Downstream Interface Research Articles

Effects of disturbed transmitted shock and interface coupling on heavy gas layer evolution

Development of a heavy gas layer with an upstream single-mode interface and a downstream planar interface accelerated by a shock wave is investigated. By considering the amplitude variation of the transmitted shock and interface coupling, a modified model is established, which provides good predictions on the linear growth rates of the perturbations on both interfaces. Through the model, the perturbation growth of the downstream interface can be frozen by choosing a suitable layer width. In such a shocked layer, interface coupling has an ignorable effect on the nonlinear evolution of the upstream interface but significantly changes the nonlinear evolution of the downstream interface. A new dimensionless approach is proposed to scale the nonlinear growth of the middle spike on the downstream interface. Finally, through modal analysis, we find that the pressure perturbations rather than interface coupling result in the formation of the small spike on the bubble head of the downstream interface.

Numerical Simulation of the Interaction between a Planar Shock Wave and a Cylindrical Bubble

Three-dimensional (3D) computational fluid dynamics (CFD) simulations have been carried out to investigate the complex interaction of a planar shock wave (Ma = 1.22) with a cylindrical bubble. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach with a level set coupled with volume of fluid (LSVOF) method has been applied in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex filaments are in very good agreement with the experimental data. The predicted non-dimensional bubble and vortex velocities also have great concordance with the experimental data compared with a simple model of shock-induced Rayleigh–Taylor instability (i.e., Richtmyer–Meshkov instability) and other theoretical models. The simulated changes in the bubble shape and size (length and width) against time agree very well with the experimental results. Comprehensive flow analysis has shown the shock–bubble interaction (SBI) process clearly from the onset of bubble compression up to the formation of vortex filaments, especially elucidating the mechanism on the air–jet formation and its development. It is demonstrated for the first time that turbulence is generated at the early phase of the shock cylindrical bubble interaction process, with the maximum turbulence intensity reaching about 20% around the vortex filament regions at the later phase of the interaction process.

Numerical investigation of shock Mach number effects on Richtmyer–Meshkov instability in a heavy square bubble

This study conducts a two-dimensional numerical investigation of incident shock Mach number effects on the Richtmyer–Meshkov (RM) instability after a shock wave impulsively drives a heavy square bubble. The square bubble is composed of SF6 gas, which is surrounded by nitrogen gas. Five different shock Mach numbers are considered: Ms=1.12, 1.22, 1.4, 1.7, and 2.1. Two-dimensional compressible Euler equations for two-component gas flows are simulated with a high-order modal discontinuous Galerkin solver. For validation, the numerical results are compared with the existing experimental results and are found to be in good agreement. The present results reveal that the incident shock Mach number is critical in the growth of RM instability in a heavy square bubble. The shock Mach number affects flow morphology significantly, resulting in complicated wave patterns, shock focusing, jet creation, bubble deformation, and vorticity generation. The convergent shape of the bubble causes shock focusing, which creates a local high-pressure zone and, as a result, an outward jet generation. It is found that the bubble deforms differently with increasing shock Mach number, and the different shock Mach numbers alter the distance between the shock focusing position and the downstream bubble interface. The effects of shock Mach numbers are investigated in depth through physical phenomena such as vorticity production, kinetic energy, and enstrophy. Finally, the shock Mach number impacts on the time-variations of the shock trajectories and interface structure are thoroughly investigated.

Fully conservative hydraulic jumps and solibores in two-layer Boussinesq fluids

We consider a special type of hydraulic jumps (internal bores) which, in the vertically bounded system of two immiscible fluids with slightly different densities, conserve not only the mass and impulse but also the circulation and energy. This is possible only at specific combinations of the upstream and downstream states. Two such combinations are identified with arbitrary upstream and downstream interface heights. The first has a cross symmetry between the interface height and shear on both sides of the jump. This symmetry, which is due to the invariance of the two-layer shallow-water system with swapping the interface height and shear, ensures the automatic conservation of the impulse and energy as well as the continuity of characteristic velocities across the jump. The speed at which such jumps propagate is uniquely defined by the conservation of the mass and circulation. The other possibility is a marginally stable shear flow which can have fully conservative jumps with discontinuous characteristic velocities. Both types of conservative jumps are shown to represent a long-wave approximation to the so-called solibores which appear as smooth permanent-shape solutions in a weakly non-hydrostatic model. A new analytical solution for solibores is obtained and found to agree very well with the previous DNS results for partial-depth lock release flow. The finding that certain large-amplitude hydraulic jumps can be fully conservative, while most are not such even in the inviscid approximation, points toward the wave dispersion as a primary mechanism behind the lossy nature of internal bores.

On the role of the laminar/turbulent interface in energy transfer between scales in bypass transition

We investigate the role of the laminar/turbulent interface in the interscale energy transfer in a boundary layer undergoing bypass transition with the aid of the Kármán–Howarth–Monin–Hill (KHMH) equation. A local binary indicator function is used to detect the interface and employed subsequently to define two-point intermittencies. These are used to decompose the standard-averaged interscale and interspace energy fluxes into conditionally averaged components. We find that the inverse cascade in the streamwise direction reported in an earlier work arises due to events across the downstream or upstream interfaces of a turbulent spot. However, the three-dimensional energy flux maps reveal significant differences between these two regions: in the downstream interface, inverse cascade is stronger and dominant over a larger range of streamwise and spanwise separations. We explain this finding by considering a propagating spot of simplified shape as it crosses a fixed streamwise location. We derive also the conditionally averaged KHMH equation, thus generalising similar equations for single-point statistics to two-point statistics. We compare the three-dimensional maps of the conditionally averaged production and total energy flux within turbulent spots against the maps of standard-averaged quantities within the fully turbulent region. The results indicate remarkable dynamical similarities between turbulent spots and the fully turbulent region for two-point statistics. This has been known only for single-point quantities, and we demonstrate here that the similarity extends to two-point quantities as well.

Numerical analysis of shock interaction with a spherical bubble

Two-dimensional and three-dimensional computational fluid dynamics studies of a spherical bubble impacted by a supersonic shock wave (Mach 1.25) have been performed to fully understand the complex process involved in shock–bubble interaction (SBI). The unsteady Reynolds-averaged Navier–Stokes computational approach with a coupled level set and volume of fluid method has been employed in the present study. The predicted velocities of refracted wave, transmitted wave, upstream interface, downstream interface, jet, and vortex ring agree very well with the relevant available experimental data. The predicted non-dimensional bubble and vortex velocities are also in much better agreement with the experiment data than values computed from a simple model of shock-induced Rayleigh–Taylor instability (the Richtmyer–Meshkov instability). Comprehensive flow visualization has been presented and analyzed to elucidate the SBI process from the beginning of bubble compression (continuous reflection and refraction of the acoustic wave fronts as well as the location of the incident, refracted and transmitted waves at the bubble compression stage) up to the formation of vortex rings as well as the production and distribution of vorticity. Furthermore, it is demonstrated that turbulence is generated with some small flow structures formed and more intensive mixing, i.e., turbulent mixing of helium with air starts to develop at the later stage of SBI.

Development of Three-Dimensional Scour below Pipelines in Regular Waves

The three-dimensional scour beneath a partially-buried pipeline in regular waves was visualized using a miniature camera installed in a transparent pipeline. The scour mechanism was analyzed based on the results. Scour development was observed to start at the upstream edge of the span shoulder when the flow in the span headed downstream. The nearby sediment scoured quickly, and a new scour front formed, which can be attributed to the deflected flow entering the scour hole. The new scour front retreated gradually. The end of the original scour front deformed and moved downstream, probably due to the enhanced seepage flow near the edge of the span shoulder. After that, the new scour front extended to the downstream interface of the sediment and the pipeline, and continued to retreat until the first half of the scour process ended. In the second half of the scour process, the sediment transportation occurred in a similar but mirror-imaged manner. The scour hole propagation rate was also determined based on visualization. The results show that the scour hole propagation rate under a pipeline decreases with an increasing pipeline embedment ratio and rises with the KC (Keulegan–Carpenter) number, which is similar to the result of a previous study.

Evolution of shock-accelerated double-layer gas cylinder

Developments of the shock-accelerated concentric double-layer gas cylinder with an air cylinder embedded into an SF6 cylinder have been experimentally investigated for the first time. The double-layer gas cylinder is created by the soap film technique. Effects of the inner cylinder on the evolution of the outer one are highlighted by changing the radius ratio, i.e., a ratio of the inner radius to the outer one. The flow features show that the two cylinders evolve independently at the early stage, whereas they couple together at the late stage. The presence of the inner cylinder changes the behavior of shock movements, and a vortex pair instead of an outward jet is generated at the downstream interface. The scale of the vortex pair is proportional to the initial radius ratio. The rarefaction waves generated from the upstream interface of the inner cylinder accelerate the upstream interface of the outer cylinder earlier than the single-layer SF6 cylinder. Depending on the radius ratio, the acceleration induced by the rarefaction wave impact either prolongs or shortens the linear phase of the upstream interface movement. The waves' effect results in the failure of the nonlinear model in predicting the upstream interface movement. For the outer cylinder, its movements in both the streamwise and spanwise directions are promoted by the inner one. For the inner cylinder, its movements in the streamwise and spanwise directions are, respectively, inhibited and promoted by the outer one. As the radius ratio increases, the effect of promotion or prohibition is stronger.

Technical Note: Small field dose correction factors for radiochromic film in lung phantoms.

Radiochromic film has been established as a detector that can be used without the need for perturbation correction factors for small field dosimetry in water. However, perturbation factors in low density media such as lung have yet to be published. This study calculated the factors required to account for the perturbation of radiochromic film when used for small field dosimetry in lung equivalent material. Monte Carlo simulations were used to calculate dose to Gafchromic EBT3 film when placed inside a lung phantom. The beam simulated had a nominal energy of 6MV and the field sizes simulated ranged from 10×10mm2 to 30×30mm2 . The lung density simulated was varied between 0.2 and 0.3g/cm3 . Each simulation was repeated with the film replaced by lung material (the same as the surrounding medium), and the required correction factors for film dosimetry in lung ( ) were calculated by dividing the dose in lung by the dose in film. For field sizes 30×30mm2 and larger, no correction factors were required. At a 20×20mm2 field size, small corrections were required, but were within the approximate accuracy of film dosimetry (~2%). For a 10×10mm2 field size, significant correction factors need to be applied (0.935 for lung density of 0.20g/cm3 to 0.963 for lung density of 0.30g/cm3 ). The values lower than one mean that the film is over-responding. At the "upstream" lung-water interface the correction factors were close to unity; while at the downstream interface the corrections required were marginally smaller to those at the center of lung. One centimeter or more away from the interfaces, the correction factor did not vary as a function distance from the interface (in the beam direction). Away from the central axis (perpendicular to the beam direction), the correction factors increased slightly (away from unity) as a function of off-axis distance, before abruptly changing direction at the penumbra, with the film actually under-responding by ~10% outside the field edges. Accurate dosimetry of very small fields (15×15mm2 or smaller) using radiochromic film requires correction factors for the perturbation of the film on the surrounding lung material. This correction factor was as high as 6.5% for a 10×10mm2 field size and a density of 0.2g/cm3 . This will increase if either the density or the field size decrease further. This correction factor does not vary as a function of depth in lung once charged particle equilibrium is established.

An Integrated Multi-Function Heterogeneous Biochemical Circuit for High-Resolution Electrochemistry-Based Genetic Analysis.

Modular construction of an autonomous and programmable multi-functional heterogeneous biochemical circuit that can identify, transform, translate, and amplify biological signals into physicochemical signals based on logic design principles can be a powerful means for the development of a variety of biotechnologies. To explore the conceptual validity, we design a CRISPR-array-mediated primer-exchange-reaction-based biochemical circuit cascade, which probes a specific biomolecular input, transform the input into a structurally accessible form for circuit wiring, translate the input information into an arbitrary sequence, and finally amplify the prescribed sequence through autonomous formation of a signaling concatemer. This upstream biochemical circuit is further wired with a downstream electrochemical interface, delivering an integrated bioanalytical platform. We program this platform to directly analyze the genome of SARS-CoV-2 in human cell lysate, demonstrating the capability and the utility of this unique integrated system.

Impact of radiopacified bone cement on radiotherapy dose calculation.

Background and purposeRadiopacifiers are introduced to bone cements to provide the appearance of bone in kilovoltage (kV) radiographic images. For higher energy megavoltage (MV) radiotherapy treatment beams, however, these radiopacifiers do not cause a bone-like perturbation of dose. This study therefore aimed to determine the impact of the barium-contrasted plastic-based cement materials on radiotherapy dose calculations.Materials and methodsThe radiological properties of a physical sample of bone cement were characterised by computed tomography (CT) imaging and transmission measurements. Monte Carlo simulations of percentage depth-dose profiles were performed to determine the possible dose error for MV treatment beams. Dose differences were then investigated for clinical volumetric modulated radiotherapy treatment plans, with and without density overrides applied.ResultsDifferences of up to 7% were observed at the downstream interface of a 0.6 cm thick bone cement layer, compared to bone. Differences in planning target volume dose-volume metrics varied between −0.5% and 2.0%.ConclusionBefore planning radiotherapy treatments for patients who have undergone cranioplasty, every effort should be made to identify whether a radiopacified bone cement has been implanted. Density overrides should be applied to minimise dose calculation errors, whenever bone cement is used.

Evaluation of the Multiple Reference Frame Approach for the Modelling of an Axial Cooling Fan

The modelling of rotating parts, such as axial fans, is one of the main challenges of current CFD simulations of industrial applications. Different methods are available, but the most commonly used is the multiple reference frame (MRF) method. This paper investigates how different flow properties, such as temperature, pressure and velocity, develop when passing through the MRF domain. The results are compared to the more physical rigid body motion (RBM) approach. It is found that the MRF method transports the upstream properties with the streamlines of the relative velocity from the upstream to the downstream interface. This leads to a non-physical rotation by an angle that is dependent on the length of the domain and the ratio between axial and tangential velocity in the MRF region. The temperature field is more affected than the flow field, since wake structures from upstream obstacles are destroyed due to the wake of the blades. Downstream structures affect the flow in the upstream region by an increase in static pressure, which causes the streamlines in the MRF zone to slow down. Depending on the size of the obstacle, this can cause substantial distortions in the upstream and downstream flow field.

Numerical study on shock–dusty gas cylinder interaction

The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caused by the particle relaxation, which is closely related to the particle radius and shock strength, on the evolution of particle cylinder is emphasized. For a very small particle radius, the particle cloud behaves like an equilibrium gas cylinder with the same physical properties as those of the gas–particle mixture. Specifically, the transmitted shock converges continually within the cylinder and then focuses at a region near the downstream interface, producing a local high-pressure zone followed by a particle jet. Also, noticeable secondary instabilities emerge along the cylinder edge and the evident particle roll-up causes relatively large width and height of the shocked cylinder. As the particle radius increases, the flow features approach those of a frozen flow of pure air, e.g., the transmitted shock propagates more quickly with a weaker strength and a smaller curvature, resulting in an increasingly weakened shock focusing and particle jet. Also, particles would escape from the vortex core formed at late stages due to the larger inertia, inducing a greater particle dispersion. It is found that a large particle radius as well as a strong incident shock can facilitate such particle escape. The theory of Luo et al. (J. Fluid Mech., 2007) combined with the Samtaney–Zabusky (SZ) circulation model (J. Fluid Mech., 1994) can reasonably explain the high dependence of particle escape on the particle radius and shock strength.

Numerical investigations of Richtmyer-Meshkov instability in different magnetic field configurations and the corresponding dynamic mode decomposition

Based on magnetohydrodynamics(MHD), the evolution of the Richtmyer-Meshkov instability in different magnetic field configurations are studied. To ensure the zero magnetic divergence, an unsplit integration algorithm is adopted by combining corner transport upwind and constrained transport (CTU+CT) algorithm. The second order Godunov flux is obtained by using piecewise parabolic method(PPM) to construct conserved variables. The numerical results show that the evolution of complex wave patterns is not affected by magnetic fields, but the interface instability is compressed by magnetic field, especially in the case of transverse magnetic fields. Specifically, whether there exists magnetic field or not, irregular reflections occur outside the cylinder. Meanwhile, the central part of incident shock wave interacts with the density interface and generates the transmitted shock wave. Subsequently, the transmitted shock wave oscillates back and forth inside the cylinder, forming a transmission-reflection structure multiple times. Besides, in the absence of magnetic field, the density interface rolls up with a series of vortex sequences and an SF<sub>6</sub> jet surrounded by vortex pairs appears. Then the SF<sub>6</sub> jet passes through the downstream interface. In a longitudinal magnetic field, although density interface is smooth, a few vortex sequences still exist in the downstream interface and SF<sub>6</sub> jet can still pass through downstream interface. However, in the case of transverse magnetic field, the interface is much smoother than in the other cases and the SF<sub>6</sub> jet cannot pass through the downstream interface. The quantitative study also indicate that the increase of characteristic sizes is suppressed by the magnetic field. In addition, because of the influence of Richtmyer-Meshkov instability, magnetic lines are distorted near density interfaces. More distortions can be observed in the upstream interfaces, resulting in strong Lorentz forces in that area, which leads to the long distance between two vortex sheets distributed along two sides of the interface. In the downstream interfaces Lorentz forces are rather small, but the forces are even smaller in the longitudinal magnetic field, as a result vortex sheets interact with each other in that area. Furthermore, the dynamic mode decomposition(DMD) is primarily used in this paper and the results illustrate that even controlled by magnetic fields, vortex sequences can still exist, especially in the case of longitudinal magnetic field. For all cases, the first DMD modes all illustrate that a stable mode is the dominated feature of fluid field, and the following second to fourth mode show that the strength of vortex sequences decreases while their frequencies increase continually. Besides, for the same modes, the frequency of vortex sequences is reduced by magnetic fields, especially by the transverse magnetic field.

Effects of aspect ratio on shock-cylinder interaction

Interaction of a planar shock wave with a discontinuous \(\hbox {SF}_6\) elliptic gas cylinder surrounded by air is investigated. Special attention is given to the effects of aspect ratio on wave pattern, interface evolution, and material mixing. An ideal discontinuous two-dimensional gas cylinder is created by the soap film technique in experiments, and the shocked flow is captured by schlieren photography combined with a high-speed video camera. The surface of the gas cylinder is clear enough to observe the shock motions, and the distinct interface boundaries allow us to extract more details. As aspect ratio varies, the shock focusing process is quite different. For the prolate gas cylinder, an inward jet is produced although an internal shock focusing firstly occurs. The inward jet has never been observed in membraneless prolate ellipse experiments probably because the inward jet is so faint due to less vorticity generation on membraneless interface that it is difficult to be observed. For the oblate gas cylinder, a secondary vortex pair, which has not been described clearly in previous work, is derived from the downstream interface. The material lines at early stages are extracted from experiments, which grow faster as aspect ratio increases. The interfacial area, the mean volume fraction and the mixing rate are presented from computations, and the results show that the increase of aspect ratio promotes the mixing between gases.

Numerical investigation of shock-SF6 bubble interaction with different mach numbers

The computational results of the shock-SF6 heavy bubble interaction are presented. Influences of different incident shock Mach numbers (Ma = 1.21, 1.7 and 2.1) on the interaction processes are clarified by using the high resolution computation schemes. It is concluded that the SF6 bubble deforms differently with the raised incident shock intensity, and the different shock Mach numbers could alter the distance between the shock focusing position and the downstream bubble interface. The minimum distance emerges when Ma = 1.7, so the jet structure in this case is the longest among the three cases. Besides, with the increasement of incident shock Mach numbers, the bubble volume (V) and effective bubble volume (Veffective) decrease, but the compression ratio, the mixedness between two different fluids and the vorticity are all raised. Furthermore, the factors affecting the vorticity evolution are also analyzed, and it is found that the compression term has a relatively stronger influence on the vorticity evolution than the baroclinic term and viscosity term.

Modeling of Solid Conveying Pressure Throughput Behavior of Single Screw Smooth Barrel Extruders under Consideration of Backpressure and High Screw Speeds

AbstractThe task of the solid conveying section is to collect the entering material and transfer it to the melt dominated sections. Therefore, its upstream interface is the hopper and its downstream interface is the section in which the first melting occurs. Beneath the hopper opening, the screw rotation collects and conveys the material forward. It is hereby assumed that the friction forces among the particles are higher than the transferring forces on the screw and barrel. For that reason commonly known models for describing the solid conveying in single screw extruders assume that the screw channel is always completely filled so that a plug flow occurs. At high screw speeds, however, these assumptions are no longer valid. To analyze and mathematically describe the solid conveying behavior at screw speeds up to 2000 rpm, simulations based on the Discrete Element Method have been executed in previous investigations. Based on this, a model for describing the solid conveying behavior was developed which enables a variation of general screw and hopper geometry parameters but neglects the backpressure that inhibits the solid movement. For that reason, further investigations based on the Discrete Element Method are presented in this paper, which enable a consideration of the backpressure and pressure build-up in the feeding zone. Astonishingly, at high screw speeds a low filling degree in the screw channel was observed which did not fulfill the expectations of an always fully filled channel due to a backpressure forced particle backlog. Based on the investigations, a mathematical model has been developed which now fully comprehends the effects occurring in the solid conveying section. The conducted simulations were subsequently validated by experimental investigations. Therefore, a test bench was designed which enables solid conveying analysis with adjustable backpressures. The results indicate a good agreement with the formulated model which now enables the calculation of solid conveying zones with consideration of the pressure build-up and filling degrees.

Development of a Methodology for Interface Boundary Selection in the Multiscale Road Tunnel Fire Simulations

The simulation of large complex dynamical systems such as a fire in road tunnels is necessary but costly. Therefore, there is a crucial need to design efficient models. Coupling of computational fluid dynamics (CFD) models and 1D network modeling simulations of a fire event, a multiscale method, can be a useful tool to increase the computational efficiency while the accuracy of simulations is maintained. The boundary between a CFD model (near field) and a 1D model (far field) plays a key role in the accuracy of simulations of large systems. The research presented in this paper develops a novel methodology to select the interface boundary between the 3D CFD model and a 1D model in the multiscale simulation of vehicle fire events in a tunnel. The development of the methodology is based on the physics of the fluid structure, turbulent kinetic energy of the dynamical system, and the vortex dynamics. The methodology was applied to a tunnel with 73.73 m2 cross section and 960 m in length. Three different vehicle fire scenarios were investigated based on two different heat reslease rates (10 MW and 30 MW) and two different inlet velocities (1.5 m/s and 5 m/s). all parameters upstream and downstream of the fire source in all scenarios were investigated at t = 900 s. The effect of changes in heat release rate (HRR) and air velocity on the selection of an interface boundary was investigated. The ratio between maximum longitudinal and transversal velocities was within a range of 10 to 20 in the quasi-1D region downstream of the fire source. The selected downstream interface boundary was 12Dh m downstream of the fire for the simulations. The upstream interface boundary was selected at 0.5 Dh m upstream the tip of the object when the velocity was greater than equal to the Vc. In the simulations with backlayering (V < Vc), the interface boundary was selected 10 m further from the tip of the backlayering (1.2 Dh). An indirect coupling strategy was utilized to couple CFD models to 1D models at the selected interface boundary; then, the coupled models results were compared to the full CFD model results. The calculated error between CFD and coupled models for mean temperature and velocity at different cross sections were calculated at less than 5%. The findings were used to recommend a modification to the selection of interface boundary in multiscale fire simulations in the road tunnels and more complex geometries such as mines.

Interaction of strong converging shock wave with SF6 gas bubble

Interaction of a strong converging shock wave with an SF6 gas bubble is studied, focusing on the effects of shock intensity and shock shape on interface evolution. Experimentally, the converging shock wave is generated by shock dynamics theory and the gas bubble is created by soap film technique. The post-shock flow field is captured by a schlieren photography combined with a high-speed video camera. Besides, a three-dimensional program is adopted to provide more details of flow field. After the strong converging shock wave impact, a wide and pronged outward jet, which differs from that in planar shock or weak converging shock condition, is derived from the downstream interface pole. This specific phenomenon is considered to be closely associated with shock intensity and shock curvature. Disturbed by the gas bubble, the converging shocks approaching the convergence center have polygonal shapes, and the relationship between shock intensity and shock radius verifies the applicability of polygonal converging shock theory. Subsequently, the motion of upstream point is discussed, and a modified nonlinear theory considering rarefaction wave and high amplitude effects is proposed. In addition, the effects of shock shape on interface morphology and interface scales are elucidated. These results indicate that the shape as well as shock strength plays an important role in interface evolution.

Numerical investigations of interactions between shock waves and triangular cylinders in magnetic field

Magnetohydrodynamic (MHD) equations are solved by using the CTU+CT (corner transport upwind + constrained transport) algorithm which guarantees the divergence-free constraint on the magnetic field. The interactions between shock wave and heavy or light triangular cylinder are investigated in detail in the cases with and without magnetic field. In the cases of hydrodynamic (B=0 T) and MHD (B=0.01 T), the numerical results indicate that heavy and light triangular cylinders have quite different wave patterns and jet structures after being impacted by a planar incident shock wave. Specifically, a regular refraction and downstream R22 jet are formed in the heavy case, whereas an irregular refraction and upstream air jet are generated in the light case. In the hydrodynamic case, the Richtmyer-Meshkov (R-M) instability and Kelvin-Helmholtz (K-H) instability are induced by the incident shock wave. Hereafter, both heavy and light density interfaces begin to roll up with a series of interfacial vortex sequences. In addition, a main vortex ring is formed in the heavy case, while a vortex dipole passing through the downstream interface is generated in the light case. In the MHD case, both heavy and light density interfaces remain smooth and interfacial vortex sequences vanish. Furthermore, the main vortex ring formed in the heavy cases and the vortex dipole generated in the light cases disappear. Moreover, in the presence of a magnetic field, a detailed investigation demonstrates that Lorentz forces give rise to the transport of baroclinic vorticities to the Alfvn waves. As a consequence, the deposition of interfacial vorticities decreases and the rolling-up of interfaces is suppressed. In the end, the vorticities are transformed into two vortex sheets travelling away from the density interfaces, and the R-M instability and K-H instability are well controlled. The quantitative investigations reveal that for both heavy and light triangular cylinders, magnetic field can accelerate the upstream interface and decelerate the downstream interface, especially for the light triangular cylinder.