Shock Wave Structure Research Articles

Numerical Simulations of Shock Waves in Viscous Carbon Dioxide Flows Using Finite Volume Method

An efficient numerical tool for studying shock waves in viscous carbon dioxide flows is proposed. The developed theoretical model is based on the kinetic theory formalism and is free of common limitations such as constant specific heat ratio, approximate analytical expressions for thermodynamic functions and transport coefficients. The thermal conductivity, viscosity and bulk viscosity coefficients are expressed in terms of temperature, collision integrals and internal energy relaxation times. Precomputed in the wide temperature range thermodynamic functions and transport coefficients are implemented to the numerical code which is used for the simulations of the shock wave structure. Including the bulk viscosity to the kinetic model results in the increasing shock width and improves the agreement with experimental data.

Morphing of an adaptive shock control bump using pressurized chambers

The dawn of research on shock and boundary layer interaction control dates back to the 1970s, when humped transonic aerofoils were first studied as a means to improve the performance of supercritical aerofoil technology at off-design conditions. Since then, shock control bumps have been found to be promising devices for such kind of flow control. They have a smearing effect on the shock wave structure achieved through isentropic pre-compression of the flow upstream of the main shock and can significantly lower wave drag without incurring unacceptable viscous losses. However, their performance is strongly dependent on a set of geometrical parameters which must be adjusted according to the ever-changing flight conditions. A concept for an adaptive shock control bump is therefore presented. The proposed actuation mechanism aims at a compact, lightweight and simple structure which could be integrated into the spoiler region of near-future aircraft without major design changes required. Numerical optimization of a simplified analytical model of the structure is used to investigate the shock control bump adaptation to various aerodynamic target shapes. Compromises between geometrical conformity and both structural and actuation related requirements are studied. Furthermore, an outlook is given on design issues related to three-dimensional effects on a finite span shock control bump.

Propagation properties of dissipative waves in non Maxwellian plasmas

The propagation of the ion-acoustic shock waves (dissipative waves) are presented in a plasma consisting of fluid ions and cold and hot electrons. Cold and hot electrons are considered as Maxwellian and kappa distribution functions, respectively. Using reductive perturbation technique, Korteweg-de-Vries-Burger (KdVB) and Burgers equations are derived for shock waves in the present plasma model. It is found that both positive (compressive) and negative (rarefactive) ion-acoustic shock waves can be propagating in present medium. Finally, the influence of different parameters on both these shock waves are studied numerically. Our results are important for the electrostatic shock wave structures in space plasmas.

Performance of wavecatcher intakes at angles of attack and sideslip

A wavecatcher type scramjet intake, that reduces the Mach number number from 4 to 1.552, is used as the basis for a study of flow starting/unstarting as affected by freestream angles of attack and sideslip. The intake design is based on a morphed streamtube consisting of two conical flow streamlines using streamline tracing and osculating axisymmetric design theory. Intake flow and performance is modeled using the numerical CFD code and the k-ε turbulence model. The intake unstarts at a sideslip angle of 2°, a positive angle of attack of 1°. Both positive angle of attack and sideslip angle have an adverse effect on the startability of the MBus intake. At negative angles, the intake initially unstarts at −5° angle of attack, due to the thickened shear layer induced by the streamwise vortex. Then it re-starts at −8° angle of attack, mainly due to the expansion fan formed at the leading edge, causing the shock wave structures inside the intake to be re-established.

Influence of viscous boundary layer on initiation zone structure of two-dimensional oblique detonation wave

The influence of the viscous boundary layer on the oblique detonation wave structure has been simulated and analyzed by solving the two-dimensional Navier–Stokes equations containing the hydrogen/air elementary reaction model. It is found that the effect of the viscous boundary layer can be neglected in the smooth transition initiation structure, but not in the abrupt transition initiation structure. The interaction of the lateral shock wave and the viscous boundary layer results in the formation of a high-temperature recirculation zone near the wall of the initiation zone, a novel structure that does not appear in inviscid formulations. Within this structure, the chemical reaction is triggered to occur in advance, eventually leading to the equilibrium initiation position relocating upstream compared with the inviscid case. Nevertheless, the viscous boundary layer has a limited impact on the main flow region downstream of the oblique detonation. The shock wave structures and pressure distributions at various Mach numbers are obtained computationally and analyzed in detail.

Study on Multiple Shock Wave Structures in Supersonic Internal Flow

Study on Multiple Shock Wave Structures in Supersonic Internal Flow

Transport properties of strongly coupled electron–phonon liquids

In this work we consider the hydrodynamic behavior of a coupled electron–phonon fluid, focusing on electronic transport under the conditions of strong phonon drag. This regime occurs when the rate of phonon equilibration due to e.g. umklapp scattering is much slower than the rate of normal electron–phonon collisions. Then phonons and electrons form a coupled out-of-equilibrium state where the total quasi-momentum of the electron–phonon fluid is conserved. A joint flow-velocity emerges as a collective hydrodynamic variable. We derive the equation of motion for this fluid from the underlying microscopic kinetic theory and elucidate its effective viscosity and thermal conductivity. In particular, we derive decay times of arbitrary harmonics of the distribution function and reveal its corresponding super-diffusive relaxation on the Fermi surface. We further consider several applications of this theory to magneto-transport properties in the Hall-bar and Corbino-disk geometries, relevant to experiments. In our analysis we allow for general boundary conditions that cover the crossover from no-slip to no-stress flows. Our approach also covers a crossover from the Stokes to the Ohmic regime under the conditions of the Gurzhi effect. In addition, we consider the frequency dependence of the surface impedance and non-equilibrium noise. For the latter, we notice that in the diffusive regime, a Fokker–Planck approximation, applied to the electron–phonon collision integral in the Eliashberg form, reduces it to a differential operator with Burgers type nonlinearity. As a result, the non-equilibrium distribution function has a shock-wave structure in the energy domain. The consequence of this behavior for the Fano factor of the noise is investigated. In conclusion we discuss connections and limitations of our results in the context of recent electron–phonon drag measurements in Dirac and Weyl semimetals, and layout directions for further extensions and developments.

Numerical Investigation on the Cold Flow Field of a Typical Cavity-based Scramjet Combustor with Double Ramp Entry

Abstract The effects of back pressure and cavity L/D ratio on the shock wave structure in the cold flow field of a typical cavity-based scramjet combustor with combined inlet and isolator is investigated numerically in the selected scramjet models. The scramjet with a throat ratio of TR 0.0 and cavity L/D 6.04 was analyzed. To perform such analysis, steady, 2-D RANS was used with SST k-ω. From the analysis, the value of static pressure along the cowl surface, contours of Mach number and pressure were obtained. The scramjet was modeled with different TR 0.1, 0.2, 0.25 and 0.3 with the same cavity L/D 6.04 and different cavity L/D 4.04, 9.04 and 12.04 with the same TR 0.25. All the models were analyzed with the same inlet conditions and the results were obtained. From the analysis, it was observed that the increase in back pressure moves the shock train towards the inlet of the isolator which leads to ‘engine unstart’ after the throat ratio of TR 0.1. Also, it is observed that there is an optimal L/D ratio of the cavity L/D 9.04 which restricts the propagation of high-pressure waves obtained in the combustor.

Theoretical study of post-shock stress relaxation and shock wave deformation around a pore in single and poly-crystalline α-RDX

The mechanical properties and shock dynamics of α-hexahydro-1,3,5-trinitro-1,3,5-triazine (α-RDX) are simulated by molecular dynamics (MD). Based on the simulation results, the equation of state, Hugoniot curve and isoentropic curve for α-RDX are calculated, and the microscopic structure of shock wave is investigated, including the wave profile and the shock front deformation. First, we prove that the shock wave profile is determined by the viscoelastic equation of α-RDX, and develop a method to inverse the viscoelastic coefficients from the velocity profile calculated by MD. Two stress relaxation mechanisms are obtained: the boundary scattering and molecular rotation. The boundary scattering mechanism shows that the damping time of stress relaxation is determined by the particle size of polycrystal. Second, we find that the pore collapse induces rarefaction wave after the shock front. The rarefaction wave function is evaluated by using the Riemann invariant method, and the shock front deformation is derived from the superposition rule of shock wave and rarefaction wave. A physical picture to describe the nanoscale pore collapse process for α-RDX is obtained.

Interaction of metastable shock waves with perturbations

The shock wave metastable behavior in equilibrium media is detected in numerical experiments. This phenomenon is directly related to the ambiguous representation of a shock wave discontinuity when the shock belongs to the S-shaped fragment of the pressure-velocity Hugoniot. After interaction with weak perturbations the metastable shock wave recovers its original form and parameters (like stable shock). If the amplitude of the perturbations exceeds some critical value, the shock wave instability is developed. The instability is accompanied by formation of the transverse secondary waves switching local post-shock parameters between two Hugoniot segments separated from each other by the absolute instability region. The problem of the metastable shock wave interaction with local entropy perturbation passing through the shock front is studied in the framework of three-dimensional problem formulation. The shock wave transition to the limiting self-oscillating mode is described. Some features of this mode are completely determined by the shape of the Hugoniot and isentropes and does not depend on the shock wave structure. Namely, the shape of the shock front corrugations and flow structure evolution are analyzed. These features may be served as marker of the corresponding thermodynamic anomalies.

Multiple temperature model of nonlinear coupled constitutive relations for hypersonic diatomic gas flows

The rotational energy of diatomic gases would be activated by the process of intermolecular collisions in high-temperature hypersonic flows. In this paper, a multi-temperature nonlinear coupled constitutive model has been proposed for simulating the transfer of energy between translational and rotational motions in hypersonic non-equilibrium flows. In this model, the nonlinear coupled constitutive equations are modified by introducing a rotational energy relaxation model and a changeable viscosity ratio related to local temperature. To confirm its accuracy, the new model is applied to investigate steady shock wave structures and high-speed gas flows around a cylinder and across a flat plate. The computational results are compared with the multi-temperature Navier–Stokes (NS) equations, the direct simulation Monte Carlo (DSMC) solutions, and the experiment data. The final results show the new model would reproduce the NS results at low Knudsen numbers but behave quite differently from the NS results as the non-equilibrium degree is enhanced. The new model is in better agreement with the DSMC solutions and the experimental data than the NS solutions in the far-from-equilibrium regions, which demonstrates the potential of the new relaxation model in the simulation of hypersonic non-equilibrium flows.

Viscous multi-species lattice Boltzmann solver for simulating shock-wave structure

The Onsager Bhatnagar Gross Krook kinetic model proposed by Mahendra et al. [32, 33] has been extended to arrive at the viscous compressible flow equations for a multi-species diffusion problem. The multi-species model ensures (i) correct exchange coefficients, (ii) positivity, (iii) that it follows indifferentiability principle and (iv) that correct amount of entropy get added as per the Onsager’s maximum entropy production principle (MEPP). A Lattice Boltzmann method (LBM) has been developed using the derived methodology within the framework of finite volume method (FVM). This solver incorporates the physics of polyatomic gases with internal degrees of freedom with flexible Prandl number. This solver can simulate the problem with species having different specific heat ratio and molecular weights. Although the equations are derived for multi-species, only binary test cases have been considered in this paper. The solver has been validated against binary shock-wave structure problems using experimental and theoretical data. Two dimensional Richtmyer Meshkov instability test case has been compared with and without viscous effects. The diffusive (viscous and mass diffusion) effects are manifested in the reduction in amplitude and increment in width of the mushroom structure. In the framework of FVM, the proposed scheme of LBM is efficient with good resolution of solutions and is easily adaptable.

Ion Temperature Gradient Mode–Driven Solitary and Shock Waves in Electron-Positron-Ion Magnetized Plasma

The characteristics of linear and nonlinear waves of ion temperature gradient mode in nonuniform electron-positron-ion magnetized plasma are investigated. A modified linear dispersion relation and its reduction in various limits are discussed. In nonlinear regime, ion temperature gradient mode–driven solitary and shock wave structures are obtained and discussed. It is found that corresponding peak potential and width of these nonlinear structures strongly depend on the positron number density and temperature. Our study reveals that in electron-positron-ion plasma, the ion energy transportation in laboratory as well as in astrophysical plasmas can be affected because of positrons.

천연가스의 고압 간접 분사에 따른 과소 팽창 제트의 충격파 구조와 천이 거동에 관한 수치적 연구

천연가스의 고압 간접 분사에 따른 과소 팽창 제트의 충격파 구조와 천이 거동에 관한 수치적 연구

On the total enthalpy behavior inside a shock wave

The total enthalpy behavior inside a shock wave in a dilute monatomic gas has been numerically studied for various values of Mach and Prandtl numbers with the continuum (the Navier–Stokes–Fourier equations) and kinetic (the Shakhov model and the direct simulation Monte Carlo method) approaches. A significant difference between the results by the continuum and kinetic approaches has been observed for the internal shock wave structure. In a wide range of the free-stream Mach numbers, the continuum approach predicts qualitatively similar behavior of total enthalpy distributions that can be of a concave, constant, or convex shape depending on the Prandtl number. The more sophisticated kinetic approach predicts a more complicated form of total enthalpy profiles: e.g., an inflection point for Mach numbers around two and Prandtl numbers close to unity. The evolution of the total enthalpy in the shock is determined by the balance of heat conduction and mechanical work of normal viscous stress—processes that are predicted inaccurately by using the Navier–Stokes–Fourier equations at high Mach numbers.

Numerical simulation of aerodynamic problems based on adaptive mesh refinement method

Numerical simulation of aerodynamic problems using an algorithm, which identifies shock regions and refines the mesh there using an adaptive mesh refinement method, is performed. The static mesh adaptation method is based on cell partitioning by adding new nodes to cell faces. The method of identification of the shock regions using a pressure and density gradient criterion and its verification are presented. The use and applications of the developed algorithm are illustrated, and supersonic and hypersonic flows with strong shock waves are calculated. The results computed explore the shock-wave structure of the flow, which develops near the nose cone section of a body and determines its aerodynamic performance. The aerodynamic performance of bodies with different nose cone designs, including a body with a spike and a pointed cone with an opposing gas jet injected from the nose section, are evaluated based on the proposed method. The method of static mesh adaptation provides a visually sharper picture of the flow around the body and reduces the numerical error of drag coefficient calculations in comparison with wind tunnel measurements. The results computed on meshes of similar resolution constructed with the adaptation method and automatic mesh generator are compared. The results computed on the adaptive mesh are similar to those computed on the mesh generated automatically, but the adaptive mesh has a smaller number of cells.

Solution of cavitating compressible flows using Discontinuous Galerkin discretisation

A methodology for modelling cavitating flows using a high-order Adaptive Mesh Refinement (AMR) approach based on the Discontinuous Galerkin method (DG) is presented. The AMR implementation used features on-the-fly adaptive mesh refinement for unstructured hybrid meshes. The specific implementation has been developed for the resolution of complex multi-scale phenomena where high accuracy p-adaptive discretisations are combined with an h-adaptive data structure. This approach accommodates the fine spatial resolution for the interface discontinuities and the shock waves observed in compressible cavitating flows. The Tait equation of state is used for the modelling of the liquid phase while an isentropic path is assumed for the liquid/vapour mixture. Second order spatial and a third order non-oscillatory temporal discretisation are used for the integration of the mass and momentum conservation equations, in order to resolve the flow structures responsible for the formation of cavitation bubbles and the resulting compression waves. Assessment of the developed methodology is performed for the one-dimensional advancement of a compressible liquid-vapour interface and the symmetric collapse of a spherical vapour bubble.Following, results obtained with the developed multi-scale modelling AMR approach has revealed a complex bubble collapse mechanism near a rigid wall, providing evidence of processes that have been unknown before due to reduced resolution and dissipative nature of past simulations. The impinging jet accompanying the collapse of a bubble near a wall, was found to induce vortical structures, which result to the formation of a secondary cavitation of a wall-attached bubble at the vicinity of the impingement jet shear layer. At the final stages of the initial bubble collapse, the impinging jet was found to penetrate the centre-line of the wall bubble inducing its partial collapse. This secondary collapse results to a rich spatial structure of shock waves, interacting with the secondary bubbles. Moreover, the calculated pressure level are found to be much higher than those reported from previous methodologies.

Interaction of a Plane Shock Wave with Regions of Varying Shape and Density in a Finely Divided Gas Suspension

A study has been made of the interaction between a plane shock wave in a gas or a gas suspension and regions of square and rhombiform cross sections differing from the environment in density. A high-stability monotonic scheme with small numerical dissipation was used for calculation. Comparisons with experiments on the refraction of the shock wave on the interface of a binary gas have confirmed the adequacy of the scheme. The influence of the density-ratio factor (Atwood number), the shape of inhomogeneities, and the particle size on the shock wave structure and the development of a Richtmyer–Meshkov instability has been shown.

Unsteady Transverse Gas Injection in a Supersonic Nozzle Flow

The gasdynamic processes accompanying the injection of a pulsed gas jet into the diffuser part of a nozzle are considered in relation to the formation of control forces in rocket engines. The gas flow through the injection nozzle is controlled by a rotary damper. The finite volume method and moving mesh technology are used to discretize the Reynolds-averaged Navier–Stokes equations and the equations of the SST turbulence model. The effect of the opening time of the damper on the dynamics of the formation of the control force, as well as the dependence of the traction and energy characteristics of the nozzle on the flow rate of the injected working fluid, are studied. The results of calculations within the non-steady-state and quasi-steady-state problem statement are compared. The formation of the shock wave and vortex structure of the flow is discussed. Conclusions are drawn about the effect of the input parameters of the problem on the coefficient of the traction change.

Shock wave compressibility of composite materials based on aramid fibers

Using a VISAR laser interferometer, the experiments on investigation of the shock wave structure, spall strength and determination of Hugoniot parameters were performed for two composite materials based on the aramid fibers. Textolite and Kevlar were made using the same epoxy resin and aramid fibers, but had a different structure - unidirectional fibers and plies of woven fibers, respectively. The density of these materials is approximately 1.27 g/cm3. To study the shock wave compressibility of composite materials under high pressure, the explosive propellant charges were used to provide a flat throw of aluminum flyer plates with velocities from 0.7 to 5.05 km/s. As a result of experiments, particle velocity profiles on the composite/water boundary were obtained. On the velocity profiles for kevlar and textolite with transverse orientation of the fibers, after the initial shock jump, oscillations are observed due to the heterogeneous structure of the investigated materials. Unlike the composite materials with transverse orientation of the fibers, in the case when a shock wave propagates along the fibers, a two-wave configuration is recorded, which is due to the anisotropic structure of material. It was found that Hugoniots of composites with perpendicular orientation of the fibers are parallel to each other and differ only in the first coefficient determined by the sound speed of the material. Also a study of spall strength of textolite and Kevlar was performed. It was found for both materials that the value of spall strength along the fibers is higher than that for the transverse direction.