Analysis of heat conduction in a rarefied gas at rest with a temperature jump at the boundary by consistent-order extended thermodynamics

In the context of the first- and second-order theories of consistent-order extended thermodynamics, a systematic approach is established for analyzing the temperature jump at the boundary through studying one-dimensional stationary heat conduction in a rarefied gas at rest. Thereby an approach to the free boundary-value problem in general is explored. Boundary values of temperature are assumed to be in the form of power expansion with respect to the Knudsen number, based on which analytical expressions of the temperature jump aswell as entropy production at the boundary are derived explicitly. Dependencies of these two boundary quantities on both the Knudsen number and accommodation factor are also extensively discussed. The present analysis is expected to be the basis for the study of higher-order theories of consistent-order extended thermodynamics.      

The Periodic BMAP/PH/c Queue

In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communication networks arrival rates and/or the service capacity usually vary periodically in time. In order to reflect this property accurately, one needs to examine periodic rather than homogeneous queues. In the present paper, the periodic BMAP/PH/c queue is analyzed. This queue has a periodic BMAP arrival process, which is defined in this paper, and phase-type service time distributions. As a Markovian queue, it can be analysed like an (inhomogeneous) Markov jump process. The transient distribution is derived by solving the Kolmogorov forward equations. Furthermore, a stability condition in terms of arrival and service rates is proven and for the case of stability, the asymptotic distribution is given explicitly. This turns out to be a periodic family of probability distributions. It is sketched how to analyze the periodic BMAP/M _t /c queue with periodically varying service rates by the same method.     

The differential perturbative method applied to the sensitivity analysis for waterhammer problems in hydraulic networks

The differential perturbative method was applied to the sensitivity analysis for waterhammer problems in hydraulic networks. Starting from the classical waterhammer equations in a single-phase liquid with friction (the direct problem) the state vector comprising the piezometric head and the velocity was defined. Applying the differential method the adjoint operator, the adjoint equations with the general form of their boundary conditions, and the general form of the bilinear concomitant were calculated for a single pipe. Considering that any hydraulic network can be built by connecting different components (reservoirs, valves, pumps, tees, etc.) through pipes, the adjoint relationships for any component, as well as the final contribution to the bilinear concomitant, were calculated. Moreover, an analogy was established in which transmission and reflection coefficients can be derived for any adjoint component. The importance or adjoint function was analyzed when the piezometric head or velocity at a given position and time is chosen as the response functional. In this case, it is shown that the importance function is represented by delta-functions travelling along the hydraulic network with the propagation speed. The calculation of the sensitivity coefficients takes into account the cases in which the parameters under consideration influence the initial condition. For these cases, the calculation can be performed by solving sequentially two perturbative problems: the first one is non-steady, while the second one is steady, with an appropriate selection of a weight function coming from the unsteady perturbative problem. The discretized adjoint equations and the corresponding boundary conditions were programmed and solved by using the method of characteristics. As an example, a constant-level tank connected through a pipe to a valve discharging to atmosphere was considered. The corresponding sensitivity coefficients due to the variation of different parameters by using both the differential method and the response surface generated by the computer code WHAT, solver of the direct problem, were also calculated. The results obtained with these methods show excellent agreement.     

On stability of elastic domain during isothermal solid-solid phase transformation in a tube configuration

Under isothermal quasi-static stretching the phasetransition of a superelastic NiTi tube involves the formation(during loading) and vanishing(in unloading) of a high strain(martensite) domain.The two events are accompanied by arapid stress drop/rise due to the formation/vanishing of domain fronts.From a thermodynamic point of view,both areinstability phenomena that occur once the system reaches itscritical state.This paper investigates the stability of a shrinking cylindrical domain in a tube configuration during unloading.The energetics and thermodynamic driving force of thecylindrical domain are quantified by using an elastic inclusion model.It is demonstrated that the two domain fronts exhibit strong interaction when they come close to each other,which brings a peak in the total energy and a sign changein the thermodynamic driving force.It is proved that suchdomain front interaction plays an important role in controlling the stability of the domain and in the occurrence of stressjumps during domain vanishing.It is also shown that the process is governed by two nondimensional length scales(thenormalized tube length and normalized wall-thickness) andthat the length scale dependence of the critical domain lengthand stress jump for the domain vanishing can be quantifiedby the elastic inclusion model.     

Force action of discontinuous waves on a vertical wall

This paper presents the results of an experimental study of the dynamic action exerted on the vertical end wall of a rectangular channel by the wave propagating in the tailwater region after total dam break. It is shown that the results of calculations using the first shallow-water approximation differ from experimental data by not more than 5%. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 129–135, March-April, 2009.     

An asymptotic iteration method for the numerical analysis of near-critical free-surface flows

Satisfying the boundary conditions at the free surface may impose severe difficulties to the computation of turbulent open-channel flows with finite-volume or finite-element methods, in particular, when the flow conditions are nearly critical. It is proposed to apply an iteration procedure that is based on an asymptotic expansion for large Reynolds numbers and Froude numbers close to the critical value 1.The iteration procedure starts by prescribing a first approximation for the free surface as it is obtained from solving an ODE that has been derived previously by means of an asymptotic expansion (Grillhofer and Schneider, 2003). The numerical solution of the full equations of motion then gives a surface pressure distribution that differs from the constant value required by the dynamic boundary condition. To determine a correction to the elevation of the free surface we next solve an ODE that is obtained from the asymptotic analysis of the flow with a prescribed pressure disturbance at the free surface. The full equations of motion are then solved for the corrected surface, and the procedure is repeated until criteria of accuracy for surface elevation and surface pressure, respectively, are satisfied.The method is applied to an undular hydraulic jump as a test case.     

Parametric vibrations of flexible hoses excited by a pulsating fluid flow,Part I: Modelling,solution method and simulation

The article presents an analysis of a model describing lateral vibrations of a pipe induced by fluid flow velocity pulsation. The motion has been described with a set of two non-linear partial differential equations with periodically variable coefficients. In the analysis Galerkin method has been applied using orthogonal polynomials as shape function. To determine instability regions Floquet theory has been employed. The effect of selected parameters on parametric resonance ranges and regions of increased vibration level has been investigated. The character and form of vibrations have been investigated indicating the possibility of excitation of sub-harmonic and quasi-periodic vibrations in the combination resonance ranges.     

On the motion of a fluid-saturated porous solid

Two-parameter structure model of a porous solid is proposed as an approximation of a real porous structure and the macroscopic mass and momentum balance equations are derived for such a medium filled with liquid. The approach presented leads to the equations of motion for a fluid-saturated porous medium with coupling terms via cross-mass couplings. The linear form of these equations is equivalent to the well-known Biot equations.     

HCCB TBM屏蔽块热工水力分析

介绍了HCCB TBM屏蔽块初步设计阶段的最新设计,对比了概念设计评审阶段设计方案在结构上的差别,并对其进行了热工水力的分析。结果表明：温度最高处位于下防剪切键顶端,为246.9℃。速度、压强和对流换热系数均满足ITER标准。另外,根据温度分析计算结果,在下防剪切键处增加了挡板,其对于防剪切键的温度降低有显著效果。     

耗散两态系统的动力学特性

利用Born-Oppenheimer近似研究了零温时耗散两态系统的动力学特性.在不同环境谱分布下,给出了两态之间的跃迁几率随时间的变化.数值结果表明:当环境的谱分布为Ohmic形式时,跃迁几率是一个衰减的函数;而当谱分布为随机取值时,跃迁几率具有“量子跳跃”的特性.与之相对比,我们还给出了当把环境等价成无穷多个谱振子的集合时,跃迁几率随时间的变化.