Equilibrium Speed Of Sound Research Articles

Lifting the Veil on Quark Matter in Compact Stars with Core g-mode Oscillations

Abstract Compact stars containing quark matter may masquerade as neutron stars in the range of measured mass and radius, making it difficult to draw firm conclusions on the phase of matter inside the star. The sensitivity of core g-mode oscillations to the presence of a mixed phase may alleviate this difficulty. In hybrid stars that admit quark matter in a mixed phase, the g-mode frequency rises sharply due to a marked decrease in the equilibrium sound speed. Resonant excitation of g-modes can leave an imprint in the waveform of coalescing binary compact stars. We present analytic and numeric results to assess the sensitivity displayed by g-mode oscillations to quark matter in a homogeneous or mixed phase and also compute relevant damping times in quark matter due to viscosity.

CO<sub>2</sub> Emission and Energy Assessments of a Novel Pre-Purification Unit for Cryogenic Air Separation Using Supersonic Separator

Thermal power plants with oxy-combustion CO2 capture are featured by large scale oxygen demand, where cryogenic air separation is most suitable. In such context, a Pre-Purification Unit (PPU) is required, prior to air fractionation, to remove hazardous air contaminants – H2O, CO2 and several trace-species – preventing ingress into the Cold Box. The conventional PPU – named FULL-TSA – remove those contaminants by means of Temperature Swing Adsorption (TSA), ordinarily using double-layered bed with activated alumina for adsorbing H2O and zeolitic molecular sieve for adsorbing CO2 and further trace-species, which implicates in relatively high demand of low-pressure steam for impurities desorption. A novel pre-purification concept (SS-TSA) embraces a Supersonic Separator (SS) performing the bulk of separation service, abating nearly 98.5% of H2O, followed by a finishing single-bed molecular sieve (MS) TSA step, which is featured by its relatively small size, for removing CO2 and remaining impurities. This work presents the energy analysis, as well as the related indirect CO2 emissions, of such a novel concept (SS-TSA) comprising air compression, cooling, SS dehydration and finishing MS-TSA against the conventional method fully based in TSA purification (FULL-TSA). Process simulation in HYSYS 8.8 assisted technical evaluation and comparison of alternatives, which included the use of two Hysys Unit Operation Extensions – SS-UOE and PEC-UOE – for rigorous thermodynamic SS modeling with phase equilibrium sound speed. SS was designed to impose only 1.4% of head loss, while shrinking TSA service to about 10% of FULL-TSA counterpart, also recovering super-cooled aqueous condensate that reduces water make-up and N2 consumption for cooling. Changing from FULL-TSA to SS-TSA the average demand of low-pressure steam reduced from 1.37 to 0.16 MW. In terms of electricity demand the difference was quite small, referring to a tiny increase of 0.07 MW in SS-TSA comparatively to total power demand of 14.97 MW in FULL-TSA. Assuming a natural gas combined cycle cogeneration plant matching requirements to air compression and pre-purification process, equivalent reduction in CO2 indirect emission was 20 kg/h for SS-TSA. These results point superiority of SS-TSA.

Shear thickening fluid impregnated ballistic fabric composites for shock wave mitigation

This study reports on the shock wave protective performance of woven Twaron fabric impregnated with shear thickening fluid (STF). The STF was prepared from a combination of mechanical and ultrasonic mixing of fumed silica nanoparticles dispersed in liquid polyethylene glycol (PEG) polymer. The shear thickening characteristics were determined from rheological tests. Two shock wave parameters governing blast related injuries are used to evaluate the performance of the STF treated fabrics – peak pressure and rate of pressure rise. The results of our shock tube tests demonstrate that the STF treated fabric composites offer superior shock wave protection as compared to untreated (neat) fabric and fabric impregnated with PEG only. After STF treatment, the normalised average peak pressure amplification is significantly reduced from 2.46 to 1.49 while the attenuation in normalised maximum rate of pressure rise is even more pronounced – from 2.3 to 0.76. Apparent material density is found to correlate with the average peak pressure and maximum rate of pressure rise. This implies that the density increases enough to increase the equilibrium sound speed in the fabric, and therefore preclude the formation of shock wave in the fabric. Ballistic tests using steel projectiles were also conducted to check that the STF treated fabrics continued to enhance ballistic protection as reported by other researchers. Overall, the results show that the STF treated fabrics have potential applications not only for ballistic protection but also for shock wave mitigation.

A wave equation model for retrograde media with a bubble structure

A nonlinear wave equation is obtained for liquid-vapor mixtures with regard to arbitrary change of equilibrium sound speed in a mixture with growth and condensation of vapor bubbles, which has a limit transition to a wave equation for pure liquid at full collapse of vapor cavities. A particular case of a collapsing wave equation (CWE) of retrograde media is considered, e.g., liquid-vapor media with low vaporization heat and low dissipation, observed near the critical liquid-vapor point, where the main effect is variable sound speed. Based on the CWE numerical solutions it is shown that in such liquid-vapor media, one can observe previously unknown nonlinear wave structures with depression waves.

高速ミスト流中に発生する斜め衝撃波に関する研究(流体工学,流体機械)

High-speed two-phase mist flow is very important in developing the ejector of a refrigeration cycle and in the total-flow system of a geothermal power plant. Two types of sound speed in two-phase flow can be created because of the inter-phase transport phenomenon. One is equilibrium sound speed in which the inter-phase transport in the flow is in complete equilibrium. Whereas, the other one is frozen sound speed in which the inter-phase transport is completely frozen. Usually, the fluid velocity is higher than the equilibrium sound speed but lower than the frozen sound speed because the equilibrium sound speed is very low. The existence of the supersonic oblique shock waves is not certain because the fundamental equations of two-phase flow are controlled by the frozen sound speed. This paper shows that the oblique shock wave could appear at some conditions even though the frozen Mach number was less than unity. As the reference length became bigger, the inclined angle of the oblique shock wave reduced to the angle of the equilibrium one. The thickness of a shock wave is directly proportional to the product of the relaxation time and the inlet velocity. Then, the fronts of the shock waves for large relaxation times reached up the inlet. All of the flow area corresponded to subsonic state and the oblique shock wave could not exist anymore.

A modified Zel’dovich-Neumann-Döring model and its peculiarities

A detonation model whose structure includes a shock wave and a continuous combustion zone, where a chemical conversion process is governed by a reaction satisfying a kinetic formulation of the mass action law, is studied. In the framework of this model, the following two types of detonation waves with Lyapunov-stable combustion zones are found: (i) the weak detonation whose speed relative to the equilibrium detonation product flow is equal to the equilibrium speed of sound and (ii) the strong detonation whose speed relative to the flow on the critical surface is equal to the frozen speed of sound (this speed coincides in magnitude with the equilibrium speed). It is shown that the strong detonation corresponds to the condition of tangency between the Mikhelson line and the adiabat of equal sound speeds called the extreme adiabat.

Acoustic properties of a two-fluid compressible mixture with micro-inertia

We study the propagation of acoustic waves in a mixture of two compressible components with micro-inertia. A special symmetric form of linearized governing equations is found permitting us to establish the stability of plane harmonic waves in the full region of flow parameters. It is shown that in non-viscous limit the dispersion relation has two real branches. One branch is defined for all disturbance frequencies, and the other one is defined only for frequencies greater than the resonance frequency. We prove that the group velocity attains its minimal value which is less than the sound speeds of each component. It is also shown that the Wood sound speed appears in our model in the limit of low frequencies only if the dissipation is taken into account. In the dissipation-free limit the equilibrium sound speed is always greater than the Wood speed.

The structure of planar and curved detonation waves with reversible reactions

The structure of both steady planar and slowly varying weakly curved detonations with one reversible reaction are investigated. For reactive systems with reversible reactions there are two distinguished sound speeds in the equilibrium fluid; the frozen sound speed and the equilibrium sound speed. According to the Chapman–Jouguet condition, self-sustaining, steady and planar detonation waves in such systems are equilibrium sonic at the end of the reaction zone. In this paper, it is shown that for any small, but nonzero, curvature of the front, the solution passes through a frozen sonic point where the thermicity simultaneously vanishes, the so-called generalized Chapman–Jouguet condition. Hence, the structure for the steady, planar wave, which is frozen subsonic throughout and is equilibrium sonic at the end of the reaction zone, is a singular limit of the structure of curved detonation waves as the curvature tends to zero. Since in any real detonation there will always be some curvature of the front, however small, the classical equilibrium sonic Chapman–Jouguet point is unobtainable and instead the frozen sonic point of the generalized Chapman–Jouguet condition must be considered. Detonation speed-curvature relations are determined for the system. Very long-time, high resolution, one-dimensional numerical simulations, starting from a time-dependent ignition problem, in both planar and cylindrical geometry are also performed. The results are compared with the steady planar or quasisteady weakly curved solutions.

Amplification of Air Shock Waves by Textile Materials

The peak reflected pressure measured under a flexible and porous textile material exposed to air shock waves may increase by an order of magnitude over the case where no material is present. This peak pressure amplification is a result of the development of shock waves in the two phase (solid/air) material as a result of the low equilibrium sound speed in porous materials and the increase in density of the materials during the transit of the shock wave. This peak pressure amplification may increase the lung injury severity for humans with layered textile materials covering their torso who are exposed to strong air shock waves. The dynamics of shock wave propagation and reflection in flexible and porous textile materials were studied both analytically and experimentally by using an air driven shock tube. A numerical model of the human chest-lung system was adapted for evaluating the effects of different textile materials covering the human chest. Experimental shock tube results were input to the computer model of the human chest to allow a comparison between the different textile materials.

Weak Shocks Initiated by Power Deposition on a Spherical Source Boundary

An inert compressible gas external to a spherical surface is in an equilibrium state initially. Heat is added at the sphere surface during a period that is short compared to the acoustic time of the sphere $t'_a $ (the radius of the sphere divided by the equilibrium sound speed), but larger than the mean time between molecular collisions. Temperature increase in the conduction layer adjacent to the surface induces gas motion arising from thermal expansion. The motion at the layer edge has a pistonlike effect on the gas beyond, generating a thicker layer in which a linear acoustic disturbance is found. As time elapses, an accumulation of nonlinear effects leads to the development of a weak shock in the acoustic region. The subsequent nonlinear evolution of the weak shock then depends mainly on the boundary heat flux. For relatively fast boundary heating, the nonlinear evolution process is described by a planar equation. On the other hand, during relatively slow boundary power addition, disturbances are able to propagate further from the surface before nonlinear effects become important. The nonlinear evolution is then described by a spherical nonlinear equation. Solutions are sought in terms of asymptotic expansions valid when $t'_a /t'_c \to 0$, where $t'_c $ the conduction time of the sphere, is the ratio of the square of the radius to the thermal diffusivity of the gas in the initial state.

Shocks generated in a confined gas due to rapid heat addition at the boundary. I. Weak shock waves

An inert compressible gas, confined between infinite parallel planar walls, is in an equilibrium state initially. Subsequently energy is added at the boundary during a period that is short compared to the acoustic time of the slot t' a (the wall spacing divided by the equilibrium sound speed), but larger than the mean time between molecular collisions. Conductive heating of a thin layer of gas adjacent to the wall induces a gas motion arising from thermal expansion. The small local Mach number at the layer edge has the effect of a piston on the gas beyond. A linear acoustic wave field is then generated in a thicker layer adjacent to the walls. Eventually nonlinear accumulation effects occur on a timescale that is longer than the initial heating time but short compared with t' a . A weak shock then appears at some well defined distance from the boundary. If the heating rate at the wall is maintained over the longer timescale, then a high temperature zone of conductively heated expanding gas develops. The low Mach number edge speed of this layer acts like a contact surface in a shock tube and supports the evolution of the weak shock propagating further from the boundary. One-dimensional, unsteady solutions to the complete Navier-Stokes equations for an inert gas are obtained by using perturbation methods based on the asymptotic limit t' a / t' c → 0, where t' c , the conduction time of the region, is the ratio of the square of the wall spacing to the thermal diffusivity in the initial state. The shock strength is shown to be related directly to the duration of the initial boundary heating.

Relaxation effect on sound propagation in partially ionized gases

The effect of ionization-recombination processes on sound propagation in a partially ionized gas was investigated by employing the fluid model under the assumption that the ionization-recombination frequency is much lower than the collision frequency of heavy particles, and the sound speed and the absorption coefficient were obtained as functions of frequency. It is found that for low frequencies small disturbances propagate with the equilibrium sound speed and that the sound speed increases monotonically with frequency and approaches the frozen sound speed for sufficiently high frequencies. It is found also that the sound is absorbed as it propagates in the medium and the absorption coefficient increases monotonically with the frequency.

Stationary radial source flow of liquid particles into vacuum.

An analytical investigation was made of stationary radial source flow of uniform-size liquid particles into vacuum. The equations describing this system constitute a sixth-order, nonlinear, two-point boundary-value problem with a parameter-depe ndent singularity located in the vicinity of unity Mach number. A numerical procedure for the integration of this system was devised by means of which it was possible to evaluate parametrically the effects on the flow structure of such variables as the initial size^ evaporation coefficient, drag coefficient, heat-transfer coefficient, initial volume fraction, injection velocity, and temperature. It is shown that the flowfield is characterized by a rapid departure from initial dynamic and thermal with the action of interphase mass, momentum, and energy transfer providing the throat through which supersonic flow is attained. For the case of vanishingly small size, it is demonstrated that the original sixth-order boundary-value problem degenerates to a third-order initial value type. Moreover, for the resulting quasi-equilibrium flow, an exact analytic solution was obtained and the limiting speed (at infinity) established. Nomenclature ae — equilibrium sound speed a/ = sound speed Cps = specific heat Cpv — vapor specific heat CD ~ drag coefficient fp = drag force per unit volume of particles h = specific enthalpy k = vapor thermal conductivity ]Vf = frozen Mach number Mp — particle Mach number (Nup~] = Nusselt number P = local pressure PO — vapor pressure qp = heat-transfer rate per unit volume of particles R = gas constant r = radial coordinate s = specific entropy T = temperature u = velocity w = mass rate evaporated per unit volume of particles a = volume fraction; volume/total volume (3 = liquid volume fraction; liquid vol

Gas particle nozzle flows

The equations governing the one-dimensional flow of gas-particle mixtures are discussed. It is shown that the sound velocity in the mixture is the frozen sound velocity in the gas alone and is unaffected by the presence of the particles unless the mixture is always in equilibrium. The equilibrium sound velocity in the mixture is derived and is shown to be lower than the frozen sound velocity. Shock waves in gas-particle mixtures are discussed and it is shown that two shock structures are possible. When the flow velocity in front of the shock is supersonic (based on the frozen speed of sound), the shock consists of a discontinuous shock front followed by a relaxation zone. When the flow velocity in front of the shock is greater than the equilibrium sound speed but less than the frozen sound speed, the shock is fully diffuse and consists of a relaxation zone in which both the gas and particle properties vary continuously. The frozen sound velocity is found to occur downstream of the nozzle throat for all gas-particle nozzle flows. It is shown that the throat conditions depend on the nozzle inlet geometry and that the nozzle mass flow and performance are determined by the nozzle inlet geometry. Analytical and numerical solutions to the equations governing the one-dimensional flow of gas-particle mixtures through nozzles are presented. The particle velocity and thermal lags are found to be greatest at the nozzle throat and expressions are given for estimating these lags. The equations governing axially symmetrical flows of gas-particle mixtures are briefly discussed. These equations are of hyperbolic type when the flow is supersonic (based on the frozen speed of sound in the gas) and can be solved by the method of characteristics. A sample nozzle calculation is given and compared with one-dimensional calculations. A summary is given of all gas-particle nozzle experiments and the results are compared to the calculated gas-particle nozzle flows. It is found that the calculations and experiments are in agreement within the accuracy of the experimental measurements. It is concluded that the flow of gas-particle mixtures can be accurately predicted by the present analysis.