Numerical simulation of incompressible flow driven by density variations during phase change1

A change in density during the solidification of alloys can be an important driving force for convection, especially at reduced levels of gravity. A model is presented that accounts for shrinkage during the directional solidification of dendritic binary alloys under the assumption that the densities of the liquid and solid phases are different but constant. This leads to a non‐homogeneous mass conservation equation, which is numerically treated in a finite element formulation with a variable penalty coefficient that can resolve the velocity field correctly in the all‐liquid region and in the mushy zone. The stability of the flow when shrinkage interacts with buoyancy flows at low gravity is examined. Copyright © 1999 John Wiley & Sons, Ltd.     

基于压力相移辅助的超流体陀螺

超流体陀螺是新一代惯性传感器,面临的关键问题是:在幅值锁定控制系统中,热相移的注入存在较大延时,引起其动态测量性能急剧下降。为此,在研究了超流体压力相移产生原理的基础上,提出采用静电力产生压力差的方法,并根据超流体的理论,构建了压力相移的数学模型。为解算角速度,提出了基于压力相移辅助的算法,锁定了超流体相移。仿真结果表明,基于该方法,超流体陀螺测量角加速度变化的信号时,测量误差减小了约一个数量级。因此,超流体陀螺的动态性能得到了很大改善,测量精度有了显著提高。     

Effect of disjoining pressure on the instability of a charged thin liquid film on a spherical rigid core

It is shown that the critical Rayleigh number which characterizes the stability of a thin charged viscous fluid film on the surface of a rigid spherical core develops rapidly with decrease in the film thickness to 100 nm when the effect of the disjoining pressure becomes significant. The dependence of the instability growth rate on the thickness of the fluid layer is obtained by analyzing the dispersion relation numerically. Yaroslavl’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 102–106, January–February, 1999.     

Migration and deformation of leukocytes in pressure driven flows

Direct numerical simulations (DNS) are used to study the motion and deformation of leukocytes in pressure driven flows in parallel plate channels. The influence of the adhesion force between the leukocytes and the channel wall on such motion and deformation is also investigated. Leukocytes are represented by two composite fluid models, consisting of a membrane, a cytoplasm and a nucleus. The adhesion force is computed using two adhesion force models. In the first model, the adhesion force is given by a potential, and in the second one it is given by Dembo’s kinetic adhesion model. The numerical code is based on the finite element method and the level set technique is used to track the cell membrane position. In the absence of the adhesion force, the leukocyte moves away from the wall to an equilibrium location that depends on the ratio of the cell to plasma viscosities. In presence of the adhesion force, the leukocyte is attracted to the layer of endothelial cells and, as it gets closer, it flattens under the action of hydrodynamic forces. This deformation, in turn, further increases the adhesion force. The leukocyte, however, can be captured only when it is placed sufficiently close to the wall, which for the kinetic model is of the order of 30 nm. We also find that for the normal parameter values and flow rates the adhesive force given by the kinetic model is too small to capture the leukocyte.     

A robust numerical method for flow through a pipe driven by an oscillating pressure gradient

The problem of periodic flow of an incompressible fluid through a pipe, which is driven by an oscillating pressure gradient (e.g. a reciprocating piston), is investigated in the case of a large Reynolds number. This process is described by a singularly perturbed parabolic equation with a periodic right‐hand side, where the singular perturbation parameter is the viscosity ν. The periodic solution of this problem is a solution of the Navier–Stokes equations with cylindrical symmetry. We are interested in constructing a parameter‐robust numerical method for this problem, i.e. a numerical method generating numerical approximations that converge uniformly with respect to the parameter ν and require a bounded time, independent of the value of ν, for their computation. Our method comprises a standard monotone discretization of the problem on non‐standard piecewise uniform meshes condensing in a neighbourhood of the boundary layer. The transition point between segments of the mesh with different step sizes is chosen in accordance with the behaviour of the analytic solution in the boundary layer region. In this paper we construct the numerical method and discuss the results of extensive numerical experiments, which show experimentally that the method is parameter‐robust. Copyright © 2006 John Wiley & Sons, Ltd.     

FEM application in phase change exchangers

Application of FEM in the analysis of condenser and vaporizer has been illustrated taking into account property variation with temperature. Accurate shell side pressure drop in a condenser has been determined by the present method taking into account the gradual reduction in vapour flow due to condensation from inlet to outlet. As the present method analyses the exchanger in small elements, analysis of an evaporator working under the conditions of partial vapour blanketing is also possible.

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Anwendung der Finite Elemente Methode bei Wärmetauschern mit Phasenwechsel

Zusammenfassung Die Verwendung der Finite Elemente Methode zur Berechnung von Kondensator und Verdampfer unter Berücksichtigung von temperaturabhängigen Stoffwerten ist hier dargestellt worden. Mit dem dargestellten Verfahren ist der genaue Druckverlust im Rohrraum eines Kondensators bestimmt worden, wobei die schrittweise Verminderung der Dampfströmung aufgrund der Kondensation von Ein-zu Auslaß mit berücksichtigt wurde. Mit der gegenwärtigen Methode, die einen Wärmeaustausch mittels kleiner Elemente berechnet, ist ebenso eine Auslegung eines Verdampfers mit einer partiellen Dampfabdeckung möglich.

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Nomenclature A heat transfer area in an elment upto any section, m² - A _c elemental heat transfer area, m² - B weightage - C UA/2 - D _e characteristic dimension, m - D _s shell diameter, cm - F _t temperature correction factor - f friction factor, m²/cm² - G mass velocity, kg/m² sec - G W/LN ^2/3 - g acceleration of gravity, m/sec² - h condensing coefficient, W/m²°C - h ₀ boiling coefficient, W/m²°C - k ₁ thermal conductivity of condensate atT _f , W/m°C - L length of tubes in the element, m - l distance of the fluid stream traverses in the element, m - LMTD log mean temperature difference, °C - N ₁,N ₂ shape functions - N _t number of tubes effective for condensation - P pressure drop, N/cm² - P _shell shell side vapour pressure drop, N/cm² - P _tube tube side stream pressure drop, N/cm² - q heat flux in the element, W/m² - S specific gravity of vapour - T _c tube side stream temperature, °C - T _c2 tube side stream exit temperature, °C - T _f (T _w +T _s )/2 - T _s saturation temperature, °C - T _w mean wall temperature in an element, °C - T ₁,T ₂ temperatures at nodes 1 and 2, °C - U overall heat transfer coefficient, W/m²°C - W ₁ tube side fluid thermal capacity rate, W/°C - W ₂ vapour mass flow rate, kg/hr - W mass of vapour condensed in any element, kg/sec - _f viscosity of condensate atT _f , N sec/m² - _f density of condensate atT _f , kg/m³     

Time-shifting correcting method of phase difference on discrete spectrum

Ｎｏｍｅｎｃｌａｔｕｒｅｘ(ｔ)　Ｏｎｅｓｅｇｍｅｎｔｏｆｃｏｎｔｉｎｕｏｕｓｓｐｅｃｉｍｅｎｇｏｔｔｅｎｂｙｓａｍｐｌｉｎｇｔｈｅｈａｒｍｏｎｉｃｓｉｇｎａｌθ　Ｐｈａｓｅｏｆｓａｍｐｌｅｄｓｉｇｎａｌθ0 　ＰｈａｓｅｏｆｓｉｇｎａｌａｆｔｅｒｓｈｉｆｔｉｎｇＡ　ＡｍｐｌｉｔｕｄｅｏｆｓｉｇｎａｌΔｆ　Ｃｏｒｒｅｃｔｉｏｎｏｆｆｒｅｑｕｅｎｃｙ△φ　ＣｏｒｒｅｃｔｉｏｎｏｆｐｈａｓｅΦ　ＰｈａｓｅａｆｔｅｒＦｏｕｒｉｅｒＴｒａｎｓｆｏｒｍΔΦ　ＰｈａｓｅＤｉｆｆｅｒｅｎｃｅｆｘ 　Ｓａｍｐｌｉｎ…     

Calculation of single phase pressure drop in heat exchangers considering the change of fluid properties along the flow path

The cost-optimized design of heat exchangers requires a fast but reliable calculation of pressure drop which makes a major contribution to running costs. For cocurrent and counter-current flow a simple approximating calculation method is presented, taking into account the variation of the fluid properties along the flow path. For any practical case reliable results are obtained only by calculating both the pressure drop and the local overall heat transfer coefficient at least at two points of the heat exchanger. In the special case of a gas in a turbulent flow and when, as usual, the major resistance to heat transfer is caused by the gas, it is sufficient to calculate only the pressure drop and at one point only. Pressure drops calculated exactly or by the proposed approximation compare well.     

Normal stress difference in liquid lubricants sheared under high pressure

Although normal stress differences in liquids have conventionally been associated with polymers, aspects of rheological behavior in lubricated concentrated contacts suggest that normal stress difference may be significant in even low molecular weight liquids sheared under high pressure and high shear stress. A torsional flow rheogoniometer was constructed for use at high (300 MPa) pressure. Four typical liquid lubricants were investigated, including one polymer/mineral oil solution. Shear stress and N ₂-N ₂ are reported as functions of shear rate. The effect of pressure variation is reported for two liquids. Results are compared with predictive techniques and a molecular dynamics simulation. Simple low molecular weight lubricant base oils can generate measurable and significant normal stress differences when sheared at high shear stress.     

A reference solution for phase change with convection

A reference solutions for phase change involving convection in the melt is currently missing. In the present study, we focus on the problem of melting of pure tin in a square cavity heated from the side, which is used as a benchmark test problem. The mathematical model used for the simulations is based on the enthalpy formulation. Extensive numerical computations are performed with grids as fine as 800 × 800. The convergence of the numerical solution is demonstrated and its level assessed. Data values and plots are provided for use as a reference solution. Copyright © 2005 John Wiley & Sons, Ltd.     

Finite element modelling of natural-convection-controlled change of phase

The problem of phase change in the presence of natural convection has been investigated. A model has been proposed based on the treatment of the release/absorption of latent heat as a heat source/sink in combination with the standard Galerkin finite element method with a primitive variable formulation on a fixed grid. To demonstrate the capabilities of the model, three cases of phase change of an aluminium alloy in the presence of natural convection arc considered, i.e. solidification, melting and combined solidification and melting. The solidification of water in a square cavity is modelled as another example, taking into account the density extremum, and the results are compared with a previously published work.     

用互谱密度函数估算两同频振动信号的相位差

根据振动实验教学中数字信号分析系统的需要,提出了用互谱密度函数估算两个同频信号相位差的方法,提高了测量精度. 应用于振动实验教学,取得了良好的效果.     

Localized modes in a variety of driven long Josephson junctions with phase shifts

We study both analytically and numerically the localized modes in long Josephson junctions with phase shift formations, so-called \(0{-}\pi {-}0\) and \(0{-}\kappa \) junctions. The system is described by an inhomogeneous sine-Gordon equation with a variety of time-periodic drives. Perturbation technique, together with multiple-scale expansions, is applied to obtain the amplitude of oscillations. It is observed that the obtained amplitude equations decay with time due to radiative damping and emission of high harmonic radiations. It is also observed that the energy taken away from the internal mode by radiation waves can be balanced by applying either direct or parametric drives. The appropriate external drives are applied to re-balance the dissipative and radiative losses. We discuss in detail the excitation by direct and parametric drives with frequencies to be either in the vicinity or double the natural frequency of the system. It is noted that the presence of external applied drives stabilizes the nonlinear damping, producing stable breather modes in long Josephson junctions. It is also noted that in the presence of parametric drives, the amplitudes of the driving forces are much more sensitive than in the case of external ac drives; that is, in the case of parametric drives, a small change in the amplitudes of the driving forces can make a drastic change in the system behavior and the system becomes unstable as compared to the case of the direct ac driving. Furthermore, we noticed that, in the presence of external driving, the driving effect is stronger for the case of driving frequency nearly equal to the system frequency as compared to that of the driving frequency nearly equal to twice the frequency of the oscillatory mode.