Isentropic Gas Flow Research Articles

Numerical Study of Plasma Behavior and Power Generation Characteristics in a Disk MHD Generator With Xenon-Seeded Neon Gas

Plasma behavior and power generation characteristics in a disk-shaped magnetohydrodynamic (MHD) power generator with xenon (Xe)-seeded neon (Ne) working gas have been examined by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$</tex-math> </inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $</tex-math> </inline-formula> 2-D numerical simulation under the assumptions of isentropic gas flow and a non-MHD interaction. The seed fraction (mole% of Xe in the mixture) is varied from 0.0% (pure Ne) to 100.0% (pure Xe) to assess the effect that Xe seeding has on plasma behavior and power generation characteristics. Adding a small amount of Xe to Ne improves the power performance due to the resulting enhancement of electrical conductivity, whereas adding an excessive amount (over 5.0%) deteriorates the performance. At an appropriate load resistance, uniform plasma structure occurs for low seed fractions. However, the plasma structure becomes nonuniform for excessively high seed fractions (over 5.0%). This result suggests that adding an excessive amount of Xe can reduce the uniformity of the plasma structure in the generator. On the other hand, at low load resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&lt;$</tex-math> </inline-formula> the appropriate load resistance) and high load resistance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$&gt;$</tex-math> </inline-formula> the appropriate load resistance), a nonuniform plasma structure occurs for any seed fraction and results in the deterioration of generator performance. The electron temperature ranges for maintaining uniform plasma structure become narrower as the seed fraction increases which can be attributed to the low ionization potential of Xe and its large atomic weight.

Global Existence of a Solution for Isentropic Gas Flow in the Laval Nozzle with a Friction Term

We are concerned with isentropic gas flow in the Laval nozzle with a friction term due to viscosity. It is well known that the flow attains the sonic state at the throat, where the cross section is minimum in the Laval nozzle. However, the present friction term changes the position of the sonic state into downstream, which is called chooking. Our goal in this paper is to investigate these phenomena mathematically. From the mathematical point of view, the friction term is different from normal friction terms such as $-\alpha m$ and difficult to treat with. In spite of its physical importance, the friction term has not received much attention until now. For the case without the friction term, the global existence of a solution was obtained by the author. However, for the case with the friction term, there are only restrictive results. The most difficult point is to obtain the bounded estimate of solutions. To solve this problem, we introduce an invariant region depending on the mass. Adjusting the invariant region, we invent a new difference scheme, which yields approximate solutions including the mass.

The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field

Abstract We analyse exact solutions to the Riemann problem for a one-dimensional isentropic and perfectly conducting non-ideal dusty gas flow in the presence of a transverse magnetic field. We give the expression of wave curves as well as the behaviors of these wave curves. A new technique is provided to get a complete list of analytical solutions with the corresponding criteria. Moreover, the numerical solutions to the Riemann problem are also given. It is shown that the analytical solutions match well with the corresponding numerical solutions.

Global Solutions to Isothermal System with Source

In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x,t,ρ,u)=b(x,t)ρ+(a′(x)/a(x))*ρu^2+α(x,t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.

Radon measures as solutions of the Cauchy problem for evolution equations

We consider a standard Navier–Stokes system on the n-D torus $${\mathbb {T}}^n={\mathbb {R}}^n/{\mathbb {Z}}^n$$ , valid when the flow is not very compressible and the temperature does not vary too much. We construct a sequence of approximate solutions that tend to satisfy the equations in a weak sense for arbitrary physical initial conditions. By weak compactness, we obtain Radon measure solutions in density and momentum when the velocity of the flow is finite, as numerically observed in all tests, and the absence of void regions in the flow. We notice that the method also applies without viscosity and complements results on other systems of evolution equations such as the systems of isothermal and isentropic gas flows considered in Colombeau (Z Angew Math Phys 66(5):2575–2599, 2015).

Existence of global solutions for isentropic gas flow with friction

In this paper, we study the existence of global entropy solutions for the Cauchy problem of the extended river flow system with a friction α(x) depending on the space variable x. First, under the boundedness of , we apply the viscosity-flux approximation method coupled with the maximum principle to obtain the a priori L∞ estimates for the approximation solutions. Second, we prove the pointwise convergence of the approximation solutions by using the compactness framework from the compensated compactness theory. Finally, as a by-product, we obtain the existence of global solutions for isentropic gas flow in the Laval nozzle with friction.

A Typical Dropping Cusp Singularity of Solutions to Equations of a One-Dimensional Isentropic Gas Flow

Solutions are considered for the system of nonlinear equations of a one-dimensional isentropic gas flow with low densities. A typical singularity of these solutions corresponding to a cusp catastrophe is described. A model solution with such a singularity was obtained for the special case of shallow-water equations. Within the terms of this model solution, an asymptotic solution is obtained for the system of nonlinear equations of a one-dimensional isentropic gas flow.

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

The Riemann problem for an isentropic ideal dusty gas flow with a magnetic field

Amplitude Blowup in Radial Isentropic Euler Flow

We show that the compressible Euler system for isentropic gas flow admits unbounded solutions. The examples are radial flows of similarity type and describe a spherically symmetric and continuous w...

The well-posedness of solution to a compressible non-Newtonian fluid with self-gravitational potential

AbstractWe study the initial boundary value problem of a compressible non-Newtonian fluid. The system describes the motion of the compressible viscous isentropic gas flow driven by the non-Newtonian self-gravitational force. The existence of strong solutions are derived in one dimensional bounded intervals by constructing a semi-discrete Galerkin scheme. Moreover, the uniqueness of solutions are also investigated. The main point of the study is that the viscosity term and potential term are fully nonlinear, and the initial vacuum is allowed.

Invariant Plane Steady Isentropic Vortical Gas Flows

Elements of group analysis are given for a submodel of plane steady isentropic gas flows. The problem of group classification by arbitrary elements of the equation of state and the values of the Bernoulli and vortex integrals is solved. Optimal systems of subalgebras for two four-dimensional Lie algebras arising in the group classification are constructed. For some cases, the classification of invariant solutions by the optimal system is carried out. Physical interpretation of some solutions is given.

Riemann problem and elementary wave interactions in dusty gas

The present paper concerns with the study of the Riemann problem for a quasi-linear hyperbolic system of partial differential equations governing the one dimensional isentropic dusty gas flow. The shock and rarefaction waves and their properties for the problem are investigated. We also examine how some of the properties of shock and rarefaction waves in a dusty gas flow differ from isentropic ideal gas flow. The solution of Riemann problem of dusty gas flow for different initial data is discussed. Under certain conditions, the uniqueness and existence of the solution of the Riemann problem has been analyzed. Finally, all possible interactions of elementary waves are discussed.

Unified solver for fluid dynamics and aeroacoustics in isentropic gas flows

The high computational cost of solving numerically the fully compressible Navier–Stokes equations, together with the poor performance of most numerical formulations for compressible flow in the low Mach number regime, has led to the necessity for more affordable numerical models for Computational Aeroacoustics. For low Mach number subsonic flows with neither shocks nor thermal coupling, both flow dynamics and wave propagation can be considered isentropic. Therefore, a joint isentropic formulation for flow and aeroacoustics can be devised which avoids the need for segregating flow and acoustic scales. Under these assumptions density and pressure fluctuations are directly proportional, and a two field velocity-pressure compressible formulation can be derived as an extension of an incompressible solver. Moreover, the linear system of equations which arises from the proposed isentropic formulation is better conditioned than the homologous incompressible one due to the presence of a pressure time derivative. Similarly to other compressible formulations the prescription of boundary conditions will have to deal with the backscattering of acoustic waves. In this sense, a separated imposition of boundary conditions for flow and acoustic scales which allows the evacuation of waves through Dirichlet boundaries without using any tailored damping model will be presented.

Classification of the Riemann problem for compressible two-dimensional Euler system in non-ideal gas

This work is devoted to the study of two-dimensional Riemann problem modeled by compressible Euler system for the non-ideal gas. The initial constant data are divided in four quadrants in such a way that only one planar elementary wave connects two neighboring states. We classify the different combinations of planar elementary waves and subsequently discuss one by one using the method of generalized characteristic analysis. Attention is drawn to the changes in elementary waves, with regard to their shape, speed and strength, under the influence of the van der Waals parameter b. It has been shown that only sixteen (respectively, fifteen) distinct combinations of planar elementary waves exist for isentropic (respectively, non-isentropic) non-ideal gas flows.

A one-dimensional analytical calculation method for obtaining normal shock losses in supersonic real gas flows

The calculation of isentropic flow and normal shock waves of real gases are important, especially in the preliminary design of turbo-machinery and test rigs. In an ideal gas, the relations for one-dimensional isentropic flow and normal shock waves are well known and can be found in standard textbooks. However, for fluids exhibiting strong deviations from the ideal gas assumption universal relations do not exist due to complex equations of state. This paper presents a analytical method for the prediction of isentropic real gas flows and normal shock waves, based on the Redlich-Kwong (RK) equation of state. Explicit expressions based on a series expansion for describing isentropic flow of Novec™ 649 are compared to Refprop data and ideal gas equations. For moderate pressures the RK method is in very good agreement with the Refprop data, while the ideal gas equations fail to predict the real gas behaviour. The same observations are made for normal shock calculations, where both real gas methods yield very close results. Especially the predicted stagnation pressure losses across a shock wave are in excellent agreement.

ApproximateWeakly NonlinearModel of gas Dynamics EquationsWith Utilized Korobeinikov’s Chemical Reaction

The main purpose is to develop an analytic approach for investigating the wave front propagation on a surface of a cylinder that can be used a descriptor of a detonation engine. The analysis is based on a weakly nonlinear approximated gas dynamic equations with incorporated approximation of the Korobeinkov’s chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. We found that the wave fronts can be expressed analytically in explicit form for special classes of flow (e.g. isentropic gas flow). In more general cases, the dynamics of wave fronts can still be determined explicitly provided that the wave front is known at initial time and the exact solution, or its approximation is known a priori, e.g. from experimental or numerical analysis.

Multidimensional wave fronts propagation along the beams associated with thermodynamic model of a rotating detonation engine

The main purpose here is to develop an analytic approach for investigating the wave front propagation on a surface of a cylinder that can be used as a descriptor of a detonation engine. The analysis is based on a weakly nonlinear approximated gas dynamic equations with incorporated approximation of the Korobeinikov’s chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. We found that the wave fronts can be expressed analytically in explicit form for special classes of flow (e.g. isentropic gas flow). In more general cases, the dynamics of wave fronts can still be determined explicitly provided that the wave front is known at initial time and the exact solution is either known a priori, e.g. from experimental or numerical analysis.

Existence of global solutions for isentropic gas flow in a divergent nozzle with friction

We study isentropic gas flow in a divergent nozzle with friction. It is physically known that the flow is influenced by friction. In this paper, we investigate the mathematical effect of the friction on solutions. We first construct approximate solutions by using the Godunov scheme and the fractional step procedure. We obtain the bounded estimate by the invariant region. This is the difficult point of the present paper. We use the compensated compactness to prove their convergence. Finally, we prove the existence of global solutions with arbitrary L∞ data.

Isentropic Gas Flow for the Compressible Euler Equation in a Nozzle

We study the motion of isentropic gas in a nozzle. Nozzles are used to increase the thrust of engines or to accelerate a flow from subsonic to supersonic. Nozzles are essential parts for jet engines, rocket engines and supersonicwind tunnels. In the present paper, we consider unsteady flow, which is governed by the compressible Euler equation, and prove the existence of global solutions for the Cauchy problem. For this problem, the existence theorem has already been obtained for initial data away from the sonic state, (Liu in Commun Math Phys 68:141–172, 1979). Here, we are interested in the transonic flow, which is essential for engineering and physics. Although the transonic flow has recently been studied (Tsuge in J Math Kyoto Univ 46:457–524, 2006; Lu in Nonlinear Anal Real World Appl 12:2802–2810, 2011), these papers assume monotonicity of the cross section area. Here, we consider the transonic flow in a nozzle with a general cross section area. When we prove global existence, the most difficult point is obtaining a bounded estimate for approximate solutions. To overcome this, we employ a new invariant region that depends on the space variable. Moreover, we introduce a modified Godunov scheme. The corresponding approximate solutions consist of piecewise steady-state solutions of an auxiliary equation, which yield a desired bounded estimate. In order to prove their convergence, we use the compensated compactness framework.

On the strong solutions of one-dimensional Navier-Stokes-Poisson equations for compressible non-Newtonian fluids

We study the strong solutions of 1D Navier-Stokes-Poisson equations for compressible non-Newtonian fluids in bounded intervals. The model is raised from the viscous isentropic gas flow under considering an external force and the non-Newtonian gravitational force term. By using the iterative method we prove the local existence and uniqueness of strong solutions based on some compatibility condition. The main condition is that the initial density vacuum is allowed.