Showing papers on "Rarefaction published in 2018"
TL;DR: In this article, the development of central cooling catastrophe and how a subsequent powerful AGN jet event averts cooling flows, with a focus on complex gasdynamical processes involved.
Abstract: The cooling flow problem is one of the central problems in galaxy clusters, and active galactic nucleus (AGN) feedback is considered to play a key role in offsetting cooling. However, how AGN jets heat and suppress cooling flows remains highly debated. Using an idealized simulation of a cool-core cluster, we study the development of central cooling catastrophe and how a subsequent powerful AGN jet event averts cooling flows, with a focus on complex gasdynamical processes involved. We find that the jet drives a bow shock, which reverses cooling inflows and overheats inner cool core regions. The shocked gas moves outward in a rarefaction wave, which rarefies the dense core and adiabatically transports a significant fraction of heated energy to outer regions. As the rarefaction wave propagates away, inflows resume in the cluster core, but a trailing outflow is uplifted by the AGN bubble, preventing gas accumulation and catastrophic cooling in central regions. Inflows and trailing outflows constitute meridional circulations in the cluster core. At later times, trailing outflows fall back to the cluster centre, triggering central cooling catastrophe and potentially a new generation of AGN feedback. We thus envisage a picture of cool cluster cores going through cycles of cooling-induced contraction and AGN-induced expansion. This picture naturally predicts an anti-correlation between the gas fraction (or X-ray luminosity) of cool cores and the central gas entropy, which may be tested by X-ray observations.
54 citations
TL;DR: A new interface discretisation method is proposed, derived from an analogy with a contact discontinuity, that performs local changes to the discrete values of density and total enthalpy based on the assumption of thermodynamic equilibrium, and does not require a Riemann solver.
39 citations
TL;DR: It is proved that the time-asymptotically nonlinear stability of the planar rarefaction wave to the two-dimensional compressible and isentropic Navier-Stokes equations is given, which gives the first stability result of the Planar Rarefaction Wave to the multi-dimensional system with physical viscosities.
Abstract: It is well known that the rarefaction wave, one of the basic wave patterns of the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional compressible Navier--Stokes equations (c...
36 citations
TL;DR: Simulation results demonstrate that the present exact Riemann solver is capable of reproducing the complete wave propagation using the current drift-flux equations as the numerical resolution.
34 citations
TL;DR: Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh-Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave as mentioned in this paper.
Abstract: Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number, , where and are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of , , and . Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber, , experiments and simulations, where is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.
28 citations
TL;DR: In this article, the authors prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain.
Abstract: We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain $${\mathbb{R} \times \mathbb{T}^2}$$
. Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x2 and x3 and its interactions with the planar rarefaction wave in x1 direction.
28 citations
TL;DR: It is demonstrated that square signal enhances temperature and pressure growth inside the bubble, as well as mass transfer by evaporation and condensation, which leads to an improvement of produced quantities of free radicals but also to a selectivity of O as a major product in the detriment of HO2 and OH.
24 citations
TL;DR: In this paper, small perturbations in the forms of graded intersite stiffnesses and graded on-site potentials are introduced to a lattice composed of bistable unit cells under elastic interactions.
Abstract: In this study we introduce small perturbations in the forms of graded intersite stiffnesses and graded on-site potentials to a lattice composed of bistable unit cells under elastic interactions. Based on a known soliton solution in the $\ensuremath{\phi}$-4 model, we use a perturbation approach to approximate the effects of the perturbations on the propagation speeds of transition waves. Numerical validations follow on the exact discrete equations of motion, from which we observe eventual stoppage of transition waves in the periodic lattice under physical damping, unidirectional propagation of the waves in the direction of softening properties, and boomerang-like reflection of the waves in the stiffening direction. Finally, we present three-dimensional-printed experimental lattices, confirming the theoretical and numerical results. The observed behaviors imply the extreme controllability of solitary waves through slight engineering manipulations in material-level structures. We further find that both kink (rarefaction) and antikink (compression) waves are allowed at any site in the lattice, extending the functionality of the lattice in engineering applications such as energy harvesting.
23 citations
TL;DR: In this paper, the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation was studied, and the existence and uniqueness of delta shocks for the Riemann problem was established under the generalized Rankine-Hugoniot relation and entropy condition.
Abstract: The relativistic full Euler system with generalized Chaplygin proper energy density–pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine–Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine–Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.
23 citations
23 citations
TL;DR: The piston shock problem is a prototypical example of strongly nonlinear fluid flow that enables the experimental exploration of fluid dynamics in extreme regimes, such as Bose-Einstein condensate.
Abstract: The piston shock problem is a prototypical example of strongly nonlinear fluid flow that enables the experimental exploration of fluid dynamics in extreme regimes. Here we investigate this problem for a nominally dissipationless, superfluid Bose-Einstein condensate and observe rich dynamics including the formation of a plateau region, a non-expanding shock front, and rarefaction waves. Many aspects of the observed dynamics follow predictions of classical dissipative—rather than superfluid dispersive—shock theory. The emergence of dissipative-like dynamics is attributed to the decay of large amplitude excitations at the shock front into turbulent vortex excitations, which allow us to invoke an eddy viscosity hypothesis. Our experimental observations are accompanied by numerical simulations of the mean-field, Gross-Pitaevskii equation that exhibit quantitative agreement with no fitting parameters. This work provides an avenue for the investigation of quantum shock waves and turbulence in channel geometries, which are currently the focus of intense research efforts. There is increasing interest in understanding the non-equilibrium phenomena in quantum fluids. Here, the authors show dissipative, viscous shock and rarefaction wave dynamics emerging from the turbulent, superfluid flow of an elongated BEC of ultracold Rb atoms driven by a quantum-mechanical piston.
TL;DR: Li et al. as mentioned in this paper investigated the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system.
Abstract: The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov–Poisson–Boltzmann (VPB) system. To this end, motivated by the micro–macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133–179, 2004) and Liu et al. (Physica D 188:178–192, 2004), we first set up a new micro–macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ
Math J 65(2):665–725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.
TL;DR: The new DG scheme not only meets the demand for high order accuracy and the positivity/monotonicity preserving property for accurately simulating dusty gas flows, but it can also handle the numerically problematic source terms efficiently, without resorting to the complicated operator splitting method commonly employed in the conventional finite volume method (FVM).
TL;DR: In this paper, the authors studied the clearance flow in dry running positive displacement vacuum pumps and compared the results with experimental investigations varying the pressure ratio and the circumferential speed of a clearance boundary in a wide range of the gas rarefaction.
Abstract: Clearance flows are the main loss mechanism in dry running positive displacement vacuum pumps. In order to calculate the operation of those pumps, a detailed knowledge of the clearance mass flow rates is crucial. The dimensions of such pumps and the large pressure range of the operating points require a wide range of gas rarefaction to be taken into account. The clearance flow can be described by a combined Couette Poiseuille flow due to the pressure gradient between two chambers and the rotation of the rotary pistons. These clearance flows are studied experimentally and theoretically in the present work. Therefore, a suitable experimental setup is described together with the requirements of sensors and the necessity of a low leakage. A theoretical approach is presented, and the results are compared to experimental investigations varying the pressure ratio and the circumferential speed of a clearance boundary in a wide range of the gas rarefaction.
TL;DR: In this article, the one-dimensional interaction of a detonation wave with a contact discontinuity was investigated analytically and experimentally for oxyhydrogen detonations, and it was shown that the transmitted shock can either be amplified or attenuated depending on the reflection type at the contact surface and on the ratio of acoustic impedance across it.
Abstract: The one-dimensional interaction of a detonation wave with a contact discontinuity was investigated analytically and experimentally for oxyhydrogen detonations. The analytical and experimental results showed that the transmitted shock through the contact surface and into a non-combustible gas can either be amplified or attenuated depending on the reflection type at the contact surface and on the ratio of acoustic impedance across it. Experiments were performed with a detonation-driven shock tube facility to determine the transmitted shock velocity into a non-combustible He/air mixture. The oxyhydrogen equivalence ratio in the detonation section was varied from 0.5 to 1.5, and the driven section He mole fraction was varied from 0.0 to 1.0 to test a broad range of acoustic impedance ratios ranging from approximately 0.36 to 1.69. The analytical results were shown to have acceptable agreement with the measured transmitted shock wave velocity in the case of a reflected rarefaction from the contact surface. Additionally, the results indicated that the detonation wave reaction zone properties could have an important role that influences the transmitted shock properties in the case of a reflected shock from the contact surface.
25 Dec 2018
TL;DR: In this paper, the high-order moments in the Lattice Boltzmann method were considered for gas flows in ultra-tight media and the influence of Reynolds number (Re) on the intrinsic permeability was discussed.
Abstract: Lattice Boltzmann method (LBM) has been applied to predict flow properties of porous media including intrinsic permeability, where it is implicitly assumed that the LBM is equivalent to the incompressible (or near incompressible) Navier-Stokes equation. However, in LBM simulations, high-order moments, which are completely neglected in the Navier-Stokes equation, are still available through particle distribution functions. To ensure that the LBM simulation is correctly working at the Navier-Stokes hydrodynamic level, the high-order moments have to be negligible. This requires that the Knudsen number (Kn) is small so that rarefaction effect can be ignored. In our study, we elaborate this issue in LBM modeling of porous media flows, which is particularly important for gas flows in ultra-tight media. The influence of Reynolds number (Re) on the intrinsic permeability is also discussed.
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TL;DR: In this article, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different $m$--fold symmetries, $m\ge 1$.
Abstract: This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different $m$--fold symmetries, $m\ge 1$. In particular, a complete study is provided for the truncated quadratic density $(A|x|^2+B){\bf{1}}_{\mathbb{D}}(x)$, with $\mathbb{D}$ the unit disc. We exhibit different behaviors with respect to the coefficients $A$ and $B$ describing the rarefaction of bifurcating curves.
TL;DR: Two-dimensional simulations are carried out to assess standard grid adaptation criteria for steady inviscid flows in the proximity of the liquid-vapor saturation curve, where non-ideal compressible-fluid behavior is expected.
TL;DR: In this paper, the authors examine the transport in a homogeneous porous medium of a finite slice of a solute which adsorbs on the porous matrix following a Langmuir adsorption isotherm and can influence the dynamic viscosity of the solution.
Abstract: We examine the transport in a homogeneous porous medium of a finite slice of a solute which adsorbs on the porous matrix following a Langmuir adsorption isotherm and can influence the dynamic viscosity of the solution. In the absence of any viscosity variation, the Langmuir adsorption induces the formation of a shock layer wave at the frontal interface and of a rarefaction wave at the rear interface of the sample. For a finite width sample, these waves interact after a given time that varies nonlinearly with the adsorption properties to give a triangle-like concentration profile in which the mixing efficiency of the solute is larger in comparison to the linear or no-adsorption cases. In the presence of a viscosity contrast such that a less viscous carrier fluid displaces the more viscous finite slice, viscous fingers are formed at the rear rarefaction interface. The fingers propagate through the finite sample to preempt the shock layer at the viscously stable front. In the reverse case i.e. when the shock layer front features viscous fingering, the fingers are unable to intrude through the rarefaction zone and the qualitative properties of the expanding rear wave are preserved. A non-monotonic dependence with respect to the Langmuir adsorption parameter $b$ is observed in the onset time of interaction between the nonlinear waves and viscous fingering. The coupled effect of viscous fingering at the rear interface and of Langmuir adsorption provides a powerful mechanism to enhance the mixing efficiency of the adsorbed solute.
01 Jan 2018
TL;DR: In this article, the authors prove the time-asymptotic stability of the planar rarefaction wave for the three-dimensional full compressible Navier-Stokes equations in an infinite long flat nozzle domain.
Abstract: We prove the time-asymptotic stability toward planar rarefaction wave for the three-dimensional full compressible Navier-Stokes equations in an infinite long flat nozzle domain $\mathbb{R}\times\mathbb{T}^2$. Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial to overcome the difficulties due to the wave propagation along the transverse directions $x_2$ and $x_3$ and its interactions with the planar rarefaction wave in $x_1$ direction.
TL;DR: In this article, the authors studied the interaction of a strong converging shock wave with an SF6 gas bubble, focusing on the effects of shock intensity and shock shape on interface evolution.
Abstract: 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.
TL;DR: The smoothed particle hydrodynamics (SPH) method, which has been employed in the arbitrary Lagrangian Eulerian (ALE) framework, offers numerical efficiency, compared to grid related discretization methods, in terms of deformation handling of the droplet.
Abstract: The impact of a laser pulse onto a liquid metal droplet is numerically investigated by utilising a weakly compressible single phase model; the thermodynamic closure is achieved by the Tait equation of state (EoS) for the liquid metal. The smoothed particle hydrodynamics (SPH) method, which has been employed in the arbitrary Lagrangian Eulerian (ALE) framework, offers numerical efficiency, compared to grid related discretization methods. The latter would require modelling not only of the liquid metal phase, but also of the vacuum, which would necessitate special numerical schemes, suitable for high density ratios. In addition, SPH-ALE allows for the easy deformation handling of the droplet, compared to interface tracking methods where strong mesh deformation and most likely degenerate cells occur. Then, the laser-induced deformation of the droplet is simulated and cavitation formation is predicted. The ablation pattern due to the emitted shock wave and the two low pressure lobes created in the middle of the droplet because of the rarefaction waves are demonstrated. The liquid metal droplet is subject to material rupture, when the shock wave, the rarefaction wave and the free surface interact. Similar patterns regarding the wave dynamics and the hollow structure have been also noticed in prior experimental studies.
TL;DR: In this paper, the authors predict the significant alteration of mass deposition rate attending extensive aggregation in a gaseous mainstream, at the same total spherule volume fraction as in a Gaseous Mainstream.
Abstract: At the same total spherule volume fraction in a gaseous mainstream, we predict the significant alteration of mass deposition rate attending extensive aggregation—illustrating our methods and result...
TL;DR: In this paper, a 3D-printed soft chain of hollow elliptical cylinders was used to demonstrate dispersive rarefaction shocks (DRS) in 3D printed soft chain.
Abstract: We report an experimental and numerical demonstration of dispersive rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical cylinders. We find that, in contrast to conventional nonlinear waves, these DRS have their lower amplitude components travel faster, while the higher amplitude ones propagate slower. This results in the backward-tilted shape of the front of the wave (the rarefaction segment) and the breakage of wave tails into a modulated waveform (the dispersive shock segment). Examining the DRS under various impact conditions, we find the counterintuitive feature that the higher striker velocity causes the slower propagation of the DRS. These unique features can be useful for mitigating impact controllably and efficiently without relying on material damping or plasticity effects.
TL;DR: In this paper, generalized simple waves of the gas dynamics equations in Lagrangian and Eulerian descriptions are studied in the context of collision of a shock wave and a rarefaction wave.
Abstract: Generalized simple waves of the gas dynamics equations in Lagrangian and Eulerian descriptions are studied in the paper. As in the collision of a shock wave and a rarefaction wave, a flow becomes nonisentropic. Generalized simple waves are applied to describe such flows. The first part of the paper deals with constructing a solution describing their adjoinment through a shock wave in Eulerian coordinates. Even though the Eulerian form of the gas dynamics equations is most frequently used in applications, there are advantages for some problems concerning the gas dynamics equations in Lagrangian coordinates, for example, of being able to be reduced to an Euler–Lagrange equation. Through the technique of differential constraints, necessary and sufficient conditions for the existence of generalized simple waves in the Lagrangian description are provided in the second part of the paper.
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TL;DR: In this paper, the authors used the Fast Marching method to factor the rarefaction fans arising due to nonsmoothness of domain boundaries or discontinuities in PDE coefficients.
Abstract: In Eikonal equations, rarefaction is a common phenomenon known to degrade the rate of convergence of numerical methods. The `factoring' approach alleviates this difficulty by deriving a PDE for a new (locally smooth) variable while capturing the rarefaction-related singularity in a known (non-smooth) `factor'. Previously this technique was successfully used to address rarefaction fans arising at point sources. In this paper we show how similar ideas can be used to factor the 2D rarefactions arising due to nonsmoothness of domain boundaries or discontinuities in PDE coefficients. Locations and orientations of such rarefaction fans are not known in advance and we construct a `just-in-time factoring' method that identifies them dynamically. The resulting algorithm is a generalization of the Fast Marching Method originally introduced for the regular (unfactored) Eikonal equations. We show that our approach restores the first-order convergence and illustrate it using a range of maze navigation examples with non-permeable and `slowly permeable' obstacles.
TL;DR: In this paper, the authors apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice with steplike initial data corresponding to a rarefaction wave.
Abstract: We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice with steplike initial data corresponding to a rarefaction wave.