Relaxing Gas Research Articles

Evolution of acceleration waves in non-ideal relaxing gas subjected to the transverse magnetic field

Evolution of acceleration waves in non-ideal relaxing gas subjected to the transverse magnetic field

Interaction of steepened wave with a strong shock in van der Waals stiffened relaxing gases

We consider the interaction problem of a steepened wave with a strong shock in the planar and radially symmetric flow of a van der Waals stiffened relaxing gases. An exact solution to the considered system is used to investigate the evolution of a steepened wave. The significance of van der Waals excluded volume, density, and velocity of solid crystals on a steepened wave is determined. Attention is drawn to analyzing the interaction between steepened wave and blast wave. The amplitudes of reflected and transmitted waves along with the bounce in shock acceleration, originating from collision between steepened wave and strong shock, are also computed.

More relaxed intracluster gas than galaxies in clusters in quasi-equilibrium

ABSTRACT During cluster mergers, the intracluster gas and member galaxies undergo dynamic evolution, but at different time-scales and reach different states. We collect 24 galaxy clusters in quasi-equilibrium state as indicated by the X-ray image, and calculate the cluster orientations and three kinds of dynamical parameters, i.e. the normalized centroid offset, the sphere index, and the ellipticity, for these clusters from the distributions of member galaxies and also the intracluster gas. We find consistent alignments for the orientations estimated from the two components. However, the three kinds of dynamical parameters indicated by member galaxies are systematically larger than those derived from the gas component, suggesting that the gas component is more relaxed than member galaxies. Differences of dynamical features between the intracluster gas and member galaxies are independent of cluster mass and concentration. We conclude that the intracluster gas reaches the dynamic equilibrium state earlier than the almost-collisionless member galaxies.

On the relaxation wave equation of G. G. Stokes

In 1851 G. G. Stokes obtained a relaxation wave equation, which has been overlooked by many modern-day researchers but, nevertheless, its form has been applied to a variety of problems of weak waves propagating in relaxing gases. The present contribution is to elucidate features of the Stokesian relaxation wave equation in a straightforward manner and to point out other physical problems relatable to the Stokesian relaxation wave equation.

Shock wave solution for the planar, cylindrically, and spherically symmetric flows of non-ideal relaxing gas

In the present article, we investigate one-dimensional non-ideal relaxing gas to study solution of shocks for planar and non-planar flows, more specifically cylindrically symmetric, and spherically symmetric flows. The analytic solution of the problem is determined in the characteristic plane. It signifies that linear solution in this plane reveals non-linear behavior in the physical plane. Also, the condition of shock formation has been determined by analyzing the growth and deterioration of shocks using transport equations. It is observed that nature of the solution completely depends upon relaxing gas parameters and non-idealness. All computations are done using computational package MATHEMATICA. • Shock wave solution to the non-ideal relaxing gasdynamic system is studied. • The condition of shock formation is determined. • The growth and deterioration of shocks is discussed. • Impact of relaxing gas and non-ideal parameters on the evolution of shock is studied.

Comparison of stationary and transient kinetic methods in determining the rate of surface exchange reaction between molecular oxygen and MIEC perovskite

The kinetic parameters of the reaction of nonstoichiometric oxide Ba0.5Sr0.5Co0.75Fe0.2Mo0.05O3-δ with molecular oxygen were determined by two independent methods: the steady-state oxygen permeability of the hollow fiber membrane and the transient kinetics of re-equilibration. To analyze the results, we used mathematical models that take into account the inhomogeneity of conditions in the relaxation reactor and gas flows in the tubular membrane. For a correct comparison of the two methods, the same formulation of the surface reaction rate was used in both models, taking into account the dependence of the reaction rate constant on oxide stoichiometry. As a result, a quantitative agreement was obtained between the values of the equilibrium exchange rate R0, including its activation energy, and the dependence on the oxygen partial pressure.

A numerical study of the expansion of a gas-particles mixture with axial symmetry

The article deals with the study of new phenomena that accompany the free or wall-bounded expansion of a nonequilibrium in terms of velocities and temperatures mixture of gas and particles of various sizes with axial symmetry. The dynamics of the gas suspension is considered in the multifluid model of a calorically perfect inviscid gas and incompressible monodisperse spherical particles. The Eulerian approach is used to describe the motion of each phase of the mixture. For numerical simulation, a hybrid large-particle method of the second order of approximation in space and time with nonlinear correction of artificial viscosity, an additive combination of fluxes, and a semi-implicit scheme for calculating interfacial friction and heat transfer are implemented. The efficiency and accuracy of the method for a two-dimensional problem with axial symmetry are confirmed by comparing the solutions obtained in a one-dimensional formulation in a cylindrical coordinate system. In the case of small particles (with a diameter of d = 0.1 µm), the relaxation time of the phases is much less than the characteristic time of the problem and the gas and particles mixture behaves as a homogeneous medium similar to the gas flow. For sufficiently large particles (d = 20 µm), the effects of the difference in the inertia of the phases and nonequilibrium, associated with the mismatch of the velocities and temperatures of the gas and particles, are manifested. These effects cause the splitting of the initial interface of the media into a contact discontinuity in the gaseous phase and the surface between the suspension and the pure gas (a jump in porosity). At subsequent moments, the flow pattern changes to the opposite, which is explained by the deceleration of the gas, the appearance of a reverse flow to the center of expansion due to rarefaction in the vicinity of the axis of symmetry, and the formation of a secondary shock wave. Then there are fluctuations with a change in the relative position of the phase boundaries. In this case, fractures of the gas contact trajectories (the break of the first derivative) are observed, which are associated with the passage of the shock wave reflected from the wall and the plane of symmetry. Over time, due to baroclinic instability (the mismatch of density and pressure gradients), vortex structures begin to appear at the interface boundaries. In addition, in the case of expansion of the gas suspension in a closed volume, a complex shock-wave structure is formed, due to multiple reflections of shock waves from the walls and their interaction with the contact surfaces. The practical significance of the results obtained is to identify the fundamental physical effects that should be taken into account when setting and solving problems in chemical technologies, pneumatic transport, and other areas. In addition, the numerical solutions can be useful in testing the resolution of other difference schemes for reproducing the vortex instability of contact boundaries and shock wave structures in the flows of relaxing gas suspensions.

Performance assessment and evaluation of SOC stacks designed for application in a reversible operated 150 kW rSOC power plant

The coupling of renewable energy sources with reversible operated high temperature solid oxide cells (rSOC) seems to be a promising option to store and supply clean energy in the future. This work provides the results of experimental investigations on the performance of a rSOC stack as a main unit of a large-scale module installed at a real industrial power plant. In order to determine the requirements as well as to propose strategies for safe and stable operation of the large-scale module the stack was tested under system relevant gas mixtures and operational conditions. Hereby, the focus was on steam electrolysis (EC) and fuel cell (FC) operation utilizing a H2/H2O/CO/CO2/N2 gas mixture, predefined by the reformer installed within the module at the power plant. Furthermore, the alternating operation between EC and FC mode was analyzed. The comprehensive analysis of the performance of the stack includes polarization curves, electrochemical impedance spectroscopy (EIS), distribution of relaxation times (DRT), gas analysis and temperature measurements. Thus, numerous combinations of operational parameters are linked to the individual processes within the stack. During EC operation higher hydrogen partial pressures presented significantly lower diffusion losses especially at low current densities, whereby in FC mode low fuel flows presented increased concentration losses. During alternating operation, prolonged voltage stabilization periods with increasing operation time were observed. Additionally, the processes represented by the peaks calculated from the DRT showed enhanced unstable behavior and presented a significant shift towards higher frequencies compared to constant mode operation.

Similarity solutions of converging shock waves in an ideal relaxing gas with dust particles

The present paper demonstrates the analysis of converging shock wave in an ideal relaxing gas with dust particles via Lie group theoretic method. The Lie group of transformations is used to determine the whole range of self-similar solutions to a problem involving both planar and non-planar flows in an ideal, relaxing and dusty gas involving strong converging shocks. For the strong shock waves, all the necessary group invariance properties associated with ambient gas are presented and the general form of rate of relaxation for which the self-similar solutions exist is determined. By using the invariance surface conditions, we determine the infinitesimal generators of Lie group of transformations associated with the system of partial differential equations and on the basis of arbitrary constants occurring in the expressions for the generators, four different possible cases involving self-similar solutions are reckoned. For the different values of dust parameters, the similarity exponents are obtained numerically and comparison is made with the similarity exponents obtained from the characteristic rule (or CCW method). The effects of mass fraction of dust particle, relative specific heat and ratio of density of dust particle to density of gas, on the flow variables and shock formation, have been shown. The patterns of all flow variables behind the shock are analyzed graphically.

Specific features of the gas-dynamic structure of supersonic axisymmetric microjets of a nonequilibrium SF6 gas

The effect of vibrational nonequilibrium of SF${}_{6}$ molecules on the gas dynamic structure of microjets is revealed, manifesting in a decrease in the longitudinal cell size of the wave structure and weakening of variations in flow parameters along the axis of the microjet compared to the equilibrium flow. The physical justification is found for the diameter of the nozzle, which is the boundary value between the macro- and microjets of vibrationally relaxing gases.

A series multi-step approach for operation Co-optimization of integrated power and natural gas systems

Power to gas units and gas turbines have provided considerable opportunities for bidirectional interdependency between electric power and natural gas infrastructures. This paper proposes a series of multi-step strategy with surrogate Lagrange relaxation for operation co-optimization of an integrated power and natural gas system. At first, the value of coordination capacity is considered as a contract to avoid dysfunction in each system. Then, the uncertainties and risks analysis associated with wind speed, solar radiation, and load fluctuation are implemented by generating stochastic scenarios. Finally, before employing surrogate Lagrange relaxation, the non-linear and non-convex gas flow constraint is linearized by two-dimension piecewise linearization. In the proposed procedure, constraints for energy storages and renewable energy sources are included. Two case studies are employed to verify the effectiveness of the proposed method. The surrogate Lagrange relaxation approach with coordination branch & cut method enhances the accuracy of convergence and can effectively reduce the decision-making time.

Impact of dust in the decay of blast waves produced by a nuclear explosion.

In this paper, we have studied the impact created by the introduction of up to 5% dust particles in enhancing the decay of blast waves produced by a nuclear explosion. A mathematical model is designed and modified using appropriate assumptions, the most important being treating a nuclear explosion as a point source of energy. A system of partial differential equations describing the one-dimensional, adiabatic, unsteady flow of a relaxing gas with dust particles and radiation effects is considered. The symmetric nature of an explosion is captured using the Lie group invariance and self-similar solutions obtained for the gas undergoing strong shocks. The enhancements in decay caused by varying the quantity of dust are studied. The energy released and the damage radius are found to decrease with time with an increase in the dust parameters.

Nonlinear magnetoacoustic waves in plasma with isentropic thermal instability.

Evolution of magnetoacoustic (MA) waves in the heat-releasing plasma is analyzed. Due to the temperature and density dependence of the heating and cooling processes, the dispersion properties of MA waves in the considered medium is rather specific. The dispersion of phase velocity can be either positive or negative, and waves can be further damped or amplified. The amplification of MA waves takes place in the case of isentropic instability. In order to analyze waves in such a medium, we use an approach based on an analogy between nonequilibrium relaxing gas and heat-releasing plasma. The uncompensated isentropic instability restricts the applicability of linear equations describing evolution of magnetoacoustic waves. It appears that for a stabilization of the isentropic instability to be reached, the inclusion of quadratic nonlinear terms is sufficient. In the current research, we derive the nonlinear magnetoacoustic equation (NMAE), which can describe evolution of fast and slow MA waves. The obtained nonlinear equation is different from the known analogues used for the analysis of waves in the considered type of medium, which are modifications of Korteweg-de Vries or Burgers equations. In contrast to the known analogues, it is obtained without the restrictions on wave spectrum and takes into account the main features of nonadiabatic processes that affect the formation of stationary wave structures. We describe analytical solutions of this equation in the form of shock waves including the self-sustained (autowave) pulse and investigate the dependence of these waves on the direction and magnitude of the external magnetic field. The evolutionary stability of the obtained structures is confirmed with the help of numerical solutions of the NMAE. The applicability of NMAE and the correctness of its solutions have been confirmed by the numerical solution of the initial system of magnetohydrodinamic equations. It is shown that the self-sustained (autowave) pulses, which may be realized only in the case of isentropic instability, completely recover their shape after the collision.

Invariant solutions of one‐dimensional equations of two‐temperature relaxation gas dynamics

The group analysis method is applied to the plane one‐dimensional equations of two‐temperature gas dynamics. The complete classification of the equations with respect to admitted Lie group is studied. All invariant solutions are analyzed and their comparisons with the known invariant solutions of the ideal gas dynamics system are presented.

Propagation of non-planar weak and strong shocks in a non-ideal relaxing gas

In this article, the kinematics of one-dimensional motion have been applied to construct evolution equations for non-planar weak and strong shocks propagating into a non-ideal relaxing gas. The approximate value of exponent of shock velocity, at the instant of shock collapse, obtained from systematic approximation method is compared with those obtained from characteristic rule and Guderley’s scheme. Computation of exponent is carried out for different values of van der Waals excluded volume. Effects of non-ideal and relaxation parameters on the wave evolution, governed by the evolution equations, are analyzed.

Interaction of a Singular Surface with a Characteristic Shock in a Relaxing Gas with Dust Particles

Abstract A system of hyperbolic differential equations outlining one-dimensional planar, cylindrical symmetric and spherical symmetric flow of a relaxing gas with dust particles is considered. Singular surface theory used to study different aspects of wave propagation and its culmination to the steepened form. The evolutionary behavior of the characteristic shock is studied. A particular solution of the governing system of equations is used to discuss the steepened wave form, characteristic shock and their interaction. The results of the interaction between the steepened wave front and the characteristic shock using the general theory of wave interaction are discussed. Also, the influence of relaxation and dust parameters on the steepened wave front, the formation of a characteristic shock, reflected and transmitted waves after interaction and a jump in shock acceleration are investigated.

Shock Wave Kinematics in a Relaxing Gas with Dust Particles

Abstract In this article, we considered the evolutionary behaviour of one-dimensional shock waves propagating through a relaxing gas with dust particles in a duct with spatially varying cross section. We adopted the procedure based on the kinematics of a one-dimensional motion to derive an infinite hierarchy of transport equations, which describe the evolutionary behaviour of shock of arbitrary strength propagating through the medium. The first three truncation approximations are considered, and the results are compared with existing results in the absence of relaxation and dust particles. The effects of dust particles and relaxation are studied using numerical computations. The results are depicted for different values of dust and relaxation parameters.

Linear Stability of the Boundary Layer of Relaxing Gas on a Plate

The development of inviscid and viscous two-dimensional subsonic disturbances in the supersonic flat-plate boundary layer of a vibrationally excited gas is investigated on the basis of the linear stability theory. The system of two-temperature gas dynamics which includes the Landau-Teller relaxation equation is used as the initial model. Undisturbed flow is described by the self-similar boundary-layer solution for a perfect gas. It is shown that in the inviscid approximation excitation decreases the maximum growth rate of the most unstable second mode by 10–12% as compared with an ideal gas. The neutral stability curves are calculated for the first and second most unstable modes at the Mach numbers M = 2.2, 4.5, and 4.8. For both modes the critical Reynolds numbers at maximum excitation are greater by 12–13% than the corresponding values for the perfect gas.

Propagation of non-linear waves in a non-ideal relaxing gas

ABSTRACTWe have derived an evolution equation governing the far-field behaviour of small amplitude waves in a non-ideal relaxing gas for planar and converging flow. Asymptotic expansions of the flow variables for small amplitude waves have been used to derive the evolution equation. This equation turns out to be a generalized Burger's equation. The numerical solution of this equation is obtained by using the homotopy analysis method (HAM) proposed by Liao with two different initial conditions. Using the HAM, we have studied the effect of relaxation and nonlinearity. The convergence control parameter enables us to find a good approximate solution for such a complex flow problem. This method also confirms the capabilities and usefulness of convergence control parameter and HAM for complex and highly non-linear problems.

WISDOM Project – II. Molecular gas measurement of the supermassive black hole mass in NGC 4697

As part of the mm-Wave Interferometric Survey of Dark Object Masses (WISDOM) project, we present an estimate of the mass of the supermassive black hole (SMBH) in the nearby fast-rotating early-type galaxy NGC4697. This estimate is based on Atacama Large Millimeter/submillimeter Array (ALMA) cycle-3 observations of the 12CO(2-1) emission line with a linear resolution of 29 pc (0.53"). We find that NGC4697 hosts a small relaxed central molecular gas disc with a mass of 1.6x10^7 Msun, co-spatial with the obscuring dust disc visible in optical Hubble Space Telescope (HST) imaging. We also resolve thermal 1mm continuum emission from the dust in this disc. NGC4697 is found to have a very low molecular gas velocity dispersion, $\sigma_{gas}=1.65^{+0.68}_{-0.65}$ km/s. This seems to be partially because the giant molecular cloud mass function is not fully sampled, but other mechanisms such as chemical differentiation in a hard radiation field or morphological quenching also seem to be required. We detect a Keplerian increase of the rotation of the molecular gas in the very centre of NGC4697, and use forward modelling of the ALMA data cube in a Bayesian framework with the KINematic Molecular Simulation (KinMS) code to estimate a SMBH mass of ($1.3_{-0.17}^{+0.18})\times10^8$ Msun and an i-band mass-to-light ratio of $2.14_{-0.05}^{+0.04}$ Msun/Lsun (at the 99% confidence level). Our estimate of the SMBH mass is entirely consistent with previous measurements from stellar kinematics. This increases confidence in the growing number of SMBH mass estimates being obtained in the ALMA era.