Shock Angle Research Articles

Control of quasi-monoenergetic electron beams from laser-plasma accelerators with adjustable shock density profile

The injection physics in a shock-induced density down-ramp injector was characterized, demonstrating precise control of a laser-plasma accelerator (LPA). Using a jet-blade assembly, experiments systematically varied the shock injector profile, including shock angle, shock position, up-ramp width, and acceleration length. Our work demonstrates that beam energy, energy spread, and pointing can be controlled by adjusting these parameters. As a result, an electron beam that was highly tunable from 25 to 300 MeV with 8% energy spread (ΔEFWHM/E), 1.5 mrad divergence, and 0.35 mrad pointing fluctuation was produced. Particle-in-cell simulation characterized how variation in the shock angle and up-ramp width impacted the injection process. This highly controllable LPA represents a suitable, compact electron beam source for LPA applications such as Thomson sources and free-electron lasers.

Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach

Shock-dominated hypersonic laminar flows over a double cone are investigated using time accurate direct simulation Monte Carlo combined with the residuals algorithm for unit Reynolds numbers gradually increasing from 9.35 × 104 to 3.74 × 105 m−1 at a Mach number of about 16. The main flow features, such as the strong bow-shock, location of the separation shock, the triple point, and the entire laminar separated region, show a time-dependent behavior. Although the separation shock angle is found to be similar for all Re numbers, the effects of Reynolds number on the structure and extent of the separation region are profound. As the Reynolds number is increased, larger pressure values in the under-expanded jet region due to strong shock interactions form more prominent λ-shocklets in the supersonic region between two contact surfaces. Likewise, the surface parameters, especially on the second cone surface, show a strong dependence on the Reynolds number, with skin friction, pressure, and surface heating rates increasing and velocity slip and temperature jump values decreasing for increasing Re number. A Kelvin-Helmholtz instability arising at the shear layer results in an unsteady flow for the highest Reynolds number. These findings suggest that consideration of experimental measurement times is important when it comes to determining the steady state surface parameters even for a relatively simple double cone geometry at moderately large Reynolds numbers.

DC Discharge Electronic Non-equilibrium Effects Investigations on a M = 2 Rarefied Supersonic Flow Over a Flat Plate

This work aims at studying the effects of a low-pressure Argon discharge (P = 0.5 Torr) on a supersonic Argon flow (M = 2) around a flat plate. The observed phenomena during high speed-flow control with a plasma discharge are exhaustively described. The present investigation is of great interest not only to aviation but also to numerous other areas like the wind power industry. The computations have been carried out using the DC discharge and the High Mach Number Flow Comsol Multiphysics modules. To simulate the DC discharge, chemical reactions near the cathode region along with their corresponding Townsend coefficients need to be defined. The latter are calculated using the Bolsig + computer code. The other reactions cross sections are imported from the LXCAT data base. The imported data are used to calculate the reactions rates. The plasma discharge effects on the rarefied supersonic flow are described using a 2D hydrodynamical model under the Drift–Diffusion approximation. The hydrodynamical model was validated by comparing its results for a supersonic air flow with experiments. The main results on an Argon supersonic flow coupled to an Argon discharge show an increase in the pitot pressure and the shock angle.

A unified description of oblique waves in ideal and non-ideal steady supersonic flows around compressive and rarefactive corners

According to classical gas dynamic theory, if a steady supersonic parallel flow encounters a sudden change in the wall slope, two very different phenomena may occur. If the flow expands around a sharp corner, the well-known isentropic Prandtl–Meyer fan is observed. Conversely, a shock wave occurs if the flow is compressed: for wedge angles smaller than the detachment value, which depends on the uniform upstream state, an oblique shock originates at the corner; at larger deviation angles, a detached shock is formed. A unified description of these flows is presented here to extend the validity of the common $$\beta $$ – $$\vartheta $$ (shock angle–deflection angle) diagram for shocked non-isentropic flows into the realm of isentropic expansions. The new graph allows for a straightforward identification of the wave angles for self-similar flow fields around compressive and rarefactive corners. Besides, it clarifies the relation between shock waves and rarefaction fans in the neighbourhood of the $${\vartheta =0}$$ axis, where shock waves are weak enough to be fairly well approximated by isentropic compressions. At $${\vartheta =0}$$ , indeed, shock and rarefaction curves are demonstrated to be first order continuous. This result is interpreted in view of the bisector rule for oblique shock waves. Exemplary diagrams are reported for both ideal-gas flows, dilute-gas flows and non-ideal flows of dense vapours in the close proximity of the liquid–vapour saturation curve and critical point. The application of the new diagram is illustrated for the textbook case of the supersonic flow past a diamond-shaped airfoil.

Simulation and stability analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92

We investigate flow instability created by an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The adverse pressure gradient of the oblique shock causes the boundary layer to separate from the wall, resulting in the formation of a recirculation bubble. For sufficiently large oblique shock angles, the recirculation bubble is unstable to three-dimensional perturbations and the flow bifurcates from its original laminar state. We utilize Direct Numerical Simulation (DNS) and Global Stability Analysis (GSA) to show that this first occurs at a critical shock angle of $\theta = 12.9^o$. At bifurcation, the least stable global mode is non-oscillatory, and it takes place at a spanwise wavenumber $\beta=0.25$, in good agreement with DNS results. Examination of the critical global mode reveals that it originates from an interaction between small spanwise corrugations at the base of the incident shock, streamwise vortices inside the recirculation bubble, and spanwise modulation of the bubble strength. The global mode drives the formation of long streamwise streaks downstream of the bubble. While the streaks may be amplified by either the lift-up effect or by G\"ortler instability, we show that centrifugal instability plays no role in the upstream self-sustaining mechanism of the global mode. We employ an adjoint solver to corroborate our physical interpretation by showing that the critical global mode is most sensitive to base flow modifications that are entirely contained inside the recirculation bubble.

Effect evaluation of a novel dehumidification structure based on the modified model

In the course of energy conversion, steam turbine is one of the most important equipment, but the wet steam at the low-pressure stage will cause losses. The losses caused by condensing flow not only reduce the efficiency of steam turbine but also influence reliability. This paper firstly numerically investigated the Dykas cascade using the modified model, and compared with the experimental data. The results showed that the modified model had an enormous advantage in predicting the condensing flow. Besides, the advantage was obvious in calculating the pressure distribution of the blade and shock angle emerged in the blade trailing edge. Secondly, a novel dehumidification structure was proposed and the effect was calculated and discussed. The result showed that the novel structure had a positive effect on reducing the nucleation zone and the liquid mass fraction. Besides, the influence of different passage diameters was investigated, the conclusion can be drawn: both the liquid mass fraction of the outlet and the nucleation zone decrease with the increment of the passage diameter. Finally, an improved dehumidification structure which can be easily manufactured was presented and the structure with different φ was calculated. The results showed that when φ=0, the dehumidification efficiency was remarkable, and the structure can be easily manufactured. However, the decrement of the liquid mass fraction was inconspicuous with the further increment of φ.

Mitigation of Turbine Vane Shock Waves Through Trailing Edge Cooling

The immense market demand on the high efficiency and lightweight aero-engines results in designs with compact high-pressure turbine stages experiencing supersonic flow field. In supersonic turbines, shocks appear at the vane trailing edges. The interaction of these shock with the neighbouring airfoils and blades on the adjacent rotor row and consequently create considerable amount of losses on the aerodynamic performance of the turbine. Moreover, periodic excitation created by the interaction of the shock waves and the motion of the turbine rotor causes fatigue problems and reduces the lifetime of the engine. Current study aims to alter the vane shock waves through blowing at the trailing edge. In order to characterize the effect of active blowing on the trailing edge flow field, a series of URANS simulations were conducted on OpenFOAM solver platform. Various blowing schemes were simulated over a simplified trailing edge geometry exposed in supersonic flow. The computations were compared in terms of shock intensity, oscillation frequency and exerted pressure forcing over the downstream components. The results showed that unsteady trailing edge blowing were able to modify the fluctuations observed on the shocks by altering the shock intensity, angle and frequency of oscillations. The classification of the wake unsteadiness, i.e. vortex shedding, in terms of trailing edge characteristics were also accomplished through frequency domain analysis of simulations.

Shock Wave Mitigation by Air Plasma Deflector

When the spacecraft flies much faster than the sound speed (~1200 km/h), the airflow disturbances deflected forward from the spacecraft cannot get away from the spacecraft and form a shock wave in front of it. Shock waves have been a detriment for the development of supersonic aircrafts, which have to overcome high wave drag and surface heating from additional friction. Shock wave also produces sonic booms. The noise issue raises environmental concerns, which have precluded routine supersonic flight over land. Therefore, mitigation of shock wave is essential to advance the development of supersonic aircrafts. A plasma mitigation technique is studied. A theory is presented to show that shock wave structure can be modified via flow deflection. Symmetrical deflection evades the need of exchanging the transverse momentum between the flow and the deflector. The analysis shows that the plasma generated in front of the model can effectively deflect the incoming flow. A non-thermal air plasma, generated by on-board 60 Hz periodic electric arc discharge in front of a wind tunnel model, was applied as a plasma deflector for shock wave mitigation technique. The experiment was conducted in a Mach 2.5 wind tunnel. The results show that the air plasma was generated symmetrically in front of the wind tunnel model. With increasing discharge intensity, the plasma deflector transforms the shock from a welldefined attached shock into a highly curved shock structure with increasing standoff distance from the model; this curved shock has increased shock angle and also appears in increasingly diffused form. In the decay of the discharge intensity, the shock front is first transformed back to a well-defined curve shock, which moves downstream to become a perturbed oblique shock; the baseline shock front then reappears as the discharge is reduced to low level again. The experimental observations confirm the theory. The steady of the incoming flow during the discharge cycle is manifested by the repeat of the baseline shock front.

Shock Train Unsteadiness Characteristics, Oblique-to-Normal Transition, and Three-Dimensional Leading Shock Structure

The structure and unsteadiness characteristics of a shock train in a constant-area ducted flow are studied experimentally as a function of duct back pressure, which is mechanically controlled by a valve. Increasing the back pressure pushes the shock train upstream where the approach conditions (including Mach number and boundary-layer momentum thickness) are different, as these quantities vary along the duct length. Despite nominally constant boundary conditions during a run, the shock train fluctuates about its time-averaged position. Schlieren imaging reveals that the unsteadiness characteristics, including the fluctuation amplitude and frequency content, are independent of back pressure. However, changes in the Mach stem length and shock angles demonstrate that the leading shock structure transitions from oblique to normal as back pressure increases. Time-averaged pressure profiles show that the shock train length decreases and the pressure rise across the shock train increases during this process, but these quantities are nominally constant when normalized by the approach conditions. Finally, stereo particle image velocimetry is used to study the three-dimensional structure of a normal leading shock. The velocity fields show a large separation region on the side-wall of the duct and a degree of axisymmetry that indicates a nominally conical shock structure.

Streamlines behind curved shock waves in axisymmetric flow fields

Streamlines behind axisymmetric curved shock waves were used to predict the internal surfaces that produced them. Axisymmetric ring wedge models with varying internal radii of curvature and leading-edge angles were used to produce numerical results. Said numerical simulations were validated using experimental shadowgraph results for a series of ring wedge test pieces. The streamlines behind curved shock waves for lower leading-edge angles are examined at Mach 3.4, whereas the highest leading-edge angle cases are explored at Mach 2.8 and 3.4. Numerical and theoretical streamlines are compared for the highest leading-edge angle cases at Mach 3.6. It was found that wall-bounding theoretical streamlines did not match the internal curved surface. This was due to extreme streamline curvature curving the streamlines when the shock angle approached the Mach angle at lower leading-edge angles. Increased Mach number and internal radius of curvature produced more reasonable results. Very good agreement was found between the theoretical and numerical streamlines at lower curvatures before the influence of the trailing edge expansion fan.

Study of Oblique Shock Wave Control by Surface Arc Discharge Plasma

The mechanism of oblique shock wave control by surface arc discharge plasma is explored through a combined numerical and experimental study. The experiments are conducted in a supersonic wind tunnel with Mach number of 2.5, total pressure of 3.5–6.4 bar, and total temperature of 300 K. An oblique shock is formed by a compression ramp with an angle of 7 deg mounted on the lower wall of the wind tunnel. Six electrodes are arranged equally in the spanwise direction and upstream of the compression ramp. The schlieren images show that the angle of the original oblique shock is increased, and the surface pressure measurements indicate that the oblique shock is weakened by the addition of the stable discharge arc. The reason is that the arc heating decreases the Mach number upstream of the oblique shock; thus, the oblique shock is weakened and the shock angle is increased. A three-dimensional numerical simulation is performed using experimental configuration. Results show that the static pressure increases in front of the oblique shock and decreases after the shock, which is in good agreement with the experimental measurements. This validates that the numerical model presents a reasonable approach for the arc discharge plasma and further confirms the predominant role of the thermal effects of plasma on shock manipulation.

Marangoni elasticity of flowing soap films

We measure the Marangoni elasticity of a flowing soap film to be 22 mN/m irrespective of its width, thickness, flow speed, or the bulk soap concentration. We perform this measurement by generating an oblique shock in the soap film and measuring the shock angle, flow speed, and thickness. We postulate that the elasticity is constant because the film surface is crowded with soap molecules. Our method allows nondestructive measurement of flowing soap film elasticity and the value 22 mN/m is likely applicable to other similarly constructed flowing soap films.Received 3 October 2016DOI:https://doi.org/10.1103/PhysRevFluids.2.082001©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCompressible flowsShock wavesSurface tension effectsFluid DynamicsStatistical PhysicsInterdisciplinary Physics

Shock-Wave-Detection Technique for High-Speed Rarefied-Gas Flows

This paper introduces a shock-wave-detection technique based on the schlieren imaging for continuum and rarefied-gas flows. The scheme is applicable for any existing two-dimensional flowfields obtained by experimental or numerical approaches. A Gaussian distribution for a schlieren function within the shock-wave region is considered. This enables the authors to access any desired locations through the shock (e.g., shock center, or leading- and trailing-edge locations). The bow shock-wave profile is described via a rational function, which could be employed for the estimation of shock angle. The relation between pre- and postshock flow properties along the shock wave with a high resolution can be investigated by using this technique. The technique is verified in a novel way based on the well-known gas dynamics curves (i.e., flow-deflection angle vs shock angle and shock polar diagrams). High-speed continuum, near continuum, and rarefied-gas flows over a wedge and cylinder are considered for evaluation of the proposed technique. The results show a very good agreement with existing analytical relations for continuum flow.

Shock transformation and hysteresis in underexpanded confined jets

This study investigates the shock transformation in an underexpanded jet in a confined duct when the jet total pressure is increased. Experimental study reveals that the Mach reflection (MR) in the fully underexpanded jet transforms to a regular reflection (RR) at a certain jet total pressure. It is observed that neither the incident shock angle nor the upstream Mach number varies during the MR–RR shock transformation. This is in contradiction to the classical MR–RR transformations in internal flow over wedges and in underexpanded open jets. This transformation is found to be a total pressure variation induced transformation, which is a new kind of shock transformation. The present study also reveals that the critical jet total pressures for MR–RR and RR–MR transformations are not the same when the primary pressure is increasing and decreasing, suggesting a hysteresis in the shock transformations.

Electron Scattering by High-frequency Whistler Waves at Earth’s Bow Shock

Abstract Electrons are accelerated to non-thermal energies at shocks in space and astrophysical environments. While different mechanisms of electron acceleration have been proposed, it remains unclear how non-thermal electrons are produced out of the thermal plasma pool. Here, we report in situ evidence of pitch-angle scattering of non-thermal electrons by whistler waves at Earth’s bow shock. On 2015 November 4, the Magnetospheric Multiscale (MMS) mission crossed the bow shock with an Alfvén Mach number ∼11 and a shock angle ∼84°. In the ramp and overshoot regions, MMS revealed bursty enhancements of non-thermal (0.5–2 keV) electron flux, correlated with high-frequency (0.2–0.4 , where is the cyclotron frequency) parallel-propagating whistler waves. The electron velocity distribution (measured at 30 ms cadence) showed an enhanced gradient of phase-space density at and around the region where the electron velocity component parallel to the magnetic field matched the resonant energy inferred from the wave frequency range. The flux of 0.5 keV electrons (measured at 1 ms cadence) showed fluctuations with the same frequency. These features indicate that non-thermal electrons were pitch-angle scattered by cyclotron resonance with the high-frequency whistler waves. However, the precise role of the pitch-angle scattering by the higher-frequency whistler waves and possible nonlinear effects in the electron acceleration process remains unclear.

Aerodynamic Analysis Over Double Wedge Airfoil

Aeronautical studies are being focused more towards supersonic flights and methods to attain a better and safer flight with highest possible performance. Aerodynamic analysis is part of the whole procedure, which includes focusing on airfoil shapes which will permit sustained flight of aircraft at these speeds. Airfoil shapes differ based on the applications, hence the airfoil shapes considered for supersonic speeds are different from the ones considered for Subsonic. The present work is based on the effects of change in physical parameter for the Double wedge airfoil. Mach number range taken is for transonic and supersonic. Physical parameters considered for the Double wedge case with wedge angle (ranging from 5 degree to 15 degree.Available Computational tools are utilized for analysis. Double wedge airfoil is analysed at different Angles of attack (AOA) based on the wedge angle. Analysis is carried out using fluent at standard conditions with specific heat ratio taken as 1.4. Manual calculations for oblique shock properties are calculated with the help of Microsoft excel. MATLAB is used to form a code for obtaining shock angle with Mach number and wedge angle at the given parameters. Results obtained from manual calculations and fluent analysis are cross checked.

Control of Triple-Shock Configurations and Vortex Structures Forming in High Speed Flows of Gaseous Media past an AD Body under the Action of External Energy Sources

The problem of supersonic streamlining of an aerodynamic (AD) body, “a plate blunted by a cylinder”, by a flow with the freestream Mach number M = 4 containing an external energy source has been studied, taking into account physicochemical transformations. The results of the effect of the ratio of specific heats γ changing in the range from 1.1 to 1.4 on the dynamics of triple-shock configurations and vortex-contact structures are presented for the interaction of an energy source with the bow shock wave. The energy source is modeled via the heated rarefied layer (filament). The angles in the triple-shock configurations, the stagnation pressure, together with the frontal drag force, have been studied dependent on the specific heats ratio γ, the characteristics of the energy source, and also on the angle of the incident shock. Vortex-contact structures have been researched for the Mach numbers 7, 8, 9, as well as the generation of the Richtmyer-Meshkov instability accompanying the formation of a triple-shock configuration. The results show a strong influence of the specific heats ratio of the gas medium and the parameters of the energy source on the triple-shock configuration and aerodynamic characteristics of the body. This conclusion can be useful for aerospace applications in the area of the design of nozzles, intakes, and high speed flying vehicles. Additionally, the results show the possibility of flow control in the atmospheres of other planets using external energy deposition.

Systematic Application of Background-Oriented Schlieren for Isolator Shock Train Visualization

The background-oriented schlieren technique is applied to visualize Mach 2.5 isolator shock train structures in 3.0- and 6.0-aspect-ratio rectangular cross-section ducts. To optimize the background pattern, a parametric study is performed by using a 10 deg compression ramp calibration flowfield producing a reference density gradient. In conjunction with a multigrid cross-correlation algorithm, the optimized background pattern adheres to three classic particle image velocimetry design rules: 1) interrogation window width four times the expected particle displacement, 2) magnified particle diameter between 2 and 5 pixels, and 3) image density greater than 10. A modified -factor analysis and qualitative observations of the density gradient range resolved suggest an optimal image density of 75 and a magnified particle diameter range of 2–5 pixels. Background-oriented schlieren visualization of the primary shock train element in both aspect ratio ducts shows the strongest density gradients to be located in the refracted shock region between the oblique shock intersection and the primary normal shock. A previous study confirms that this region is characterized by an increasing shock angle and Mach number as it approaches the duct centerline.

Strong magnetic fields generated with a metal wire irradiated by high power laser pulses and its effect on bow shock

Laboratory astrophysics is a rapid developing field studying astrophysical or astronomical processes on a high-power pulsed facility in laboratory. It has been proved that with the similarity criteria, the parameters in astrophysical processes can be transformed into those under laboratory conditions. With appropriate experimental designs the astrophysical processes can be simulated in laboratory in a detailed and controlled way. Magnetic fields play an important role in many astrophysical processes. Recently, the generation of strong magnetic fields and their effects on relevant astrophysics have attracted much interest. According to our previous work, a strong magnetic field can be induced by a huge current formed by the background cold electron flow around the laser spot when high power laser pulses irradiate a metal wire. In this paper we use this scheme to produce a strong magnetic field and observe its effect on a bow shock on the Shenguang II (SG II) laser facility. The strength of the magnetic field is measured by B-dot detectors. With the measured results, the magnetic field distribution is calculated by using a three-dimension code. Another bunch of lasers irradiates a CH planar target to generate a high-speed plasma. A bow shock is formed in the interaction of the high-speed plasma with the metal wire under the strong magnetic condition. The effects of the strong magnetic field on the bow shock are observed by shadowgraphy and interferometry. It is shown that the Mach number of the plasma flow is reduced by the magnetic field, leading to an increase of opening angle of the bow shock and a decrease of the density ratio between downstream and upstream. In addition, according to the similarity criteria, the experimental parameters of plasma are scaled to those in space. The transformed results show that the magnetized plasma around the wire, produced by X-ray emitted from the laser-irradiated planar target in the experiment, is suitable for simulating solar wind in astrophysics. In this paper, we provide another method to produce strong magnetic field, apply it to a bow shock laboratory astrophysical study, and also generate the magnetized plasma which can be used to simulate solar wind in the future experiments.

Dependence of the Spectrum of Shock-Accelerated Ions on the Dynamics at the Shock Crossing.

Diffusive shock acceleration (DSA) of ions occurs due to pitch-angle diffusion in the upstream and downstream regions of the shock and multiple crossing of the shock by these ions. The classical DSA theory implies continuity of the distribution at the shock transition and predicts a universal spectrum of accelerated particles, depending only on the ratio of the upstream and downstream fluid speeds. However, the ion dynamics at the shock front occurs within a collision-free region and is gyrophase dependent. The ions fluxes have to be continuous at the shock front. The matching conditions for the gyrophase-averaged distribution functions at the shock transition are formulated in terms of the transition and reflection probabilities. These probabilities depend on the shock angle and the magnetic compression as does the power spectrum of accelerated ions. Their spectral index is expressed in terms of the reflectivity. The spectrum is typically harder than the spectrum predicted by the classical DSA theory.