Hypersonic Boundary Layer Transition Research Articles

Dynamic large-eddy simulation of hypersonic transition delay over broadband wall impedance

Three-dimensional numerical simulations of hypersonic boundary layer transition delay due to porosity representative of carbon-fibre-reinforced carbon-matrix ceramics (C/C) were carried out on a 7 $^{\circ {}}$ half-angle cone for unit Reynolds numbers $Re_m=2.43 \times 10^6$ – $6.40\times 10^6\ \text {m}^{-1}$ , at the free-stream Mach number $M_\infty =7.4$ , for both sharp and 2.5 mm nose tip radii. A broadband time-domain impedance boundary condition was used to model the acoustic effects of the porous surface on the flow field. A quasi-spectral sub-filter-scale dynamic closure was adopted to stabilize the computations upon turbulent breakdown under extreme cooling conditions, with wall-to-adiabatic temperature ratio of $T_{w}/ T_{ad} \simeq 0.08 $ , while accurately recovering the growth rates of the unstable modes present in the early transition stages. Good agreement is observed with the reference experimental data, both in terms of the predicted extent of the transition delay and the measured second-mode frequency spectrum. The latter is strongly modulated by the formation of near-wall low-temperature three-dimensional streaks. Pressure disturbances concentrate in corridors of locally thickened boundary layer, with frequencies lower than what predicted by linear theory. Here, trapped wavetrains are formed, which can persist long into the turbulent region. Finally, it is shown that the presence of a porous wall simply shifts the onset of turbulence downstream, without affecting its structure.

Local-Variable-Based Transition Model for Hypersonic Flows Considering Wall Mass Injection

Pyrolysis gas injection during the ablation process will affect the hypersonic boundary-layer transition. This paper proposes a three-equation γ-Reθ-fb transition model that considers wall mass injection. First, the boundary conditions of wall mass injection are established and verified. Second, based on analysis of the compressible boundary-layer solutions under wall mass injection, new transition correlations are developed. This allows an injection factor transport equation to be constructed using strictly local variables, and this equation is coupled with the γ-Reθ transition model. Additionally, to model the wall mass injection effects in the fully turbulent zone, the wall boundary conditions for the specific turbulence dissipation rate are amended. The results of numerical simulations show that the transition onset locations and the changes in the heat transfer rate are reasonably consistent with experimental data.

Interaction of second-mode instability and distributed roughness elements in the hypersonic boundary layer over a sharp cone

The ablation of the thermal protection system (TPS) on the aircraft surface generates distributed roughness elements (DRE), which is expected to affect the hypersonic boundary-layer instability seriously. This work presents the experimental investigation of hypersonic boundary-layer instability waves on a 7° half-angle sharp cone with DRE allocated downstream of synchronization point at 0° angle of attack using surface flush-mounted pressure sensors, focused laser differential interferometer (FLDI), infrared thermography and schlieren technique. The experimental results showed that when the DRE (lower than the local boundary-layer height) was located downstream of the synchronization point, the Mack second mode still dominate the boundary-layer instability, and the transition onset was not significantly affected by DRE at various Reynolds numbers. Based on further analysis in the region downstream of roughness, the DRE didn't influence the nonlinear interaction among instability waves materially, although it promoted the growth of instability waves compared with the smooth case. However, the nonlinear interactions were decaying adjacent to the DRE, as the Mack second-mode instability waves cannot penetrate into the separation bubble because of the flow separation induced by the DRE. The FLDI measurement along the wall-normal direction revealed the second-mode instability waves were suppressed close to the wall by the complex roughness surface at the DRE region, and also confirmed the existence of second-mode instability waves at these streamwise locations. The evolution of instability waves followed the linear stability theory (LST), despite the existence of complex wall surfaces. This work enriches the understanding of the effect of DRE on hypersonic boundary-layer transition and demonstrates the spatial characteristics of instability waves above the complex surface.

Development of the BOLT-2 Roughness Experiment for Flight

A sounding rocket research flight called BOLT-2, which stands for Boundary Layer Turbulence 2, was initiated with the goal of studying hypersonic boundary-layer transition and turbulence. The BOLT-2 research vehicle is based on a three-dimensional geometry with concave surfaces and swept leading edges that provides two separate and distinct, also redundant, flowpaths for conducting measurements. One side of BOLT-2 is dedicated to smooth surface transition and turbulence, to better study the natural instability processes, whereas the other has been assigned to study forced transition and turbulence using discrete roughness trips. The present paper is intended to document the primary drivers and decisions made that lead up to finalizing the roughness-side experiment for the BOLT-2 flight.

Experimental study on influences of steps on hypersonic boundary layer transition at different angles-of-attack

Experimental study on influences of steps on hypersonic boundary layer transition at different angles-of-attack

Amplification factor transport equation modelling of Mack mode disturbances in hypersonic boundary layers

In the hypersonic boundary layer, the streamwise instability modes are mainly the Mack first mode and the Mack second mode. After the Mach number exceeds 4.0, the Mack second mode becomes the dominant instability mode for boundary layer transition. Currently, there is no complete analytical method to establish an amplification factor transport equation for the second mode. In order to improve the application of the amplification factor transport (AFT) model in hypersonic boundary layer transition prediction, this paper employs boundary layer similarity solutions to conduct stability analysis on the second mode and introduces a function to calculate the growth rate of disturbances. Additionally, a transport equation for the amplification factor of the second mode is formulated. For the non-local variables appearing in the equation, a local calculation method is provided. Combined with the intermittency factor transport equation, a transition prediction model for the second mode is formed. Hypersonic flat plate, wedge, and flared wedge are selected for model validation. The computed results show good agreement with standard stability analysis or experimental results, demonstrating the rationality of the transition model and its high prediction accuracy and reliability.

Controlling hypersonic boundary layer transition with localized cooling and metasurface treatments

This study investigates a novel method to control hypersonic boundary layer transition using a combined local cooling and local metasurface treatment. The method’s effectiveness was investigated on a 5-degree half-angle blunt wedge with a nose radius of 0.0254 mm at a freestream Mach number of 6.0 using direct numerical simulations and linear stability theory. We explored four cases: (i) adiabatic baseline case, (ii) locally cooled case, (iii) local metasurface case, and (iv) combined local cooling-local metasurface case. Results showed that the combined local cooling-local metasurface treatment significantly reduced both wall pressure disturbance amplitude and the density perturbation amplitude around the sonic line, indicating a potential for controlling hypersonic boundary layer transition. In the local cooling-local metasurface case, the disturbance amplitude at the end of the computational domain was 270 times lower than the baseline case. The study also examined the impact of Reynolds numbers, ranging from 25.59 million per meter to 32.80 million per meter. Unsteady simulations revealed that the Reynolds number had a negligible effect on the local cooling-local metasurface performance, indicating that the proposed method applies to a wide range of flight conditions.

Centralized gradient-based reconstruction for wall modeled large eddy simulations of hypersonic boundary layer transition

In this study, we introduce a robust central Gradient-Based Reconstruction (GBR) scheme for the compressible Navier-Stokes equations. The method leverages transformation to characteristic space, allowing selective treatment of waves from the compressible Euler equations. By averaging left- and right-biased state interpolations, a central scheme is achieved for all but the acoustic waves, which require upwinding for stability. Distinct differences were observed between transformations using either primitive or conservative variables. We evaluated the method's robustness and superiority using benchmark problems, including the two-dimensional shock entropy problem, two-dimensional viscous shock tube, and three-dimensional inviscid Taylor-Green vortex. Subsequently, we assessed the method in the context of Wall Modeled Large Eddy Simulations (WMLES), where coarse grids are used to reduce computational cost but also introduce substantial numerical dissipation. Using WMLES, we simulated oblique shock impingement on a Mach 6 disturbed boundary layer and a Mach 7.7 flow over a 15∘ compression ramp. Our findings reveal that: 1) transformation to characteristic space using conservative variables leads to more accurate results; 2) minimizing numerical dissipation through centralized interpolation is crucial. In the compression ramp case, boundary layer separation was shifted slightly upstream, and there was an over-prediction of wall heating, likely attributable to the equilibrium-assuming wall model. Overall, this work showcases the method's potential in accurately capturing complex flow dynamics with reduced numerical dissipation.

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.

Effect of wall-seeping gas film under different working media on stability of conical hypersonic boundary layer

Wall-seeping gas film (WSGF) is a promising method of controlling hypersonic boundary layer transition and reducing friction drag and heat transfer. Experiments are conducted in a Mach 6 hypersonic quiet wind tunnel by using nano-tracer planar laser scattering (NPLS) and high-frequency fluctuating pressure measuring technique. This work investigates the effects of wall-seeping helium, air, and carbon dioxide gas films under identical volume flow rate condition on conical boundary layer thickness, disturbance wave structure, wavelength, frequency, amplitude, and nonlinear interaction. The experimental results reveal that the WSGF significantly thickens the hypersonic boundary layer, with the thickest position appearing at the downstream boundary of the seeping zone. The boundary layer thickness is thinnest for helium gas film but thickest for carbon dioxide gas film. Generally, air gas film and carbon dioxide gas film induce the regular, rope-like, and interlaced second-mode waves to appear in advance in the boundary layer. However, under a higher volume flow rate for carbon dioxide gas film, the disturbance wave structure resembles interface fluctuations, with a characteristic wavelength of approximately 18 mm and a peak frequency as low as about 35 kHz, but no the rope-like interlaced characteristic. At this time, the influence of shear layer instability becomes significant. The disturbance waves do not exhibit second-mode wave characteristics for wall-seeping helium gas film, whose shape is irregular and undergoes deformation with time and space. Additionally, the power spectral density of wall fluctuating pressure exhibits insignificant variation with volume flow rate and flow direction, which is similar to the characteristic of power spectral density in the laminar boundary layer and has no peak frequency. The wavelength of second-mode waves is about 2－3 times the boundary layer thickness for air gas film, and increases to more than 3 times for carbon dioxide gas film. The application of carbon dioxide gas film results in smaller peak frequency and bandwidth of disturbance wave, larger characteristic wavelength and amplitude, longer propagation distance, and stronger nonlinear interaction than the application of air gas film. In the future, attention should be paid to understanding disturbance wave characteristics in the boundary layer for the helium gas film and shear layer instability under larger volume flow rates.

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.