Interaction Of Shock Wave Research Articles

Simulation of High-Enthalpy Turbulent Shock Wave/Boundary Layer Interaction Using a RANS Approach

In the era of space exploration, the scientific community is strongly focusing on the analysis of hypersonic flows in the presence of shock wave/boundary layer interaction. In these conditions, the flow field presents a complex shock structure due to the interaction of different shock waves with the boundary layer. The strong adverse pressure gradient makes the boundary layer separate, giving rise to a separation bubble. In the reattachment zone, the temperature can reach very high values, inducing thermochemical non-equilibrium effects. This research field is recently achieving more and more relevance in aerospace research, as the analysis of turbulent shock wave/boundary layer interaction so far has been mainly focused on perfect gas flows. In this manuscript, a Reynolds averaged Navier–Stokes (RANS) approach is considered, the shear stress transport (SST) model being coupled with the multitemperature approach proposed by Park to investigate thermochemical non-equilibrium effects in hypersonic turbulent shock wave/boundary layer interaction. The first part of the manuscript is devoted to the validation of the solver, and results for low enthalpy flat plate and compression ramp flows are presented. The numerical results are shown to be in good agreement with numerical solutions and experimental measurements. Afterward, the free stream conditions are modulated to make non-equilibrium relevant and analyze a reacting flow.

Wall pressure fluctuations in wall heated and cooled shock wave and turbulent boundary layer interactions

Wall pressure fluctuations in shock wave and turbulent boundary layer interactions on heated and cooled walls are investigated by performing direct numerical simulations. The objectives of this study are to identify flow dynamics causing low- and high-frequency wall pressure fluctuations and evaluate wall heating and cooling effects on the wall pressure fluctuations. The wall pressure spectra highlight two characteristic low-frequency spectral peaks at the separation point and below the expansion waves. Conditional analysis reveals that the two spectral peaks originate from the oscillations of the reflected shock and expansion waves, coupled with the expansion and contraction motions of the separated turbulent shear layer. Regarding wall temperature effects, wall cooling enhances the magnitude of the wall pressure fluctuations regardless of the low- and high-frequency components. Furthermore, influences of the expansion waves are also enhanced by wall cooling, which increases the wall pressure fluctuations locally after the separation.

Interaction of shock wave with closed cell foams: Effect of foam material, microstructure, and specimen configuration

This article discusses the experimental investigation of the dynamic mechanical behavior of polyethylene (PE) foam under shock wave loading. The experiments were conducted using a two-stage light shock tube, and the dynamic response of the foam was characterized by measuring the pressure wave transmitted through the foam and the load on the foam specimen using a pressure sensor and a load cell, respectively. High-speed imaging was also used to capture the deformation of the foam specimen during the shock loading. The results show that the deformation of the foam under shock wave loading is non-uniform along the length of the specimen and is influenced by the presence of metal plates inserted along the length of the foam specimen. The degree of compression of the foam specimen was quantified and found to depend on the number of segments and the presence of metal caps on the specimen. The results provide insight into the mechanical behavior of PE foam under dynamic loading conditions and can be useful for designing protective structures for impact and blast resistance applications.

Optimization of Johnson-Cook Constitutive Model Parameters Using the Nesterov Gradient-Descent Method.

Numerical simulation of impact and shock-wave interactions of deformable solids is an urgent problem. The key to the adequacy and accuracy of simulation is the material model that links the yield strength with accumulated plastic strain, strain rate, and temperature. A material model often used in engineering applications is the empirical Johnson-Cook (JC) model. However, an increase in the impact velocity complicates the choice of the model constants to reach agreement between numerical and experimental data. This paper presents a method for the selection of the JC model constants using an optimization algorithm based on the Nesterov gradient-descent method. A solution quality function is proposed to estimate the deviation of calculations from experimental data and to determine the optimum JC model parameters. Numerical calculations of the Taylor rod-on-anvil impact test were performed for cylindrical copper specimens. The numerical simulation performed with the optimized JC model parameters was in good agreement with the experimental data received by the authors of this paper and with the literature data. The accuracy of simulation depends on the experimental data used. For all considered experiments, the calculation accuracy (solution quality) increased by 10%. This method, developed for selecting optimized material model constants, may be useful for other models, regardless of the numerical code used for high-velocity impact simulations.

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

AbstractThe mathematical description of localized solitons in the presence of large‐scale waves is a fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear optics, and condensed matter physics. Here, the evolution of a soliton as it interacts with a rarefaction wave or a dispersive shock wave, examples of slowly varying and rapidly oscillating dispersive mean fields, for the Korteweg–de Vries equation is studied. Step boundary conditions give rise to either a rarefaction wave (step up) or a dispersive shock wave (step down). When a soliton interacts with one of these mean fields, it can either transmit through (tunnel) or become embedded (trapped) inside, depending on its initial amplitude and position. A topical review of three separate analytical approaches is undertaken to describe these interactions. First, a basic soliton perturbation theory is introduced that is found to capture the solution dynamics for soliton–rarefaction wave interaction in the small dispersion limit. Next, multiphase Whitham modulation theory and its finite‐gap description are used to describe soliton–rarefaction wave and soliton–dispersive shock wave interactions. Lastly, a spectral description and an exact solution of the initial value problem is obtained through the inverse scattering transform. For transmitted solitons, far‐field asymptotics reveal the soliton phase shift through either type of wave mentioned above. In the trapped case, there is no proper eigenvalue in the spectral description, implying that the evolution does not involve a proper soliton solution. These approaches are consistent, agree with direct numerical simulation, and accurately describe different aspects of solitary wave–mean field interaction.

Energy transformations accompanying a shock wave distortion and disappearance during the interaction with thermally stratified plasma

The results of experiments and numerical simulations of the interaction of a plane shock wave with an area of ionization strata formed by a glow gas discharge are presented. For the experimentally obtained phenomena transformations of kinetic and internal energy have been studied numerically using Euler and Navier-Stokes approaches under the assumption that ionization unstable plasma has stratified gas temperature. Energy transfer between a region of layered energy deposition and heated gas zone behind the shock wave was considered. It has been established that a layered energy deposition can provide the distortion and destruction of a shock wave front and in addition, to create a lot of zones with higher internal and kinetic energy beyond it. These phenomena were shown to be connected with generation in many points of the Richtmyer-Meshkov instability resulting from the interaction of thermal strata with a front of the shock wave.

Numerical investigation of the interaction between a converging shock wave and an offset cylindrical bubble containing different gases

A numerical study investigating the interaction process between a converging shock wave and a gas bubble placed at an offset location is presented. As a first step, for proofing the reliability of the used numerical scheme, a simulation of relevant available experimental findings of Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000] is conducted; the tested gases were helium (He) and sulfur hexafluoride (SF6). The converging shock wave had a Mach number of 1.18 prior to its impact on the 50 mm diameter gas bubble. Achieving good agreement with the experimental findings ensures the reliability of the applied numerical scheme. After the converging shock wave impacted the gas bubble, different shock waves are created. These shock waves propagate differently than those observed in the case of planar shock wave impacting a cylindrical gas bubble or that of a converging shock wave where the gas bubble is located at the center. Furthermore, once the converging shock wave converged, a diverging shock wave expands and again impacts the remaining gas bubble, thus creating more complex shock wave patterns. The gas contained inside the bubble has an effect on the location of the converging shock wave focus point. In the case of the heavy gas SF6, the focus point is near the center of the converging shock wave, but in the case of light gas He, it is offset from the converging shock wave focus point and outside of the initial location of the He bubble. The new results from the current numerical simulation include more detailed results for both bubbles, which were not reported in Hosseini and Takayama [“Richtmyer–Meshkov instability induced by cylindrical shock wave loading of cylindrical gaseous inhomogeneities,” AIAA Paper No. 2000-2464, 2000] and Hosseini and Takayama [“Study of a converging shock wave interaction with a gaseous interfaces in an eccentric arrangement,” in Japanese Symposium on Shock Waves, 2000]. In addition, a shock wave focusing of the transmitted shock wave inside the SF6 bubble is observed. This later creates a secondary diverging shock wave. Higher pressure is achieved in the SF6 case.

Experimental investigation of nanosecond laser-induced shock waves in water using multiple excitation beams.

Revealing the expansion and interaction dynamics of multiple shock waves induced by a nanosecond laser is important for controlling laser surgery. However, the dynamic evolution of shock waves is a complex and ultrafast process, making it difficult to determine the specific laws. In this study, we conducted an experimental investigation into the formation, propagation, and interaction of underwater shock waves that are induced by nanosecond laser pulses. The effective energy carried by the shock wave is quantified by the Sedov-Taylor model fitting with experimental results. Numerical simulations with an analytic model using the distance between adjacent breakdown locations as input and effective energy as fit parameters provide insights into experimentally not accessible shock wave emission and parameters. A semi-empirical model is used to describe the pressure and temperature behind the shock wave taking into account the effective energy. The results of our analysis demonstrate that shock waves exhibit asymmetry in both their transverse and longitudinal velocity and pressure distributions. In addition, we compared the effect of the distance between adjacent excitation positions on the shock wave emission process. Furthermore, utilizing multi-point excitation offers a flexible approach to delve deeper into the physical mechanisms that cause optical tissue damage in nanosecond laser surgery, leading to a better comprehension of the subject.

Experimental and Numerical Study on Perforated Plate Mitigation Capacity to Near-Field Blasts.

Based on the analysis of existing collective shockwave protection methods worldwide, this paper addresses the mitigation of shock waves by means of passive methods, namely the use of perforated plates. Employing specialized software for numerical analysis, such as ANSYS-AUTODYN 2022R1®, the interaction of shock waves with a protection structure has been studied. By using this cost-free approach, several configurations with different opening ratios were investigated, pointing out the peculiarities of the real phenomenon. The FEM-based numerical model was calibrated by employing live explosive tests. The experimental assessments were performed for two configurations, with and without a perforated plate. The numerical results were expressed in terms of force acting on an armor plate placed behind a perforated plate at a relevant distance for ballistic protection in engineering applications. By investigating the force/impulse acting on a witness plate instead of the pressure measured at a single point, a realistic scenario can be considered. For the total impulse attenuation factor, the numerical results suggest a power law dependence, with the opening ratio as a variable.

WITHDRAWN: Effets synergiques des concentrés plaquettaires autologues et des ondes de choc extra-corporelles dans le traitement des pseudarthroses aseptiques diaphysaires des os longs

IntroductionUnion of long bone fractures is a complicated biological mechanism affected by numerous systemic and local variables. Disruption of any of these components may result in fracture nonunion. There are various types of clinically available treatment strategies for aseptic nonunion. Both activated platelet plasma and extracorporeal shock waves play important roles in fracture healing. This study aimed to investigate the interaction of Platelet-rich plasma (PRP) and extracorporeal shock wave (ESW) in bone healing of nonunion. HypothesisPRP and ESW have synergistic effects in treating long bone nonunion. MethodsBetween January 2016 and December 2021, a total of 60 patients with established nonunion of a long bone (18 tibias, 15 femurs, 9 humerus, 6 radii, and 12 ulnae) were included in this study, comprising 31 males and 29 females, ranging from 18 to 60 years old. Patients with bone nonunion were separated into two groups: PRP alone (Monotherapy group) and those treated with PRP combined with ESW (Combined treatment group). The two groups were compared to assess the therapeutic benefits, callus development, local problems, bone healing time, and Johner Wruhs functional classification of operated limbs. ResultsFifty-five patients were followed up, 5 patients were lost to follow-up, two in the PRP group and three in the PRP+ESW group, the follow-up time varied from 6 to 18 months, with an average of 12.7±5.2months. At 8, 12, 16, 20, and 24weeks following intervention, the callus score in the monotherapy group was significantly lower than in the combined treatment group (p<0.05). Both groups had no swelling and infection in the soft tissue of the nonunion operation site. In the PRP+ESW group, the fracture union rate was 92.59 % and the healing time was 16.3±5.2 weeks. In the PRP group, the fracture union rate was 71.43 % and the healing time was 21.5±3.7 weeks. The clinical healing time of the monotherapy group was significantly longer than the combined treatment group (p<0.05). All the nonunion patients with no signs of healing were treated with revision surgery. The excellent and good rate of Johner-Wruhs functional classification of affected limbs in the monotherapy group was significantly lower than in the combined treatment group (p<0.05). ConclusionPRP combined with ESW has a certain synergistic effect in treating aseptic nonunion after fracture surgery. It can significantly improve the formation of new bone, it is a minimally invasive and effective strategy to treat aseptic nonunion in a clinical setting. Level of evidenceIII, retrospective, single-centre, case-control study.

Microramp wake impinging on canonical shock/boundary-layer interaction

We analyze the influence of microramp vortex generators (mVGs) on a canonical oblique shock wave/turbulent boundary-layer interaction (SBLI) in terms of mean flow field and unsteady dynamics. The flow configuration of our wall-resolved large-eddy simulations (LES) reproduces the experiment of Bo et al. [“Experimental investigation of the micro-ramp based shock wave and turbulent boundary-layer interaction control,” Phys. Fluids 24, 055110 (2012)]: a rake of microramps is inserted upstream of the SBLI, protruding by 0.476δ in a turbulent boundary layer (TBL) at free-stream Mach number M = 2.7 and corresponding to a Reynolds number based on the displacement thickness of Reθ=3600. The long integration time of 1672 Lsep/U∞ allows an accurate characterization of the low-frequency dynamics of the SBLI under the influence of the microramps. With respect to the reference SBLI without control devices, the mean flow field shows a new spatial organization of the recirculation bubble due to the mVGs' wake. The alternating high and low-speed zones in the near-wall region of the incoming TBL, induced by the counter-rotating streamwise vortices generated by the mVGs, trigger spanwise corrugations of the separation and reattachment lines and locally alter the reverse flow region. Tornado-like vortices are found in the vicinity of these zones, yielding a new fluid collection mechanism of the reverse flow region. These vortices redirect the fluid coming from regions outside of the wake in the incoming TBL to three key spanwise exit locations located in between the mVGs and at their centerline. Interestingly, power spectral densities of wall-pressure probes show a damping of the low-frequency dynamics of the reflected shock foot for spanwise stations aligned with the mVGs' wake, whereas this activity appears to be reinforced in the planes located in between the mVGs. However, we found no evidence of unsteady forcing linked to the high-frequency shedding of the coherent structures developing in the wake of the microramps. Dynamic mode decomposition highlights a significant change in the low-frequency dynamics, mostly affecting the mass budget of the recirculation bubble. The breathing of the recirculation zone that occurs at StL=0.1 for the SBLI without control devices (with StL=fLsep/U∞) appears to shift toward a lower frequency of StL=0.05. Remembering that the reflected shock foot motion is related to frequencies in the range StL=[0.03−0.05], the SBLI with upstream mVGs seems to highlight a synchronization of this motion with the breathing of the separation bubble.

Structure of shock wave in tungsten and titanium metals by using navier-stokes equation

Using the Navier–Stokes equation, we present the structure of a one-dimensional stationary shock wave formed in condensed alloy materials such as tungsten and titanium. In this study, the shock wave structure in the mentioned materials has been analysed by using several important parameters such as material viscosity, the Mie-Gruneisen parameter, and Mach number (M). One of our derived results is shock thickness, which is found to be of the order of 10−6 meters. In addition, we address a number of key insights into the shock wave interaction with tungsten and titanium. It should be noted that the validity of the model discussed in this study is limited to high M values, i.e., M ≥ 2.0.

Baroclinic interaction of forced shock waves with random thermal gradients

Density gradients aligned at an angle to pressure gradients result in baroclinic torque in fluid flows, generating vorticity. In this work, we study the vorticity generated by the baroclinic torque exerted by the interaction of pressure jumps across random two-dimensional shock waves with density gradients. A field of random two-dimensional shock waves has acoustic spectral energy scaling as Êk∼ε2/3ℓ−1/3k−2, where k is the wavenumber, ε is the energy dissipation, and ℓ is the integral length scale of the field. Since the acoustic energy is broadband, pressure and velocity gradients exist in a wide range of length scales. We study the interaction of these broadband gradients with isobaric thermal gradients localized at a length scale in the spectral space. We show that the method of generating shock waves or injection of wave energy in the system governs the baroclinic interactions. For stochastically forced shock waves, baroclinic terms are negligible. Broadband vorticity with energy at least two orders of magnitude smaller is generated due to continuous variation in curvature of shock waves caused by stochastic forcing. On the other hand, shock waves maintained by energy rescaling result in the generation of coherent vorticity. We also discuss the relative magnitude of the baroclinic torque generated due to total density gradients compared to the one generated due to non-isentropic density gradients within the shock waves interacting with the pressure gradients.

On the propagation and interaction of ion-acoustic solitary, periodic, shock, and breather waves in a non-Maxwellian electron–positron–ion magnetoplasma

This investigation analyzes the propagation of nonlinear ion-acoustic waves (IAWs) in an unmagnetized, collisionless plasma composed of inertial positive ions and inertialess Maxwellian positrons as well as the inertialess non-Maxwellian electrons that obey (r, q)-distribution. To observe the impact of particle trapping on the nonlinear IAWs in an electron–positron–ion plasma, the Korteweg–De Vries (KdV) and modified KdV (mKdV) equations are derived using a reductive perturbation method. In the distribution function, the spectral parameters (r, q) put up their contribution to the flatness and high-energy tails, respectively. An important aspect of this investigation is the determination of well-known quasi-periodic solutions, multi-soliton solutions, breathers, and shocks under the variation of different physical parameters, especially spectral indices (r, q). Finally, the interaction of solitons is also presented for discussion of the complete profile. In addition, a detailed comparison, especially in a periodic wave, is made between the generalized (r, q)-distribution and the limiting cases of Kappa and Maxwellian distributions. The results presented in this study contribute to a better understanding of the characteristics of both high- and low-energy parts of the electron distribution function as well as the formation of periodic, soliton, multi-soliton, breathers, and shocks in space and astrophysical plasmas.

Ultrafast observation of multiple shock waves evolution and interaction processes in femtosecond laser processing

Revealing the expansion and interaction dynamics of multiple shock waves (SWs) induced by a femtosecond laser is important for controlling laser processing. However, the dynamics of SWs is a complex and ultrafast process, making it difficult to determine the specific laws that govern their evolution. In this study, we observed the various evolutionary and interaction processes of SWs generated by a femtosecond laser on fused quartz using pump–probe shadowgraphy. First, we discovered a time-invariant hemispherical plasma chamber (HPC) composed mainly of air plasma before the expansion of material SW, differing from other studies wherein the plasma chamber is usually not observed. Second, the coupling process between the plasma pressure waves (PPWs) and the material SW was studied. After the expansion of material SW, the front plasma of the HPC was ionized again, generating two PPWs in opposite directions and affecting the further expansion of material SW. Eventually, the material SW broke through the HPC and PPWs and evolved into a single SW that expanded continuously. Additionally, it was demonstrated that double pulses with different time delays could effectively control the SW coupling process and plasma evolution, thereby improving the laser-processing efficiency.

Influence of vehicle length on the aerothermodynamic environment of the Hyperloop

Hyperloop has received much attention as a futuristic mode of transportation because of its energy efficiency and high speed, among other advantages. The length of the capsule vehicle has essentially little influence on the distribution of the aerodynamic environment, but makes significant differences in the evolution of waves and in the fluctuations of pressure and temperature in the aerodynamic environment. This study employs fluid simulation to learn the aerothermodynamic effects of a capsule vehicle traveling in an evacuated tube of Hyperloop. Based on a validation of CFD simulations via wind-tunnel test measurements, a meshing strategy was designed to ensure that errors in the computational results were minimized. An axisymmetric model of the capsule vehicle was used to reduce computational costs. The results show that different capsule vehicle lengths affect the formation of pressure and temperature flow fields, boundary-layer thickness of the capsule-vehicle surface, and interference of shock waves and expansion waves in Hyperloop. As the vehicle length increased, the pressures at the vehicle head and tail gradually decreased, whereas the middle of the vehicle did not undergo this decrease in pressure. Inside the tube, the high temperature and pressure upstream of the vehicle head decreased slightly as the vehicle length increased. The temperature and pressure around the vehicle tended to increase, whereas at the tail of the vehicle, the pressure tended to decrease, and the temperature to increase. For short, medium and long vehicles, the shock waves were 1.06, 1.120, and 1.243 m, respectively, from the top of the tail, from which it is inferred that the flow separation point moved forward as the length of the vehicle increased. The wake widened as the length of the capsule vehicle increased. The boundary layer at the vehicle tail gradually thickened along the contour. Before separation, the maximum difference in boundary-layer thickness was able to reach 50.3 %, after separation, the difference decreased to a minimum of 8.8 %. The interaction (IE1) and reflection (RE2) of the expansion wave led to pressure decreases of 5.86 % and 4.07 %, respectively, whereas the interaction of shock wave (IS1) and reflection of shock wave (RS1) led to pressure decreases of 4.15 % and 3.67 %, respectively. The interaction had a greater effect on the Hyperloop flow field than that of the reflection.

Study of jet tabs in 2D convergent–divergent nozzle for thrust vectoring in aerial vehicles

PurposeIn this study, 2D density-based SST K-turbulence model with compressibility effect is used to observe the flow separation and shock wave interactions of the flow. The wall static pressure and Mach number differences are also evaluated. This study aims to discuss the aforementioned objectivesDesign/methodology/approachThis study outlines the evaluation of the performance of a 2D convergent–divergent nozzle with various triangular jet tab configurations that can be used for effective thrust vectoring of aerial vehicles.FindingsFrom the study, it is seen that the shadow effect induced by the tab with a height of 30% produces higher oblique wave deflection and higher thrust deflection at the exit nozzle. The numerical calculation concluded that thrust vector efficiency of 30% jet tab is, 0.46%. In the case of 10% jet tab height the thrust vector efficiency is higher, i.e. 1.647%.Research limitations/implications2D study.Practical implicationsThe optimization will open up a new focus in TVC that can be implemented for effective attitude control in aircrafts.Social implicationsUsed in future aircrafts.Originality/valueThe influence of shadowing ratio with different tab heights at different Mach numbers has not been reported in the previous studies. Few of the studies on jet tab are focused on the acoustic studies and not pertaining to the aerodynamic aspects. The multi jet configuration, the combination of location, shapes and other parametric analysis have not been covered in the previous studied.

Shock impingement on a transitional hypersonic high-enthalpy boundary layer

Shock-wave boundary layer interactions are of utmost importance for both aeronautical and aerospace applications. The dynamics of high-speed compressible turbulent boundary layers becomes tightly coupled with strong gradients of thermodynamic properties, leading to an increase of thermomechanical loads. In the contextual presence of hypersonic and high-enthalpy regimes, thermochemical nonequilibrium effects must be considered as well. This work is a first step toward the fundamental understanding of this configuration.

KdV breathers on a cnoidal wave background

Using the Darboux transformation for the Korteweg–de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character, these wave patterns are referred to as breathers. Both elevation (bright) and depression (dark) breather solutions are obtained. The nonlinear dispersion relations demonstrate that the bright (dark) breathers propagate faster (slower) than the background cnoidal wave. Two-soliton solutions are obtained in the limit of degeneration of the cnoidal wave. In the small amplitude regime, the dark breathers are accurately approximated by dark soliton solutions of the nonlinear Schrödinger equation. These results provide insight into recent experiments on soliton-dispersive shock wave interactions and soliton gases.

Amplification of turbulent kinetic energy and temperature fluctuation in a hypersonic turbulent boundary layer over a compression ramp

In this paper, direct numerical simulations in a Mach 6.0 hypersonic turbulent boundary layer over a 30 ° compression ramp are performed. The influence of shock wave/boundary layer interactions on the amplification of turbulent kinetic energy (TKE) and temperature fluctuation (TF) is explored, to provide an insight into the physical mechanism. In the initial part of the interaction region before the detachment of the shear layer, the amplification of the TKE and TF is found, via a frequency spectrum analysis, to be closely related to the low-frequency unsteadiness of the shock wave. Once the free shear layer is established, the shear component of the TKE production defined in the shear layer coordinate appears to act as the main contributor for the TKE amplification, owing to the mixing layer turbulence and the resultant Kelvin–Helmholtz instability. This is consistent with the result from the spectrum analysis that the TKE and TF amplification and their streamwise evolution are dominated by the spectral energy in the median-frequency range, arising from the mixing layer turbulence. As the flow moves downstream along the shock wave, the high-frequency spectral energy content of TF shows a decreasing trend, while the low-frequency spectral energy tends to increase gradually, implying that the shock wave low-frequency unsteadiness exists not only in the initial stage of the interaction region but also around the main shock wave. Under the combined influence of the shock wave intensity and interaction intensity, the median-frequency content appears to weaken first and then tends to increase before decreasing again. The variation amplitude appears to be small and generally dominates the distribution of the TF intensity.