Showing papers on "Rarefaction published in 1996"

Rarefied gas flow through a long tube at any temperature ratio

Abstract: The mass flow rate of a rarefied gas through a long capillary caused by small pressure and temperature gradients has been calculated based on the s‐model for the diffuse specular gas‐surface interaction in the range of the rarefaction parameter from 0.005 to 50. A simple method of calculation of the thermomolecular pressure effect and the thermal creep caused by a large temperature ratio have been elaborated. Numerical calculations of both phenomena for the temperature ratio T2/T1=3.8—usually realized in experiments—have been carried out. It has been determined that the nonlinear thermomolecular pressure effect does not depend on the temperature distribution along the capillary. The nonlinear thermal creep has been calculated for two different temperature distributions along the capillary. A dependence of the creep on the temperature distribution has been found. It has been shown that the application of the linear theory based on the average rarefaction parameter to the gas flow at a large temperature rat...

Stability of rarefaction waves in viscous media

Abstract: We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, “Burgers” rarefaction wave, for initial perturbations w 0 with small mass and localized as w 0(x)= $$\mathcal{O}(|x|^{ - 1} )$$ The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error. This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass $$\mathcal{O}$$ (log (t)). These “diffusion waves” have amplitude $$\mathcal{O}$$ (t -1/2logt) in linear degenerate transversal fields and $$\mathcal{O}$$ (t -1/2logt) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof.

Analytic theory of Richtmyer–Meshkov instability for the case of reflected rarefaction wave

Abstract: An analytic theory of the Richtmyer–Meshkov (RM) instability for the case of reflected rarefaction wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock wave case of the RM instability and for stability analysis of a ‘‘stand‐alone’’ rarefaction wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two rarefaction waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration of the interface. This confirms that the RM instability is not caused by the instant normal acceleration of the interface, and hence, is not a type of Rayleigh–Taylor instability. The RM instability is related to the growth of initial transverse velocity perturbations at the interface, which may be either present initially as in symmetrical Riemann problem, or be induced by a shock passing a corrugated interface.

The behaviour of a gas cavity impacted by a weak or strong shock wave

Abstract: Two-dimensional simulations of gas cavity responses to both weak shocks (p ≤ 30 MPa) and strong shocks (p ranging from 500 to 2000 MPa) are performed using a finite volume method. An artificial viscosity to capture the shock and a simple, stable, and adaptive mesh generation technique have been developed for the computations. The details of the shock propagation, rarefaction, transmission and bubble wall motions are obtained from the numerical computations. A weak shock is defined in the present context as one that does not cause liquid jet formation upon impact with the bubble. For this case, a large pressure is created within the gas upon collapse due to rapid compression of the gas, ultimately causing the re-expansion of the bubble. The bubble collapse and re-expansion time predicted by this model agree well with spherically symmetric computations. When impacted by strong shock waves, the bubble will collapse and a liquid jet is formed that propagates through the bubble to the opposite bubble wall. Jet speeds as high as 2000 m s -1 are predicted by this model.

Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws

Abstract: We consider the problem of self-similar zero-viscosity limits for systems ofN conservation laws. First, we give general conditions so that the resulting boundary-value problem admits solutions. The obtained existence theory covers a large class of systems, in particular the class of symmetric hyperbolic systems. Second, we show that if the system is strictly hyperbolic and the Riemann data are sufficiently close, then the resulting family of solutions is of uniformly bounded variation and oscillation. Third, we construct solutions of the Riemann problem via self-similar zero-viscosity limits and study the structure of the emerging solution and the relation of self-similar zero-viscosity limits and shock profiles. The emerging solution consists ofN wave fans separated by constant states. Each wave fan is associated with one of the characteristic fields and consists of a rarefaction, a shock, or an alternating sequence of shocks and rarefactions so that each shock adjacent to a rarefaction on one side is a contact discontinuity on that side. At shocks, the solutions of the self-similar zero-viscosity problem have the internal structure of a traveling wave.

An experimental investigation of screech noise generation

Abstract: The screech noise generation process from supersonic underexpanded jets, issuing from a sonic nozzle at pressure ratios of 2.4 and 3.3 (fully expanded Mach number, Mj = 1.19 and 1.42), was investigated experimentally. The extremely detailed data provide a fresh, new look at the screech generation mechanism. Spark schlieren visualization at different phases of the screech cycle clearly shows the convection of the organized turbulent structures over a train of shock waves. The potential pressure field (hydrodynamic fluctuations) associated with the organized structures is fairly intense and extends outside the shear layer. The time evolution of the near-field pressure fluctuations was obtained from phase-averaged microphone measurements. Phase-matched combined views of schlieren photographs and pressure fluctuations show the sound generation process. The individual compression and rarefaction parts of the sound waves are found to be generated from similar hydrodynamic fluctuations. A partial interference between the upstream-propagating sound waves and the downstream-propagating hydrodynamic waves is found to be present along the jet boundary. The partial interference manifests itself as a standing wave in the root-mean-square pressure fluctuation data. The standing wavelength is found to be close to, but somewhat different from, the shock spacing. An outcome of the interference is a curious 'pause and go' motion of the sound waves along the jet periphery. Interestingly, a length scale identical to the standing wavelength is found to be present inside the jet shear layer. The coherent fluctuations and the convective velocity of the organized vortices are found to be modulated periodically, and the periodicity is found to match with the standing wavelength distance rather than the shock spacing. The reason for the appearance of this additional length scale, different from the shock spacing, could not be explained. Nevertheless, it is demonstrated that an exact screech frequency formula can be derived from the simple standing wave relationship. The exact relationship shows that the correct spacing between the sources, for a point source model similar to that of Powell (1953), should be a standing wavelength (not the shock spacing).

Impact of Relativistic Fireballs on External Matter : Numerical Models of Cosmological Gamma-Ray Bursts

Abstract: We numerically model the interaction between an expanding fireball and a stationary external medium whose density is either homogeneous or varies with distance as a power-law. The evolution is followed until most of the fireball kinetic energy is converted into internal energy. The density, pressure and flow Lorentz factor profiles are shown at different stages, including shock and rarefaction wave reflections, for a fireball of initial bulk Lorentz factor Gamma = 100, both in the adiabatic and non-adiabatic (radiative) regimes. For cooling times shorter than the dynamic time, bolometric light-curves are computed for values of Gamma = 50, 100 and 200. We compare the numerical light-curves with analytic results, and find that for a homogeneous external medium there is a simple scaling relationship among light-curves obtained for different parameters. The light-curves for power-law external densities are similar in shape to those in the homogeneous case. We discuss the implications of a comparison of the results with observed Gamma-Ray Burst time histories.

Heliospheric termination shock motion due to fluctuations in the solar wind upstream conditions: Spherically symmetric model

Abstract: Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Review of blunt body wake flows at hypersonic low density conditions

Abstract: Recent results of experimental and computational studies concerning hypersonic flows about blunted cones including their near wake are reviewed. Attention is focused on conditions where rarefaction effects are present, particularly in the wake. The experiments have been performed for a common model configuration (70 deg spherically-blunted cone) in five hypersonic facilities that encompass a significant range of rarefaction and nonequilibrium effects. Computational studies using direct simulation Monte Carlo (DSMC) and Navier-Stokes solvers have been applied to selected experiments performed in each of the facilities. In addition, computations have been made for typical flight conditions in both Earth and Mars atmospheres, hence more energetic flows than produced in the ground-based tests. Also, comparisons of DSMC calculations and forebody measurements made for the Japanese Orbital Reentry Experiment (OREX) vehicle (a 50 deg spherically-blunted cone) are presented to bridge the spectrum of ground to flight conditions.

Optimal shock-wave systems under constraints on the total flow turning angle

Abstract: A “shock and subsequent rarefaction wave” shock-wave system in a plane supersonic inviscid non-heat-conducting gas flow is considered. An exact analytic solution of the problem of determining the intensities of the waves leading to extreme values of the gasdynamic variables (static pressure, temperature, etc.) behind the wave is found using Lagrangian multipliers. These systems are related to the optimal ones [1, 2]. The parameters of the problem are the free-stream Mach number, the specific heat ratio, and the total flow turning angle in the wave system. Analytic solutions determining the boundaries of monotonic and nonmonotonic behavior of the gasdynamic variables behind the system are presented. The effect of the specific heat ratio on the dimensions of the domains of existence of the optimal waves is investigated.

Asymptotic measurements of free surface instabilities in laser-induced shock waves

Abstract: An experimental technique based on optical scattering to detect melting in release of strongly shocked materials is presented. This method is used to study the asymptotic behavior of the free surface of shock-loaded materials. After reflection of a shock wave from a metallic sample free surface, occurrence of a solid to liquid transition will induce a dynamic behavior-such as mass ejection and development of instabilities. A study of the mass ejection due to laser-induced shock waves in aluminium, copper, and tin targets is presented. Shock waves of order of hundreds of kilobars to more than one megabar are produced by a Nd :YAG laser system with a wavelength of 1.06 μm, pulse width of 7 ns FWHM focused to spot of 200 μm. The velocities, size, and topological structure of the ejected particles are measured. The radii of the ejecta are in the range 0.5-7 μm. The size distribution of the ejected particles, moving ahead of the free surface, fit well to a power scaling law N(r) ∼ r -b , characteristic of percolation theories. The experimental values for b are in the range 3-4, depending on the material. Calculations of the threshold pressure for melting, based on realistic equations of state (EOS), predict that in the experiments reported here the Sn samples melt during the laser-induced shock wave, while the Al and Cu samples melt during the release (rarefaction wave) following the shock wave. Two topological patterns of the ejecta clouds were observed : a shell-like pattern in Al and Cu and a jet-like pattern in Sn.

Convection in a porous medium with velocity slip and temperature jump boundary conditions

Abstract: The onset of convection in a rarefield gas saturating a horizontal layer of a porous medium has been investigated using both Darcy and Brinkman models. It is assumed that due to rarefaction both velocity slip and temperature jump exist at the boundaries. The results show that (i) when the degree of rarefaction increases the critical Rayleigh number as well as the critical wave number for the onset of convection increases, (ii) stabilizing effect of temperature jump is more than that of velocity slip, (iii) Darcy model is seen to be the most stable one when compared to Brinkman model or the pure gaseous layer (i.e. in the absence of porous medium).

Development and Calibration of a Super Large Scale Gap Test (SLSGT).

Abstract: : Numerical simulations of eight inch (203 mm) diameter gap test experiments employing heavily confined donors have been conducted. They reveal that strong convergence of lateral rarefaction waves results in transmitted shocks with latent high pressure regions which exceed the amplitude of the leading edge of the shock wave, and are transmitted into the gap attenuator. Since gap tests are calibrated using TOA measurement of the transmitted shock wave, into the attenuating material, the complex wave structure may lead to erroneous gap pressure assignments in the eight inch gap test. These simulations further indicate that this complex shock wave structure is attributable to the heavy steel case confinement, as donors without it exhibit minimal perturbations from lateral rarefaction. This results in a transmitted shock which is characterized by a smooth time decay profile. Therefore a new eight inch gap test using uncased Comp-B donors was developed, calibrated, and evaluated. TNT and AFX-1100 were used as baseline standard acceptors. The test is designated the 'Super Large Scale Gap Test' (SLSGT). Results indicate that the sensitivity of TNT to shock initiation is somewhat greater than previously observed.

A characteristic based numerical method with tracking for nonlinear wave equations

Abstract: Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function. Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

One-dimensional linear waves with axial and central symmetries in saturated porous media

Abstract: The features of propagation of one-dimensional monochromatic waves and dynamics of weak perturbations with axial and central symmetries in liquid-saturated porous medium are investigated. Non-stationary interaction forces and viscoelastic skeleton characteristics are taken into account. The research is carried out within the two-velocity, two-stress tensor model by applying methods of multiphase media mechanics. The system of equations is solved numerically by applying Fast Fourier Transform (FFT) algorithm. The influence of geometry of the process on wave propagation behavior is studied. It is shown that the initial pressure perturbation splits into two waves: fast (deformational) wave and slow (filtrational) one. Each of them is followed by the balance wave: that is, rarefaction wave after compression wave and compression wave after rarefaction wave; at that slow wave and balance one following fast wave may interfere.

Microwave compatible electromagnetic valve for plasma deposition studies

Abstract: A microwave compatible electromagnetic valve capable of discharging saturated vapors in vacuum for shock wave formation and subsequent pulsed plasma deposition is presented. The valve discharges vapors of 1–5 atm and 75 °C with open duration times of 36–178 μs into vacuum. A theoretical model describing rarefaction wave motion coupled with a valve dynamic model was used to determine critical open duration time required for driving a shock wave in the experimental system. Valve design, operating characteristics, and rarefaction wave dynamics for H2, He, Ar, and CO2 internal to the valve are described.

Theory of embedded shock formation in rarefaction waves by homogeneous condensation

Abstract: A theory of embedded shock formation by homogeneous condensation in the centered rarefaction wave of a shock tube is presented. The necessary and sufficient conditions for the existence of such embedded shock waves are exhibited in a parabolic approximation to the family of intersecting characteristics. In particular the coordinates of the embedded shock origin are derived explicitly by the construction of the envelope of the family. Predictions of the theory, including an estimate for the average embedded shock speed, are substantiated by comparison of the results obtained employing the classical nucleation theory and Hertz-Knudsen droplet growth law for the condensation model with those of typical experiments showing visualized shocks formed by homogeneous condensation during the expansion of water vapor in nitrogen (or air).

Low Density Drivers of Strong Interplanetary Shocks

Abstract: The theory that most, if not all, interplanetary shocks are caused by coronal mass ejections (CMEs) faces serious problems in accounting for the strongest shocks. The difficulties include (i) a remarkable absence of very strong shocks during solar maximum 1980 when CMEs were prolific, (ii) unrealistic initial speeds near the Sun for impulsive models, (iii) the absence of rarefaction zones behind the shocks and (iv) sustained high speed flows following shocks which are not easily explained as consequences of CME eruptions. Observations of the proton temperature near 1 AU indicate that strong shock drivers have properties similar to high speed streams emitted by coronal holes. Eruptions of fast solar wind from coronal holes influenced by solar activity can explain the occurrence of the strongest interplanetary shocks.

Item-by-item delivery of flat articles from pile

Abstract: FIELD: radioelectronic industry; production of printed circuit boards. SUBSTANCE: rarefaction is built in chambers 4 and 5 by fans 7 and 8. Pile 2 of flat articles placed on lifting-lowering table 1 is lifted to definite distance between upper plane of pile and roller conveyor 3 providing lifting of flat article from pile. With article gripped, break contact of grip sensor 9 operates, and motor of fan 8 is switched off by control unit 11. As a result, lifting force decreases, as rarefaction is preserved only in chambers 5, but force remains sufficient to hold flat article on conveyor. When article passes through last suction chamber, make contact of article take off sensor 10 operates, and motor of fan 8 is switched on. Rarefaction is built in chambers 4 again with resulting increase in lifting force. Next article is gripped, and cycle repeats. EFFECT: reduced power consumption, increased efficiency. 2 cl, 2 dwg

A modification of the non-reflecting boundary conditions for gas-dynamic simulation in astrophysics

Abstract: A new formulation of non-reflecting boundary conditions on open outlet boundaries of domains of gas-dynamic flow is proposed. A combination of three strictly non-reflecting conditions is used: the known condition for supersonic flow, which gives a typically consistent approximation of the equations on the boundary, the condition for the conservation ofhomogeneous equilibrium subsonic flow, and a new condition, connected with the use of gas-dynamic parameters in the boundary rarefaction wave at the sonic point. A comparison is made between the non-reflecting properties of the proposed approach and several known formulations using the example of calculations of the interaction between supersonic flow and a spherically symmetric source, simulating the stellar wind/interstellar medium interaction. In the parameter range under consideration, for practically all the generally accepted formulations this problem is critical, and it is used as the basis for developing the proposed approach.

Nucleation and condensation rate measurement by condensation wave

Abstract: Publisher Summary This chapter experimentally and theoretically investigates the homogeneous nucleation with subsequent spontaneous condensation of the vapors of water, molecular mass Mv, in a carrier gas, Ar and He with molecular mass Mc,, in the expansion part of a shock tube The amount of condensate produced in the condensation wave (CW) is evaluated by the principle of minimum entropy production and by measurement of the time of onset and termination of the CW The homogeneous nucleation of water vapor in a carrier gas was first studied experimentally in the expansion part of a shock tube using light scattering by Barschdorff, and the numerical solution was added by Sislian and Glass The nucleation and growth rate of droplets in argon were measured by Peters using the Mie-scattering method Theoretical analysis and semianalytical solution (asymptotic expansion) of the embedded condensation shock wave formation in a rarefaction fan were given by Delale

Statistical physics approach to heat transfer in gases

Abstract: In view of the difficulty encountered in extending the electrical analogy approach to study axial heat transfer in a cylindrical column of rarefied gas, a statistical physics approach is proposed for evaluating the thermal conductivity of a gas in terms of the probability for collision free travel of a gas molecule in the gaseous column. The resulting expression for thermal conductance of a gas is found to be more realistic than some existing interpolation formulas, as it uniquely defines the criterion for rarefaction. Moreover, acoustic mode of heat transport can be readily incorporated to understand anomalous heat transfer during heat pulse propagation in gaseous columns.