Piston Problems of Two-Dimensional Chaplygin Gas

In this paper, the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas. The angle of the piston is allowed to vary in a wide range. The piston can be pushed forward into the static gas, or pulled back from the gas. The global existence of solution to the piston problem with any initial speed is established, and the structures of the global solutions are clearly described. The authors find that for the proceeding piston problem the front shock can be detached, attached or even adhere to the surface of the piston depending on the parameters of the flow and the piston; while for the receding problem the front rarefaction wave is always detached and the concentration will never occur.     

A REMARK ON HOFER-ZEHNDER SYMPLECTIC CAPACITY IN SYMPLECTIC MANIFOLDS M×R~(2n)

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Global existence of shock front solutions in 1-dimensional piston problem in the relativistic Euler equations

The paper studies the 1-D piston problem of the relativistic Euler equations when the speed of the piston is a perturbation of a constant. A sequence of approximate solutions constructed by a modified Glimm scheme is proved to be convergent to the weak solution (which includes a strong leading shock) to the piston problem. In particular, we give the precise estimates on the reflection of the perturbed waves on the piston and the leading shock.     

双缸单作用活塞泵中活塞匀速运动的探讨

通常双缸单作用活塞泵的恒转速运行会导致管路流量波动,使之在恒流量场合较少应用.对双缸单作用活塞泵的运动建立微分方程,给出了MATLAB7的仿真结果,提出了活塞近似匀速运动的条件,并对电动机转轴的角速度的计算方法作了讨论,得出了在中、低速运行时采用变角速度控制能近似实现恒流量的结论.     

Global existence of shock front solutions in 1-dimensional piston problem in the relativistic Euler equations

The paper studies the 1-D piston problem of the relativistic Euler equations when the speed of the piston is a perturbation of a constant. A sequence of approximate solutions constructed by a modified Glimm scheme is proved to be convergent to the weak solution (which includes a strong leading shock) to the piston problem. In particular, we give the precise estimates on the reflection of the perturbed waves on the piston and the leading shock. The paper is supported by the National Natural Science Foundation of China (Grant 10626034) and the Special Research Fund for Selecting Excellent Young Teachers of the Universities in Shanghai.     

一维活塞问题激波解的整体存在性

本文用改进的Glimm格式的方法,研究一维活塞问题当活塞的运动速度是一个常数的扰动时含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射作出了精确的估计,在对主激波的强度不加限制的情况下证明了激波解的整体存在性.     

Approximate calculation method for one-dimensional gas flows induced by nonmonotonic motion of a piston : PMM vol. 40, n 6, 1976, pp. 1058–1064

The problem of one-dimensional piston which at the beginning moves with increasing velocity into a gas at rest, then is decelerated, and finally stops, is solved by means of special series. The gas flow field is constructed by a successive joining of three characteristic Cauchy problems in terms of their characteristic solutions. Generalized solution of the problem of instantaneous arrest of the piston is derived. Obtained equations are used for the approximate calculation of the motion of generated shock waves.Representation of solutions of certain boundary value problems for nonlinear equations of the hyperbolic kind in the form of special series was proposed in [1, 2], The problem of the piston moving into a gas at rest is solved there, and the obtained solution was used for an approximate determination of the generated shock wave. The piston velocity was assumed to be monotonically increasing. That problem is solved here with the use of similar series in the case when the piston velocity is nonmonotonous,Numerical methods make it possible at present to determine one-dimensional flows similar to that considered below, and multidimensional problems can be solved by the method proposed in [1, 2]. The use of the proposed scheme for solving the problem of the multidimensional piston, whose velocity is nonmonotonous, does not present theoretical difficulties, but except that the formulas are more cumbersome.     

On a free piston problem for potential ideal fluid flow

Our goal was to model and analyze a stationary and evolutionary potential ideal fluid flow through the junction of two pipes in the gravity field. Inside the ‘vertical’ pipe, there is a heavy piston that can freely move along the pipe. In the stationary case, we are interested in the equilibrium position of the piston in dependence on the geometry of junction, and in the evolutionary case, we study motion of the piston also in dependence on geometry. We formulate corresponding initial and boundary value problems and prove the existence results. The problem is nonlinear because the domain is unknown. Furthermore, we study some qualitative properties of the solutions and compare them with the qualitative properties of a free piston problem for Newtonian fluid flow. All theoretical results are illustrated with numerical experiments. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of the adiabatic piston problem via methods of continuum mechanics

We consider a system modelling the motion of a piston in a cylinder filled by a viscous heat conducting gas. The piston is moving longitudinally without friction under the influence of the forces exerted by the gas. In addition, the piston is supposed to be thermally insulating (adiabatic piston). This fact raises several challenges which received a considerable attention, essentially in the statistical physics literature. We study the problem via the methods of continuum mechanics, specifically, the motion of the gas is described by means of the Navier–Stokes–Fourier system in one space dimension, coupled with Newton's second law governing the motion of the piston. We establish global in time existence of strong solutions and show that the system stabilizes to an equilibrium state for $t\to \infty$.     

强引力场中的一维活塞过程

本文在直角坐标系、柱坐标及球坐标系中研究一维匀速活塞在强引力场中的动力学过程.用特征线法数值求解流体力学方程组,得出符合活塞速度条件及联结条件的解.分析讨论了不同坐标系对压缩区,常流区,稀疏区流场、激波传播速度及活塞面上声速的影响.     

A complete analysis of axial piston pump leakage and output flow ripples

The paper is focused on understanding the flow losses and the resulting flow/pressure dynamics in a piston pump. Initially, equations to evaluate leakages in all piston pump gaps will be presented and tested against numerical models, later the equations will be linked to determine the general pressure/flow pump dynamic characteristics. The model will also provide the temporal pressure in each piston/cylinder chamber and the temporal leakage in all pump clearances. A test rig able to measure the dynamic pressure inside a piston chamber was build and employed to evaluate pressure ripple dynamics as a function of turning speed, outlet pressure and swash plate angle. The comparison between experimental and simulated results is very good, giving confidence to the model presented. The advantage of using the analytical approach is that explicit equations allow a more direct understanding of the effect of dimension changes and operating conditions on pump dynamics. Fluid used hydraulic oil ISO 32.     

Non-formation of a vacuum state in a standing piston problem

When boundary data is introduced, additional terms are introduced into the weak formulation of the Navier-Stokes conservation law. We examine the example of single standing piston problem. The single piston problem corresponds to a fixed boundary problem.It is intuitively clear when a single piston filled with gas is pulled apart, even though gas becomes sparse in density, a vacuum state is never formed, because of viscosity. To study this rigorously, the Navier-Stokes equations are used to describe the gas's density and velocity, subject to the presence of viscosity. We prove that, given reasonable assumptions on the boundary data, vacuum states cannot form, if they are not present initially.     

Stability of Rarefaction Wave to the 1-D Piston Problem for the Pressure-Gradient Equations

The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the piston are both sufficiently small, the author establishes the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength by employing a modified wave front tracking method.     

Stability of contact discontinuities to 1-D piston problem for the compressible Euler equations

We consider 1-D piston problem for the compressible Euler equations when the piston is static relatively to the gas in the tube. By a modified wave front tracking method, we prove that a contact discontinuity is structurally stable under the assumptions that the total variation of the initial data and the perturbation of the piston velocity are both sufficiently small. Meanwhile, we study the asymptotic behavior of the solutions by the generalized characteristic method and approximate conservation law theory as $t\to +\infty$.     

An approximate solution of one-dimensional piston problem

A new theory of shock dynamics has been developed in the form of a finite number of compatibility conditions along shock rays. It has been used to study the growth or decay of shock strength for accelerating or decelerating piston starting with a nonzero piston velocity. The results show good agreement with those obtained by Harten's high resolution TVD scheme.     

Effects of mean piston speed,equivalence ratio and cylinder wall temperature on performance of an Atkinson engine

The performance of an air standard Atkinson cycle is analyzed using finite-time thermodynamics. In the model, the linear relation between the specific heat ratio of the working fluid and its temperature, the friction loss computed according to the mean velocity of the piston, the internal irreversibility described by using the compression and expansion efficiencies and the heat transfer loss are considered. The relations between the power output and the compression ratio and between the power output and the thermal efficiency are derived by detailed numerical examples. The results show that if the compression ratio is less than a certain value, the power output decreases with increasing mean piston speed, while if the compression ratio exceeds a certain value, the power output first increases and then starts to decrease with increasing mean piston speed. With further increase in the compression ratio, the increase of mean piston speed results in decreasing the power output. Throughout the compression ratio range, the power output increases with increasing cylinder wall temperature while it first increases and then starts to decrease with the increase of equivalence ratio. The conclusions of this investigation are of importance when considering the designs of actual Atkinson engines.     

Self-similar solutions of the Euler equations with spherical symmetry

We consider self-similar flows arising from the uniform expansion of a spherical piston and preceded by a shock wave front. With appropriate boundary conditions imposed on the piston surface and the spherical shock, the isentropic compressible Euler system is transformed into a nonlinear ODE system. We formulate the problem in a simple form in order to present the analytic proof of the global existence of positive smooth solutions.     

Definition of boundary values of thickness of chrome coverings of piston rings

An approach to the definition of adhesion and cohesion stresses that appear in a piston ring after chroming and its mounting on the piston, its performance in a motor, and corresponding conditions of the critical thicknesses of the covering on the basis of a representation of the ring as a two-layer beam is described.Translated from Dinamicheskie Sistemy, No. 9, pp. 72–76, 1990.     

Stability of rarefaction wave to the 1-D piston problem for exothermically reacting Euler equations

This paper is to devoted to the stability of the rarefaction wave for one dimensional piston problem of the exothermically reacting Euler equations. When the total variation of the initial data and the perturbation of the piston velocity are sufficiently small, we employ fractional wave front tracking scheme to establish the global existence and study the asymptotic behavior of entropy solutions as \(t\rightarrow +\infty \).     

Global existence of shock front solution to axially symmetric piston problem in compressible flow

In this paper we study the global existence of BV solution to two-dimensional piston problem in fluid dynamics. Different from previous results on related problems we remove the restriction on the strength of the leading shock and require the velocity of the piston is rather fast or the density is quite small instead. The main tool in our proof is Glimm Scheme with some improvement. To define the Glimm functional we derive more precise estimates for the interaction of elementary waves, particularly in the region near the leading shock.