Hypersonic Boundary Layer Transition Research Articles

Coherent structure tracking of the second Mack mode in transitional hypersonic boundary layers

The natural transition of hypersonic boundary layers (HBLs) is often expressed in terms of discrete modes and their linear stability. A frequent interpretation revolves around fast and slow acoustic modes interacting in the vicinity of the vortical/entropic branches of the continuous spectrum found from stability analyses. Yet several transition scenarios are contingent upon factors such as the spectral content of the free-stream disturbances, or the interactions between the discrete modes within the boundary layer and the free-stream disturbances near the leading edge which can be decomposed into vortical, acoustic and entropic nature based on the fluid-thermodynamic (FT) components. Yet the interpretations of linear stability applied to discrete modes can lead to semantic conflicts with the terminology of FT components. To clarify the current description of the processes involved, this study chooses an approach aimed at characterizing the dynamics of the second Mack mode in transitional HBLs through coherent structure tracking. The method involves decomposing the flow perturbations into acoustic, vortical and entropic content, and following their associated coherent structures over time. For this purpose, direct numerical simulations are carried out to investigate the dynamics of the second Mack mode instability in two-dimensional HBLs, considering a flow at Mach 6 over a cooled and an insulated wall. It is found that vortical structures coexist at different heights along the wall surface, forming alternating sign doublets around the critical layer and above the relative sonic line. These structures are found to merge in the region of maximum second Mack mode instability.

Gas Kinetic Scheme Coupled with High-Speed Modifications for Hypersonic Transition Flow Simulations.

The issue of hypersonic boundary layer transition prediction is a critical aerodynamic concern that must be addressed during the aerodynamic design process of high-speed vehicles. In this context, we propose an advanced mesoscopic method that couples the gas kinetic scheme (GKS) with the Langtry-Menter transition model, including its three high-speed modification methods, tailored for accurate predictions of high-speed transition flows. The new method incorporates the turbulent kinetic energy term into the Maxwellian velocity distribution function, and it couples the effects of high-speed modifications on turbulent kinetic energy within the computational framework of the GKS solver. This integration elevates both the transition model and its high-speed enhancements to the mesoscopic level, enhancing the method's predictive capability. The GKS-coupled mesoscopic method is validated through a series of test cases, including supersonic flat plate simulation, multiple hypersonic cone cases, the Hypersonic International Flight Research Experimentation (HIFiRE)-1 flight test, and the HIFiRE-5 case. The computational results obtained from these cases exhibit favorable agreement with experimental data. In comparison with the conventional Godunov method, the new approach encompasses a broader range of physical mechanisms, yielding computational results that closely align with the true physical phenomena and marking a notable elevation in computational fidelity and accuracy. This innovative method potentially satisfies the compelling demand for developing a precise and rapid method for predicting hypersonic boundary layer transition, which can be readily used in engineering applications.

Experimental study of the effects of isolated roughness elements on the stability and transition of a hypersonic boundary layer on a flat plate

Surface roughness elements on hypersonic vehicles can cause early boundary layer transition, increasing wall skin friction and heat flux and affecting aircraft range and thermal protection systems. Accurate prediction of the transition caused by these roughness elements is crucial for the design of hypersonic vehicles. In this work, wind tunnel experiments on isolated roughness-induced boundary layer transition at Ma = 6 are conducted. Infrared thermography and high-frequency pressure sensors are utilized to investigate the effects of different roughness element configurations (cylindrical, diamond, ramp) on the hypersonic boundary layer instability and transition. The experimental results show that all three roughness elements can effectively enhance the generation of second mode waves and promote boundary layer transition. Compared to smooth surfaces, they exhibit similar frequency band range, faster growth, and earlier saturation. Among them, the ramp roughness element most effectively triggers the boundary layer transition, with a relatively small heat flux increase. Furthermore, bispectral analysis illustrates that all three roughness elements undergo self-interactions that lead to spectral broadening, ultimately resulting in boundary layer transitions.

Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint

The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$ , and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.

The Experiments and Stability Analysis of Hypersonic Boundary Layer Transition on a Flat Plate

Experimental and linear stability theory (LST) investigation of boundary layer transition on a flat plate was conducted with a flow of Mach number 5. The temperature distributions and second-mode disturbances on the flat plate surface at different unit Reynolds number (Reunit) values were captured by infrared thermography and PCB technology, respectively, which revealed the transition location of the flat-plate boundary layer. The PCB sensors successfully captured the second-mode disturbances within the boundary layer initially at a frequency of about 100 kHz, with a gradually expanding frequency range as the distance travelled downstream increased. The evolution characteristics of the second-mode instabilities were also investigated by LST and obtained for the second mode, ranging from 100 to 250 kHz. The amplitude amplification factor (N-factor) of the second-mode instabilities was calculated by the eN method. The N-factor of the transition location in the wind tunnel experiment predicted by LST is about 0.98 and 1.25 for Reunit = 6.38 × 106 and 8.20 × 106, respectively.

Correlated off-body density fluctuations and surface heating in hypersonic boundary layer transition

Correlated off-body density fluctuations and surface heating in hypersonic boundary layer transition

Hypersonic boundary-layer instability characterization and transition downstream of distributed roughness

Hypersonic boundary-layer instability characterization and transition downstream of distributed roughness

Numerical Investigation of Hypersonic Flat-Plate Boundary Layer Transition Subjected to Bi-Frequency Synthetic Jet

Transition delaying is of great importance for the drag and heat flux reduction of hypersonic flight vehicles. The first mode, with low frequency, and the second mode, with high frequency, exist simultaneously during the transition through the hypersonic boundary layer. This paper proposes a novel bi-frequency synthetic jet to suppress low- and high-frequency disturbances at the same time. Orthogonal table and variance analyses were used to compare the control effects of jets with different positions (USJ or DSJ), low frequencies (f1), high frequencies (f2), and amplitudes (a). Linear stability analysis results show that, in terms of the growth rate varying with the frequency of disturbance, an upstream synthetic jet (USJ) with a specific frequency and amplitude can hinder the growth of both the first and second modes, thereby delaying the transition. On the other hand, a downstream synthetic jet (DSJ), regardless of other parameters, increases flow instability and accelerates the transition, with higher frequencies and amplitudes resulting in greater growth rates for both modes. Low frequencies had a significant effect on the first mode, but a weak effect on the second mode, whereas high frequencies demonstrated a favorable impact on both the first and second modes. In terms of the growth rate varying with the spanwise wave number, the control rule of the same parameter under different spanwise wave numbers was different, resulting in a complex pattern. In order to obtain the optimal delay effect upon transition and improve the stability of the flow, the parameters of the bi-synthetic jet should be selected as follows: position it upstream, with f1 = 3.56 kHz, f2 = 89.9 kHz, a = 0.009, so that the maximum growth rate of the first mode is reduced by 9.06% and that of the second mode is reduced by 1.28% compared with the uncontrolled state, where flow field analysis revealed a weakening of the twin lattice structure of pressure pulsation.

Effect of local wall temperature on hypersonic boundary layer stability and transition

Wall temperature significantly affects stability and receptivity of the boundary layer. Changing the wall temperature locally may therefore be an effective laminar flow control technique. However, the situation is complicated when the wall temperature distribution is nonuniform, and researchers have experimentally found that local wall cooling may delay the onset of transition. We attempt to clarify the physical mechanisms whereby the local wall temperature affects the transition and the stability of a hypersonic boundary layer. A numerical investigation of the disturbance evolution in a Mach-6 sharp cone boundary layer with local wall heating or cooling is conducted. Direct numerical simulation (DNS) is performed for the single-frequency and broadband disturbance evolution caused by random forcing. We vary the local wall temperature and the location of heating/cooling, and then use the e N method to estimate the transition onset. Our results show that local wall cooling amplifies high-frequency unstable waves while stabilizing low-frequency unstable waves, with local heating amplifying all unstable waves locally. The disturbance amplitude and second-mode peak frequency obtained by DNS agree well with the previous experimental results. Local cooling/heating has a dual effect on the stability of the hypersonic boundary layer. For local cooling, while it effectively inhibits the growth of the low-frequency unstable waves that dominate the transition downstream, it also further destabilizes the downstream flow. In addition, while upstream cooling can delay the transition, excessive cooling may promote it; local heating always slightly promotes the transition. Finally, recommendations are given for practical engineering applications based on the present results.

Numerical Investigations of Nonlinearly Generated Disturbance Waves in High-Speed Boundary Layers

In several experimental investigations of hypersonic boundary-layer transition, higher harmonics of the linearly unstable second mode waves as well as low-frequency waves, which are not related to first mode waves, have been observed. It has been conjectured that the higher harmonics are nonlinearly generated by a self-interaction mechanism of the linearly amplified second mode waves. Several hypotheses regarding the origin of the low-frequency waves and their role in the transition process have been put forth. However, a clear understanding of the origin and role of these low-frequency disturbances in the transition process is difficult to attain from experiments and thus still not completely achieved. The nonlinear generation of higher harmonics and low-frequency disturbances is relevant because in high-speed boundary layers, second modes can reach very large amplitudes, which can lead to a considerable stretching of the transitional regime where these nonlinearly generated waves can then reach significant amplitudes and participate in the transition process. To shed light on this unresolved issue, numerical investigations were carried out for a flared cone at Mach 6. These calculations have shown that nonlinear interactions of sufficiently large-amplitude second mode waves can generate low-frequency disturbances. This was confirmed by a theoretical nonlinear interaction model.

Stabilization of hypersonic boundary-layer instability using porous coatings under thermochemical nonequilibrium

In this study, the suppression of the instability of the hypersonic boundary-layer transition under thermochemical nonequilibrium (TCNE) using a porous coating configuration is examined through linear stability theory (LST) and direct numerical simulation (DNS). Fedorov's admittance model is applied in LST to account for the porous coating effect. The model is modified accordingly such that the flow condition simulated under the TCNE assumption is considered. The results are compared with the case under the calorically perfect gas (CPG) assumption. Conditions of Mach 20-6 degree wedge flow and Mach 45-10 degree wedge flow are chosen for this study. In general, the second mode instability is destabilized and shifts upstream under the TCNE effect. Through the comparison between the DNS and LST results in the presence of a porous coating, it is concluded that the effect of suppressing the instability is very similar under both the CPG and TCNE assumptions. The TCNE effect has minimal impact on the acoustic attenuation of the instability within the cavity. Furthermore, the use of the admittance models in LST can fairly predict the trend of disturbance growth in DNS if the porous coating region is sufficiently long, validating the feasibility of extending the application of the admittance model to a different thermochemical state in addition to the CPG assumption. Examination of the perturbation contours under different state assumptions reveals the absence of second-mode wave structure in the region of microcavities, confirming the stabilization of hypersonic boundary-layer instability.

Direct numerical simulation of slender cones with variable nose bluntness based on graphics processing unit computation

Direct numerical simulation with up to 10×109 scale grid points based on graphics processing unit computation is carried out to investigate the bluntness effect on the hypersonic boundary-layer transition over a slender cone with zero angle of attack at Mach 6. Four cases with the nose radii of 1, 10, 20, and 40 mm are conducted, and the corresponding Reynolds number based on the nose radius varies from 1.0×104 to 4.0×105. Random disturbances with a broad spectrum of frequencies and a wide range of azimuthal wavenumbers were applied to the wall to simulate disturbances caused by wall roughness. The numerical results show that as the nose tip radius increases, the transition position gradually moves downstream with increased transition region. For the case with a nose radius of 1 mm, the flow transition and entropy swallowing occur almost simultaneously, while for other cases, the transition takes place earlier than the entropy swallowing. In consequence, the disturbance amplitude upstream of the transition in the 1 mm case is much larger than that of other cases. To further study the mechanism of the transition, the frequency spectrum analysis is carried out. It is found that all cases exhibit two characteristic frequencies within the transition region, i.e., the high frequency and extremely low frequency. Owing to the influence of the entropy layer, the characteristic high frequency of the 1 mm case is significantly higher than that of other cases. With the increase in the nose radius, the characteristic frequency of the high frequency decreases gradually.

Direct-Numerical Simulation with the Stability Theory for Turbulent Transition in Hypersonic Boundary Layer

Direct-Numerical Simulation with the Stability Theory for Turbulent Transition in Hypersonic Boundary Layer

Plate boundary layer transition regulation based on plasma actuation array at Mach 6

An experimental study on controlling hypersonic boundary layer transition using a surface arc plasma actuation array was conducted. First, base boundary transition characteristics were analyzed in virtue of various sensors and high-speed schlieren, and the transition criterion was established based on the critical value of schlieren spatial power spectral density resolution. Then, the influence of three different actuation frequencies (8, 34, and 55 kHz) was studied based on linear stability theory analysis. The impact of different actuation frequencies on the dominant unstable waves in the boundary layer was analyzed, and a transition criterion under the regulation of plasma actuation was proposed. Finally, the proper orthogonal decomposition method was used to analyze the influence of different actuation frequencies on the unstable characteristic structures. Based on the research, the efficacy of plasma actuation array in promoting transition is verified, the corresponding regulation mechanism is summarized, and transition regulation mechanization is refined.

Direct numerical simulations of hypersonic boundary layer transition over a hypersonic transition research vehicle model lifting body at different angles of attack

This paper performs direct numerical simulations of hypersonic boundary layer transition over a Hypersonic Transition Research Vehicle (HyTRV) model lifting body designed by the China Aerodynamic Research and Development Center. Transitions are simulated at four angles of attack: 0°, 3°, 5°, and 7°. The free-stream Mach number is 6, and the unit Reynolds number is 107 m−1. Four distinct transitional regions are identified: the shoulder cross-flow and vortex region and the shoulder vortex region on the leeward side, the windward vortex region and the windward cross-flow region on the windward side. As the angle of attack increases, the transition locations on the leeward side generally move forward and the transition ranges expand, while the transition locations generally move backward and the transition ranges decrease on the windward side. Moreover, the shoulder vortex region moves toward the centerline of the leeward side. At large angles of attack (5° and 7°), the streamwise vortex on the shoulder cross-flow and vortex region will enable the transition region to be divided into the cross-flow instability region on both sides and the streamwise vortex instability region in the middle. In addition, the streamwise vortex also leads to a significant increase in cross-flow instability in their upper region, which can generate a new streamwise vortex instability region between the two transition regions on the leeward side. Furthermore, since the decrease in the intensity and the range for the cross-flow on the windward side, the windward cross-flow region tends to become narrow and ultimately disappears.

The stabilizing effect of grooves on Görtler instability-induced boundary layer transition in hypersonic flow

Görtler vortex-induced hypersonic boundary layer transition controlled by grooves is investigated using direct numerical simulations and spatial bi-global stability analysis. In the simulations, Görtler vortices are excited by wall steady blowing and suction with spanwise wavelengths of 3 mm. It is found that when the wall is covered with grooves, the Görtler streaks keep more regular even at the end of the model. In addition, the skin friction coefficient is reduced efficiently. Furthermore, the wall-normal and spanwise velocity shear are both reduced, suppressing growths of secondary instabilities. In conclusion, grooves can delay Görtler vortex-induced transition by modifying the Görtler streaks structure and instability, which would shed light on hypersonic boundary layer transition control.

Experimental study on the hypersonic boundary layer transition induced by tandem cylinders

The flow field structure and heat flux distribution around an isolated cylinder and tandem cylinders on a flat plate at different angles of attack (AoA) and inflow conditions are investigated in a Mach 6 low-noise wind tunnel, using nano-tracer-based planar laser scattering (NPLS) techniques and the temperature sensitive paint (TSP) technique. The results reveal that, first, at AoA = 10°, the downstream cylinder will cause a horseshoe vortex formed by the upstream cylinder, which originally propagates parallel to the downstream, to expand to both sides. Subsequently, when the number of cylinders increases, the spanwise width of the affected area is increased further. In addition, a low-heat flux region caused by the recirculation region appears behind the cylinder; downstream of the low-heat flux region, the heat flux distribution of the isolated cylinder model forms a parallel stripe structure, while in the tandem cylinder model, it resembles a “Λ-shaped” distribution. A second key finding is that, with the decrease in AoA, the region of influence of the cylinder decreases. Moreover, the “Λ-shaped” heat flux structure in the wake of the downstream tandem cylinders gradually disappears, and the stripe structure near the second cylinder is in a “shuttle-shaped” distribution. Notably, with the increase in the spacing between the two tandem cylinders, the spanwise width of the “shuttle-shaped” distribution increases. The low-heat flux area behind the second cylinder initially increases with an increase in the spacing, but when the spacing is too large, a high-heat flux stripe begins to appear in the centre of the low-heat flux region. In addition, placing a third cylinder on the wake centreline of the tandem cylinder has a slight impact on the flow, but its effect is enhanced when the third cylinder is located outside the recirculation region of the tandem cylinder.

Experimental Investigation of the Hypersonic Boundary-Layer Transition Induced by the Wall-Mounted Cylinder

The flowfield structure, heat flux distribution, and pressure fluctuations of the wall-mounted cylinder-induced hypersonic boundary-layer transition are investigated at a 10 deg angle of attack. Experiments are conducted in a Mach 6 low-noise wind tunnel using the nanotracer-based planar laser scattering (NPLS) technique, temperature-sensitive paints (TSP), and high-frequency pressure sensors. First, the streamwise and spanwise NPLS images, TSP results, and power spectral density results of isolated cylinders at different heights show that with the increase of the cylinder height , the size of the separated region and the spanwise width of the horseshoe vortex increase, and the transition moves forward. Second, the flowfield structure and wall heat flux distribution around the streamwise cylinder arrays are investigated. The results demonstrate that the downstream cylinder will destroy the development of the hairpin vortex in the upstream cylinder wake but will expand the horseshoe vortex to both sides, increasing the influence area of the cylinder.

Improvement of transition prediction model in hypersonic boundary layer based on field inversion and machine learning framework

The classical four-equation γ−Reθ transition model has presented excellent accuracy in low-speed boundary layer transition prediction. However, once the incoming flow reaches hypersonic speed, the original model is no longer applicable due to the compressibility problem and the appearance of multiple instability modes. Recently, there has been widespread interest in data-driven modeling for quantifying uncertainty or improving model prediction accuracy. In this paper, a data-driven framework based on field inversion and machine learning is performed to extend the prediction capability of the original γ−Reθ transition model for the hypersonic boundary layer transition. First, the iterative regularized ensemble Kalman filter method is applied to obtain the spatial distribution of the perturbation correction term β for the switching function Fonset1, and the effectiveness of this method is initially verified in the hypersonic flat plate case. Then, the random forest algorithm is adopted to construct a mapping from the average flow features to β. The generalizability of the well-trained learning model is fully validated in the blunt cone cases with different unit Reynolds numbers, free-stream flow temperature, and bluntness. The simulation results indicate that the performance of the original γ−Reθ transition model in the hypersonic boundary layer transition prediction is significantly improved, and the boundary layer transition onset location and the length of transition zone can be correctly obtained. In addition, the machine learning model investigates the importance of the input features and confirms that the effective length scale plays a significant role in the numerical simulation of the hypersonic boundary layer transition.

Wall temperature effects on the hypersonic boundary-layer transition over an inclined, blunt cone

Wall temperature is a crucial factor for the transition of hypersonic boundary layers. This paper investigates the wall temperature effects on the hypersonic boundary-layer transition over an inclined blunt cone with two wall temperatures by direct numerical simulations and instability analysis. The breakdown processes of leeward streamwise vortices and crossflow vortices are both studied. Inner modes with lower phase velocities and outer modes with higher phase velocities are responsible for the breakdown of leeward streamwise vortices, respectively, in cooled- and heated-wall cases. A higher wall temperature will promote the boundary layer transition in the vicinity of the leeward centerline due to the collision of nearby crossflow vortices with the leeward mushroom structure, instead of by destabilizing inner and outer modes. In the crossflow-dominated region, the transition is triggered by the interaction between second modes and crossflow vortices for the cooled-wall case. Increasing the wall temperature will promote the transition in this region even though second modes are suppressed.