Shock Oscillations Research Articles

Shock buffet onset prediction with flow feature-informed neural network

Transonic shock buffet is a significant self-excited shock oscillations and aerodynamic instability phenomenon induced by shock-boundary layer interaction, which limits the flight envelope and even causes flight accidents. The aviation industry has a significant interest in accurately predicting the shock buffet onset boundary, defined by a specific combination of Mach number and angle of attack. While the current methods of steady and unsteady numerical simulation suffer from a contradiction of efficiency and accuracy. In the current paper, a flow feature-informed neural network (FINN) model is constructed to predict the buffet onset boundary over airfoils. Typical features associated with buffet onset are extracted from the steady base flow and subsequently integrated into the hidden layer of the neural network to impose physical constraints. With the test cases of the NACA0012 airfoil at various Mach numbers, the FINN model can accurately predict the damping representing the unsteady instability margin. Compared to the direct mapping input-output neural network (NN) model, the proposed method with shock wave feature-informed has enhanced accuracy, with an average relative error decreased by 70% at extrapolated Mach numbers. This research demonstrates the effectiveness of the FINN model in predicting the buffet onset, which leverages physics features derived from the more economical steady solution far from the onset boundary at a given predicted Mach number.

Flowfield reconstruction in a supersonic isolator based on proper orthogonal decomposition and sensor compression coupling under variable Mach numbers

The supersonic inflow passes through the shock train in the isolator of the scramjet to complete deceleration and pressurization, followed by combustion and energy release, providing strong thrust. When the back pressure generated by combustion is disturbed forward, the location of shock train leading edge (STLE) will also change accordingly. Once it moves to the entrance of the isolator, it will cause unstart. Accurately detecting STLE in the isolator of a scramjet is crucial for controlling the shock train and preventing the inlet from unstart. Therefore, based on the sparse reconstruction of compressive sensing and sensor compression coupling, a supersonic flowfield reconstruction model (POD-STLE) based on proper orthogonal decomposition (POD) was constructed to reconstruct the supersonic flowfield and detect the location of STLE in the supersonic isolator. The experiments were conducted on the shock oscillation under variable Mach numbers and back pressures, to construct the experimental dataset. Combining supersonic flowfield reconstruction and matrix decomposition, different sensor layouts were constructed, which can ensure accuracy and stability while saving sensor resources. The POD-STLE was applied to the flowfield reconstruction of the supersonic isolator, and the location of STLE was detected under variable and constant conditions, ultimately achieving the expected reconstruction effect and detection accuracy. This study provides a new research method for detecting the location of STLE in the supersonic isolator of a scramjet and provides technical for exploring supersonic flowfield.

OpenSBLI v3.0: High-Fidelity Multi-Block Transonic Aerofoil CFD Simulations using Domain Specific Languages on GPUs

OpenSBLI is an automatic code-generation framework for compressible Computational Fluid Dynamics (CFD) simulations on heterogeneous computing architectures (previous release: Lusher et al, CPC (2021)). OpenSBLI is coupled to the Oxford Parallel Structured (OPS) Domain Specific Language (DSL), which uses source-to-source translation to enable parallel execution of the code on large-scale supercomputers, including multi-GPU clusters. To date, OpenSBLI has largely been applied to compressible turbulence and shock-wave/boundary-layer interactions on very simple geometries comprised of single mesh blocks with essentially orthogonal grid lines. OpenSBLI has been extended in this new release to target strongly curvilinear cases, including transonic aerofoils using multi-block grids. In addition to multi-block mesh support, more efficient numerical shock-capturing methods and filters have been added to the codebase. Improvements to post-processing, reduced-dimension data output, and coupling to a modal decomposition library are also included. A set of validation cases are presented to showcase the new code features. Furthermore, state-of-the-art wide-span transonic aerofoil simulations on up to N=2.5×109 grid points demonstrate that wider aspect ratios can alter buffet predictions and increase the regularity of the low-frequency shock oscillations by accommodating fully-developed trailing edge flow separation. Spectral Proper Orthogonal Decomposition (SPOD) analysis showed that overly-narrow aerofoil simulations contain additional domain-dependent energy content at a Strouhal number of St≈3 associated with wake modes.

The Unsteady Shock-Boundary Layer Interaction in a Compressor Cascade – Part 3: Mechanisms of Shock Oscillation

Abstract The shock-boundary layer interaction in transonic flows is known to cause strong unsteady flow effects that negatively affect the performance and operability of blade and cascade designs. Despite decades of research on the subject, little is still known about the physical mechanisms that drive the different oscillation frequencies observed with different designs. In the conclusion of this three-part series, the experimental and numerical data obtained with the Transonic Cascade TEAMAero are analyzed together in detail in order to test the main theories of continuous shock oscillation. This analysis exposes a main mechanism of shock oscillation, where pressure waves generated inside the passage of the cascade propagate upstream and interact strongly with the main shock when the latter is also in the passage. The interaction of these features causes a breakdown of the flow that is shown to propagate upstream, inevitably causing strong variations in the inflow angle and therefore on the operating conditions of the cascade. The high frequency content of these pressure waves is also shown to be responsible for weaker high-frequency variations of the shock movement throughout the cycle. Parallels are also drawn with previous experimental campaigns in order to search for a global understanding of the different observations made. Although various parts of the described interaction are not fully understood yet, and the dataset of experimental measurements compiled is still rather small, a good basis is provided on which to further study the underlying mechanisms of unsteady flows in transonic cascades.

Effect of Tripping and Domain Width on Transonic Buffet on Periodic NASA-CRM Airfoils

Transonic buffet is an instability characterized by shock oscillations and separated boundary layers. High-fidelity simulations have typically been limited to narrow domains to be computationally feasible, overly constraining the flow and introducing modeling errors. Depending on the boundary-layer state upstream of the interaction, different buffet features are observed. High-fidelity simulations (implicit large-eddy simulation) were performed on the periodic (infinite) NASA-CRM wing at a moderate Reynolds number to assess the sensitivity of the two-dimensional transonic buffet to boundary-layer state and domain width. Simulations were cross-validated against low-fidelity Reynolds-averaged Navier–Stokes (RANS)/unsteady RANS and global stability analysis, and excellent agreement was found near the onset. By varying the boundary-layer tripping amplitude, laminar, transitional, and turbulent buffet interactions were obtained. All cases consisted of a single shock and low-frequency oscillations (St≈0.07). The transitional interaction also exhibited reduced shock movement, a 15% increase in CL¯, and energy content at higher frequencies (St≈1.3). Spanwise domain studies showed sensitivity at the shock location and near the trailing edge. We conclude that the span width must be greater than the trailing-edge boundary-layer thickness to obtain span-independent solutions. For largely separated cases, the sensitivity to span width increased, and variations across the span were observed. This was found to be associated with a loss of two-dimensionality in the flow.

Synchronized shock wave and compliant wall interactions: Experimental characterization and aeroelastic modeling

The static and dynamic interaction of a normal shock wave (upstream Mach number 1.35) with a compliant wall is characterized experimentally by schlieren visualizations and an optical displacement sensor. Depending on the location of the shock wave along the compliant wall, three different regimes of interaction are found: large-amplitude synchronized regime, small-amplitude synchronized regime and unsynchronized regime. The regime of large-amplitude synchronized oscillations is found for shock locations close to the mid-point of the compliant wall along the streamwise direction; at this location, the coupled system locks to the second vibration frequency of the structure. Three regimes of small-amplitude synchronized oscillations are found depending on the shock position. When the shock is located upstream the center of the compliant wall, the shock may oscillate either periodically at the frequency of the first vibration mode or quasi-periodically with highest amplitudes at the three frequencies of the vibration modes. When the shock is located downstream the center of the compliant wall, the shock oscillates periodically at the frequency of the third vibration mode. Finally, close to the trailing edge of the compliant wall, the shock oscillation is not synchronized with the compliant wall which oscillates with a very small amplitude. An empirical model is proposed to investigate the energy exchange between the flow and the compliant wall during the limit cycle oscillations. A negative aerodynamic damping – and, hence, the possibility of a limit cycle – is observed when a sufficiently extended separation is considered in the model for the pressure distribution at the wall.

Alleviation of SWBLI over the payload of a launch vehicle by change of nose shape

Wind tunnel tests on a typical heavy-lift launch vehicle configuration featuring a core vehicle flanked by two strap-on boosters showed very high levels of unsteady pressures over the payload region at transonic Mach numbers when the nose had a cone-cylinder shape. This was due to very high levels of Shock Wave Boundary Layer Interactions (SWBLI) associated with the conical shape, which caused alternating flow featuring the formation of a unsteady λ-shock system over the payload region and a pair of counter-rotating vortices. The phenomenon was found to strongly depend on the proximity of the noses of the strap-on boosters to the boat tail downstream of the payload region. When the conical nose was replaced by an ogive-shaped nose, significant reduction in SWBLI occurred, with dramatic reduction of shock oscillations, pressure fluctuations, replacement of alternating flow by steady flow and disappearance of the vortex-pair. Time-averaged pressure fluctuations indicate reduction in pressure gradients due to a more gradual expansion of flow over the ogive nose compared to conical nose, an observation also supported by CFD simulations. The alleviation of SWBLI with ogive nose was so effective that the presence or absence of strap-on boosters had practically no effect on pressure fluctuations over the payload region. Unlike the conical shape, the ogive nose cone shape seems to meet both the shape and pressure parameter-criteria of NASA to ensure buffet-free environment.

Numerical study on ignition start-up process of an underwater solid rocket motor across a wide depth range

Solid rocket motors have important applications in the propulsion of trans-media vehicles and underwater launched rockets. In this paper, the ignition start-up process of an underwater solid rocket motor across a wide depth range has been numerically studied. A novel multi-domain integrated model has been developed by combining the solid propellant ignition and combustion model with the volume of fluid multiphase model. This integrated model enables the coupled simulation of the propellant combustion and gas flow inside the motor, along with the gas jet evolution in the external water environment. The detailed flow field developments in the combustion chamber, nozzle, and wake field are carefully analyzed. The variation rules of the internal ballistics and thrust performance are also obtained. The effects of environmental medium and operating depth on the ignition start-up process are systematically discussed. The results show that the influence of the operating environment on the internal ballistic characteristics is primarily reflected in the initial period after the nozzle closure opens. The development of the gas jet in water lags significantly compared with that in air. As the water depth increases, the ignition delay time of the motor is shortened, and the morphology evolution of the gas jet is significantly compressed and accelerated. Furthermore, the necking and bulging of the jet boundary near the nozzle outlet and the consequent shock oscillations are intensified, resulting in stronger fluctuations in the wake pressure field and motor thrust.

Proposing a physical mechanism to explain various observed sources of QPOs by simulating the dynamics of accretion disks around the black holes

We propose a mechanism to explain the low-frequency QPOs observed in X-ray binary systems and AGNs. To achieve this, we perturbed stable accretion disks around Kerr and EGB black holes at different angular velocities, revealing characteristics of shock waves and oscillations on the disk. By applying this perturbation to scenarios with varying alpha values for EGB black holes and different spin parameters for Kerr black holes, we numerically observed changes in the disk dynamic structure and its oscillations. Through various numerical models, we found that the formation of one- and two-armed spiral shock waves on the disk serves as a mechanism for generating QPOs. We compared the QPOs obtained from numerical calculations with the low-frequency QPOs observed in X-ray binary systems and AGN sources, finding high consistency with observations. We observed that the shock mechanism, leading to QPOs, explains the X-ray binaries and AGNs studied in this article. Our numerical findings indicate that QPOs are more strongly dependent on the EGB constant than on the black hole spin parameter. However, we highlighted that the primary impact on oscillations and QPOs is driven by the perturbation angular velocity. The results from the models showed that the perturbation asymptotic speed at V∞=0.2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{\\infty }=0.2$$\\end{document} independently generates QPO frequencies, regardless of the black hole spin parameter and the EGB coupling constant. Therefore, for the moderate value of V∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{\\infty }$$\\end{document}, a two-armed spiral shock wave formed around the black hole is suggested as a decisive mechanism in explaining low-frequency QPOs.

Effect of Transition on Self-Sustained Shock Oscillations in Highly Loaded Transonic Rotors

Recent trends in numerical studies suggest the possible need for scale-resolving simulations for resolving shock oscillations on transonic compressors, the sources of which are unclear. The effect of promoting transition on the suction side upstream of self-sustained shock oscillations from a laminar shock/boundary-layer interaction (altitude conditions) in transonic compressors is studied using implicit large-eddy simulation, as well as experiments in a transonic cascade. The experiment is performed at conditions leading to different shock structures, and the shock behavior is captured with high-speed schlieren imaging. The Rolls-Royce HYDRA in-house code is employed for the numerical simulations. Trends in the change of oscillation behavior are discussed. The work addresses the fundamentally different behavior between an idealized quasi-2D LES case and an experimental cascade. This suggests that a simplification of the shock oscillation problem to a more canonical form is needed in order to investigate the oscillation mechanism itself experimentally and validate the CFD of the mechanism before returning to more complex cases. The reader is referred to youtu.be/CNRz7IYl1Pk for a condensed summary of the work with flow visualization.

Magnetoacoustic waves in spin-1/2 dense quantum degenerate plasma: nonlinear dynamics and dissipative effects

Abstract Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev’s potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments.

Diaphragm-Induced Attenuation in Shock Tubes

This is a numerical and experimental study on shock attenuation in shock tubes. Tube geometry, boundary layer, and reduction in cross-sectional area induced by burst diaphragms are often considered the main causes of shock speed reduction (or shock attenuation) observed during the experiments. In order to distinguish how each single phenomenon contributes toward shock attenuation, the National Cheng Kung University shock tube is simulated for driver and test (driver–test) gas pairs involving air–air and He–air. For low pressure ratios, the diaphragm effect was found to be negligible. For a pressure ratio of 200 and helium as driver gas, the shock speed was found to decrease linearly with the size of the diaphragm orifice. In general, wall viscous effects caused a 2.5% decrease in shock speed, while an additional 7% reduction was caused by the presence of the diaphragm. The gradual opening of the diaphragm mainly contributed to a decrease in shock oscillations.

Oscillatory and regularized shock waves for a modified Serre–Green–Naghdi system

AbstractThe Serre–Green–Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre–Green–Naghdi system incorporating the effect of an artificial term that results in dispersive and dissipative dynamics. We show that the modified system effectively approximates the classical Serre–Green–Naghdi equations over sufficiently extended time intervals and admits dispersive–diffusive shock waves as traveling wave solutions. The traveling waves converge to the entropic shock wave solution of the shallow water equations when the dispersion and diffusion approach zero in a moderate dispersion regime. These findings contribute to an understanding of the formation of dispersive shock waves in the classical Serre–Green–Naghdi equations and the effects of diffusion in the generation and propagation of undular bores.

Transonic buffet simulation using a partially-averaged Navier-Stokes approach

The present article assesses the capability of the partially averaged Navier-Stokes (PANS) method to reproduce accurately the self-sustained shock oscillations, also known as transonic buffet, occurring on airfoils and wings at transonic regime under certain conditions of Mach number and angle of attack. The test case under analysis is an OAT15A unswept wing at Mach number M∞=0.73 and Reynolds number Rec=3×106. The three-dimensional flow is studied by accounting for the wind tunnel walls adopted in the experiments of Jacquin et al. [1] in the simulations. The computations on a large-span, confined configuration reveal a strong three-dimensionality of the flow both before and after the buffet onset. Attention is paid to the comparison with unsteady Reynolds-averaged Navier Stokes (URANS) results, to show the benefits of PANS in resolving flow unsteadiness at different flow resolutions, especially on affordable CFD grids, at limited additional cost. In this context, the role of the mesh metrics and the local turbulence level in the formulation of the model is described, as well as the relation of this latter with the spatiotemporal discretization used for the numerical simulations. The aim is to extend the use of PANS and obtain accurate predictions of flow cases involving shock-wave boundary layer interactions without expensive approaches.

The role of superthermal electrons and positrons on magnetised oscillatory shock waves

The role of superthermal electrons and positrons on magnetised oscillatory shock waves

Oscillating shocks in the transonic viscous, variable Γ accretion flows around black holes

ABSTRACT We investigate the time evolution of the transonic-viscous accretion flow around a non-rotating black hole. The input parameters used for the simulation are obtained from semi-analytical solutions. This code is based on the total variation diminishing routine and correctly handles the angular momentum transport due to viscosity. The thermodynamic properties of the flow are described by a variable adiabatic index equation of state. We regenerate the inviscid and viscous steady-state solutions, including shocks, using the simulation code and compare them with the semi-analytical solutions. The angular momentum piles up across a shock due to shock-jump conditions and viscous transport of angular momentum. This will push the shock-front outward and can result in shock oscillation or a complete destabilization of shock. We study how shocks behave in the presence of viscosity. As the viscosity parameter (α) crosses a critical value, the previously steady shock becomes time-dependent, eventually leading to oscillations. The value of this critical viscosity depends on the injection angular momentum (λou) and the specific energy (ϵ). We estimated the posteriori bremsstrahlung and synchrotron cooling, and the net radiative output also oscillates with the frequency of the shock. We also study the variation of frequency, amplitude, and mean position of oscillation with α. Considering a black hole with a mass of 10 M⊙, we observed that the power spectrum exhibits a prominent peak at the fundamental frequency of a few to about tens of Hz, accompanied by multiple harmonics. This characteristic is frequently observed in numerous accreting black hole candidates.

Aerodynamic Instabilities in High-Speed Air Intakes and Their Role in Propulsion System Integration

High-speed air intakes often exhibit intricate flow patterns, with a specific type of flow instability known as ‘buzz’, characterized by unsteady shock oscillations at the inlet. This paper presents a comprehensive review of prior research, focused on unraveling the mechanisms that trigger buzz and its implications for engine stability and performance. The literature survey delves into studies concerning complex-shaped diffusers and isolators, offering a thorough examination of flow aerodynamics in unstable environments. Furthermore, this paper provides an overview of contemporary techniques for mitigating flow instability through both active and passive flow control methods. These techniques encompass boundary layer bleeding, the application of vortex generators, and strategies involving mass injection and energy deposition. The study concludes by discussing future prospects in the domain of engine-intake aerodynamic compatibility. This work serves as a valuable resource for researchers and engineers striving to address and understand the complexities of high-speed air induction systems.

Experimental study on spatiotemporal correlation and similarity law of transonic buffeting loads

The spatiotemporal correlation of transonic buffet, driven by strong shock waves and boundary-layer separation, plays a critical role in causing structural vibrations in launch vehicles. To investigate this correlation, a wind tunnel experiment was conducted to measure the time-frequency characteristics of wall fluctuation pressures. The phase array approach was employed to obtain the spatial correlation of buffeting load. The results indicate that the low-frequency hydrodynamic modes dominate the separation flow and shock oscillation, while the attached flow is predominantly influenced by broadband acoustic modes. The space-time correlation analysis reveals that the peak buffeting load, for typical flows, results from the convergence of energy beneath the turbulent boundary layer. Furthermore, a similarity law for the spatial correlation of buffeting load was derived and validated by the measurement data. Based on the measured buffeting load data, an improved W–F (Wavenumber–Frequency spectrum) model with scaling spatiotemporal correlation was developed. This model serves as a theoretical foundation for predicting buffeting loads under flight conditions.

Comparison of shock-buffet dynamics on a supercritical airfoil with and without a pitching degree of freedom

With the goal of understanding the dynamics of the transonic flow around an OAT15A airfoil model, velocity field measurements were performed by means of high repetition rate particle image velocimetry. The experiments were performed at free-stream Mach numbers from 0.70 to 0.77 and at a Reynolds number of Rec≈3×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\ extrm{c}\\approx 3\ imes 10^6$$\\end{document}. The variation of the Mach number allowed for an investigation in the pre-buffet, buffet and close to buffet-offset regime. A fixed version and a spring mounted version of the model were used to investigate the effect of the pitching degree of freedom on the shock buffet. The dominant structural frequency of the airfoil’s pitch motion was adjusted to be in the range of the natural buffet frequency of the flow with inhibited pitching motion of the model. Flow field measurements with an acquisition rate of 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\,$$\\end{document} kHz allowed for the detection and analysis of the shape and the motion of the compression shock. With released pitching degree of freedom, shock buffet started at a lower Mach number and showed a larger amplitude for the shock oscillation. Furthermore, the shock motion appeared more harmonic compared to the model without pitching degree of freedom. For a Mach number of M∞=0.72\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\\infty =0.72$$\\end{document} and 0.74, the change of the angle of attack and the shock location correlated strongly with each other. From the measurements, the phase lag between both quantities during the coupled motion could be determined. From the correlation of the shock position at different heights, it can be concluded that the shock motion is controlled by events at the shock foot. The movement of the upper shock part is only a reaction to the movement of the lower part.

Numerical Analysis of Unsteady Characteristics of the Second Throat of a Transonic Wind Tunnel

The unsteady characteristics of the second throat of a transonic wind tunnel have an important influence on the design and test of the wind tunnel. Therefore, the forced oscillation characteristics were studied by a numerical simulation method. The governing equation was the viscous compressible unsteady Navier–Stokes equation. Under the sinusoidal pressure disturbance of the computational domain exit, the shock wave presents a clear forced oscillation state, and the shock wave periodically changes its position. Under a pressure disturbance of 1%, the shock wave displacement reaches 150 mm. Additionally, overshoot occurs when the shock moves upstream or downstream. The shock-boundary layer interference is very sensitive to the motion characteristics of the shock wave, resulting in a transformation of the flow field symmetry. The flow field downstream of the shock wave exhibits periodic structural changes. Compared with the pressure change at the outlet, the pressure change near the shock wave has a phase delay. The increasing disturbance near the shock wave shows a clear amplification effect. The pressure disturbance near the shock wave had an obvious amplification effect, and its fluctuation amount reached 16% under the pressure disturbance of 1%. The variation trend of the second throat wall force, wavefront Mach number, and Mach number in the test section with time is similar to that of the downstream disturbance, but it does not have a complete follow-up effect, which indicates that the pressure disturbance can propagate into the test section through the boundary layer or the shock gap. Nevertheless, the second throat choking can still control the Mach number stability of the test section. The dynamic characteristics of shock oscillation are related to the amplitude and frequency of the applied pressure disturbance. The shock displacement decreases with the increase in the excitation frequency. When the excitation frequency is higher than 125 Hz, the flow field basically does not change.