Showing papers on "Rarefaction published in 2002"

Application of the Cercignani-Lampis scattering kernel to calculations of rarefied gas flows. I. Plane flow between two parallel plates

Abstract: The Cercignani–Lampis scattering kernel of the gas-surface interaction was applied to numerical calculations of the plane Poiseuille flow, thermal creep, mechanocaloric flux and heat flux. The S model of the Boltzmann equation was numerically solved by the discrete velocity method. The calculations have been carried out in wide ranges of the rarefaction parameter and of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data the value of the accommodation coefficients can be calculated.

Rarefaction Shocks, Shock Errors, and Low Order of Accuracy in ZEUS

Abstract: We show that there are simple one-dimensional problems for which the MHD code, ZEUS, generates significant errors, whereas upwind conservative schemes perform very well on these problems.

Strongly underwound magnetic fields in co-rotating rarefaction regions: Observations and Implications

Abstract: [1] Observations of the magnetic field orientation in co-rotating rarefaction regions (CRRs) reveals that the field can be significantly more radial than predicted by the Parker model. In particular, CRRs sampled by the Ulysses spacecraft beyond 4 AU from the sun often show average field orientations deviating by more than 30° from the expected Archimedian spiral and lasting many days. These observations are explained by a model combining footpoint motion between fast and slow solar wind streams at the source surface with the effects of velocity shear across coronal hole boundaries.

Rarefaction Shocks, Shock Errors and Low Order of Accuracy in ZEUS

Abstract: We show that there are simple one dimensional problems for which the MHD code, ZEUS, generates significant errors, whereas upwind conservative schemes perform very well on these problems.

Numerical Simulation of Detonation Initiation with a Shock Wave Entering a Cloud of Aluminum Particles

Abstract: Based on the mathematical model of a reacting two-phase medium in the two-velocity, two-temperature approximation, the process of planar shock wave entering a cloud of aluminum particles is numerically studied. The incident shock wave may have either a rectangular or a triangular profile, i.e., it may be accompanied by a rarefaction wave. An analysis of numerical data allowed us to determine conditions of possible establishment of a steady detonation regime in the cloud. Scenarios of initiation and types of detonation flows in the cloud are determined as functions of the amplitude of the incident shock wave and initiation energy. Criteria of detonation initiation for various fractions of particles are obtained, which express the dependence of the energy stored in the shock wave on its Mach number.

The fluid-dynamic paradigm of the dust-acoustic soliton

Abstract: In most studies, the properties of dust-acoustic solitons are derived from the first integral of the Poisson equation, in which the shape of the pseudopotential determines both the conditions in which a soliton may exist and its amplitude. Here this first integral is interpreted as conservation of total momentum, which, along with the Bernoulli-like energy equations for each species, may be cast as the structure equation for the dust (or heavy-ion) speed in the wave. In this fluid-dynamic picture, the significance of the sonic points of each species becomes apparent. In the wave, the heavy-ion (or dust) flow speed is supersonic (relative to its sound speed), whereas the protons and electrons are subsonic (relative to their sound speeds), and the dust flow is driven towards its sonic point. It is this last feature that limits the strength (amplitude) of the waves, since the equilibrium point (the centre of the wave) must be reached before the dust speed becomes sonic. The wave is characterized by a compression in the heavies and a compression (rarefaction) in the electrons and a rarefaction (compression) in the protons if the heavies have positive (negative) charge, and the corresponding potential is a hump (dip). These features are elucidated by an exact analytical soliton, in a special case, which provides the fully nonlinear counterpoint to the weakly nonlinear sech 2 -type solitons associated with the Korteweg-de Vries equation, and indicates the parameter regimes in which solitons may exist.

The Evolution of Shocks in Blazar Jets

Abstract: We consider the shock structures that can arise in blazar jets as a consequence of variations in the jet flow velocity. There are two possible cases: (1) A double shock system consisting of both a forward and reverse shock (2) A single shock (either forward or reverse) together with a rarefaction wave. These possibilities depend upon the relative velocity of the two different sections of jet. Using previously calculated spherical models for estimates of the magnetic field and electron number density of the emission region in the TeV blazar Markarian 501, we show that this region is in the form of a thin disk, in the plasma rest frame. It is possible to reconcile spectral and pair opacity constraints for MKN 501 for Doppler factors in the range of 10--20. This is easiest if the corrections for TeV absorption by the infrared background are not as large as implied by recent models.

The Evolution of Shocks in Blazar Jets

Abstract: We consider the shock structures that can arise in blazar jets as a consequence of variations in the jet flow velocity. There are two possible cases: (1) a double shock system consisting of both a forward and reverse shock, and (2) a single shock (either forward or reverse) together with a rarefaction wave. These possibilities depend upon the relative velocity of the two different sections of jet. Using previously calculated spherical models for estimates of the magnetic field and electron number density of the emission region in the TeV blazar Mkn 501, we show that this region is in the form of a thin disk in the plasma rest frame. It is possible to reconcile spectral and pair opacity constraints for Mkn 501 for Doppler factors in the range of 10–20. This is easiest if the corrections for TeV absorption by the infrared background are not as large as implied by recent models.

Directional dependence of nonlinear surface acoustic waves in the (001) plane of cubic crystals.

Abstract: Spectral evolution equations are used to perform analytical and numerical studies of nonlinear surface acoustic waves in the (001) plane of a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, and quasilinear solutions of the equations are presented. Expressions are also developed for a characteristic length scale for nonlinear distortion and a nonlinearity coefficient. A time-domain equation corresponding to the spectral equations is derived. Numerical calculations based on measured second- and third-order elastic constants taken from the literature are performed to predict the evolution of initially monofrequency surface waves. Nonlinearity matrix elements that indicate the coupling strength of harmonic interactions are shown to provide a useful tool for characterizing waveform distortion. The formation of compression or rarefaction shocks can be strongly dependent on the direction of propagation, and harmonic generation is suppressed or increased in certain directions.

Application of the Cercignani-Lampis scattering kernel to channel gas flows

Abstract: The Poiseuille flow, the thermal creep and the heat flux between two parallel plates are calculated applying the S model of the Boltzmann equation and the Cercignani-Lampis scattering kernel. The calculations have been carried out in wide ranges of the rarefaction parameter and of the accommodation coefficients of momentum and energy. Comparing the present results with experimental data the value of the accommodation coefficients can be calculated.

Nonlinear waves and solitons propagating perpendicular to the magnetic field in bi-ion plasma with finite plasma pressure

Abstract: . We investigate the nature of nonlinear waves propagating transverse to the magnetic field in a bi-ion plasma including plasma pressure. By using the conservation laws derived from the multi-ion fluid equations the system may be described by a single order differential equation whose properties control the structure of the flow and the magnetic field. Compressive solitons exist in specific ranges of the characteristic Mach numbers. Various features of solitons differ in different existence "windows". For example, there are solitons that contain a strong proton rarefaction core embedded in the main compressional structure. Compressive solitons are found in a wide range of flow parameters. Finite ion pressure introduces critical Mach numbers. In contrast to a plasma consisting only of protons and electrons these singular points are reached where a specific combination of ion and electron speeds lies on particular locii, in multi-parameter space, which corresponds to the generalized "sonic point" of the compound system.

Microscopic structure of the k-step exclusion process

Abstract: We review the hydrodynamics and discuss the shock, rarefaction fan and contact discontinuity at a microscopic level for a one-dimensional totally asymmetric k-step exclusion process. In particular we define a microscopical object that identifies the shock in the decreasing case.

Stability of the rarefaction wave for the generalized kdv-burgers equation

Abstract: This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equationRoughly speaking, under the assumption that u_ < u+, the solution u(x,t) to Cauchy problem (1) satisfying sup \u(x,t) -uR(x/t)| -0 as t - , where uR(x/t) is the rarefac-tion wave of the non- viscous Burgers equation ut + f(u)x=0 with Riemann initial data

Cavitation Thresholds, Free Surface and Cavity Cluster Dynamics in Liquids at Shock Wave Reflection

Abstract: Cavitation cluster dynamics and cavitation thresholds under plane short shock waves reflected from the free surface of various liquids is investigated experimentally By means of capacity and light absorption methods it is shown that the free-surface velocity is directly connected to the volume concentration of cavitation bubbles in the cavitating area and an expression for it was found. An effect of the time of contact of water and atmosphere on the dynamics of cavitation development is revealed. It was found that one hour is enough to change the free-surface velocity dynamics from monotonous to oscillating, which is characteristic for spalling damage of metals. High-speed filming showed that in the first case, the bubble distribution over the volume is uniform, while in the second case a dense layer of bubbles is formed under the free surface and partly reflects the rarefaction wave which continues moving freely in the formed liquid layer. This effect is probably associated with the changes in the structure of a near-surface layer due to air saturation. It is shown experimentally that for transformer oil, the previous loading history and the time interval between the experiments are essential considerations and the intensity of cavitation is increased under multiple sequential loading.

Nonlinear stability of centered rarefaction waves of the Jin-Xin relaxation model for conservation laws.

Abstract: We study the asymptotic equivalence of the Jin-Xin relaxation model and its formal limit for genuinely nonlinear 2 2 conservation laws. The initial data is allowed to have jump discontinuities corresponding to centered rarefaction waves, which includes Riemann data connected by rarefaction curves. We show that, as long as the initial data is a small perturbation of a constant state, the solution for the relaxation system exists globally in time and converges, in the zero relaxation limit, to the solution of the corresponding conservation law uniformly except for an initial layer.

Influence of rarefaction on the computation of aerodynamic parameters in hypersonic flow

Abstract: The results from two well-known and widely accepted codes, the Navier—Stokes solver FLUENT and the direct simulation Monte Carlo (DSMC) solver DS2G, have been analysed in order to fix the levels of the flow field rarefaction where the codes can work properly for the computation of aerodynamic forces and heat flux on a spacecraft during the re-entry. This subject has already been widely investigated; thus the purpose of the present work is to provide a further contribution. In order to make realistic computations, a probable path of a typical capsule, returning from an interplanetary mission to Earth, has been considered in the altitude range 50—120 km. Proper use of FLUENT was fixed at the free-stream Knudsen number Kn∞ < 7×10−5. Attempts have been made to increase this limit, but with no success. More specifically, a finer mesh as well as a slip velocity and temperature jump were considered. Physical conditions like the lack of isotropy of the pressure tensor and the failure of the classical phen...

DSMC calculation of supersonic expansion at a very large pressure ratio

Abstract: Supersonic expansion of room temperature argon from a sonic orifice at a very large pressure ratio up to 16000 for different stagnation Knudsen numbers, 2×10−3 and 4×10−4 is simulated by the DSMC method. In order to calculate a large flowfield different sized cells and a different time-step scheme were adopted. It was shown that the effects of rarefaction and background gas to the jet size can be evaluated using a rarefaction parameter or a local Knudsen number. The calculation was also made for the expansion to a vacuum for a wide range of the stagnation Knudsen number, 4×10−4–0.1. The terminal parallel temperature dependence to the stagnation Knudsen number agrees well with the sudden freezing model.

Dust‐ion‐acoustic precursor of a shock wave

Abstract: The effect of charged dust particles on the structure of the plasma precursor of a strong shock wave is studied. The conditions of formation of a weak discontinuity front are obtained. It is shown that resonant modes can occur in which the concentration of dust particles in the neighborhood of the front increases. In the case of positively charged particles of dust, the formation of a localized compaction region in the form of a soliton “bunch” is possible and the dependence of the amplitude of the soliton on shock‐wave velocity is nonmonotonic. In the case of negatively charged particles of dust, a rarefaction wave is formed. The indicated phenomena can substantially affect the concentration of the neutral component in a slightly ionized plasma.

Dynamics of Formation and Parameters of a Fog upon Abrupt Expansion of a Compressed Vapor–Gas Volume

Abstract: This paper deals with an experimental investigation of structural changes in the compressed vapor–gas volume of a water vapor–hydrogen–air system, which are caused by an abrupt expansion of the volume due to the loss of integrity of the confinement shell. A homogeneous system transforms to a heterogeneous water vapor–microdroplets–hydrogen–air mixture behind the rarefaction wave. The microdroplet sizes and their bulk concentration are measured during the formation of a fog. A method is proposed for estimating the volume fraction of microdroplets from the measurements of light absorption on one wavelength of the IR region.

Method of film cooling and appliance for its implementation

Abstract: A cooling by a film method includes blowing of the cooling air onto a hot blade surface. By delivering a hot air to the blade surface across the main gas flow at least one row of the pulsed vortexes is formed. A device for the cooling by a film method implementation contains a gas turbine blade with the grooves, in which on the rarefaction and pressure surface along the blade height the pits are disposed, and in every of which at the upper by the flow direction half the holes are made for introducing the cooling air.

Molecular Dynamics Modeling of Impact‐Induced Shock Waves in Hydrocarbons

Abstract: We use nonequilibrium molecular dynamics (MD) simulations to study the behavior of hydrocarbons under shock compression and spallation processes in shock and rarefaction waves generated by the high‐velocity impact of a flyer plate into a target material. The interatomic forces were introduced using a recently modified reactive empirical bond order (REBO) potential with intermolecular interactions, termed the adaptive intermolecular REBO potential (AIREBO). This potential allows us to simulate as many as ten thousand molecules on a single processor, providing a relatively large cross‐section at the shock front in hydrocarbon solids. We performed plane‐wave impact experiments with different flyer velocities and observed the chemical dissociation of methane and acetylene molecules in the shock layer, followed by polymerization into carbon chains for certain flyer velocities. The hydrocarbon oligomers survive into the rarefaction region, indicating that stable molecular products have been formed. These result...

Method for performing healing cosmetic rarefaction massage

Abstract: medicine. SUBSTANCE: method involves applying to skin surface controllable rarefaction in continuous and pulsating mode. The treatment is carried out with rarefaction intensity of 85-830 mbar/mm2 during less than 1 h. pulsating action is carried out at 0.1 to 5 Hz cyclically varying suction force from some selected minimum value to maximum one. EFFECT: eliminated neuro-microcirculation blockage zones on the skin; enhanced effectiveness in evacuating toxins and softening subcutaneous fat. 5 cl

Stability of the rarefaction wave for the generalized BBM-Burgers equation

Abstract: This paper is concerned with the stability of the rarefaction wave for the generalized BBM-Burgers equationu t+f(u) x=u xx+u xxt, u| t=0=u o(x)→u ±, x→∞.(1)under the assumption of u -u +, the solution u(x,t) to Cauchy problem (1) satisfies supx∈R|u(x,t)- uR(x/t)|→0 as t→∞, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation u t+ f(u) x=0 with Riemann initial data u(x,0)=u -, x0, u +, x0.

A New Type of Interaction of a Moving Shock with an Unsteady Boundary Layer

Abstract: In this paper, a new type of interaction of a moving shock with an unsteady boundary layer had been studied theoretically and experimentally. This type of shock wave and boundary layer interaction describes a moving shock interacts with an unsteady boundary layer which is induced by another shock wave and rarefaction waves. So it is different from the interaction of a stationary shock with steady boundary layer, also different from the interaction of a reflected moving shock on the end of a shock tube with an unsteady boundary layer induced by an incident shock. The geometrical shock dynamics was used for the theoretical analysis to the shock wave and unsteady boundary layer interaction, and a double driver shock tube with rarefaction waves bursting diaphragm was used for the experimental investigation.

Low density heat transfer to blunt cylinders

Abstract: Experimental studies of heat transfer to blunt bodies were performed in the transition regime. The studies were at Mach numbers of 6.38 and 7.6 at stagnation temperatures of 500, 600 and 700 K. The heat flux was measured using slug gauges inserted in Macor models. The data is presented in terms of non dimensional parameters such as Stanton number, Knudsen number and Cheng’s rarefaction parameter.

Interaction of a simple Prandtl-Meyer wave with a weakly vortexed layer

Abstract: The problem of interaction of a centered wave of rarefaction with a shear layer is solved in the case of a small flow vorticity in the shear layer. The solution is found in the form of an asymptotic series with respect to a small parameter of the problem. A system of equations derived in the zero approximation describes the flow in a simple wave. A uniformly applicable first-order expansion is constructed using the method of deformed coordinates.