchronization between the two modes under this condition, which is similar to multiple Görtler modes and thus referred to as Görtler–crossflow modes. Three scenarios are presented to describe the possible development of these modal instabilities. In addition, increasing the concave curvature destabilizes the instability, while introducing a pressure gradient stabilizes the instability and results in a shrinkage of the unstable band of the spanwise wavenumber, as reported in the literature. In supersonic and hypersonic boundary layers, synchronization can occur near specific sweep angles and under cold wall conditions in supersonic boundary layers. As Mach number increases, the synchronization regime shifts toward lower sweep angles and wall temperature, in which the former reflects a decline in crossflow strength relative to Görtler instability, while the latter indicates the influence of thermal effects on synchronization. In hypersonic boundary layers, the crossflow instability is insignificant compared with the Görtler instability. No synchronization is identified under various parameter changes, and the first Görtler–crossflow mode dominates across the entire spanwise wavenumber ranges.

Influence of distributed hydrogen injection and combustion on supersonic boundary layer stability and transition

This theoretical study recorded the influence of the distributed injection of hydrogen through a permeable surface and its combustion on the stability and transition of a supersonic boundary layer (BL). The laminar base flow for a multicomponent flat-plate BL was computed using the computational fluid dynamics solver with finite-rate chemistry for free-stream Mach number (M) = 2. Linear stability theory (LST) equations for a reactive gas mixture were derived in the local parallel base flow approximation. Stability calculations based on the developed theory revealed the possibility of a decrease in the local spatial amplification rates of unstable perturbations. A double reversal in the maximal amplification rate magnitudes of perturbations was obtained, wherein at first, they increased, then decreased to zero, and then rose again. The influence of the distributed injection and combustion of hydrogen in the supersonic BL on the position of the laminar-turbulent transition was estimated using the LST-based eN-method. Calculated and experimentally obtained dependencies of the relative transition Reynolds number on the relative mass flow rate of injected hydrogen were compared. It was found that depending upon the flow conditions, the hydrogen diffusion flame could accelerate or decelerate the transition in the supersonic M = 2 BL, when compared to absence of hydrogen burning. Two counteracting effects compete: heat supply by combustion exerts stabilizing influence, while low-molecular-weight gas blowing from the surface exerts destabilizing influence. Depending on the interplay of these two factors, it would be possible to obtain acceleration or deceleration of transition.

Response of a supersonic turbulent boundary layer to different streamwise adverse pressure gradients

An adverse pressure gradient (APG) has an impact on the boundary layer, increasing the turbulent intensity of the layer. The mean and turbulent properties of the turbulent boundary layer on a flat plate with different APGs were investigated at Mach 2.7 in the present work utilizing the particle image velocimetry and nanoparticle-based planar laser scattering techniques. According to analysis, the changing trends of boundary layer parameters are different depending on whether the local mainstream velocity or freestream velocity of the wind tunnel is used to normalize. Using the former might make the enhanced effect of the rising APG more visible. With the rise in APG, the principal strain rate, turbulent fluctuation, Reynolds stress, and turbulence production in the boundary layer all increased, while the turbulent boundary layer's thickness dropped. Furthermore, the heightened upward ejection and downward sweep events caused the streamwise turbulence intensity to reach its outer peak under the influence of strong APG. The characteristics of the spanwise vortex in the boundary layer are investigated in conjunction with the probability density function analysis. The growing APG, which primarily promote negative vorticity, can strengthen the rotational strength of spanwise vortices, which are a component of hairpin vortices. As APG rises, the number of small-scale vortices in the boundary layer increases and the fractal dimension grows. The increase in small-scale vortices tends to induce strong transportation and promotes turbulence intensity. Further investigation reveals that the increased volume change caused by the enhanced compression effect with increasing APG exacerbated the vorticity.

Conditional space-time POD extensions for stability and prediction analysis

The correlation and extraction of coherent structures from a turbulent flow is a principal objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CST-POD) offers insight into transient dynamics, revealing the causes of specific flow phenomena, or events, in a customizable manner. This work targets the temporal evolution of CST-POD modes in a reduced subspace, resulting in new extensions and adaptations that are distinct from capabilities of other decomposition methods. First, the properties of CST-POD and its relation to the ensemble average are instantiated with a simple Lorenz system. Other CST-POD properties are examined with applications to problems displaying intermittent properties that test data-driven methods, including transitional supersonic boundary layers and schlieren video processing of unstarted inlet buzz. These examples also explore the pragmatic concerns of oversampling and offer theoretical connections to the sub-sampling of a larger Hankel space through time-delay embedding. Through these insights, it is demonstrated that the subsequent application of dynamic mode decomposition (DMD) to CST-POD modes, provides a flexible tool to investigate targeted flow instabilities, both absolute (tonal) and convective in nature. It is shown, using a resonating jet as an example, that Spectral POD modes associated with tones can be recovered if the time-horizon of CST-POD is suitably extended. Regarding convective instabilities, a multi-resolution framework (CST-mrDMD) yields a refined “cause and effect” stability analysis, capable of diagnosing the natural forcing mechanisms within the jet, and the resulting unstable shear-layer mode. In the final interpretation, the potential for real-time flow prediction of extreme events is derived from an active sensor correlated to a CST-POD mode using the example of bluff-body wake structures impinging on a channel wall.

Control of Cowl Shock/Boundary Layer Interaction in Supersonic Inlet Based on Dynamic Vortex Generator

A shock wave/boundary layer interaction (SWBLI) is a common phenomenon in supersonic inlet flow, which can significantly degrade the aerodynamic performance of the inlet by inducing boundary layer separation. To address this issue, in this paper, we propose the use of a dynamic vortex generator to control the SWBLI in a typical supersonic inlet. The unsteady simulation method based on dynamic grid technology was employed to verify the effectiveness of the proposed method of control and investigate its mechanism. The results showed that, in a duct of finite width at the inlet, the SWBLI generated complex three-dimensional (3D) flow structures with remarkable swirling properties. At the same time, vortex pairs were generated close to the side wall as a result of its presence, and this led to the intensification of transverse flow and, in turn, the formation of a complex 3D structure of the flow of the separation bubble. The dynamic vortex generator induced oscillations of variable intensity in the vortex system in the supersonic boundary layer that enhanced the mixing between the boundary layer flow and the mainstream. Meanwhile, the unique effects of “extrusion” and “suction” in the oscillation process continued to charge the airflow, and the distribution of velocity in the boundary layer significantly improved. As the oscillation frequency of the vortex generator increased, its charging effect on low-velocity flow in the boundary layer increased, and its control effect on the flow field of the SWBLI became more pronounced. The proposed method of control reduced the length of the separation bubble by 31.76% and increased the total pressure recovery coefficient at the inlet by 6.4% compared to the values in the absence of control.

Experimental study on combustion within a supersonic boundary layer and its effect on laminar-turbulent transition

Experimental study on combustion within a supersonic boundary layer and its effect on laminar-turbulent transition

Experimental Investigation of the Structure of Disturbances from Two Pulsed Sources in the Flat-Plate Supersonic Boundary Layer

The work is devoted to the development of a new experimental method for entering controlled disturbances with a given frequency-wave structure into a supersonic boundary layer. Experimental data on the formation of disturbances from two pulsed sources (pulsed glow discharge) in the laminar flat-plate boundary layer at the Mach number equal to 2 are given. The experiments were carried out in the T-325 wind tunnel of ITAM SB RAS. The localized sources were spaced out at the same distance from the leading edge of the plate at 6 mm from each other spanwise. Flow pulsations were measured using a hot-wire probe of constant temperature anemometer, the signal was recorded synchronously with ignition of the discharges. This made it possible to distinguish the pulsations from the discharges against the background of random uncontrolled “natural” pulsations of the boundary layer. The spatial-temporal and frequency-wave structure of the generated disturbances from a single or two discharges, operating synchronously or with a time delay, are analyzed. It is found that the maximum difference in the structure of disturbances from one and two sources is observed in the central region, while at the side boundaries of the disturbances, the pulsations are close in all considered cases. In the wave spectra of disturbances from two discharges, nodes and antinodes are formed. Their position is determined by the distance between the sources and the time delay in their operation.

Controlling second-mode oblique breakdown in high-speed boundary layers using streak: A direct numerical simulation study

The suppression effect of streaks on the second mode has been studied by the stability analysis in the past decade. In the present study, we conduct direct numerical simulations (DNS) to investigate the direct nonlinear control in the complete laminar-to-turbulence transition scenario within a high Mach number supersonic boundary layer. Our study aims to provide a comprehensive understanding of the mechanisms underlying the influence of streaks on the transition of high-speed boundary layers. Our work demonstrates the effective control effect of the streaks generated by blowing and suction strips on laminar-to-turbulence transition via the second-mode oblique breakdown at a Mach number 4.5 high-speed boundary layer using DNS. Modal analysis, nonlinear disturbance formulation, and stability analysis are used to provide insight into the stabilization effect of control streaks. Crucially, the role of three-dimensional control modes and mean-flow distortion generated by the control streak are investigated. Our findings indicate that both mean-flow distortion and three-dimensional control modes effectively stabilize the fundamental oblique second mode, particularly when the amplitude of control streaks is strong.

Experimental Investigation of the Structure of Disturbances from Two Pulsed Sources in the Flat-Plate Supersonic Boundary Layer

The work is devoted to the development of a new experimental method for entering controlled disturbances with a given frequency-wave structure into a supersonic boundary layer. Experimental data on the formation of disturbances from two pulsed sources (pulsed glow discharge) in the laminar flat-plate boundary layer at the Mach number equal to 2 are given. The experiments were carried out in the T-325 wind tunnel of ITAM SB RAS. The localized sources were spaced out at the same distance from the leading edge of the plate at 6 mm from each other spanwise. Flow pulsations were measured using a hot-wire probe of constant temperature anemometer, the signal was recorded synchronously with ignition of the discharges. This made it possible to distinguish the pulsations from the discharges against the background of random uncontrolled “natural” pulsations of the boundary layer. The spatial-temporal and frequency-wave structure of the generated disturbances from a single or two discharges, operating synchronously or with a time delay, are analyzed. It is found that the maximum difference in the structure of disturbances from one and two sources is observed in the central region, while at the side boundaries of the disturbances, the pulsations are close in all considered cases. In the wave spectra of disturbances from two discharges, nodes and antinodes are formed. Their position is determined by the distance between the sources and the time delay in their operation.

Secondary Instabilities in Supersonic Boundary Layers over Microporous Surfaces

Secondary Instabilities in Supersonic Boundary Layers over Microporous Surfaces

Decomposition of mean skin friction in incident shock wave/turbulent boundary layer interaction flows at Mach 2.25

The evolution characteristics of the mean skin friction beneath the supersonic turbulent boundary layer that interacts with incident shock waves at Mach 2.25 are analyzed using Direct Numerical Simulation (DNS). The separated and attached boundary layers in the interaction region that respectively correspond to 33.2° and 28° incident shock angles are considered. The mean skin friction recovery rate for the separated boundary layer is much gentler and distinctly less than that for the attached case where the skin friction completes its recovery within one boundary layer thickness. The novel mean skin friction decomposition method for compressible flows proposed by the recent research is applied in the interaction region to investigate the internal evolution characteristics quantitatively. The results reveal that the three decomposition components are distinctly unequal between the two cases. The contributions of the turbulent motions at different scales to the associated term are focused on using empirical mode decomposition technology. It indicates that the outer large-scale structures dominate separation and reattachment regions, while contributions from inner small-scale structures are limited. In contrast, contributions from the outer large-scale structures are dramatically reduced in the attached case, which results in the outer large-scale and inner small-scale motions being of equal importance.

Effect of Small Angles of Attack on Turbulence Generation in Supersonic Boundary Layers on Swept Wings

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability.

Effect of wall temperature in streamwise supersonic corner flow

The interaction between corner flow and heat transfer is very common in the internal and external flow of hypersonic vehicle surface, but it is not clear how the wall thermal boundary condition affects the supersonic corner flow boundary layer. In the present study, the Reynolds stress model is used to solve the Reynolds-averaged Navier–Stokes equations. The results show that when the symmetrical wall temperature Tw is less than or equal to the recovery temperature Taw, the mean velocity profile in the corner zone is similar to the plate zone, and the temperature is higher in the corner zone. At heating wall condition of Tw>Taw, both velocity and temperature profile of outer corner boundary layer are different from that in the plate zone. The near-wall temperature distribution increases relatively, and the temperature profile is no longer similar to the law of the wall when Tw rises. Along the spanwise wall, the deviation of the velocity–temperature quadratic curve and the generalized Reynolds analogy (GRA) relation is within 10%. In the supersonic corner flow, the velocity–temperature relation under non-adiabatic wall condition satisfies the GRA relation. The effect of wall temperature on corner boundary layer velocity and temperature is significant. It is necessary to consider wall thermal boundary condition in the supersonic corner flow boundary layer analysis.

Influence of optical aperture sizes on aero-optical effects induced by supersonic turbulent boundary layers.

With the increase of flight speed, aero-optical effects induced by the turbulent boundary layer near the optical window become increasingly significant. The density field of the supersonic (Mach 3.0) turbulent boundary layer (SPTBL) was measured by nano-tracer-based planar laser scattering technique, and the optical path difference (OPD) was obtained through ray-tracing method. The influence of the optical aperture size on the aero-optical effects of SPTBL was studied in detail, and the underlying mechanisms were analyzed from the perspective of the turbulent structure scales. The influence of the optical aperture on the aero-optical effects is mainly due to turbulent structures with different scales. The beam center jitter (s x¯) and offset (x¯) are mainly caused by turbulent structures larger than the optical aperture size, while the beam spread about the center (x ' 2¯) is mainly caused by turbulent structures smaller than the optical aperture size. With the increase of optical aperture size, the proportion of turbulent structures larger than the optical aperture size decreases, which can suppress the beam jitter and the beam offset. Meanwhile, since the beam spread is primarily induced by small-scale turbulent structures with relatively strong density fluctuation intensity, the spread increases rapidly to its peak and then gradually stabilizes as the optical aperture size grows.

Effect of Small Angles of Attack on Turbulence Generation in Supersonic Boundary Layers on Swept Wings

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability.

Gas Injection and Suction Effect on the Instability of a Supersonic Boundary Layer

We present the results of an investigation of the boundary layer stability on a flat plate having a region of gas injection/suction normal to the wall at a large supersonic freestream Mach number. The laminar flow past a flat plate having a region of distributed injection/suction of fixed intensity is modeled numerically using the integration of Navier—Stokes equations. The unstable disturbances in the boundary layer distorted by injection/suction are analyzed within the framework of the linear stability theory and the eN{{e}^{N}} method for compressible flows. High-frequency disturbances belonging to the plane second mode of the boundary layer, which are the most unstable at high velocities, are considered. It is shown that gas injection/suction leads to a nonmonotonic variation of disturbance growth rates with the appearance of stabilization/destabilization regions, as compared with the case in which injection/suction is absent.

Numerical Investigation of Asymmetric Mach 2.5 Turbulent Shock Wave Boundary Layer Interaction

Supersonic shock wave boundary layer interactions are common to inlet flows of supersonic and hypersonic vehicles. This paper reports on wall-resolved implicit large-eddy simulations of a canonical Mach 2.5 turbulent shock wave boundary layer interaction experiment at the NASA Glenn Research Center. The boundary layer upstream of the interaction was nominally axisymmetric and two-dimensional. A conical centerbody with a 16 deg half-angle and a maximum radius of 0.147D of the test section diameter was employed to generate a conical shock wave, where D is the test section diameter. Asymmetric (swept) interactions were obtained by displacing the shock generator away from the test section centerline. The present simulation is for a shock generator displacement of D/6. Results from the asymmetric simulation are compared with results from an earlier simulation of a corresponding axisymmetric interaction. The experimental Reynolds number based on test section diameter was ReD=4×106. For the simulations, the Reynolds number was lowered to ReD=4×105 to keep the computational expense of the simulations within limits. Compared to the axisymmetric interaction, the streamwise extent of the separation varies considerably in the azimuthal direction for the asymmetric interaction. The separation is strongest at the azimuthal location that is closest to the shock generator. The streamwise extent of the separated flow regions is noticeably reduced and substantial crossflow is observed between the locations that are closest and farthest from the shock generator. A Fourier analysis of the unsteady flow data indicates low-frequency content for the separated region that is closest to the shock generator. Away from this region, with increasing sweep angle and cross-flow, the low-frequency content is diminished. A proper orthogonal decomposition captures spanwise coherent structures for the more two-dimensional parts of the interaction.