Strong Shock Interactions Research Articles

Misaligned precessing jets are choked by the accretion disc wind

ABSTRACT We analytically and numerically study the hydrodynamic propagation of a precessing jet in the context of tidal disruption events (TDEs) where the star’s angular momentum is misaligned with the black hole spin. We assume that a geometrically thick accretion disc undergoes Lense–Thirring precession around the black hole spin axis and that the jet is aligned with the instantaneous disc angular momentum. At large spin-orbit misalignment angles $\theta _{\it LS}$, the duty cycle along a given angle that the jet sweeps across is much smaller than unity. The faster jet and slower disc wind alternately fill a given angular region, which leads to strong shock interactions between the two. We show that precessing jets can only break out of the wind confinement if $\theta _{\it LS}$ is less than a few times the jet opening angle $\theta _{\rm j}$. The very small event rate of observed jetted TDEs is then explained by the condition of double alignment: both the stellar angular momentum and the observer’s line of sight are nearly aligned with the black hole spin. In most TDEs with $\theta _{\it LS}\gg \theta _{\rm j}$, the jets are initially choked by the disc wind and may only break out later when the disc eventually aligns itself with the spin axis due to the viscous damping of the precession. Such late-time jets may produce delayed radio rebrightening as seen in many optically bright TDEs. Our model is also applicable to jets associated with (stellar mass) black hole-neutron star mergers where the black hole’s spin is misaligned with the orbital angular momentum.

High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of flow variables construct a time-accurate evolution solution of gas distribution function at a cell interface and obtain the corresponding flux function; 2). Introduce the WENO-type weighting functions into the high-order time-derivative of the cell interface flux function in the multistage multi-derivative (MSMD) time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step, and update the cell-averaged conservative flow variables inside each control volume; 3). Model the time evolution of the gas distribution function on both sides of a cell interface separately, take moments of the inner cell interface gas distribution function to get flow variables, and update the cell-averaged gradients of flow variables inside each control volume; 4). Based on the cell-averaged flow variables and their gradients, develop compact initial data reconstruction to get initial condition of flow distributions at the beginning of next time step. A compact gas-kinetic scheme (GKS) up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh. In this paper, the compact GKS up to fourth-order accuracy on three-dimensional tetrahedral mesh will be further constructed with the focus on the WENO-type initial compact data reconstruction. Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions. The fourth-order compact GKS uses a large time step with a CFL number 0.6 in the simulations from subsonic to hypersonic flow. A series of test cases are used to validate the scheme. The high-order compact GKS can be used in 3D applications with complex geometry.

Seven Years of Coordinated Chandra–NuSTAR Observations of SN 2014C Unfold the Extreme Mass-loss History of Its Stellar Progenitor

We present the results from our 7 yr long broadband X-ray observing campaign of SN 2014C with Chandra and NuSTAR. These coordinated observations represent the first look at the evolution of a young extragalactic SN in the 0.3–80 keV energy range in the years after core collapse. We find that the spectroscopic metamorphosis of SN 2014C from an ordinary type Ib SN into an interacting SN with copious hydrogen emission is accompanied by luminous X-rays reaching L x ≈ 5.6 × 1040 erg s−1 (0.3–100 keV) at ∼1000 days post-explosion and declining as L x ∝ t −1 afterwards. The broadband X-ray spectrum is of thermal origin and shows clear evidence for cooling after peak, with . Soft X-rays of sub-keV energy suffer from large photoelectric absorption originating from the local SN environment with . We interpret these findings as the result of the interaction of the SN shock with a dense (n ≈ 105 − 106 cm−3), H-rich disk-like circumstellar medium (CSM) with inner radius ∼2 × 1016 cm and extending to ∼1017 cm. Based on the declining NHint(t) and X-ray luminosity evolution, we infer a CSM mass of ∼(1.2 f–2.0 , where f is the volume filling factor. We place SN 2014C in the context of 121 core-collapse SNe with evidence for strong shock interaction with a thick circumstellar medium. Finally, we highlight the challenges that the current mass-loss theories (including wave-driven mass loss, binary interaction, and line-driven winds) face when interpreting the wide dynamic ranges of CSM parameters inferred from observations.

Study on afterbody-effects of multi-stage separation at high-speed

The stage separation of high-speed vehicle is complicated at high dynamic pressure, usually accompanied by strong shock and vortex interaction. There exists a strong interaction between first stage and second stage, which called “afterbody-effects”. The aerodynamic mechanism of “afterbody-effects” is studied in this paper based on numerical simulation. The aerodynamic characteristics of a simplified three-dimensional projectile model at different distances between stages at 0° angle of attack is researched with structural mesh. The results show that the vortexes of stages have a significant impact on the aerodynamic characteristics of different stages, As the distance between stages increases, the drag coefficient of the first stage increases, and the drag coefficient of the second stage increases first and then decreases.

Numerical simulation of compressible multifluid flows using an adaptive positivity‐preserving RKDG‐GFM approach

SummaryThe Runge‐Kutta discontinuous Galerkin method together with a refined real‐ghost fluid method is incorporated into an adaptive mesh refinement environment for solving compressible multifluid flows, where the level set method is used to capture the moving material interface. To ensure that the Riemann problem is exactly along the normal direction of the material interface, a simple and efficient modification is introduced into the original real‐ghost fluid method for constructing the interfacial Riemann problem, and the initial conditions of the Riemann problem are obtained directly from the solution polynomials of the discontinuous Galerkin finite element space. In addition, a positivity‐preserving limiter is introduced into the Runge‐Kutta discontinuous Galerkin method to suppress the failure of preserving positivity of density or pressure for the problems involving strong shock wave or shock interaction with material interface. For interfacial cells in adaptive mesh refinement, the data transfer between different grid levels is achieved by using a L2 projection approach along with the least squares fitting. Various numerical cases, including multifluid shock tubes, underwater explosions, and shock‐induced collapse of a underwater air bubble, are computed to assess the capability of the present adaptive positivity‐preserving RKDG‐GFM approach, and the simulated results show that the present approach is quite robust and can provide relatively reasonable results across a wide variety of flow regimes, even for problems involving strong shock wave or shock wave impacting high acoustic impedance mismatch material interface.

On the carbuncle instability of the HLLE-type solvers

The carbuncle phenomenon is a numerical instability that affects the numerical capturing of shock waves when low-dissipative upwind scheme is used. This paper investigates shock instabilities of the HLLE-type methods for the Euler equations under the strong shock interaction, where the HLLE-type methods include the HLLE, HLLC, HLLEM, HLLCM and HLLEC Riemann solvers with specific wavespeed estimates. Based on a matrix stability analysis for two dimensional steady shocks, a new factor to influence carbuncle phenomenon is pointed out and the choice of the signal velocity plays an important role. A numerical flux function with wave velocity estimates which can crisply resolve shocks seems to be vulnerable to the shock anomalies even if the numerical fluxes to be regarded to be free from the carbuncle phenomenon. A suggestion to the choice of the wave speed is proposed when calculating strong shock wave problems.

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

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

A Few Benchmark Test Cases for Higher-Order Euler Solvers

AbstractThere have been great efforts on the development of higher-order numerical schemes for compressible Euler equations in recent decades. The traditional test cases proposed thirty years ago mostly target on the strong shock interactions, which may not be adequate enough for evaluating the performance of current higher-order schemes. In order to set up a higher standard for the development of new algorithms, in this paper we present a few benchmark cases with severe and complicated wave structures and interactions, which can be used to clearly distinguish different kinds of higher-order schemes. All tests are selected so that the numerical settings are very simple and any higher order scheme can be straightforwardly applied to these cases. The examples include highly oscillatory solutions and the large density ratio problem in one dimensional case. In two dimensions, the cases include hurricane-like solutions; interactions of planar contact discontinuities with asymptotic large Mach number (the composite of entropy wave and vortex sheets); interaction of planar rarefaction waves with transition from continuous flows to the presence of shocks; and other types of interactions of two-dimensional planar waves. To get good performance on all these cases may push algorithm developer to seek for new methodology in the design of higher-order schemes, and improve the robustness and accuracy of higher-order schemes to a new level of standard. In order to give reference solutions, the fourth-order gas-kinetic scheme (GKS) will be used to all these benchmark cases, even though the GKS solutions may not be very accurate in some cases. The main purpose of this paper is to recommend other CFD researchers to try these cases as well, and promote further development of higher-order schemes.

Optical and IR observations of SN 2013L, a Type IIn Supernova surrounded by asymmetric CSM

We present optical and NIR photometry and spectroscopy of SN 2013L for the first four years post-explosion. SN 2013L was a moderately luminous (M$_{r}$ = -19.0) Type IIn supernova (SN) that showed signs of strong shock interaction with the circumstellar medium (CSM). The CSM interaction was equal to or stronger to SN 1988Z for the first 200 days and is observed at all epochs after explosion. Optical spectra revealed multi-component hydrogen lines appearing by day 33 and persisting and slowly evolving over the next few years. By day 1509 the H$\alpha$ emission was still strong and exhibiting multiple peaks, hinting that the CSM was in a disc or torus around the SN. SN 2013L is part of a growing subset of SNe IIn that shows both strong CSM interaction signatures and the underlying broad lines from the SN ejecta photosphere. The presence of a blue H$\alpha$ emission bump and a lack of a red peak does not appear to be due to dust obscuration since an identical profile is seen in Pa$\beta$. Instead this suggests a high concentration of material on the near-side of the SN or a disc inclination of roughly edge-on and hints that SN 2013L was part of a massive interactive binary system. Narrow H$\alpha$ P-Cygni lines that persist through the entirety of the observations measure a progenitor outflow speed of 80--130 km s$^{-1}$, speeds normally associated with extreme red supergiants, yellow hypergiants, or luminous blue variable winds. This progenitor scenario is also consistent with an inferred progenitor mass-loss rate of 0.3 - 8.0 $\times$ 10$^{-3}$ M$_{sun}$ yr$^{-1}$.

Power spectra of outflow-driven turbulence

We investigate the power spectra of outflow-driven turbulence through high-resolution three-dimensional isothermal numerical simulations where the turbulence is driven locally in real-space by a simple spherical outflow model. The resulting turbulent flow saturates at an average Mach number of ~2.5 and is analysed through density and velocity power spectra, including an investigation of the evolution of the solenoidal and compressional components. We obtain a shallow density power spectrum with a slope of ~-1.2 attributed to the presence of a network of localised dense filamentary structures formed by strong shock interactions. The total velocity power spectrum slope is found to be ~-2.0, representative of Burgers shock dominated turbulence model. The density weighted velocity power spectrum slope is measured as ~-1.6, slightly less than the expected Kolmogorov scaling value (slope of -5/3) found in previous works. The discrepancy may be caused by the nature of our real space driving model and we suggest there is no universal scaling law for supersonic compressible turbulence. We find that on average, solenoidal modes slightly dominate in our turbulence model as the interaction between strong curved compressible shocks generates solenoidal modes, and compressible modes decay faster.

A method for compressible multimaterial flows with condensed phase explosive detonation and airblast on unstructured grids

An efficient method for the simulation of compressible multimaterial flows with a general form of equation of state is presented for explosive detonation and airblast applications. Multimaterial flows are modeled with a volume-fraction type approach for immiscible fluids governed by the compressible Euler equations on three-dimensional unstructured grids. The five-equation quasi-conservative system is discretized in space using an edge-based finite volume approach with a second-order accurate HLLC approximate Riemann solver and temporal discretization with an explicit multistage Runge–Kutta method. The computational model is robust enough to handle flows with strong shocks, while being general enough to model materials with different equations of state and physical states. Numerical tests demonstrate the accuracy of the method for strong shock and interface interactions. A program burn method is implemented to describe the conversion of solid unreacted explosive to reacted gases in condensed phase detonations. The accuracy of the burn model is validated by comparison with published numerical results of flow profiles during detonation and for near-field airblast. Numerical simulations of hemispherical and plate-shaped explosive charge detonations are performed to investigate the influence of charge shape on airblast. The predicted pressure and impulse from simulation compare well with published experimental data.

Investigation of strong shock wave interactions with CeO2 ceramic

Strong shock wave interactions with ceramic material ceria (CeO2) in presence of O2 and N2 gases were investigated using free piston driven shock tube (FPST). FPST is used to heat the test gas to very high temperature of about 6800–7700 K (estimated) at pressure of about 6.8–7.2 MPa for short duration (2–4 ms) behind the reflected shock wave. Ceria is subjected to super heating and cooling at the rate of about 106 K/s. Characterization of CeO2 sample was done before and after exposure to shock heated test gases (O2 and N2). The surface composition, crystal structure, electronic structure and surface morphology of CeO2 ceramic were examined using X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectrometry, scanning electron microscopy (SEM) and high resolution transmission electron microscopy (HRTEM). Results obtained from the experimental investigations show that CeO2 can withstand high pressure accompanied by thermal shock without changing its crystal structure. Reducible CeO2 releases lattice oxygen making it possible to shift between reduced and oxidized states upon the interaction with shock heated gas. Due to such reaction mechanism, CeO2 ceramic undergoes nitrogen doping with decrease in lattice parameter. Investigations reveal that CeO2 retains its crystal structure during strong shock interaction, even at elevated pressure.

A robust and contact resolving Riemann solver on unstructured mesh, Part II, ALE method

This paper investigates solution behaviors under the strong shock interaction for moving mesh schemes based on the one-dimensional Godunov and HLLC Riemann solvers. When the grid motion velocity is close to Lagrangian one, these Godunov methods, which updates the flow parameters directly on the moving mesh without using interpolation, may suffer from numerical shock instability. In order to cure such instability, a new cell centered arbitrary Lagrangian Eulerian (ALE) algorithm is constructed for inviscid, compressible gas flows. The main feature of the algorithm is to introduce a nodal contact velocity and ensure the compatibility between edge fluxes and the nodal flow intrinsically. We establish a new two-dimensional Riemann solver based on the HLLC method (denoted by the ALE HLLC-2D). The solver relaxes the condition that the contact pressures must be the same in the traditional HLLC solver and constructs discontinuous fluxes along each sampling direction of the similarity solution. The two-dimensional contact velocity of the grid node is determined via enforcing conservation of mass, momentum and total energy. The resulting ALE scheme has a node instead of grid edge conservation properties. Numerical tests are presented to demonstrate the robustness and accuracy of this new solver. Due to the multi-dimensional information introduced and consistency between the fluxes and nodal contact velocity, the developed ALE algorithm performs well on both quadrilateral and triangular grids and reduces numerical shock instability phenomena.

Effect of multi-bend geometry on deflagration to detonation transition of a hydrocarbon-air mixture in tubes

We present a numerical investigation of gaseous deflagration-to-detonation transition (DDT) triggered by a shock in a multi-bend geometry. The ethylene-air mixture filled rigid tube with obstacles is considered for understanding the effects of complex confinement and initial flame size on DDT. Our calculations show generation of hot spots by flame and strong shock interactions, and flame propagation is either restrained or accelerated due to the wall obstacles of both straight and bent tubes. The effect of initial flame size on DDT in complex confinement geometry is analyzed as well as the hot spot formation on promoting shock–flame interaction, leading to a full detonation.

Differential evolution based soft optimization to attenuate vane–rotor shock interaction in high-pressure turbines

This article presents a soft computing methodology to design turbomachinery components experiencing strong shock interactions. The study targets a reduction of unsteady phenomena using evolutionary optimization with robust, high fidelity, and low computational cost evaluations. A differential evolution (DE) algorithm is applied to optimize the transonic vane of a high-pressure turbine. The vane design candidates are examined by a cost-effective Reynolds-averaged Navier–Stokes (RANS) solver, computing the downstream pressure distortion and aerodynamic efficiency. A reduction up to 55% of the strength of the shock waves propagating downstream of the stand-alone vane was obtained. Subsequently to the vane optimization, unsteady computations of the vane–rotor interaction were performed using a non-linear harmonic (NLH) method. Attenuation above 60% of the unsteady forcing on the rotor (downstream of the optimal vane) was observed, with no stage-efficiency abatement. These results show the effectiveness of the proposed soft optimization to improve unsteady performance in modern turbomachinery exposed to strong shock interactions.

Sharp interface simulations with Local Mesh Refinement for multi-material dynamics in strongly shocked flows

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) is developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. In addition, the Riemann solver based GFM approach is augmented with a quadtree (octree in three-dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions. The paper reports on a conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundaries. The numerical examples presented in this paper clearly demonstrate that the methodology produces accurate benchmark solutions and effectively captures fine structures in the flow field.

Energetic electron response to ULF waves induced by interplanetary shocks in the outer radiation belt

Strong interplanetary shock interactions with the Earth's magnetosphere have great impacts on energetic particle dynamics in the magnetosphere. An interplanetary shock on 7 November 2004 (with the maximum solar wind dynamic pressure of ∼70 nPa) was observed by the Cluster constellation to induce significant ULF waves in the plasmasphere boundary, and energetic electrons (up to 2 MeV) were almost simultaneously accelerated when the interplanetary shock impinged upon the magnetosphere. In this paper, the relationship between the energetic electron bursts and the large shock‐induced ULF waves is studied. It is shown that the energetic electrons could be accelerated and decelerated by the observed ULF wave electric fields, and the distinct wave number of the poloidal and toroidal waves at different locations also indicates the different energy ranges of electrons resonating with these waves. For comparison, a rather weak interplanetary shock on 30 August 2001 (dynamic pressure ∼2.7 nPa) is also investigated. It is found that interplanetary shocks or solar wind pressure pulses with even small dynamic pressure change can have a nonnegligible role in the radiation belt dynamics.

Turbulence Model Studies to Investigate the Aerodynamic Performance of a NASA Dual Control Missile at Supersonic Mach Numbers

This paper contains an investigation of the ability of some of the current turbulence models to predict viscous effects in supersonic Mach number regimes. In most cases, these turbulence models have been derived and validated in traditional subsonic to transonic Mach number regimes and their application to supersonic and hypersonic regimes is assumed valid without a proper recourse to understanding the wider implications of the viscous flow field at high Mach numbers. In such flow regimes, such characteristics as the strong shock interactions with control surfaces and evolving vortices present in the flow, or other large entropy gradient effects brought about by the forebody or other fin surfaces, produce non-trivial challenges for the turbulence models. This study was aimed at interrogating the strength of the turbulence models to model such physics. The Applied Vehicle Technology Panel Group 082 of the Research Technology Organisation selected a dual control NASA missile to investigate the capabilities of Computational Fluid Dynamics (CFD) to predict the flow field and performance characteristics of complex-shaped projectiles at high Mach numbers. There are two types of difficulties that are encountered when computing such problems. The first type are geometry based, and are related to the shape of the nose and forebody, number and types of strakes or forward control mechanisms, fin geometry deployment, and shape and design of the cowls and intakes. The second type of difficulty deals with flow complexities such as the heat transfer (M > 4) implications; the vortices shed from the forebody and other control surfaces; the interaction of these vortices with the body structures, the free stream, and with each other; the base flow interaction with the free stream; the boundary-layer development; and, in the case of supersonic flows, the shock boundary-layer interactions. Air-breathing missiles with intakes or missiles with jet-controlled guidance systems add to the flow complexities. Various turbulence models employed in current CFD codes are tested for their ability to address these viscous issues.

Numerical experiments on the accuracy of a discontinuous Galerkin method for the Euler equations

In this paper, a discontinuous Galerkin approximation to the weak solutions of hyperbolic system of conservation laws is presented. This work is a part of the thesis of the first author. The method is essentially viewed as a second order accurate upwind spatial discretization of the governing equations. Although the present approach, like MUSCL, is based on linear spatial interpolation, it avoids the use of limiters owing to its good stability property. To evaluate the accuracy and the robustness of the present method, a series of detailed comparisons has been carried out with two MUSCL approaches, using a directionwise or a truly two-dimensional limiter. Various severe unsteady test cases, including strong shock and contact discontinuity interactions, demonstrate the capabilities of the present method, on both regular and disturbed meshes.

Variations in Upstream Vane Loading With Changes in Back Pressure in a Transonic Compressor

Dynamic loading of an inlet guide vane (IGV) in a transonic compressor is characterized by unsteady IGV surface pressures. These pressure data were acquired for two spanwise locations at a 105 percent speed operating condition, which produces supersonic relative Mach numbers over the majority of the rotor blade span. The back pressure of the compressor was varied to determine the effects from such changes. Strong bow shock interaction was evident in both experimental and computational results. Variations in the back pressure have significant influence on the magnitude and phase of the upstream pressure fluctuations. The largest unsteady surface pressure magnitude, 40 kPa, was obtained for the near-stall mass flow condition at 75 percent span and 95 percent chord. Radial variation effects caused by the spanwise variation in relative Mach number were measured. Comparisons to a two-dimensional nonlinear unsteady blade/vane Navier–Stokes analysis show good agreement for the 50 percent span results in terms of IGV unsteady surface pressure. The results of the study indicate that significant nonlinear bow shock influences exist on the IGV trailing edge due to the downstream rotor shock system. [S0889-504X(00)00303-2]