Shock Wave Structure Research Articles

Mechanism of shock-train/boundary-layer interaction in spanwise concave isolator channels

A series of spanwise concave channel models of isolators with different radii were investigated to reveal the mechanism of shock train/boundary layer interaction in the inward-turning inlet. Numerical simulations of the shock train flow under different incoming Mach numbers, incoming static pressures, and backpressure ratios were performed. The results show that the shock train leading edge exhibits a “λ” shape in the concave channel, and that a Mach stem is present at the intersection of the shock waves on the top and bottom walls. As the radius of the concave wall is increased, the streamwise force generated by the wall decreases and the upward force perpendicular to the wall increases, which leads to an increase in the thickness of the boundary layer and weakening of the ability of the boundary layer fluid to resist the pressure gradient. Owing to the increase in the radius of the concave channel, the shock train moves upstream, the Mach stem in the shock train leading edge becomes shorter, the distance between the reflection shock waves increases, and the shock train becomes longer. Compared with the concave bottom wall, the separation flow at the flat top wall extends further streamwise. As the incoming Mach number increases, the inertial effect is strengthened, and the shock train evolves towards a normal shock wave structure. As the incoming static pressure decreases, the viscous effect is enhanced, and the flow field of the shock train tends to evolve to reflect more shock waves with compression over longer streamwise distances.

Discrete Boltzmann modeling of high-speed compressible flows with various depths of non-equilibrium

The non-equilibrium high-speed compressible flows present wealthy applications in engineering and science. With the deepening of Thermodynamic Non-Equilibrium (TNE), higher-order non-conserved kinetic moments of the distribution function are needed to capture the main feature of the flow state and the evolution process. Based on the ellipsoidal statistical Bhatnagar–Gross–Krook model, Discrete Boltzmann Models (DBMs) that consider various orders of TNE effects are developed to study flows in various depths of TNE. In numerical tests, DBMs including the first up to the sixth order TNE effects are demonstrated. Specifically, at first, the model's capability to capture large flow structures with zeroth-order TNE effects in two types of one-dimensional Riemann problems is demonstrated. The ability to capture large flow structures with first-order TNE effects is also shown in the Couette flow. Then, a shock wave structure given by Direct simulation Monte Carlo is used to verify the model's capability to capture fine structures at the level of the mean free path of gas molecules. Furthermore, we focus on the TNE degree of two colliding fluids mainly decided by two parameters: the relaxation time τ and relative speeds Δu of two fluids. Consequently, three numerical tests for flows with various depths of TNE are constructed. Due to any definition of the TNE strength is dependent on the perspective of investigation, we propose to use a N-component vector STNE to describe the TNE system from N perspectives. As specific applications, we use a three-component vector STNE=(τ,Δu,Δ2*) to roughly characterize three cases for numerical tests in this work. Then, we check the system TNE behavior from the perspective of the xx component of the TNE quantity, viscous stress Δ2*. It is found that, for the first two cases, at least up to the second-order TNE effects, i.e., the second-order terms in Knudsen number in the CE expansion, should be included in the model construction, while for the third case, at least up to the third-order TNE effects should be included. Similar to Δ2*, three numerical tests for flows in various depths of Δ3,1* are constructed. It is found that from the perspective of Δ3,1,x*, for case 1 and case 3, at least up to the second-order TNE effects should be required, while for case 2, the first-order TNE effects are enough. These findings demonstrate that the inadequacy of focusing only on the few kinetic moments appearing in Navier–Stokes increases with the degree of discreteness and deviation from thermodynamic equilibrium. Finally, a two-dimensional free jet is simulated to indicate that, to obtain satisfying hydrodynamic quantities, the DBM should include at least up to the third-order TNE effects. This study is meaningful for the understanding of the TNE behavior of complex fluid systems and the choice of an appropriate fluid model to handle desired TNE effects.

Physics and flame morphology of supersonic spontaneously combusting hydrogen spouting into air

Spontaneous ignition resulting from the accidental release of high-pressure hydrogen is an important safety issue, and the self-ignition flame can eventually induce a jet flame. However, the links between the self-ignition flame inside a tube and an external jet flame are unclear. Hence, this paper presents a study on how the self-ignition flame transforms into the jet flame in the near-field region of the nozzle. Effects of release pressure and tube length are investigated. Changes in release conditions can lead to changes in the flow characteristics of the self-combustible jet at the nozzle. Results show that the difference in the flow parameters is manifested in three aspects, which directly contribute to the diversity of transition forms. The expansion processes and shock structure govern the flame transition. The expansion process consists of two typical stages, which lead to two different flame morphologies. Besides, the presence of discontinuous surfaces in the shock wave structure can cause the self-ignition flame to extinguish or re-ignition in some transition processes, resulting in the flame appearing in different zones during different transitions. Finally, five forms of flame transition are proposed and their formation reasons are analyzed. Dominant factors and links between different transitions are eventually identified.

Non-premixed flame propagation inside and outside the different three-way tubes after the self-ignition of pressurized hydrogen

Accidental leakage of pressurized hydrogen into the pipeline is often accompanied by the non-premixed self-ignition flame, whilst the complex structure of pipeline affects the flame propagation. In this study, the propagation of self-ignition hydrogen flame in different three-way tubes is studied and the flame evolution near the two exits is compared. Effects of the tube length and the location of bifurcation points are investigated. Results show that the bifurcation structure has the attenuation effect on the intensity of flame and shock wave, and they attenuate more sharply in the branch pipeline. But the flame intensity can increase again downstream the bifurcation point in the trunk pipeline, and this increase is not continuous and decrease again as the tube length increases. In addition, the flame evolution can be different near two exits of the tube. As the bifurcation point moves downstream, the number of Mach disk and the time required to form the stable flame will increase near the exit of branch pipeline. Despite different flame evolution, the flame morphology and propagation are all controlled by the shock wave structures before the formation of the vortex, but the flame changes dramatically and grows rapidly to form the stable lift-off flame after the formation of the vortex.

Research on inner flow and energy characteristics of air ejector for liquid-ring vacuum pump

To analyze the complex flow characteristics, and reveal the mechanisms of energy transfer and hydraulic loss of the liquid-ring pump ejector. The numerical simulation and experiment were applied to analyze the complex shock wave structure, vortex evolution characteristics in the ejector and its influence on hydraulic performance, which provides a novelty reference for the optimization design of the ejector. Furthermore, novelty is expressed in the performance analysis of the ejector based on the performance of its matching liquid-ring pump. The results show that the λ-shock wave and Mach disk are formed inside the nozzle under the action of supersonic jet, and the triple point is formed as the incident shock wave, the reflected shock wave and the Mach disk intersect. The shock wave, as it propagates, changes from Mach reflection to regular reflection, and meanwhile, the position of triple point moves from the initial Mach disk to the new Mach disk. With the interaction of shock wave and jet boundary layer, the shock train is formed in the core region of the jet. The pressure, density and Mach number are oscillatory distributed in the shock wave region. There is a relatively large velocity gradient between the high speed primary flow and the low speed secondary flow near the outlet of nozzle, which induces the formation of opposite rotating vortices in the shear layer of the cylinder. With the evolution of the vortex, the high speed jet transfers energy through the cylindrical shear layer and is accompanied by the large hydraulic loss. The total entropy production of the ejector increases with the increase of primary flow pressure. The entropy production rate has a strong correlation with the vorticity magnitude.

Dynamic compaction of aluminum with nanopores of varied shape: MD simulations and machine-learning-based approximation of deformation behavior

We compare two machine-learning-based approaches, artificial neural network (ANN) and micromechanical model with automatic Bayesian identification of the model parameters, in application to mimicking the deformation behavior of nanoporous aluminum extracted from molecular dynamics (MD) simulations. Reference data are generated by means of MD simulation of both hydrostatic and uniaxial deformation with compression of representative volume elements of aluminum single crystal with nanopores of spherical, cubic and cylindrical shapes at the temperatures of 300, 500, 700 and 900 K. Several typical sizes of the nanopores are considered: The smallest one corresponds to the initial porosity less than 1%, while the largest one gives the initial porosity in the range of 30–50%. Plastic collapse of nanopores in all cases occurred by the mechanism of emission of partial Shockley dislocation half-loops from the pore surface. The emission of initial loop occurred earlier in the case of cylindrical pore; however, this did not lead to an explosive increase in the number of dislocations in the system at this stage. In general, flat free surfaces of pores are less subjected to the dislocation nucleation than the rounded ones. A new physically-based micromechanical model of the plastic compaction of nanoporous metal is formulated with accounting of different pore shapes and anisotropy of the compaction process. Both tested machine-learning approaches show an adequate approximation of MD data. The developed ANN and parameterized micromechanical model are applied to simulate the propagation of a shock wave in nanoporous aluminum in comparison with direct MD simulations of this process; this comparison shows an adequate description of the shock wave structure by means of both approaches incorporated into continuum mechanics modeling. Thus, the developed machine-learning-based approaches can be applied as constitutive equations of nanoporous aluminum in macroscopic simulations of the dynamic compaction and shock-wave processes in this material.

Shock-wave structure in non-polar diatomic and polyatomic dense gases under rotation and vibration

This study investigates the effect of rotation and vibration on the structure of shock waves in moderately dense diatomic and polyatomic non-polar gases using the one-temperature Navier–Stokes–Fourier approach. The modified Enskog equation of state of the gas is taken to include the denseness and shielding effects. The specific heat at constant volume has been taken to be temperature-dependent. The shear viscosity, the bulk viscosity, and the thermal conductivity have been assumed to follow the temperature-dependent power-law model. Nitrogen and oxygen gas have been taken as the test cases for diatomic gases while carbon dioxide was taken for the polyatomic gases. The implicit system of equations is derived and solved numerically for density and temperature. The inclusion of denseness, rotational, and vibrational modes of molecular motion have a significant effect on the density and temperature profiles, the inverse shock thickness, the bulk to shear viscosity ratio, and the molar specific heat at constant pressure. The gas having a low characteristic vibrational temperature has been found to have a high value of inverse shock thickness. The inverse shock thickness, the bulk to shear viscosity ratio, and the molar specific heat at constant pressure for nitrogen and carbon dioxide are found to be in good agreement with the experimental values.

Numerical Investigation on the Performance of a Transonic Axial Compressor with Inlet Distortion and Low Reynolds Number

The performance and stability of the transonic fan stage with a nonuniform inflow is a key issue in aero engine operation, and the coupling of inlet distortion and low Reynolds numbers at high altitude creates more severe challenges to aero engines. This work used computational methods to explore the performance and stability of a transonic fan stage with inlet distortion and a low Reynolds number. To investigate this issue, the transonic fan stage NASA stage 67 with a 180° total pressure distortion at a low Reynolds number was selected as the test case. Full-annulus 3D unsteady simulations were conducted to reveal the details of the flow field under coupling conditions. The computational results under different conditions were analyzed and showed that the coupling effect was not linearly stacked with single factors. The low Reynolds number in the coupling case thickened the boundary layer on the blade surface, and, on the one hand, the profile loss in the hub region increased. On the other hand, the structure of shock wave was converted in the tip region, which increased the shock loss significantly. In addition, the variation in the shock wave structure reconstructed the pressure distribution on the blade surface, allowing the fluid to migrate to the tip region, which affected the tip flow structure and ultimately delayed the stability boundary.

A simple hydrodynamic-particle method for supersonic rarefied flows

In the practical aerospace industry, the supersonic rarefied effect presents multiscale characteristics from the near-continuum regime to the free molecular regime. In this paper, a simple hydrodynamic-particle method (SHPM) is proposed to efficiently capture the multiscale properties for the supersonic rarefied flow. To combine the conventional computational fluid dynamics solver with the particle-based method, the weights are theoretically derived from the integral solution of the Boltzmann Bhatnagar–Gross–Krook equation. The present numerical method is validated by test cases of supersonic shock wave structure, Sod shock-tube, and supersonic flow around the circular cylinder. Numerical results demonstrate that the SHPM could capture the multiscale properties from the continuum regime to the rarefied regime.

Discrete Boltzmann modeling of plasma shock wave

Plasma shock waves widely exist and play an important role in high-energy-density environment, especially in the inertial confinement fusion. Due to the large gradient of macroscopic physical quantities and the coupled thermal, electrical, magnetic, and optical phenomena, there exist not only hydrodynamic non-equilibrium (HNE) effects but also strong thermodynamic non-equilibrium (TNE) effects around the wavefront. In this work, a two-dimensional single-fluid discrete Boltzmann model is proposed to investigate the physical structure of ion shock. The electron is assumed inertialess and always in thermodynamic equilibrium. The Rankine–Hugoniot relations for single-fluid theory of plasma shock wave is derived. It is found that the physical structure of shock wave in plasma is significantly different from that in normal fluid and somewhat similar to that of detonation wave from the sense that a peak appears in the front. The non-equilibrium effects around the shock front become stronger with increasing Mach number. The charge of electricity deviates oppositely from neutrality in upstream and downstream of the shock wave. The large inertia of the ions causes them to lag behind, so the wavefront charge is negative and the waverear charge is positive. The variations of HNE and TNE with Mach number are numerically investigated. The characteristics of TNE can be used to distinguish plasma shock wave from detonation wave.

Discharge characteristics of a gliding arc discharge in a supersonic jet air flow

Whereas discharge characteristics of a gliding arc have previously been investigated in a low-speed subsonic flow without considering the effect of shock waves and extremely high turbulence, we here studied an important physical feature of the gliding arc in a supersonic flow that generates complex shock waves and extremely high turbulence. The gliding arc in a 1.2 Mach supersonic jet air flow is investigated by high-speed imaging, schlieren imaging, electrical measurements, and the large eddy simulation. The experimental results show that high-repetition transitions between the spark-type discharges and the glow-type discharge with a frequency of 1.4–2.1 MHz can be observed in the supersonic flow after the gliding arc is generated between the narrowest gap of knife-shaped electrodes, whereas the similar phenomena are invisible in a low-speed subsonic flow. It can be recognized that the high-repetition transitions occur in the region with complex structures of shock waves and expansion waves. The large velocity/density gradient generated by the complex wave structures and the small-scale vortices produced by the strong turbulence is located near the position where the high-repetition transitions occur. The high-repetition transitions between the spark-type discharges and the glow-type discharges are found to be mainly caused by the combined effects of the strong turbulent eddy transportation in the supersonic flow and the drastic change in the flow properties across the shock wave, shedding light on the mechanism of the high-repetition discharge transitions of the gliding arc in a supersonic flow.

Multi-Species Compressible Solver for Non-Continuum Flow Through a Micro-Channel

Compressible multi species flow solver, developed by the authors Kumar and Maheshwari [May 15, 2020. “Viscous Multi-Species Lattice Boltzmann Solver for Simulating Shock-Wave Structure.” Computers and Fluids 203. Article ID 104539], has been extended further to non-continuum flows. The approach uses the Onsager-BGK model, which ensures Onsager's maximum entropy production principle is followed, thus avoids unphysical solutions. Equations for velocity slip and temperature jump have been derived. The viscous slip, thermal slip and diffusion slip coefficients have been successfully validated with 13-moment solver's and experimental data. The departure from equilibrium in such flows has been approximated by a collision probability function (), instead of using the complicated second order perturbation over the Knudsen number (that leads to Burnett equations). This provided the necessary reduction in (viscous, thermal, mass) dissipation and the developed approximate solver is able to predict the thermal and viscous profiles in a non-continuum regime and validates against DSMC simulations. Test cases consisting of flow through micro-channels demonstrated the ability of solver to handle monoatomic, diatomic and poly atomic gases. The developed non-continuum solver is in a finite volume framework and is easily adaptable to legacy in-house Navier–Stokes solvers.

Numerical study of unsteady shock/mixing interaction in confined space

Unsteady shock wave enhancement is an effective technical approach to achieve air/fuel mixing under high speed and compressible conditions. However, unsteady shock/mixing interactions are always accompanied by complex wave structures, so the height of the combustion chamber will inevitably have a significant impact on shock waves and engine performance. In this regard, shock/mixing interactions in confined space are studied in this article by direct numerical simulation to investigate the effect of wall constraint on shock wave enhancement. Shock wave structure, total pressure loss, thickness of mixing layer, and turbulence intensity of flow field with different confinement degrees are calculated and compared. The results show that the unsteady shock wave can dramatically enhance the thickness of the mixing layer and the turbulence intensity, thus improving the mixing efficiency. In addition, as the wall constraint increases, the intensity of the shock wave and the total pressure loss increase; the flow field is more prone to Mach reflection. The average total pressure loss caused by steady shock wave and unsteady shock wave is essentially the same for an identical wall height, but the total pressure distortion caused by the unsteady shock wave is more substantial. Furthermore, the enhancements of mixing efficiency by the shock wave are also affected significantly by the degree of wall constraint; therefore, a suitable wall height needs to be determined in order to achieve the highest mixing efficiency.

Unsteady Motion of Shock Wave for a Supersonic Compression Ramp Flow Based on Large Eddy Simulation

A large eddy simulation (LES) is conducted to investigate shock wave/turbulent boundary layer interaction in a 24° compression ramp at a high inlet Mach number of Ma=2.9. The recycling/rescaling Method is used as the inflow turbulence generation technique. The shock wave structure and boundary layer flow in the interaction region are studied by flow visualization methods, such as vortex recognition and numerical schlieren. The distributions of turbulent kinetic energy and Reynolds normal stresses at different streamwise locations are analyzed. The results show that a strong anisotropy turbulent flow appears in the reattached boundary layer after the interaction of the shock wave. The large-scale unsteady motion of the separation shock wave is analyzed by using the intermittent factor and power spectrum. It is found that the shock moves around the averaged separation position, and the length scale is equal to 72% of the inlet boundary layer thickness. The power spectrum analysis reveals the existence of low-frequency instability in the separation region.

Numerical investigation of the influence of aerothermoelastic dynamic response on the performance of the three-dimensional hypersonic inlet

The influence of aerothermoelastic dynamic response on the performance of the three-dimensional hypersonic inlet is investigated in this paper. A dynamic aerothermoelastic analysis framework is developed. The reliability of the framework is verified. The effects of aerodynamic heating on the dynamic response, the effects of the aerothermoelastic dynamic response of the inlet on the flow field structure, and the performance parameters are studied. The results indicate that the static deformation of the leading edge structure is large while the vibration amplitude is small. Meanwhile, the vibration amplitude of the trailing edge structure is larger. The aerothermoelastic dynamic response changes the shock wave structure near the exit, strengthens the shock wave intensity, increases the length of the separated region, and changes the flow field of the exit. Simultaneously, the flow field structure also experiences obvious dynamic changes at different moments. The dynamic response increases the time-averaged flow coefficient, reduces the time-averaged total pressure recovery coefficient, and improves the time-averaged reverse pressure ratio. At the same time, the dynamic response leads to the fluctuation of performance parameters, especially the large fluctuation range of the reverse pressure ratio at the exit.

Numerical Research on the Simulation Nacelle of Ejector Engine

The numerical simulation research of single-nozzle center ejector and double-ducted multi-nozzle ejection nacelle was carried out to study the dynamic simulation nacelle under variable working conditions required by advanced aero-engine test technology. The shock wave structure and blocking effect in the supersonic central ejector are analyzed in detail, and the internal flow field characteristics of the ejector under the condition of non-central axisymmetric supersonic ejection were examined. The aerodynamic characteristics of the single-ducted and double-ducted ejector nacelles are studied; and the flow field simulation with analyzation of the inner and outer ducts under the condition of variable duct ratio was carried out. The relevant conclusions obtained from the research can provide theoretical guidance and reference for the analysis of the multi-condition test run of the aero-engine test cell.

Phase transitions in Zr at sub-nanosecond time scales

Solid-solid phase transitions are investigated in Zr thin films using shock compression induced by a short laser pulse (<1 ns). Shock wave profiles are measured at free surfaces for films of different thicknesses (a few micrometers) using chirped-pulse line velocimetry with 10 ps time resolution. Experiments are performed at pressures up to ∼50 GPa, which is sufficient to reach the ω and β phases under equilibrium conditions. The shock wave structures are analyzed using a general Lagrangian analysis method, which allows for the calculation of stress–strain paths and assessments of phase transition behavior. In agreement with recent short laser pulse experiments using ultra-fast x-ray diffraction, we do not find any clear evidence of the α–ω transition, though this would be expected from the phase diagram. Instead, we infer a direct transformation to a metastable β-phase at lower shock pressures (<20 GPa) and equilibrium β at higher pressures. Through the velocimetry analysis, we find α–β transformation onset times of less than ∼100 ps and completion times of less than ∼200 ps.

Evolution of cylindrical/spherical shock formation in a dusty plasma with nonadiabatic dust charge variation

Cylindrical/spherical dust acoustic shock waves are studied in an unmagnetized plasma consisting of Maxwellian electrons, superthermal ions under the effect of nonadiabatic dust charge fluctuation. The dissipation is introduced in the system via nonadiabaticity, a new mechanism for the formation of shock waves. Using standard reductive perturbation method, nonplanar equation namely Korteweg–de Vries Burgers (KdVB) equation is derived and solution is obtained using the Weighted residual method. By use of weighted residual method, a progressive wave solution to nonplanar modified KdV Burgers equation is presented. It is shown that dust charge fluctuation produces dissipation which is responsible for shock formation. The solution shows that as one goes towards the axis of the cylinder or center of the sphere, the wave attenuates faster and the effects are shown in some 2D figures. We have studied various parametric influences on such shock structure and also showed how the gradual variations of these parameter affect the generation and structure of the shocks in their respective domain. Our results should be applicable to the formation of nonlinear DIA shock wave structures in regions in which dust grain is embedded in a Kappa distributed plasma, such as Saturn's magnetosphere.

Simulation of the pulsed outflow of air and fine powder mixture, partially filling the discharge channel

The paper studies the regularities of the pulsed outflow of air and fine powder mixture, which partially fills the ejection cylindrical channel, in both one-dimensional and two-dimensional formulations. The dynamics of a gas-dispersed medium are described in the framework of the Eulerian continuum approach with different velocities and temperatures of gas and powder particles. Analytical self-similar solutions are constructed in the equilibrium approximation. For the numerical solution of the problem, a hybrid large-particle method of the second order of accuracy in space and time is used. Comparison of exact self-similar and numerical solutions confirmed the reliability of the method. The outflow of the mixture of high-pressure gas and powder particles has a pronounced wave character, which is associated with the decomposition of the initial discontinuity, the movement, and refraction of waves at the interface of media inside the channel, as well as the reflection of waves from its bottom. The characteristic time intervals of the wave process and the corresponding distributions of gas-dynamics quantities are established. Depending on the generalized self-similar variable, the pressure, density, and velocity of the mixture are monotonic functions, and the profile of the specific (per unit cross-section) mass flow has a maximum in the critical section. Dimensionless parameters and specific mass flow of a two-phase medium in the outlet section of the discharge channel are determined. In the case of a channel limited by the size of the high-pressure chamber, a two-dimensional physical picture of the formation and evolution of a gas-dispersed mixture was studied. At the initial stage of the outflow, an “anomalous” grouping of powder particles is observed with the formation of a shock-wave structure in the subsonic mode of the carrier gas flow. After the powder layer leaves the channel, the pure gas flowing out of it accelerates to supersonic speed and an intense vortex motion develops in the wake of the gas-dispersed jet. The calculated values of the parameters allow us to justify the achievable level of technical characteristics (speed, mass flow rate) of the flow of the working gas-dispersed medium of pulsed powder devices. The proposed methodology and the results obtained are the basis for making rational decisions at the early stages of design and preparation of initial data on design and operating parameters for testing prototypes of pulsed powder technical devices.

Analysis of Nano Order Structure of Shock Wave Front Generated by HVI and Propagating in <100> Direction of fcc Metal

It is difficult to determine experimentally the nanometer level structure of shockwave propagating in solid materials. In present study, molecular dynamics (MD) simulation is performed to clarify quantitatively the atom level structure of shockwave propagating in fcc crystalline Al or Ni in the <100> direction. Simulated metal to metal collision model is similar to the experimental equipment of the split Hopkinson pressure bar which is used for the high strain rate deformation test. The non-closed pack (100) plane of the fcc crystal is the collision plane.