Shock Wave Configuration Research Articles

Features of Supersonic Flow Around a Blunt Body in the Area of Junction with a Flat Surface

This work studies the influence of a growing boundary layer on the process of supersonic flow around an aerodynamic body. The task is to select and implement in an experiment the parameters of a supersonic flow and to study the flow pattern near the surface of an aerodynamic body at different viscosity values for the incoming flow. Visualization of the shock wave configuration in front of the body and studying the change in the pressure field in the flow region under these conditions is the main goal of this work. The experiment was carried out on an experimental stand created on the basis of a shock tube. The aerodynamic body under study (a semi-cylinder pointed along a circle or an ellipse) was placed in a supersonic nozzle. The model was clamped by lateral transparent walls, which were simultaneously a source of boundary layer growth and the viewing windows for visualizing the flow. For selected modes with Reynolds numbers from 8200 to 45,000, schlieren flow patterns and pressure distribution fields near the surface of the streamlined models and the plate of the growing boundary layer were obtained. The data show a complex, unsteady flow pattern realized near the model which was caused by the viscous-inviscid interaction of the boundary layer with the bow shock wave near the wall.

Неоднозначность решений для ударно-волновых структур, образующихся в высокоскоростных потоках газа с малым показателем адиабаты

We considered branched shock-wave structures (triple configurations of shock waves) which forms in supersonic flows of perfect gas, mainly at high flow Mach numbers and low values of the adiabatic index. Ambiguity of the solution for triple configurations of steady shock waves formed at Mach reflection, including for configurations with a negative slope angle of the reflected shock, was studied analytically and numerically. The conditions for the coexistence of triple configurations which correspond to Mach reflection with other shock-wave structures are derived and graphically demonstrated.

A cluster analysis-based shock wave pattern recognition method for two-dimensional inviscid compressible flows

Compressible flows typically exhibit multiple shock waves which interact with each other, making the detection of these shock waves crucial for various aspects of flow studies including construction of high-order numerical schemes (e.g., shock-fitting), adaptive grid refinement, and flow visualization. This study aims to effectively identify and localize multiple shock waves and their interaction points in two-dimensional inviscid steady and unsteady flows. A novel shock wave pattern recognition method based on cluster analysis is proposed, including three processes. First, a series of grid-cells located at the transition zones of captured shock waves are extracted using a shock wave detection approach based on local flow variation. Subsequently, these grid-cells are grouped into numerous clusters using the classical K-means clustering algorithm, with categorization based on nearest neighbor features. Finally, a strategy is introduced to merge relevant adjacent clusters and further localize the points where shock waves interact. The Bézier curve fitting technique is then employed to obtain the high-quality shock-lines. Several numerical cases demonstrate that this method achieves high localization accuracy for shock-lines while being minimally affected by grid type and scale variations. Moreover, it enables clear and effective identification of the shock interaction patterns in both steady and unsteady flows, providing an effective visualization means for analyzing the motion and evolution of shock wave configurations.

Method of calculation of satellite flow parameters behind the point of Mach reflection

A mathematical model for the calculation and express analysis of triple configurations of air shock waves arising from an “elevated” explosion of a condensed high-energy material is presented. The considered blast waves with a long duration of the positive phase (compression phase) can take place in industrial and agricultural applications: in the explosion of fuel-air mixtures, explosive dust in elevators and granaries, as well as high-energy materials for agricultural and industrial applications based on ammonium nitrate and explosive saltpetre mixtures with petroleum products. The developed mathematical model uses exact and semi-empirical relationships developed earlier in the theory of optimal shock wave systems.

Extreme Relations of the Dynamical Pressures Downstream the Stationary Mach Configurations of Running Shock Waves

Extreme Relations of the Dynamical Pressures Downstream the Stationary Mach Configurations of Running Shock Waves

Shock wave configuration in a transonic flow through a mid-section of a last stage turbine blade cascade equipped with a part-span connector

This paper deals with the study of a flow field and namely the configuration of shock waves in a blade cascade equipped with a part-span connector called tie-boss. The cascade consists of prismatic blades formed from the mid-section of a very long last-stage blade of a steam turbine. The study is based on numerical simulations of the flow through a cascade that was previously tested in a wind tunnel. Commercial software Ansys CFX was used for the simulations and Ansys ICEM for the mesh generation. The computational domain contains non-homogenous mesh interfaces. The simulations showed that the presence of the tie-boss has a profound effect on the configuration of the shock waves. The blade exit shock waves are disturbed and new lateral shock waves are introduced into the flow.

Computational and Experimental Modeling in Magnetoplasma Aerodynamics and High-Speed Gas and Plasma Flows (A Review)

This paper provides an overview of modern research on magnetoplasma methods of influencing gas-dynamic and plasma flows. The main physical mechanisms that control the interaction of plasma discharges with gaseous moving media are indicated. The ways of organizing pulsed energy input, characteristic of plasma aerodynamics, are briefly described: linearly stabilized discharge, magnetoplasma compressor, capillary discharge, laser-microwave action, electron beam action, nanosecond surface barrier discharges, pulsed spark discharges, and nanosecond optical discharges. A description of the physical mechanism of heating the gas-plasma flow at high values of electric fields, which are realized in high-current and nanosecond (ultrafast heating) electric discharges, is performed. Methods for magnetoplasma control of the configuration and gas-dynamic characteristics of shock waves arising in front of promising and advanced aircraft (AA) are described. Approaches to the control of quasi-stationary separated flows, laminar–turbulent transitions, and static and dynamic separation of the boundary layer (for large PA angles of attack) are presented.

Experimental study of the motion of a shock wave in the plasma of a pulsed volume discharge in air

The motion of quasi-plane shock waves with Mach numbers = 2.20–3.50 in the plasma of a nanosecond combined volume discharge in air at an initial pressure of 10–100 Torr has been experimentally studied on the basis of high-speed shadow registration of the flow field. The dynamics of shock–wave configurations after the discharge at various stages of an unsteady supersonic flow, which is formed after the diffraction of a plane shock wave by a rectangular obstacle, is studied. An increase in the velocity of the shock wave front over a time interval of up to 15 𝜇s in a plasma region of 9–40 mm long and its dependence on the plasma parameters is found. An analysis of relaxation processes in plasma showed that the acceleration of the shock wave front can be caused by air heating due to the quenching of electronically excited nitrogen molecules, in which the internal energy is converted into thermal energy at times up to 30 𝜇s.

Application of Reflected Shock Wave Configuration to Validate Nonequilibrium Models of Reacting Air

The direct simulation Monte Carlo (DSMC) method is used to model transient thermal and chemical relaxation behind reflected shock waves in oxygen–argon and air mixtures under conditions reproducing earlier shock-tube experiments. Two vibration–translation and three popular DSMC chemical reaction models are tested. Where possible, model parameters are adjusted to match equilibrium and nonequilibrium relaxation times and reaction rates. A number of factors that impact relaxation and reaction model validation are examined, including gas–surface interactions, time-varying freestream properties, location of the observation point, electronic excitation, and nonequilibrium populations of vibrational states probed in the experiments. Comparison of numerical and experimental results has demonstrated that the reflected shock configuration is a platform very convenient for validation and analysis of high-temperature chemical reaction models. Computations have shown that the Bias reaction model is superior to the total collision energy and quantum kinetic models, providing reasonable agreement with measured absorbance time histories and vibrational temperatures in oxygen–argon mixtures and pure . There are some modeling-versus-experiment differences observed for air that may warrant additional studies focused on Zeldovich reaction rates and oxygen–nitrogen vibrational excitation and nonequilibrium dissociation rate.

Lagrange Optimization of Shock Waves for Two-Dimensional Hypersonic Inlet with Geometric Constraints

The present paper focuses on the Lagrange optimization of shock waves for a two-dimensional hypersonic inlet by limiting the cowl internal angle and inlet length. The results indicate the significant influences of geometric constraints on the configuration of shock waves and performances of an inlet. Specifically, the cowl internal angle mainly affects the internal compression section; the inlet length affects both the internal and external compression sections where the intensity of internal and external compression shock waves shows a deviation of equal. In addition, the performances of optimized inlets at off-design points are further numerically simulated. A prominent discovery is that a longer inlet favors a higher total pressure recovery at the positive AOA; conversely, a shorter inlet can increase the total pressure recovery at the negative AOA.

Principles of Magnetohydrodynamical Control of Internal and External Supersonic Flows

This paper demonstrates the possibility of active magnetohydrodynamic (MHD) control of supersonic flows containing shock waves. The shock wave configurations that occur at the inlet to a supersonic diffuser and in front of a streamlined semicylindrical model are used for the purpose of investigation. The impact is carried out by organizing local gas discharge regions when applying a magnetic field transverse to gas discharge currents. It has been shown that by changing the local region of application, the intensity and the direction of the gas discharge currents, it is possible to change the intensity and direction of the ponderomotive force acting on the gas flow during MHD interaction. The ponderomotive force control allows for acting locally on the shape and position of shock waves, the speed and direction of the flow, and the increase or reduction of pressure near the surface of the streamlined body. The experiments were carried out on a gas dynamic setup based on a shock tube in a gas dynamic path, capable of creating supersonic flows in a wide range of Mach numbers at M = 4–7. There was a possibility of organizing the electric and pulsed magnetic fields with an intensity of up to 1.5 T. The given experimental Schlieren flow patterns and the analysis of the obtained data demonstrate the MHD effect on: the change in the angle of inclination of the attached shocks, both into increase and decrease; the bow shock wave approaching the body or the removal from it; and the change in the aerodynamic drag and lift force of the streamlined bodies.

Investigation on shock-induced separation loss mitigation method considering radial equilibrium in a transonic compressor rotor

AbstractA shock-induced separation loss reduction method, using local blade suction surface shape modification (smooth ramp structure) with constant adverse pressure gradient with the consideration of radial equilibrium effect to split a single shock foot into multiple weaker shock wave configuration, is investigated on the NASA Rotor 37 for promoting aerodynamic performance of a transonic compressor rotor. Numerical investigation on baseline blade and improved one with blade modification on suction side has been conducted employing the Reynolds-averaged Navier–Stokes method to reveal flow physics of ramp structure. The results indicate that the passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot generating moderate adverse pressure gradient on ramp profile, which is beneficial for mitigating the shock foot and shrinking flow separation region as well. In addition, the radial secondary flow of low-momentum fluids within boundary layer is decreased significantly in the region of passage shock-wave/boundary-layer interaction on blade suction side, which mitigates the mass flow and mixing intensity of tip leakage flow. With the reduction of flow separation loss induced by passage shock, the adiabatic efficiency and total pressure ratio of improved rotor are superior to baseline model. This study herein implies a potential application of ramp profile in design method of transonic and supersonic compressors.

Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

Mechanism of separation hysteresis in curved compression ramp

A new spatial-related mechanism is proposed to understand separation hysteresis processes in curved compression ramp (CCR) flows discovered recently (Hu et al. Phy. Fluid, 32(11): 113601, 2020). Two separation hystereses, induced by variations of Mach number and wall temperature, are investigated numerically. The two hystereses indicate that there must exist parameter intervals of Mach number and wall temperature, wherein both attachment and separation states can be established stably. The relationships between the aerodynamic characteristics (including wall friction, pressure and heat flux) and the shock wave configurations in this two hystereses are analyzed. Further, the adverse pressure gradient (APG) Isb(x) induced by the upstream separation process and APG Icw(x) induced by the downstream isentropic compression process are estimated by classic theories. The trend of boundary layer APG resistence Ib(x) is evaluated from the spatial distributions of the physical quantities such as the shape factor and the height of the sound velocity line. With the stable conditions of separation and attachment, a self-consistent mechanism is obtained when Isb, Icw and Ib have appropriate spatial distributions.

Mechanism analysis of magnetohydrodynamic shock control in hypersonic flow

The effects of external magnetic fields on the shock-wave configuration at hypersonic plasma flow field are investigated in this paper. A series of numerical simulations over various geometry configurations, namely, a blunt body and a fixed-geometry inlet forebody, have been conducted by varying the applied magnetic field under different freestream conditions. Results show that magnetohydrodynamic shock control capabilities under three types of magnetic field are ranked from weak to strong as dipole magnet, solenoid magnet, and uniform magnet field. Under the same applied magnetic field, it is easier to deflect the shock at a relatively high altitude condition, compared with the low altitude case. The bow shock standoff distance is dependent on the distribution of counter-flow Lorentz force right after shock in the stagnation region. For the oblique shock control, the function of two components of Lorentz force is different that the counter-flow one decelerates the flow and increases the shock-wave angle, while the normal one squeezes the oblique shock and deflects the streamlines.

Interaction between Shock Waves Travelling in the Same Direction

In this paper, we study the intersection (interaction) between several steady shocks traveling in the same direction. The interaction between overtaking shocks may be regular or irregular. In the case of regular reflection, the intersection of overtaking shocks leads to the formation of a resulting shock, contact discontinuity, and some reflected discontinuities. The type of discontinuity depends on the parameters of incoming shocks. At the irregular reflection, a Mach shock forms between incoming overtaking shocks. Reflected discontinuities come from the points of intersection of the Mach stem with the incoming shocks. We also consider the possible types of shockwave configurations that form both at regular and irregular interactions of several overtaking shocks. The regions of existence of overtaking shock waves with different types of reflected shock and the intensity of reflected shocks are defined. The results obtained in the study can potentially be useful for designing supersonic intakes and advanced jet engines.

Refraction of Oblique Shock Wave on a Tangential Discontinuity

The refraction of an oblique shock wave on a tangential discontinuity dividing two gas flows with different properties is considered. It is shown that its partial reflection occurs with the exception of the geometrical diffraction of an oblique shock. Another oblique shock, expansion wave or weak discontinuity that coincides with the Mach line can act as a reflected disturbance. This study focuses on the relationships that define the type of reflected discontinuity and its parameters. The domains of shock wave configurations with various types of reflected discontinuities, including characteristic refraction and refraction patterns with a reflected shock and a reflected rarefaction wave, are analyzed. The domains of existence of various shock wave structures with two types of reflected disturbance, and the boundaries between them, are defined. The domains of parameters with one or two solutions exist for the characteristic refraction. Each domain is mapped by the type of refraction with regard to the Mach number, the ratio of the specific heat capacities of the two flows and the intensity of a refracted oblique shock wave. The conditions of the regular refraction and the Mach refraction are formulated, and the boundaries between the two refraction types are defined for various types of gases. Refraction phenomena in various engineering problems (hydrocarbon gaseous fuel and its combustion products, diatomic gas, fuel mixture of oxygen and hydrogen, etc.) are discussed. The result can be applied to the modeling of the shock wave processes that occur in supersonic intakes and in rotating and stationary detonation engines. The solutions derived can be used by other researchers to check the quality of numerical methods and the correctness of experimental results.

Gasdynamic Flow Control by Ultrafast Local Heating in a Strongly Nonequilibrium Pulsed Plasma

—The paper presents a review of modern works on gasdynamic flow control using a highly nonequilibrium pulsed plasma. The main attention is paid to the effects based on ultrafast (on the nanosecond time scale for atmospheric pressure) local gas heating, since, at present, the main successes in controlling high-speed flows by means of gas discharges are associated with this thermal mechanism. Attention is paid to the physical mechanisms responsible for the interaction of the discharge with gas flows. The first part of the review outlines the most popular approaches for pulsed energy deposition in plasma aerodynamics: nanosecond surface barrier discharges, pulsed spark discharges, and femto- and nanosecond optical discharges. The mechanisms of ultrafast heating of air at high electric fields realized in these discharges, as well as during the decay of the discharge plasma, are analyzed separately. The second part of the review gives numerous examples of plasma-assisted control of gasdynamic flows. It considers control of the configuration of shock waves in front of a supersonic object, control of its trajectory, control of quasi-stationary separated flows and layers, control of a laminar–turbulent transition, and control of static and dynamic separation of the boundary layer at high angles of attack, as well as issues of the operation of plasma actuators in different weather conditions and the use of plasma for the de-icing of a flying object.

Simulation of propagation and diffraction of a shock wave in a planar curvilinear channel

Subject of Research. Numerical simulation of a shock wave propagation in a plane curved channel is considered on the basis of numerical simulation data. Method. Calculations of an inviscid compressible gas were carried out on the basis of unsteady two-dimensional Euler equations. Discretization of the basic equations was carried out using the finite volume method. Calculations were carried out for different channels with different radius of curvature and Mach numbers of the initial wave. To find the angular position of the front at the current time, the absolute value of the derivative of the density with respect to the angular coordinate was used. The calculation results were compared with the data of a physical experiment. Main Results. The features of the emerging shock-wave flow pattern and its development in time are discussed. The shock-wave configuration observed in channels with different radii of curvature is compared. Some differences in the curvature change of the front of shock waves formed in channels with different radius of curvature are shown. The size of the Mach leg and its change with time depending on the intensity of the initial wave and the size of the annular gap is the angular coordinate function corresponding to the position of the shock wave at the current time. While the maximum Mach number on the outer wall is relatively weakly dependent on the initial wave velocity, the Mach number on the bottom wall decreases with increasing Mach number at the channel entrance. The performed numerical studies show that in all variants there are no non-physical oscillations of the solution. Practical Relevance. The study of shock-wave and detonation processes is of interest for using their potential in pulsed installations and power systems for aircraft and rockets. The calculation results are important for the search of the new flow patterns that guarantee the formation of self-sustained detonation combustion in the combustion chambers of promising propulsion systems. Adjusting the size of the annular gap gives the possibility to select a geometric configuration that will provide the formation of an optimal triple shock wave structure, as well as the required intensity and size of the Mach wave.

Influence of gas-dynamic characteristics of a wide-range engine on energy-information exchange during flights at high supersonic speed

Using a conical nozzle as an example, the gas-dynamic and thrust characteristics of high-altitude nozzles are studied in a wide range of atmospheric pressures. A geometric model of the nozzle block and the computational domain is developed in a two-dimensional axisymmetric formulation. A calculation was carried out with setting the parameters of the standard atmosphere in the altitude range from 0 to 80 km. In one of the parts of this work, the most common shock-wave structures (triple configurations of shock waves) that arise during flights at supersonic and high supersonic speeds are considered, during jet outflows from propulsion systems. We also studied the influence of the extreme values of the discontinuities of the flow field parameters on the transmitted electromagnetic signals.