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.     

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.     

Zero Leakage Sealings for Reciprocating Compressors

The piston rod of a reciprocating compressor is sealed with elastic cylindrical sealing elements. Across the sealings the pressure drops from the operating pressure to the ambient pressure. The lubrication gap between the elastic sealing and reciprocating piston rod is studied with the aim to find conditions of a leakage free sealing. The flow in the lubrication gap and the elastic deformation of the sealing are determined simultaneously. The netflow during one cycle of the reciprocating piston rod is calculated. It turns out that maintaining zero leakage is very sensible. Indeed the outbound flow during out-stroke has to be equal the inbound flow during the instroke. By prescribing a special shape of the undeformed sealing zero leakage can be attained — at least theoretically for certain operating conditions. It turns out that temperature dependent material data and a model for cavitation is necessary. The model, its numerical implementation and results will be discussed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of actuator parameters on the critical flow velocity of a fluidic amplifier

The effect of actuator parameters on the critical flow velocity of the fluidic amplifier in liquid-jet hammers has been investigated numerically and experimentally. The flow in the fluidic amplifier and actuators coupled with the rigid body movement of the impacting body has been simulated using a commercial CFD software package, Fluent. The flow is modeled by the RNG-based κ–ε turbulence model and the incompressible Navier–Stokes equations. Dynamic layering method and a user-defined function written in C programming language are used to update the mesh in the simulations. The results show that, increasing the piston diameter decreases rapidly the critical flow velocity as the piston diameter is less than a certain value. The critical flow velocity increases sharply as the piston rod diameter is greater than a certain value, and increases nearly linearly with mass of the impacting body, and is independent on stroke length of the impacting body. The findings of the numerical investigations agree well with corresponding experimental results.     

Mathematical modeling of shock-wave processes under gas solid boundary interaction

The results of numerical simulations are presented for planar air flows in a bounded volume of square cross section diminishing due to a uniform motion of the walls, for a flow of a propane-air mixture under sinusoidal variation of the size of the square domain, and for three-dimensional supersonic air and propane-air flows in channels of variable square cross section. Specific features of shock-wave processes that are associated with the piston effect and cumulation are established. The hypersonic analogy between planar and spatial flows is confirmed, which allows one to use two-dimensional solutions in estimating three-dimensional flows. The equations of a multicomponent ideal perfect gas and one-stage kinetics of chemical reactions are used to describe the flows. The method of numerical simulations is based on S.K. Godunov’s scheme and implemented within an original software package.     

A low-Mach number method for the numerical simulation of complex flows

A new numerical procedure which considers a modification to the artificial acoustic stiffness correction method (AASCM) is here presented, to perform simulations of low Mach number flows with the compressible Navier–Stokes equations. An extra term is added to the energy fluxes instead of using an energy source correction term as in the original model. This new scheme re-scales the speed of sound to values similar to the flow velocity, enabling the use of larger time steps and leading to a more stable numerical method. The new method is validated performing Large Eddy Simulations on test problems. The effect of a crucial numerical parameter alpha is evaluated as well as the robustness of the method to variations of the Mach number. Numerical results are compared to the existing experimental data showing that the new method achieves good agreement increasing the time-step, and therefore accelerating the computation for low-Mach convective flows.     

Implicit fully mesh-less method for compressible viscous flow calculations

A dual-time implicit mesh-less scheme is developed for solution of governing viscous flow equations. The computational efficiency of the method is enhanced by adopting accelerating techniques such as local time stepping and residual smoothing. The Taylor series least square method is used for approximation of derivatives at each node which leads to a central difference spatial discretization. The capabilities of the method are demonstrated by flow computations about standard cases at subsonic and transonic laminar flow conditions. Results are presented which indicate good agreements with the alternative numerical and experimental data. The computational time is considerably reduced when using the proposed mesh-less method compared with the explicit mesh-less and finite-volume counterparts using the same distribution of points.     

Dynamic Modelling and Identification of a Waterjet Cutting System

This paper describes a new dynamic model for a waterjet cutting system that includes a double-acting reciprocating intensifier pump. Since the system operates at high pressures the fluid flow is assumed to be compressible. The dynamic model includes the characteristics of the intensifier pump, the check valves, the accumulator, the system piping and compressible jet flow through the nozzle. The system model is presented as a set of differential-algebraic equations. Experimental results for an actual system are used to identify the discharge coefficient of the nozzle, certain unknown parameters associated with the check valve, and to determine the velocity profile of the piston in the intensifier pump. This is accomplished by formulating and solving a parameter optimization problem. The paper also includes numerical simulation results that validate the dynamic model.     

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.     

Dynamically adapted grids for interacting discontinuous solutions

Further development of the dynamic adaptation method for gas dynamics problems that describe multiple interactions of shock waves, rarefaction waves, and contact discontinuities is considered. Using the Woodward-Colella problem and a nonuniformly accelerating piston as examples, the efficiency of the proposed method is demonstrated for the gas dynamics problems with shock wave and contact discontinuity tracking. The grid points are distributed under the control of the diffusion approximation. The choice of the diffusion coefficient for obtaining both quasi-uniform and strongly nonuniform grids for each subdomain of the solution is validated. The interaction between discontinuities is resolved using the Riemann problem for an arbitrary discontinuity. Application of the dynamic adaptation method to the Woodward-Colella problem made it possible to obtain a solution on a grid consisting of 420 cells that is almost identical to the solution obtained using the WENO5m method on a grid consisting of 12 800 cells. In the problem for a nonuniformly accelerating piston, a proper choice of the diffusion coefficient in the transformation functions makes it possible to generate strongly nonuniform grids, which are used to simulate the interaction of a series of shock waves using shock wave and contact discontinuity tracking.     

Exact solutions of accelerated flows for a Burgers’ fluid II. The cases γ = λ2/4 and γ > λ2/4

The purpose of this study is to provide the exact analytic solutions of accelerated flows for a Burgers’ fluid when the relaxation times satisfy the conditions γ = λ²/4 and γ > λ²/4. The velocity field and the adequate tangential stress that is induced by the flow due to constantly accelerating plate and flow due to variable accelerating plate are determined by means of Laplace transform. All the solutions that have been obtained are presented in the form of simple or multiple integrals in terms of Bessel functions. A comparison between Burgers’ and Newtonian fluids for the velocity and the shear stress is also made through several graphs.     

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.     

采用高分辨率数值方法重构与实测数据一致的实际爆炸波的部分流场

本文采用球面爆炸的活塞推进模型和对间断解具有高分辨率的二阶Godunov型有限差分方法,以两类化爆试验值作依据,通过恰当调整运动活塞边界条件,数值重构了实际半球形爆炸波的部分流场.方法简单、可靠,所得结果可用于评估任意同类型炸药一维爆炸波的远场效应.     

Bifurcation and chaos of an axially accelerating viscoelastic beam

This paper investigates bifurcation and chaos of an axially accelerating viscoelastic beam. The Kelvin–Voigt model is adopted to constitute the material of the beam. Lagrangian strain is used to account for the beam's geometric nonlinearity. The nonlinear partial–differential equation governing transverse motion of the beam is derived from the Newton second law. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. By use of the Poincaré map, the dynamical behavior is identified based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented in the case that the mean axial speed, the amplitude of speed fluctuation and the dynamic viscoelasticity is respectively varied while other parameters are fixed. The Lyapunov exponent is calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially accelerating viscoelastic beam.     

Square Matrix Padé Approximation and Convergence Acceleration of Sequences

This paper provides a new method for approximating matrix-valued functions — square Padéapproximation. Some computational methods of the approximants are given. For accelerating matrix sequences, a family of nonlinear extrapolation formulas based on the square Padé approximation is given, a convergence acceleration theorem is proved and numerical examples are presented.     

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.     

Gas dynamics applications of a characteristic Cauchy problem

Some initial-boundary-value problems for a system of quasilinear partial differential equations of gas dynamics with the initial data prescribed on the characteristic surface (characteristic Cauchy problem) are considered. The following three-dimensional flow problems are investigated: the flow produced by a motion of an impermeable piston; the flow produced by a permeable piston with a given pressure; and the flow produced by the moving free boundary. In the first two problems, the piston motion is prescribed; in the last problem, the free boundary motion cannot be prescribed in advance and must be determined as a part of the problem. It is shown that those problems can be reduced to a characteristic Cauchy problem of a certain standard type that satisfies the analog of Cauchy-Kowalewski's existence theorem in the class of analytical functions (Differential Equations 12 (1977) 1438-1444). Thus, it is proved that, in the case of the analyticity of the input data, the considered problems have unique piecewise analytic solutions which may be expressed by infinite power series (the procedure of constructing the power series solution is described in Differential Equations 12 (1977) 1438-1444 as a part of the proof of the theorem).     

Exact solution of a boundary value problem describing the uniform cylindrical or spherical piston motion

In this paper, we construct the exact solution for fluid motion caused by the uniform expansion of a cylindrical or spherical piston into still air. Following Lighthill [1], we introduce velocity potential into the analysis and seek a similarity form of the solution. We find both numerical and analytic solutions of the second order nonlinear differential equation, with the boundary conditions at the shock and at the piston. The results obtained from the analytic solutions justify numerical solution and the approximate solution of Lighthill [1]. We find that although the approximate solution of Lighthill [1] gives remarkably good numerical results, the analytic form of that solution is not mathematically satisfactory. We also find that in case of spherical piston motion Lighthill’s [1] solution differs significantly from that of our analytic and numerical solutions. We use Pade′ approximation to extend the radius of convergence of the series solution. We also carry out some local analysis at the boundary to obtain some singular solutions.     

Roll waves in an annular channel

The goal of this study is to analytically construct periodic wind perturbations in an annular channel that are numerically produced by a regularized model. R. Dressler’s technique in the shallow water approximation is used to prove the nonexistence of smooth periodic solutions, and discontinuous solutions related to roll waves on inclined surfaces are constructed. The constraints on the accelerating and dissipating forces are obtained under which periodic solutions can exist. A numerical analysis of the problem is carried out, and a qualitative comparison of the numerical and theoretical results is presented.