DEVELOPMENT OF INSTABILITY IN STREAM WITH NORMAL SHOCK WAVES

In a supersonic flow, disturbances of different parameters arise. These perturbations can have a significant impact on the interaction of the flow with the surface. When gas flow passes through a shock wave, perturbations are transformed depending on the initial parameters of the flow. Therefore, it is important to be able to correctly assess the intensity of these transformations. In this work, for the first time, a method has been proposed that allows us to estimate the dynamics of variation of disturbances of flow parameters when passing through an oblique shock wave. The influence of the shock wave inclination angle β, Mach number, intensity of disturbances of velocity, density, temperature, and pressure in front of the shock wave on perturbations of the flow parameters behind the shock wave was investigated. The Mach numbers ranged from 1.2 to 10 and the shock wave inclination angle varied from 15° to 90°. It was shown that the interaction of a supersonic gas flow with an oblique shock wave has a significant effect on the transformation of the perturbations of the flow parameters. The perturbations of temperature and pressure behind the shock wave increase significantly with the increasing angle β and Mach number in front of the shock wave. With the increasing Mach number, the velocity perturbations behind the shock wave first increase, then decrease, passing through a maximum, and afterwards the flow becomes more stable.

The viscosity effects on weak shock wave reflection are investigated with the Navier– Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of three-shock intersection. Instead of a singular triple point, in viscous flow there is a smooth shock transition zone, where one-dimensional shock jump relations cannot be applied. At the parameters corresponding to the von Neumann reflection, when no inviscid three-shock solution exists, the three-shock configuration is also observed. The existence of a viscous zone in the region of shock-wave interaction allows a continuous transition from the parameters behind the Mach stem to the parameters behind the reflected shock, which is impossible in the three-shock theory. I. Background and motivation Many interesting phenomena that occur in oblique shock wave reflection have been discovered in the past. The main feature herein is the existence of two possible configurations of shocks, regular and irregular. Regular reflection consists of the incident shock wave and the reflected shock wave with supersonic flow behind the reflected shock. Irregular reflection, which is in most cases called Mach reflection due to E. Mach who first discovered this phenomenon, is a complex shock wave pattern that combines the incident and reflected shock waves and the Mach stem. A contact discontinuity (slip surface) emanates from the triple point due to inequality of entropy in the flow passing through the incident and reflected shocks and the flow passing through the Mach stem. Classical theoretical methods such as shock polar analysis and the three-shock theory based on Rankine–Hugoniot jump conditions across the oblique shocks were developed by J. von Neumann to describe the shock wave configurations at various flow parameters and to predict transitions between different types of shock wave interaction. These theoretical methods predict well most of the features of shock wave interaction. Steady shock wave reflection is very important in aerodynamics and has been extensively studied in recent years with an emphasis on strong shock waves (for flow Mach numbers higher than 2.2 in air). For supersonic civil aviation, however, the lower Mach number range is of greatest interest. Regular and irregular interactions of different types are inherent in such critical phenomena as off-design inlet flows, inlet starting, and flow stalling. Interactions and reflections of weak shock waves are typical for supersonic inlet flows at low and moderate Mach numbers (M=1-2). There are many problems of irregular shock reflections in steady flows which are not yet investigated. One of the most exciting phenomena that occurs in irregular reflection of weak shock waves is a shock wave reflection in the range of flow parameters where the von Neumann’s three-shock theory does not produce any solution whereas the experiments reveal 1 a three-shock structure similar to the Mach reflection pattern. This inconsistency is referred to as the von Neumann paradox, and the observed reflection pattern is called the von Neumann reflection (vNR). Inviscid numerical simulations

This present study describes the aerodynamic characteristics of supersonic flow over biconvex and double wedge airfoils using a finite volume method-based commercial CFD code Ansys Fluent. A steady-state RANS approach is used with SST k-ω viscous modeling. A series of simulations are conducted to analyze the characteristics of shock and expansion waves formed around the airfoils for Mach numbers ranging from 1.4 to 3.4 with varying angles of attack (α) from 0° to 20°. It is observed that the lift and drag coefficients both increase with the angle of attack for a fixed Mach number and decrease with the Mach number for a fixed angle of attack. Double wedge airfoil generates about 5% more lift at a low Mach number and 1% more lift at a higher Mach number compared to the biconvex airfoil. However, the biconvex airfoil generates lesser drag than the double wedge airfoil. The maximum value of the pressure coefficient (Cp ) is found to be 1.7 for biconvex airfoil and 1.4 for double wedge airfoil. The maximum value of the lift-to-drag ratio for biconvex airfoil is 7.63, occurs at 1.4 Mach number and 3.46° angle of attack, whereas the value for double wedge airfoil is 5.19 at the same Mach number with 4.47° angle of attack, which suggest that biconvex airfoil has a higher lift-to-drag ratio and gives a better aerodynamics performance. The shock waves start to detach after an angle of attack of 5° and the shock wave is fully detached at a 15° angle of attack for biconvex airfoil for Mach number of 1.4. For the same Mach number, the double wedge airfoil, the shock wave starts to form the same as the biconvex airfoil but the waves are fully detached at a lower angle of attack of 10°. With the increasing Mach number, the shock waves remain attached to the airfoil.

This study presents a rigorous numerical investigation into the interplay between magnetic fields and high-speed flow dynamics across supersonic and hypersonic flow regimes. Employing advanced computational techniques, we quantify the impact of varying Mach (M) and Reynolds (Re) numbers on flow discontinuities, with particular focus on shock wave behavior under magnetohydrodynamics (MHD) conditions. The key solutions are derived for critical physical parameters such as compression rate (κ), Mach number ratio (M2M1), Cowling number ratio (C2C1), Reynolds number ratio (Re2Re1), pressure ratio (p2p1), magnetic pressure ratio (h2h1), and entropy production (S2−S1) across the shock wave. This study analyzes the combined effects of magnetic fields and viscous dissipation on shock waves in supersonic and hypersonic ideal MHD flows. A 1D model, solved using Rankine–Hugoniot conditions, reveals that stronger magnetic fields reduce post-shock pressure ratios by up to 20% while increasing downstream Mach numbers and generation. Notably, viscous, inviscid, and ideal gas flow simulations, both with and without magnetic coupling, exhibit strong alignment with the benchmark studies of Cavus [“On the effects of viscosity on the shock waves for a hydrodynamical case—Part I: Basic mechanism,” Adv. Astron. 2013, 1 (2013)], corroborating the numerical fidelity of our approach. This work validates its novel approach through rigorous statistical comparison with established studies, employing percentage change analysis, mean value differences, standard deviation measurements, and 95% confidence intervals. The results demonstrate significantly enhanced predictive capability relative to prior methods. Furthermore, the analysis reveals a previously under-characterized phenomenon: magnetic field effects exhibit pronounced Mach number dependence, becoming substantially more influential in hypersonic regimes compared to supersonic conditions. This finding addresses a critical gap in existing shock wave literature. This consistency underscores the robustness of our methodology in capturing MHD flow interactions under extreme velocity conditions.

A shock wave is a typical aerodynamic phenomenon in a supersonic flow, and if controlled effectively, a series of potential applications can be achieved in aerospace fields, such as reducing wave drag and sonic boom of the supersonic vehicle, optimizing shock waves of the supersonic inlet in off-design operation states, decreasing pressure loss induced by shock waves in the supersonic wind tunnel or aeroengine internal duct, controlling shock waves of the wave rider, changing shock wave symmetry to achieve flight control and inducing shock waves in the aeroengine nozzle to achieve thrust vector control. Shock wave control can be achieved by many mechanical or gas dynamic methods, such as the ramp angle control in supersonic inlet and the holl/cavum control in self-adapted transonic wing. Because the structural configurations of these methods are somewhat complex and the flow control response is also slow, plasma flow control based on gas discharge physics and electromagnetohydrodynamics (EMHD) theory has been developed recently in the shock wave control field. Using this method, substantial thermal energy can be added in the shock wave adjacent areas, then the angle and intensity of shock wave change subsequently. Meyer et al investigated whether shock wave control by plasma aerodynamic actuation is a thermal mechanism or an ionization mechanism, and the experimental results demonstrated that the thermal mechanism dominates the shock wave control process [1, 2]. Miles et al investigated the shock wave control by laser energy addition experimentally and numerically, and the research results showed that when the oblique shock wave passed by the thermal spot induced by laser ionization, the shock wave shape distorted and the shock wave intensity reduced [3]. Macheret et al proposed a new method of virtual cowl induced by plasma flow control which can optimize the shock waves of supersonic inlet when its operation Mach number is lower than the design Mach number [4]. Meanwhile, they used the combination method of e-beam ionization and magnetohydrodynamic (MHD) flow control to optimize the shock waves of supersonic inlet when operating in off-design states, and the research results demonstrated that the shock waves can reintersect in the cowl adjacent area in different off-design operation states with the MHD acceleration method and the MHD power generation method, respectively [5]. Leonov et al used a quasi-dc

This study presents flow simulation over the reentry capsule at supersonic and hypersonic speeds. Numerical algorithms solve for the CFD method, which is produced using help ANSYS Fluent 19.2. The using GPU core to get a solution faster. The main purpose – flow simulation and numerical analysis reentry capsule; understand the behavior of supersonic and hypersonic flow and its effect on the reentry capsule; compare temperature results for the range Mach numbers equals 2–6. This study showed results on velocity counters, on temperature counters and vector of velocity for range Mach numbers equals 2–6. This study demonstrates the importance of understanding the effects of shock waves and illustrates how the shock wave changes as the Mach number increases. For every solves, the mesh had adapted for pressure gradient and velocity gradient to get the exact solution. As a result of the obtained solution, it is found that a curved shock wave appears in front of the reentry capsule. The central part of which is a forward shock. An angular expansion process is observed, which is a modified picture of the Prandtl- Mayer flow that occurs in a supersonic flow near the sharp edge of the expanding region. It is revealed that with an increase in the Mach number, the shock wave approaches the bottom of the reentry capsule, and there is also a slope of the shock to the flow direction, with an increase in the Mach number. The relevance and significance of this problem for the design of new and modernization of old reentry capsules.

A double-pulse discharge method is used to simulate high-repetition-rate excitation discharge in TEA gas laser with supersonic gas flow. The supersonic gas flow is generated using a Ludwieg tube with a two-dimensional shock-free nozzle. A solid electrode with UV pins is used to generate the discharge. The test gas is a mixture of He and Ar (He:Ar = 9:1) with the density of 0.52 kg/m³ in a discharge cavity. In supersonic gas flow with the Mach number M = 2 (v = 860 m/s), not only gas density depression but also shock wave produced by the previous pulsed discharge has a key effect on stability of the subsequent discharge. For pulse repetition rate f = 60-25 kHz, the gas density depression has already been removed from the discharge cavity, whereas the traveling shock wave against the supersonic gas flow still remains. Hence the subsequent discharge becomes arc discharge. For f≤17 kHz, on the other hand, the subsequent discharge becomes glow discharge because both the shock waves and gas density depression have already been removed from the discharge cavity. A formula for estimating the maximum repetition rate of stable excitation discharge train in supersonic gas flow is proposed.

Navier-Stokes simulation of self-excited shock induced oscillations

An experimental study was done to elucidate the Mach number effects on vortex shedding of a square cylinder (side length D = 20 mm) and thick symmetrical airfoil (NACA 0018, chord length 20 mm) arranged in tandem , at free stream Mach numbers between 0.1526 and 0.9081, and at free stream Reynolds numbers (based on the side length D) between 0.702 x 105 and 4.188 x 105. The spacing ratio of the central distance, L, between the square cylinder and the airfoil to the side length, D, of the square cylinder was varied from 1.125 to 5.5. It was found that the regular vortex shedding is not suppressed by steady shock waves in the local supersonic flow regions; the periodic vortex shedding is still present, irrespective of the appearance of the shock waves. When the spacing ratio is fixed, the Strouhal number behind the square cylinder is almost constant up to the critical Mach number of about 0.70, but it increases rapidly with further increase of the Mach number. However, once the shock waves are formed on both sides of the vortex formation region, various frequency components, other than the vortex shedding frequency appear; the spectral peaks lower than those of the vortex shedding frequency were identified as frequencies of an acoustic-feedback oscillation and the resonance of the wind tunnel structural system. With increasing the Mach number, the formation region becomes small and asymmetric, and the separating shear layers become wavy. These changes result in an increase of the scale and strength of the vortices and thus enhance the vortex shedding process. However, when the Mach number exceeds the critical value, the streamwise length of the formation region increases suddenly and becomes long enough to enclose the downstream airfoil. Under this circumstance, the formation region is almost symmetrical with respect to the wake axis, and shock waves are formed on the upper and lower separating shear layers. The shock waves are almost normal to the wake axis at M = 0.7512 and 0.8215, but incline to the downstream direction at M = 0.9081. Acoustic waves travelling upstream have been observed most clearly when the vortex shed from the square cylinder hits the leading edge of the airfoil at a Mach number of about 0.63, which is close to, but slightly smaller than the critical value. The mean pressure and the amplitude of the pressure fluctuations in the test section decreases and increases, respectively, with increasing the Mach number. However, the amplitude of the pressure fluctuations decreases suddenly when the steady shock waves are formed on the upper and lower separating shear layers.

This paper presents an experimental investigation of one-dimensional moving shock waves in vertical soap films. The shock waves were generated by bursting the films with a perforating spark. Images of propagating shock waves and small disturbances were recorded using a fast line scan CCD camera. An aureole and a shock wave preceding the rim of the expanding hole were clearly observed. These images are similar to the x-t diagrams in gas dynamics and give the velocities of shock and sound waves. The moving shock waves cause jumps in thickness. The variations of the induced Mach number, M2 and the ratio of film thickness across the shock wave, δ 2/δ 1, are plotted versus the shock Mach number, M s. Both results suggest that soap films are analogous to compressible gases with a specific heat ratio of γ≅1.0.

In this paper, experimental results were reported to investigate a behavior of combustion wave when a shock wave was transmitted into a combustible premixed gas of oxygen and hydrogen. In general, phenomena occurring in the premixed gas would be classified into four types, i.e. (a) the shock wave was just transmitted without causing ignition for the shock wave propagated with low-Mach number, (b) the gas was ignited behind the shock wave and a deflagration wave was propagated following the shock wave, (c) the deflagration wave was transited to a detonation wave behind the shock wave, (d) a detonation wave was directly initiated just behind incident shock wave having high-propagation Mach number. In this study, a shock wave produced by a detonation-driven shock tube was transmitted into a premixed gas of oxygen and hydrogen varied with an equivalence ratio, initial pressure of premixed gas and Mach number of the shock wave. As a result, the phenomena of combustion wave were classified using a cell-size of steady-propagating detonation wave. For sensitive gases having small cell-size, the detonation wave was directly initiated behind the shock wave even though the Mach number of the shock wave was relatively low. Empirical equations to evaluate a Mach number and temperature behind shock wave were obtained, which are threshold parameters to cause detonation wave behind transmitted shock wave.

In problems involving strong shock waves (the problem of a strong explosion, the motion of bodies with large supersonic speeds, and the problem of supersonic piston expansion), a significant increase in temperature occurs in the disturbed flow region. It is therefore necessary to take the real properties of the gas into account when determining the parameters of the gas flow behind the front of a strong shock wave. This significantly complicates the construction of approximate analytical solutions. However, studies show that the effect of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, i.e., by introducing an effective adiabatic index. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes insignificantly in the entire flow zone. This allows us to simulate the flow behind the shock wave front using some perfect gas, whose adiabatic index is determined by the shock wave front depending on the Mach number and the thermodynamic state of the gas. To obtain more accurate solutions for problems with strong shock waves, the model must allow a discontinuity in the adiabatic index at the shock wave. An explicit expression for gas parameters behind the front of an intense shock wave is obtained in this study under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the shock wave surface. Plane and axisymmetric cases are considered.

Physical parameters of supercritical fluids change drastically near the critical region, which makes it difficult to predict and analyze the supercritical fluid flow parameters behind the normal shock wave. In this paper, in combination with supercritical fluid physical parameters database, we employed an iterative algorithm to solve the flow parameters behind normal shock by deriving shock equations. The change of normal shock parameters of six supercritical fluids with inflow state was studied by the controlled variable method and a correlation analysis. The results show that when the inflow Mach number is fixed, the normal shock parameters, such as density ratio and pressure ratio, change rapidly in the Widom zone as a result of the dramatic changes of the physical parameters. When the inflow state is the same, the normal shock pressure ratio of NH3 is the highest, whereas that of C8H24O2Si3 and C10H22 are pretty low. The normal shock intensity of supercritical fluid is better reflected by the pressure ratio rather than Mach number. According to the correlation analysis, the compressibility factor and the sound speed of inflow are the main physical factors that affect the normal shock density ratio and pressure ratio, respectively. Based on the main physical factors, empirical equations for predicting the change trend of normal shock pressure ratio and density ratio are obtained.

The three-dimensional spherical flame evolutions induced by incident and reflected shock waves in a rectangular shock tube are numerically simulated using the compressible reactive Navier–Stokes equations with a single-step Arrhenius chemical reaction. Four cases, including variable parameters of flame size and number, shock wave strength, and mixture reactivity, are considered in order to investigate the effects of these parameters on the flame evolutions and detonation onsets. The three-dimensional visualized results and the time-dependent integral and statistical results for the shock–flame interactions are obtained. The morphology of the flame evolutions for all cases studied shows the severe distortion, expansion, and corrugation of flame disturbed by shock waves, especially by a reflected shock wave. The unstable flame produces the three-dimensional reactive shock bifurcation (RSB) structure, as the flame number, the shock wave strength, or the mixture reactivity increase. Further, detonations can occur in a later stage of flame evolution at the different three-dimensional spatial locations for different cases through the shock–detonation–transition (SDT) mechanism. Unlike the three-dimensional spatial dissimilarities of flame patterns and detonation initiation locations among cases studied, the time-dependent integral and statistical properties of flame developments prior to detonation onset show the more similar behaviors for all cases. During the passage of shock and reshock waves, the spherical flames are compressed and distorted, resulting in the vorticity deposition within flame and the well-mixing between the burned and unburned gases. Physical process dominates the compression phases of the flame evolution. Following the passage of the shock and reshock waves, the well-mixing facilitates the chemical heat release and expands (accelerates) the distorted flame. The chemical process becomes more prominent, especially under the reshock condition. In the flame expansion phases, the baroclinic effect is weakened, and the vortex stretching effect is enhanced with the development of flame. In addition, the well-mixing by the passages of shock waves promotes the chemical reaction of the flame, which in turn burns out the mixing zone of flame and therefore inhibits the mixing.

A new 2D analysis of light for computing the Mach number distribution in a flow field from Schlieren images taken across the shock wave and expansion zone is proposed and verified by a 2D numerical computation Specially, inserting experimental measuring sensors inside shock wave zone and associated flow field is difficult. Across the shock wave, the pressure and density of the fluid change at extremely high rates, which affect the light refraction. The intensity of the Schlieren light is a function of the medium density, which is a function of the light ray path position. The contrast of each pixel is determined by analyzing the image. The equations of Schlieren intensity light are derivated to be a function of Mach number. These functions are applied on an image of shockwave around hemisphere-cylinder at M=1.96. To verify the results two-dimensional Navier-Stokes equations and conservation of energy equation are used to model the flow field and determine Mach number distribution around a hemisphere-cylinder of the supersonic flow, shock waves and associated flow field at the same previous conditions. The governing equations are discretized on a structured grid using an upwind difference scheme. The computational and experimental results show that there is a good matching in the iso-contour of the Mach number with difference less than 3%. The new proposed technique successfully represents the upstream region, the shock wave region, the subsonic region and the expansion fan region. This difference may be due to the noise in the image. This noise can be eliminated if Schlieren light received directly on a CCD camera. The results show that this analysis can be applied for both bright and dark regions of the Schlieren image with correcting the phase shift in the dark area. This optical technique has the advantages of optical measurements. This optical technique has all the advantages of optical measurements as does not disturb the flow and the high sensitivity to capture rapid variation.