Showing papers on "Rarefaction published in 2015"

The flexible asymmetric shock tube (FAST): A Ludwieg tube facility for wave propagation measurements in high-temperature vapours of organic fluids

Abstract: This paper describes the commissioning of the flexible asymmetric shock tube (FAST), a novel Ludwieg tube-type facility designed and built at Delft University of Technology, together with the results of preliminary experiments. The FAST is conceived to measure the velocity of waves propagating in dense vapours of organic fluids, in the so-called non-ideal compressible fluid dynamics (NICFD) regime, and can operate at pressures and temperatures as high as 21 bar and 400 ?C, respectively. The set-up is equipped with a special fast-opening valve, separating the high-pressure charge tube from the low-pressure plenum. When the valve is opened, a wave propagates into the charge tube. The wave speed is measured using a time-of-flight technique employing four pressure transducers placed at known distances from each other. The first tests led to the following results: (1) the leakage rate of 5×10?4mbarl s?1 for subatmospheric and 5×10?2mbarl s?1 for a superatmospheric pressure is compatible with the purpose of the conceived experiments, (2) the process start-up time of the valve has been found to be between 2.1 and 9.0 ms, (3) preliminary rarefaction wave experiments in the dense vapour of siloxane D6 (dodecamethylcyclohexasiloxane, an organic fluid) were successfully accomplished up to temperatures of 300?C, and (4) a method for the estimation of the speed of sound from wave propagation experiments is proposed. Results are found to be within 2.1 % of accurate model predictions for various gases. The method is then applied to estimate the speed of sound of D6 in the NICFD regime.

Uniqueness of rarefaction waves in multidimensional compressible Euler system

Abstract: We show that 1D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the shock wave solutions to the Riemann problem, where infinitely many solutions are constructed by the method of convex integration.

Stability of the Rarefaction Wave of the Vlasov--Poisson--Boltzmann System

Abstract: This paper is devoted to the study of the nonlinear stability of the rarefaction waves of the Vlasov--Poisson--Boltzmann system with slab symmetry in the case where the electron background density satisfies an analogue of the Boltzmann relation. We allow that the electric potential may take distinct constant states at both far fields. The rarefaction wave is constructed by the quasineutral Euler equations through the zero-order fluid dynamic approximation, and the wave strength is not necessarily small. We prove that the local Maxwellian with macroscopic quantities determined by the quasineutral rarefaction wave is time-asymptotically stable under small perturbations for the corresponding Cauchy problem. The main analytical tool is the combination of techniques we developed in [R.-J. Duan and S.-Q. Liu, J. Differential Equations, 258 (2015), pp. 2495--2530] for the viscous compressible fluid with the self-consistent electric field and the refined energy method based on the macro-micro decomposition of the...

Stability of the Isentropic Riemann Solutions of the Full Multidimensional Euler System

Abstract: We consider the complete Euler system describing the time evolution of an inviscid nonisothermal gas. We show that the rarefaction wave solutions of the one-dimensional (1-D) Riemann problem are stable, in particular unique, in the class of all bounded weak solutions to the associated multidimensional problem. This may be seen as a counterpart of the nonuniqueness results of physically admissible solutions emanating from 1-D shock waves constructed recently by the method of convex integration.

Stability of Superposition of Viscous Contact Wave and Rarefaction Waves for Compressible Navier-Stokes System

Abstract: This paper is concerned with the large-time behavior of solutions for the one-dimensional compressible Navier-Stokes system We show that the combination of viscous contact wave with rarefaction waves for the non-isentropic polytropic gas is stable under \emph{large} initial perturbation without the condition that the adiabatic exponent $\gamma$ is close to 1, provided the strength of the combination waves is suitably small

Lasing modes of a microdisk with a ring gain area and of an active microring

Abstract: Microcavity lasers shaped as thin circular disks are famous for the ultra-low thresholds of their whispering-gallery modes. We considered a two-dimensional model of such a laser in free space with a ring-like active region and compared the characteristics of its modes with the modes of an active microring, i.e. a similar disk with a concentric hole. The comparison showed that a microring has considerable rarefaction effect in terms of emission thresholds, accompanied by the blue-shift of emission spectra. If the ring becomes narrower than a half-wavelength in material, then all lasing modes obtain catastrophically high thresholds.

Influence of intermolecular potentials on rarefied gas flows: fast spectral solutions of

Abstract: The Boltzmann equation with an arbitrary intermolecular potential is solved by the fast spectral method. As examples, noble gases described by the Lennard-Jones potential are considered. The accuracy of the method is assessed by comparing both transport coecients with variational solutions and mass/heat flow rates in Poiseuille/thermal transpiration flows with results from the discrete velocity method. The fast spectral method is then applied to Fourier and Couette flows between two parallel plates, and the influence of the intermolecular potential on various flow properties is investigated. It is found that for gas flows with the same rarefaction parameter, di↵erences in the heat flux in Fourier flow and the shear stress in Couette flow are small. However, di↵erences in other quantities such as density, temperature, and velocity can be very large.

Role of Suction/Injection on MHD Natural Convection Flow in a Vertical Microchannel

Abstract: The present paper analyses the steady natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical parallel plate micro-channel with combined effects of transverse magnetic field and suction/injection in the presence of velocity slip and temperature jump at the micro-channel surfaces. The fully developed solutions of the velocity, temperature, volume flow rate, skin-friction and rate of heat transfer which is expressed as a Nusselt number are derived analytically. The solution obtained for the velocity has been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as suction/injection parameter, Hartmann number, rarefaction parameter, and fluid-wall interaction parameter are discussed with the aid of line graphs. During the course of numerical computations, results shows that as suction/injection, rarefaction and fluid-wall interaction increase, the volume flow rate increases while it decreases with increase in Hartmann number.

Staggered Momentum Conservative Scheme For Radial Dam Break Simulation

Abstract: The momentum conservative scheme is implemented on a staggered grid to solve the shallow water equations in the $$r$$r---$$t$$t space. The resulting scheme is used to simulate flow induced by the instantaneous collapse of a radial dam. The result shows the shock wave propagates radially outward and rarefaction wave moves inward. We demonstrate that our staggered momentum conservative scheme is able to produce the correct shock wave front and rarefaction wave, and having a good agreement with the Roe conservative method of a collocated grid. Moreover, the total fluid mass is conserved during calculations, and yet our scheme is simple and efficient.

Numerical simulations of a shock interacting with successive interfaces using the Discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities

Abstract: In this work, we investigate the growth of interface perturbations following the interaction of a shock wave with successive layers of fluids. Using the Discontinuous Galerkin method, we solve the two-dimensional multifluid Euler equations. In our setup, a shock impacts up to four adjacent fluids with perturbed interfaces. At each interface, the incoming shock generates reflected and transmitted shocks and rarefactions, which further interact with the interfaces. By monitoring perturbation growth, we characterize the influence these instabilities have on each other and the fluid mixing as a function of time in different configurations. If the third gas is lighter than the second, the reflected rarefaction at the second interface amplifies the growth at the first interface. If the third gas is heavier, the reflected shock decreases the growth and tends to reverse the Richtmyer–Meshkov instability as the thickness of the second gas is increased. We further investigate the effect of the reflected waves on the dynamics of the small scales and show how a phase difference between the perturbations or an additional fluid layer can enhance growth. This study supports the idea that shocks and rarefactions can be used to control the instability growth.

Molecular dynamics simulations of shock compressed heterogeneous materials. I. The porous case

Abstract: The propagation of an incident shock and subsequent rarefaction and compression waves in a porous media are analysed from a set of large scale molecular dynamics simulations. The porous material is modelized by a collection of spherical pores, empty or filled with dense gaseous argon, enclosed in a copper matrix. We observe that the pore collapse induces a strong local disorder in the matrix even for shock intensities below the melting point of shocked copper. Various mechanisms are considered and a detailed analysis of the numerical results shows that the melting around an isolated pore is mainly due to the plastic work induced by the collapse: a result that can be extended to more complicated pore shapes. The systematic study of the influence of the shock intensity, the pore size, and the presence of a filling gas shows that the melting is mainly inhibited by the presence of the gas. The final structure strongly depends on the interactions between the waves resulting from the various reflections of the initial shock at the sample boundaries, implying that the evaluation of the incident shock intensity based on post-mortem analyses requires a knowledge of the full history of the sample.

Relativistic Hydrodynamics and Non-Equilibrium Steady States

Abstract: We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.

Role of diffusion on molecular tagging velocimetry technique for rarefied gas flow analysis

Abstract: The molecular tagging velocimetry (MTV) is a well-suited technique for velocity field measurement in gas flows. Typically, a line is tagged by a laser beam within the gas flow seeded with light emitting acetone molecules. Positions of the luminescent molecules are then observed at successive times and the velocity field is deduced from the analysis of the tagged line displacement and deformation. However, the displacement evolution is expected to be affected by molecular diffusion, when the gas is rarefied. Therefore, there is no direct and simple relationship between the velocity field and the measured displacement of the initial tagged line. This paper addresses the study of tracer molecules diffusion through a background gas flowing in a channel delimited by planar walls. Tracer and background species are supposed to be governed by a system of coupled Boltzmann equations, numerically solved by the direct simulation Monte Carlo (DSMC) method. Simulations confirm that the diffusion of tracer species becomes significant as the degree of rarefaction of the gas flow increases. It is shown that a simple advection–diffusion equation provides an accurate description of tracer molecules behavior, in spite of the non-equilibrium state of the background gas. A simple reconstruction algorithm based on the advection–diffusion equation has been developed to obtain the velocity profile from the displacement field. This reconstruction algorithm has been numerically tested on DSMC generated data. Results help estimating an upper bound on the flow rarefaction degree, above which MTV measurements might become problematic.

Computational Network Model Prediction of Hemodynamic Alterations Due to Arteriolar Rarefaction and Estimation of Skeletal Muscle Perfusion in Peripheral Arterial Disease.

Abstract: Objective To estimate the relative influence of input pressure and arteriole rarefaction on gastrocnemius muscle perfusion in patients with PAD after exercise and/or percutaneous interventions. Methods A computational network model of the gastrocnemius muscle microcirculation was adapted to reflect rarefaction based on arteriolar density measurements from PAD patients, with and without exercise. A normalized input pressure was applied at the feeder artery to simulate both reduced and restored ABI in the PAD condition. Results In simulations of arteriolar rarefaction, resistance increased non-linearly with rarefaction, leading to a disproportionally large drop in perfusion. In addition, perfusion was less sensitive to changes in input pressure as the degree of rarefaction increased. Reduced arteriolar density was observed in PAD patients and improved 33.8% after three months of exercise. In model simulations of PAD, ABI restoration yielded perfusion recovery to only 66% of baseline. When exercise training was simulated by reducing rarefaction, ABI restoration increased perfusion to 80% of baseline. Conclusion Microvascular resistance increases non-linearly with increasing arteriole rarefaction. Therefore, muscle perfusion becomes disproportionally less sensitive to ABI restoration as arteriole rarefaction increases. These results highlight the importance of restoring both microvascular structure and upstream input pressure in PAD therapy.

The limit to rarefaction wave with vacuum for 1D compressible fluids with temperature-dependent transport coefficients

Abstract: In this paper, we study the zero dissipation limit of the one-dimensional full compressible Navier–Stokes equations with temperature-dependent viscosity and heat-conduction coefficient. It is proved that given a rarefaction wave with one-side vacuum state to the full compressible Euler equations, we can construct a sequence of solutions to the full compressible Navier–Stokes equations which converge to the above rarefaction wave with vacuum as the viscosity and the heat-conduction coefficient tend to zero. Moreover, the uniform convergence rate is obtained. The main difficulty in our proof lies in the degeneracies of the density, the temperature and the temperature-dependent viscosities at the vacuum region in the zero dissipation limit.

Recollimation Shocks in Magnetized Relativistic Jets

Abstract: We have performed two-dimensional special-relativistic magnetohydrodynamic simulations of non-equilibrium over-pressured relativistic jets in cylindrical geometry. Multiple stationary recollimation shock and rarefaction structures are produced along the jet by the nonlinear interaction of shocks and rarefaction waves excited at the interface between the jet and the surrounding ambient medium. Although initially the jet is kinematically dominated, we have considered axial, toroidal and helical magnetic fields to investigate the effects of different magnetic-field topologies and strengths on the recollimation structures. We find that an axial field introduces a larger effective gas-pressure and leads to stronger recollimation shocks and rarefactions, resulting in larger flow variations. The jet boost grows quadratically with the initial magnetic field. On the other hand, a toroidal field leads to weaker recollimation shocks and rarefactions, modifying significantly the jet structure after the first recollimation rarefaction and shock. The jet boost decreases systematically. For a helical field, instead, the behaviour depends on the magnetic pitch, with a phenomenology that ranges between the one seen for axial and toroidal magnetic fields, respectively. In general, however, a helical magnetic field yields a more complex shock and rarefaction substructure close to the inlet that significantly modifies the jet structure. The differences in shock structure resulting from different field configurations and strengths may have observable consequences for disturbances propagating through a stationary recollimation shock.

The effect of characteristic length on mean free path for confined gases

Abstract: Molecular Dynamics simulations are performed to investigate the influence of system boundaries and characteristic length (L) of the system on the mean free path (MFP) of rarefied gas confined to the walls of a nano-channel Isothermal Lennard-Jones fluid confined between Reflective walls and platinum walls at different number densities (031 atoms/nm3 and 161 atoms/nm3) are independently considered The MFP is calculated by the Lagrangian approach of tracking the trajectory of each atom and averaging the distance between successive collisions The percentage of fluid–wall collisions is observed to predominate over fluid–fluid collisions at high levels of rarefaction The influence of L (varying from 6 nm to 16 nm) on MFP is examined in this regime At lower Knudsen number (Kn), it is observed that the effect of L on MFP is minimal However, at higher rarefaction the characteristic dimension influences the MFP significantly for various wall configurations

On Knudsen-minimum effect and temperature bimodality in a dilute granular Poiseuille flow

Abstract: The numerical simulation of gravity-driven flow of smooth inelastic hard disks through a channel, dubbed ‘granular’ Poiseuille flow, is conducted using event-driven techniques. We find that the variation of the mass-flow rate ( ) with Knudsen number ( ) can be non-monotonic in the elastic limit (i.e. the restitution coefficient ) in channels with very smooth walls. The Knudsen-minimum effect (i.e. the minimum flow rate occurring at for the Poiseuille flow of a molecular gas) is found to be absent in a granular gas with , irrespective of the value of the wall roughness. Another rarefaction phenomenon, the bimodality of the temperature profile, with a local minimum ( ) at the channel centerline and two symmetric maxima ( ) away from the centerline, is also studied. We show that the inelastic dissipation is responsible for the onset of temperature bimodality (i.e. the ‘excess’ temperature, ) near the continuum limit ( ), but the rarefaction being its origin (as in the molecular gas) holds beyond . The dependence of the excess temperature on the restitution coefficient is compared with the predictions of a kinetic model, with reasonable agreement in the appropriate limit. The competition between dissipation and rarefaction seems to be responsible for the observed dependence of both the mass-flow rate and the temperature bimodality on and in this flow. The validity of the Navier–Stokes-order hydrodynamics for granular Poiseuille flow is discussed with reference to the prediction of bimodal temperature profiles and related surrogates.

Numerical simulation of shock wave and contact surface propagation in micro shock tubes

Abstract: Micro shock tubes have been widely used in many engineering and industrial applications, but their performance and detailed flow characteristics are not well known. Compared to macro shock tubes, unsteady flows related to the moving shock waves in micro shock tubes are highly complicated due to more active viscous dissipation and rarefaction effects. This makes shock wave dynamics significantly different from theoretical predictions. One of the major flow behaviors related to the shock wave propagation in micro shock tube is that the boundary layer growth leads to stronger dissipative shock wave. Due to effects of the scale, more shock wave attenuation happens in micro shock tubes. We used a CFD approach to understand the flow characteristics in a micro shock tube with finite diameter. A fully implicit finite volume scheme has been employed to solve the unsteady compressible Navier-Stokes equations. The diaphragm pressure ratio and diameter of the shock tube were varied to investigate their effects on micro shock tube flows. Based on the predicted results, some wave diagrams were built to characterize the micro shock tube flows. Detailed flow structures between the contact surface and moving shock wave were analyzed during the present study.

The interaction of rarefaction waves of a two-dimensional nonlinear wave system

Abstract: This paper is concerned with a two-dimensional Riemann problem for the nonlinear wave system which gives rise to an interaction of two planar rarefaction waves. This problem comes from the expansion of a wedge of gas with constant velocity into vacuum, which is often interpreted as the dam collapse problem in hydraulics. We establish the global existence of smooth solutions in the interaction region of rarefaction waves up to a non-trivial vacuum boundary.

Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier-Stokes-Poisson system

Abstract: This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier-Stokes-Poisson system in the half line $\mathbb{R}_{+}=:(0,+\infty)$. On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we successfully construct the boundary layer and rarefaction wave, and then we give the rigorous proofs of the stability theorems on the superposition of boundary layer and rarefaction wave under small perturbations for the corresponding initial boundary value problem of the Navier-Stokes-Poisson system, only provided the strength of boundary layer is small while the strength of rarefaction wave can be arbitrarily large. The complexity of nonlinear composite wave leads to many complicated terms in the course of establishing the {\it a priori} estimates. The proofs are given by an elementary $L^2$ energy method.

Effects of initial condition spectral content on shock-driven turbulent mixing.

Abstract: The mixing of materials due to the Richtmyer-Meshkov instability and the ensuing turbulent behavior is of intense interest in a variety of physical systems including inertial confinement fusion, combustion, and the final stages of stellar evolution. Extensive numerical and laboratory studies of shock-driven mixing have demonstrated the rich behavior associated with the onset of turbulence due to the shocks. Here we report on progress in understanding shock-driven mixing at interfaces between fluids of differing densities through three-dimensional (3D) numerical simulations using the rage code in the implicit large eddy simulation context. We consider a shock-tube configuration with a band of high density gas (SF(6)) embedded in low density gas (air). Shocks with a Mach number of 1.26 are passed through SF(6) bands, resulting in transition to turbulence driven by the Richtmyer-Meshkov instability. The system is followed as a rarefaction wave and a reflected secondary shock from the back wall pass through the SF(6) band. We apply a variety of initial perturbations to the interfaces between the two fluids in which the physical standard deviation, wave number range, and the spectral slope of the perturbations are held constant, but the number of modes initially present is varied. By thus decreasing the density of initial spectral modes of the interface, we find that we can achieve as much as 25% less total mixing at late times. This has potential direct implications for the treatment of initial conditions applied to material interfaces in both 3D and reduced dimensionality simulation models.