Strength Of Shock Wave Research Articles

Adjoint-based aerodynamic shape optimization including transition to turbulence effects

The inclusion of transition to turbulence effects in aerodynamic shape optimization makes it possible to use it as a tool for the design of airframes with laminar flow. Modified Reynolds-Averaged Navier–Stokes (RANS) models that consider transition to turbulence have gained traction in the computational fluid dynamics (CFD) community. These models enable the computation of transitional flows without the need for external modules. In this work, we use a smooth version of the amplification factor transport (AFT) model, called AFT-S, to perform gradient-based aerodynamic shape optimization (ASO) of airfoils in subsonic and transonic flow conditions. We investigate the benefits of including transition effects into the optimization process and assess the impact of losing laminar flow when early transition to turbulence occurs due to surface contamination. Our results indicate that our design optimization approach yields lower drag airfoils when transition effects are considered. For the transonic case, the optimizer trades between shock wave strength and laminar flow extension to minimize drag.

A robust and contact preserving flux splitting scheme for compressible flows

Low-dissipation shock-capturing methods usually suffer from various forms of shock instabilities, such as the notorious carbuncle phenomenon, in simulations of hypersonic flows. Many strategies for tackling the shock instability of flux difference splitting schemes, such as HLLC and Roe schemes, have been proposed while little work has been undertaken on the shock instability of flux splitting schemes. In this paper, we are concerned with the shock instability of a convection-pressure flux splitting scheme. By means of a linearized perturbation analysis, it shows that all of the perturbations in the streamwise direction are damped, while the perturbations of density and shear velocity in the transverse direction are undamped. Due to the special symmetry, the two-dimensional Sedov blast wave problem is studied to demonstrate the relation between the transverse flux and shock instability. Based on the theoretical analyses, a shock stable flux splitting scheme is presented through introducing additional viscosities of entropy wave and shear wave to damp out all perturbations in the transverse direction. For restoring the contact surface and shear layer, a pressure-based function depending on the shock-wave strength is defined to control the amount and location of additional viscosities. Numerical results of several challenging test problems demonstrate that the new scheme has greatly improved the robustness without undermining the accuracy.

Effects of micro-vortex generators on shock wave structure in a low aspect ratio duct, numerical investigation

The interaction between the shock wave and boundary layer and its induced separation is an undesirable phenomenon in the design of supersonic systems. The control of this phenomenon by active and passive methods is highly important in the design of aerodynamic systems. In the present work, different series of micro vortex generators were investigated as a passive control method (with the ability to increase the flow momentum), affecting the structure of a compressible flow at the Mach number of 2.05 in a low-aspect-ratio duct. In this regard, the finite volume method was used in the OpenFoam package. The obtained results were first validated against experimental data, and then four different vortex generators with a height of 10 μm were investigated. The results revealed that the use of vortex generators caused a reduction in the shock wave strength and energy loss across the flow. Furthermore, applying a vortex micro-generator with the outer body of national advisory committee for aeronautics 4412 airfoil led to a significant decrease in the strength of shock waves. Also, a vortex generator could shift the shock wave occurrence location to the downstream.

Spatial–temporal evolution of plasma radiation in electrical wire explosion: a morphological observation

This paper deals with an experimental study regarding the spatial–temporal evolution of single wire explosions in air and water at atmospheric pressure. Experiments were carried out with a microsecond timescale pulsed current source under 500 J stored energy. The morphology of the exploding wire with different discharge type, wire material, insulating coat, and ambient medium was intensively observed via self-emission images. The results revealed that the plasma radiation of wire explosion in air mainly contained two stages: initial intense radiation from optically thick plasma, and later decaying radiation from expanded arc-like plasma. A hollow structure was observed in a Cu exploding wire in air, and the plasma channel tended to develop inside it. As for W case, there would always be a core-corona structure, resulting in lower expansion rate and shock wave strength. Moreover, the plasma radiation of the underwater wire explosion was mainly determined by two factors: expansion rate and chemical reaction. The expansion rate of the radiant region in water was only 10–1 mm μs–1 level (1 mm μs–1 level for air), leading to the lagging radiation. No noticeable difference in morphology was found between Cu and W wire explosions in water. Particularly, the Al wire explosion generated a bright light emission due to chemical reactions. Finally, radiative characteristics in an exploding wire were preliminarily concluded and existing problems proposed.

Effect of mach number on high-subsonic and low-Reynolds-number flows around airfoils

High-subsonic and low-Reynolds-number flow is a special aerodynamic problem associated with near space propellers and Mars aircrafts. The flow around airfoils and the corresponding aerodynamic performance are different from the incompressible flow at low-Reynolds-number, due to complex shock wave-laminar separation bubble interaction. The objective of this paper is to figure out the effect of Mach number on aerodynamic performance and special flow structure of airfoil. An in-house Reynolds-averaged Navier–Stokes solver coupled with [Formula: see text] transition model is employed to simulate the flows around the E387 airfoil. The results show that the lift slope is larger than [Formula: see text] in the linear region. No stall occurs even at an attack angle of [Formula: see text]. With increase of Mach number, lift coefficient decreases when attack angle is below [Formula: see text]. However, once the angle of attack exceeds [Formula: see text], higher Mach number corresponds to higher lift coefficient. In addition, the strength and number of shock waves are very sensitive to Mach number. With increase of Mach number, the region of reverse flow vortex near transition location becomes smaller and finally disappears, while a new reverse flow vortex appears near the trailing edge and becomes larger.

The Exact Riemann Solutions to the Generalized Pressureless Euler Equations with Dissipation

The Riemann solutions for the generalized pressureless Euler equations with a dissipation term are constructed explicitly. It is shown that the delta shock wave appears in Riemann solutions in some situations. The generalized Rankine–Hugoniot conditions of the delta shock wave are established, and the exact position, propagation speed and strength of the delta shock wave are given explicitly. Unlike the homogeneous case, it is shown that the dissipation term makes contact discontinuities and delta shock waves bend into curves and the Riemann solutions are not self-similar anymore. Moreover, as the dissipation term vanishes, the Riemann solutions converge to the corresponding ones of the generalized pressureless Euler equations. Finally, we give the application of our results on two typical examples.

Shock wave interactions within concave cavities

The interaction of a plane shock wave in air with concave profiles has been used in the past mainly to understand the nature of shock wave focusing. The current study examines the complex two-dimensional flow field resulting from the interaction of a plane shock wave entering a symmetrical cavity with curved walls. Of particular interest are the development of reflection patterns of the incident shock wave at the profile wall and the process of gas dynamic focus. These principal flow features are examined across a wide range of different reflector shapes. This includes a review of previously studied profiles such as cylindrical and parabolic, and also of a number of additional profiles, including compound profiles, where an inlet profile merging with that of the main cavity is shown to have major effects on the focusing mechanism and pressures. The various reflector shapes were specified by varying the shape of the profile and the depth-to-aperture ratio. The strength of the incident plane shock wave was limited between Mach numbers of 1.04 and 1.45. The principal flow features were established and examined experimentally using a variety of qualitative and quantitative flow visualization techniques, supplemented with numerical results. Time-resolved high-speed imaging was used to capture the interaction providing the unique ability to track the various transient flow features over the course of the interaction. The three primary factors that influence the maximum pressure amplification at focus, and the focus mechanism, are the incident shock strength, the depth-to-aperture ratio of the profile and an inlet profile leading into the main cavity, if present. An inlet profile results in higher-pressure amplifications for corresponding shock strengths and depth-to-aperture ratios. Increases in the depth-to-aperture ratio increase the maximum pressure amplification observed at focus. This occurs due to a combination of factors including: the strengthening of the individual shock waves involved in focus; the duration of focus; and the strengthening of a compressive flow field that develops adjacent to the shock system during focus. The compressive flow field adjacent to the shock system at focus is shown to be of great importance to the focus process.

Aerodynamic shape optimization by continually moving ROM

This study presents a multi-round shape optimization method based on the aerodynamic reduced order model. In this method, each optimization round employs the first-order Taylor reduced order model to provide aerodynamic characteristics in the local design space around the baseline point. At the end of each optimization round, the baseline point moves toward the optima and a new reduced order model is built at the new baseline point for the next optimization round. In this way, the provided method explores the whole design space. The NACA0012 airfoils in subsonic and transonic flows are used to verify the method with the lift-drag ratio as optimization objective. The design parameters are the shape control parameters of the airfoil. The optimization algorithm is a genetic algorithm. After a total of 20 simulations by two rounds of optimizations, the lift-drag ratios increase from 0 to 25 and from 0 to 8 in the subsonic case and transonic case, respectively. An additional trick was suggested for addressing shockwave effect in the transonic case, in which the influence of the airfoil shape on the aerodynamic forces is divided into the following two parts: the smoothed part to address the influence of the shape on the smooth aerodynamic distribution, and the shockwave part to address the influence of the shape on shockwave strength, shockwave position, and their effect on the aerodynamic distribution. The optimizations of the airfoils in subsonic and transonic flows yield different trends. The results of the subsonic case tend to increase the airfoil curvature to increase the lift-drag ratio. The results of the transonic case tend to move the upper surface shockwave to the trailing edge, while moving the lower surface shockwave to the leading edge. Independent of the case, the provided optimization method can properly address the resulting trends and increase the efficiency of the optimization.

Numerical research on the trailing-edge sweep of supersonic/transonic turbines

Although the sweep design used in fans and compressors has been the subject of considerable research and development, its application in turbines is relatively rare. This paper first studies the aerodynamic effects and mechanics of a general backward sweep in supersonic plane cascades. In response to the specific challenge of severe changes in working conditions, a new structure, combined with the characteristics of an unchanged throat and sweep around the trailing-edge, is proposed and studied. After two targeted modifications, the trailing-edge sweep is applied to a turbine stage. The results show that, similar to fans and compressors, the aerodynamic influence of the sweep in the turbine changes the working conditions and spanwise loading in spanwise tubes. Proper trailing-edge sweep design can weaken the strength of the 3D shock wave under similar flow conditions, providing a new approach for shock-weakening treatments. By applying the trailing-edge sweep, the turbine stage achieves an efficiency improvement of nearly 0.4%.

Nonlinear stability of large amplitude viscous shock wave for general viscous gas

In the present paper, it is shown that the large amplitude viscous shock wave is nonlinearly stable for isentropic Navier-Stokes equations, in which the pressure could be general and includes γ-law, and the viscosity coefficient is a smooth function of density. The strength of shock wave could be arbitrarily large. The proof is given by introducing a new variable, which can formulate the original system into a new one, and the elementary energy method introduced in [21].

Delta-Shock Solution to the Eulerian Droplet Model by Variable Substitution Method

Abstract By introducing a special kind of variable substitution, we skillfully solve the delta-shock and vacuum solutions to the one-dimensional Eulerian droplet model. The position, propagation speed, and strength of the delta shock wave are derived under the generalised Rankine–Hugoniot relation and entropy condition. Moreover, we show that the Riemann solution of the Eulerian droplet model converges to the corresponding the pressureless Euler system solution as the drag coefficient goes to zero.

Drift wave in strong collisional dusty magnetoplasma

The study about the wave mechanism of magnetized dusty plasmas has important value to related experiment, industrial processing and exploring celestial space. The linear and nonlinear fluctuation characteristics of the nonuniform magnetized dust plasma system are researched in this paper. For the homogeneous external magnetic field and the nonuniform environment with density and temperature gradients, a two-dimensional nonlinear dynamic magnetoplasma equation is derived considering the strong impact between dust and neutral particles. The linear dispersion relation is obtained by the linearized method. There are both the damping wave causing by strong collision and the harmonic wave by particle drift. Employing the typical numerical parameters for analysis, the results display that the quantum parameter modifies the system lengths; the real wave frequency is proportion to the drift frequency; the imaginary wave frequency has complex relationship with the collision frequency between dust and neutrals, and the collision of particles causes the dissipation effects to the system. Besides, the analytical solutions of drift shock wave and explosive wave are solved by function change method. The variation about the electrostatic potential with the main physical parameters is discussed in detail. It is shown that the strength of the electrostatic shock wave and the width of the explosive wave increase with increasing the dust density and magnetic field intensity, decrease with increasing the collision frequency, change with the drift velocity. When the space-time phase is small, the electrostatic potential changes quickly; once big enough, the potential tends to be stable value and reaches stable state eventually. Finally, the stability of the system is discussed. It is found that the dusty charge, quantum parameter, drift velocity all appear in the disturbed solution. All these results in the paper show that the strong collision effect, quantum effect, particle drift and magnetic field all play important role to the generation, evolution and stability of drift waves.

Influence of parallel shearing flow on the switch-off effect of magnetic reconnection

Parallel shearing flows significantly affect the structure of the magnetic reconnection layer and generate new shock structures such as intermediate shock (IS) and time-dependent IS. The strength of shock waves (such as slow shock) can be changed and result in the switch-off of magnetic reconnection under certain conditions. In this study, we perform numerical simulations of one-dimensional resistive magnetohydrodynamic equations by using the total variation diminishing algorithm to investigate the influence of parallel shear flow on the switch-off effect of magnetic reconnection on both asymmetric and symmetric magnetic reconnection layers. Numerical results show that there exists a critical shear velocity Vzc that equals VA in symmetrical antiparallel magnetic reconnection, where VA denotes the inflow Alfvén velocity. For symmetric component magnetic reconnection, Vzc drops with the increase in guide magnetic field strength, which also equals the component of inflow Alfvén velocity along the z-axis. In regard to asymmetric magnetic reconnection, the critical shear velocity, Vzc, that leads to the switch-off of magnetic reconnection, ranging between the z-axis components of inflow Alfvén velocity in the magentosheath and in the magnetosphere. A new parameter associated with the Alfvén velocity on both sides is proposed; for both antiparallel reconnection and component reconnection, this new parameter equals the critical shear velocities.

A Novel Three-Dimensional Inverse Method for Axial Compressor Blade Surface Design

A novel three-dimensional inverse method based on the time-accurate solution of Navier–Stokes equations for axial compressor design is proposed in this work. The main novelty lies in the derivation of an inverse design boundary condition established on the conservation of Riemann invariant in order to directly design the blade surface. Specifically, a dynamic mesh technique is employed to update the grids and reduce the computational costs. In addition, some restrictions are imposed on the blade surface movement in order to avoid unrealistic airfoil profiles and guarantee computational robustness. Two redesign procedures are presented, including shock wave strength restrain for the NASA Rotor 37 stage and integrated controlled diffusion airfoil concept design for the Stage 35. Results indicate that this novel inverse method is effective for detailed axial compressor design.

The Riemann problem for the Suliciu relaxation system with the double-coefficient Coulomb-like friction terms

We solve the Riemann problem for the Suliciu relaxation system with the Coulomb-like friction terms containing two constant friction coefficients. The exact Riemann solutions involving delta shock waves and contact discontinuities are obtained constructively. Via deriving the generalized Rankine–Hugoniot relations of delta shock waves in detail, all of the position, propagation speed and strength of the delta shock wave are given concretely under a suitable entropy condition. Based on this, we clearly analyze the influence of the Coulomb-like friction terms on the Riemann solutions of the Suliciu relaxation system.

Simulation of Hypersonic-Shock-Wave–Laminar-Boundary-Layer Interaction over Blunt Fin

Shock-wave–boundary-layer interaction is one of the most important phenomena in hypersonic flights due to its ubiquitous presence and its extreme effects on the aerothermodynamic loads on the aircraft surfaces. Low-frequency oscillations in separated flows in addition to high localized pressure and heat transfer as a result of such interactions make the ability to predict the flow with shock-wave–boundary-layer interaction highly essential in design of any hypersonic aircraft. To further investigate three-dimensional shock-wave–hypersonic-boundary-layer interaction, a cylindrically blunt fin–plate junction with three different sweep angles, 0, 22.5, and 45 deg, of the fin relative to the plate is chosen to numerically simulate. An MPI code written by the authors was used to solve the unsteady Navier–Stokes and ideal gas equations. The blunt fin shock wave with strength depending on the sweep angle of the fin interacts with the boundary layer on the plate and creates a separated region with a complex flow structure. The extent of the separated region decreases with increase in the sweep angle of the fin and decrease in the strength of the blunt fin shock wave. Localized high pressure forms at the reattachment point of the boundary layer by formation of a reattachment shock wave, with its maximum peak decreasing by increase in the sweep angle of the fin. The boundary-layer thickness on the blunt fin reaches its minimum at the reattachment point, where the heat transfer rate reaches its maximum value. Unsteady oscillations are observed in the 0 deg sweep angle configuration. The unsteady oscillations significantly subside with increase in the sweep angle of the fin. Time-averaged normalized heat transfer of the numerical simulations shows good agreement with the experimental data, except for the peak heat transfer for the 0 deg sweep angle case.

Pressure dependency on a nanosecond pulsed dielectric barrier discharge plasma actuator

The behavior of a nanosecond pulsed dielectric barrier discharge (ns-DBD) plasma actuator with the ambient pressure from 30 to 100 kPa was characterized with Schlieren images. Shock wave propagation speed and strength were recorded, showing clear trends with decreasing ambient pressure. Higher ambient pressures result in stronger shock waves; this has been observed irrespective of the actuator thickness. This might be explained with fewer air molecules to ionize at lower ambient pressures and hence a lower temperature from the exothermal recombination reactions. The thickness of the dielectric barrier also influences the shock strength. In accordance with previous findings, it was confirmed that a thinner dielectric barrier results in a greater shock strength. NS-DBD shock waves were modeled numerically using OpenFOAM through a source term added to the energy equation, which controls the amount of thermal energy added to the near-wall deposition region. The compressible, unsteady sonicFoam solver was used with second order schemes. A mesh sensitivity study gives confidence that the solution is grid independent. The overall shock wave structure and propagation speed match well with experimental data. The heat addition required to reproduce experimental results varied with ambient pressure. Less heating of the near-wall region was needed with lower ambient pressures.

Connecting the Properties of Coronal Shock Waves with Those of Solar Energetic Particles

Abstract We develop and exploit a new catalog of coronal pressure waves modeled in 3D to study the potential role of these waves in accelerating solar energetic particles (SEPs) measured in situ. Our sample comprises modeled shocks and SEP events detected during solar cycle 24 observed over a broad range of longitudes. From the 3D reconstruction of shock waves using coronagraphic observations we derived the 3D velocity along the entire front as a function of time. Combining new reconstruction techniques with global models of the solar corona, we derive the 3D distribution of basic shock parameters such as Mach numbers, compression ratios, and shock geometry. We then model in a time-dependent manner how the shock wave connects magnetically with spacecraft making in situ measurements of SEPs. This allows us to compare modeled shock parameters deduced at the magnetically well-connected regions, with different key parameters of SEPs such as their maximum intensity. This approach accounts for projection effects associated with remote-sensing observations and constitutes the most extensive study to date of shock waves in the corona and their relation to SEPs. We find a high correlation between the maximum flux of SEPs and the strength of coronal shock waves quantified, for instance, by the Mach number. We discuss the implications of that work for understanding particle acceleration in the corona.

L2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

We consider a L2-contraction (a L2-type stability) of large viscous shock waves for the multi-dimensional scalar viscous conservation laws, up to a suitable shift by using the relative entropy methods. Quite different from the previous results, we find a new way to determine the shift function, which depends both on the time and space variables and solves a viscous Hamilton-Jacobi type equation with source terms. Moreover, we do not impose any conditions on the anti-derivative variables of the perturbation around the shock profile. More precisely, it is proved that if the initial perturbation around the viscous shock wave is suitably small in L2-norm, then the L2-contraction holds true for the viscous shock wave up to a suitable shift function. Note that BV-norm or the L∞-norm of the initial perturbation and the shock wave strength can be arbitrarily large. Furthermore, as the time t tends to infinity, the L2-contraction holds true up to a (spatially homogeneous) time-dependent shift function. In particular, if we choose some special initial perturbations, then L2-convergence of the solutions towards the associated shock profile can be proved up to a time-dependent shift.

Computational analysis of shock-induced flow through stationary particle clouds

We investigate the shock-induced flow through random particle arrays using particle-resolved Large Eddy Simulations for different incident shock wave Mach numbers, particle volume fractions and particle sizes. We analyze trends in mean flow quantities and the unresolved terms in the volume averaged momentum equation, as we vary the three parameters. We find that the shock wave attenuation and certain mean flow trends can be predicted by the opacity of the particle cloud, which is a function of particle size and particle volume fraction. We show that the Reynolds stress field plays an important role in the momentum balance at the particle cloud edges, and therefore strongly affects the reflected shock wave strength. The Reynolds stress was found to be insensitive to particle size, but strongly dependent on particle volume fraction. It is in better agreement with results from simulations of flow through particle clouds at fixed mean slip Reynolds numbers in the incompressible regime, than with results from other shock wave particle cloud studies, which have utilized either inviscid or two-dimensional approaches. We propose an algebraic model for the streamwise Reynolds stress based on the observation that the separated flow regions are the primary contributions to the Reynolds stress.