幂率流体圆管非定常流动的数值分析

本文讨论水平圆管中幂率流体的起动问题。用显式和隐式两种格式,我们得到了问题的数值解并从而得到流动建立时间的近似公式。     

A finite element explicit algorithm for solving the temporal temperature fields

Practical calculations and numerical experiments in this paper have shown that in elements relating to a common node it is acceptable and reasonable for derivaties of temperature with respect to time on nodes of those elements to be presented with one on common node, if linear interpolation shape function is taken. The relation between the derivative of temperature to time on a certain node and the temperature on other nodes around that node may therefore be established after discretization of the differential equation is made in space by the finite element method. Then an explicit scheme for calculating the temperature fields may be constructed. The obtained algebraic equations. being simple and the procedure being straight will be its two tangible advantages and its calculating will, therefore, be fast. The stability analysis by the maximum principle, as in the example quoted, proves that the stability condition is similar to that in implicit algorithms.     

Steady and modulated flow of an Ostwald fluid around a rotating disk

The solutions of the continuity equation and the equations of motion of the flow in the vicinity of a rotating disk have been established for an Ostwald fluid under steady-state conditions and in modulated flow around a mean value. Under steady-state conditions, the kinematics of the flow is scarcely dependent on the rheological parameters close to the disk, however, for n < 1 long-range effects have been put forward. For modulated flow, in the high-frequency range, a behaviour very different from that observed for a Newtonian fluid was found. In the low-frequency range an asymptotic solution has been proposed which is of special interest in mass transfer problems.Presented at the Second Conference of European Rheologists, Prague, June 17–20, 1986     

Averaging methods for numerical simulations of flows through heterogeneous porous media

Many natural rock systems contain small patches of different permeability which affect the flow of fluids through them. As these heterogeneities become smaller and more numerous, they become harder to model numerically. We consider how to reduce the computational effort required in simulations by incorporating their effects in the boundary conditions at the edges of each grid block. This is in contrast with current methods which involve often arbitrary changes in the fluid properties. The method is restricted to the case of widely-spaced patches, which simplifies interaction effects. The system then reduces to an array of dipoles, and two averaging methods are proposed for finite grid blocks. Several infinite systems, including vertical and horizontal bands, are also considered as further approximations. There is a great wealth of existing results from different fields which lead to identical mathematical problems and which can be used in these cases. Finally, we consider how to use these techniques when the precise configuration of the grid block is not known, but only its statistical properties. This can lead to results which are very different from the deterministic case.     

Response of an elastic Bingham fluid to oscillatory shear

The response of an elastic Bingham fluid to oscillatory strain has been modeled and compared with experiments on an oil-in-water emulsion. The newly developed model includes elastic solid deformation below the yield stress (or strain), and Newtonian flow above the yield stress. In sinusoidal oscillatory deformations at low strain amplitudes the stress response is sinusoidal and in phase with the strain. At large strain amplitudes, above the yield stress, the stress response is non-linear and is out of phase with strain because of the storage and release of elastic recoverable strain. In oscillatory deformation between parallel disks the non-uniform strain in the radial direction causes the location of the yield surface to move in-and-out during each oscillation. The radial location of the yield surface is calculated and the resulting torque on the stationary disk is determined. Torque waveforms are calculated for various strains and frequencies and compared to experiments on a model oil-in-water emulsion. Model parameters are evaluated independently: the elastic modulus of the emulsion is determined from data at low strains, the yield strain is determined from the phase shift between torque and strain, and the Bingham viscosity is determined from the frequency dependence of the torque at high strains. Using these parameters the torque waveforms are predicted quantitatively for all strains and frequencies. In accord with the model predictions the phase shift is found to depend on strain but to be independent of frequency.Notation A plate strain amplitude (parallel plates) - A _R plate strain amplitude at disk edge (parallel disks) - G elastic modulus - m torque (parallel disks) - M normalized torque (parallel disks) = 2m/R ³₀ - N ratio of viscous to elastic stresses (parallel plates) =µ A/ ₀ ratio of viscous to elastic stresses (parallel disks) =µ A _R/₀ - r normalized radial position (parallel disks) =r/R - r radial position (parallel disks) - R disk radius (parallel disks) - t normalized time = t — /2 - t time - _E elastic strain - _P plate strain (displacement of top plate or disk divided by distance between plates or disks) - _PR plate strain at disk edge (parallel disks) - ₀ yield strain - _E normalized elastic strain = _E/₀ - _P normalized plate strain = _P/₀ - _PR normalized plate strain at disk edge (parallel disks) = _PR/₀ - ₀ normalized plate strain amplitude (parallel plates) =A/ ₀ — normalized plate strain amplitude at disk edge (parallel disks) =A _R/₀ - phase shift between _P andT (parallel plates) — phase shift between _PR andM (parallel disks) - µ Bingham viscosity - stress - ₀ yield stress - T normalized stress =/ ₀ - frequency     

Some further observations on the creeping motion of spheres through Ellis model fluids

Using the formulation of Hopke and Slattery, upper and lower bounds on the drag coefficient of a sphere moving slowly in Ellis model fluids have been calculated, over wide range of conditions, and compared with the suitable experimental data available in the literature. C _D drag coefficient - d diameter of sphere - El Ellis number - Re Reynolds number based on zero-shear viscosity - V terminal falling velocity of a sphere - X drag correction factor - Ellis model parameter - ₀ zero-shear viscosity - _1/2 Ellis model parameter     

Computational and experimental studies of convective fluid motion and heat transfer in inclined non-rectangular enclosures

Computational and experimental studies of the fluid motion and heat transfer characteristics of an incompressible fluid contained in a non-rectangular inclined enclosure are described in this paper. The enclosure has two 45° inclined side walls one of which was heated and the other cooled. The remaining two sides of the enclosure are parallel and insulated. The enclosure was rotated about the long axis in steps of 30° through 360°. Experiments were performed to study the effects of Rayleigh number, aspect ratios and orientation of the enclosure. The computational method uses a mesh transformation technique coupled with the introduction of ‘false transient’ parameters for the steady state solution of the problem. The experimental method uses smoke for flow visualization studies. With aspect ratios of 3 and 6, the results indicate that the heat transfer and fluid motion within the enclosure is a strong function of both the Rayleigh number and the cavity orientation angle. A minimum and a maximum mean Nusselt number occurred as the angle of inclination was increased from 0 to 360°. A transition in the mode of circulation occurred at the angle corresponding to the minimum or maximum rate of heat transfer. Stream lines and isotherms are presented for the most representative cases     

Flow of viscoelastic fluid between confocal elliptic cylinders

Summary Using elliptic coordinates, the flow pattern of a fluid of grade four between two elliptic tubes is determined. A comparison between the position of the maximum of the axial velocity in the present case and in the case of two concentric circular tubes shows a basic difference. In the elliptic case the maximum is shifted towards the external wall, while in the case of concentric circular tubes the shift is in the direction of the internal wall. The secondary flow shows dissymmetry with reference to the intermediate line , which itself lies nearer to the external wall.

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Zusammenfassung Unter Benutzung elliptischer Koordinaten wird die Strömung zwischen zwei elliptischen Rohren bestimmt. Ein Vergleich zwischen der Lage des axialen Geschwindigkeitsmaximums im vorliegenden Fall und im Fall zweier konzentrischer Kreisrohre ergibt einen grundsätzlichen Unterschied: Das Maximum ist im elliptischen Fall zur äußeren Wand hin verschoben, während die Verschiebung im Fall der konzentrischen Kreisrohre zur inneren Wand hin erfolgt. Die Sekundärströmung ist unsymmetrisch relativ zur mittleren Stromlinie , die selbst näher zur äußeren Wand liegt.

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A planar domain representing the annular region - vector inx ₁,x ₂-plane - x _i rectangular coordinates - rectangular unit vectors - , elliptic coordinates - ₁, ₂ ellipses representing respectively the internal and external tubes - = ₂ – ₁ annular widthy = ( – ₁)/ - µ 1^st grade material constant - _i 2^nd grade material constants - _i 3^rd grade material constants - _i 4^th grade material constants - I unit tensor - T _E extra stress (T + pI) - V potential of body forces - material density = (p/) + V = –ax ₃ + () - a specific driving force - arbitrary scalar function - A _k Rivlin-Eriksen tensors - S stress scalar defined onA - t stress vector defined onA - P stress tensor defined onA - v axial velocity - v _i i ^th term in the approximation ofv - u velocity vector perpendicular to the axis 4( ₃ + ₄ + ₅ + 1/2₆) –2/µ(2 ₁ + ₂)( ₂ + ₃) - T stress tensor - p arbitrary hydrostatic pressure - u _i i ^th term in the approximation ofu - stream function definingu - _i i ^th term in the approximation of With 8 figures and 1 table     

半球蓝宝石整流罩制造技术研究

整流罩在高速飞行中既要对空气进行整流,同时又起光学窗口的作用。蓝宝石材料硬度高,加工非常困难。分别从精磨模、精磨磨料、抛光膜层、抛光辅料、机床速度和压力等方面介绍了一种加工蓝宝石整流罩的工艺方法。     

Laurdan in Fluid Bilayers: Position and Structural Sensitivity

Laurdan (2-dimethylamino-6-lauroylnaphthalene) is a hydrophobic fluorescent probe widely used in lipid systems. This probe was shown to be highly sensitive to lipid phases, and this sensitivity related to the probe microenvironment polarity and viscosity. In the present study, Laurdan was incorporated in 1,2-dipalmitoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DPPG), which has a phase transition around 41°C, and DLPC (1,2-dilauroyl-sn-glycero-3-phosphocholine), which is in the fluid phase at all temperatures studied. The temperature dependence of Laurdan fluorescent emission was analyzed via the decomposition into two gaussian bands, a short- and a long-wavelength band, corresponding to a non-relaxed and a water-relaxed excited state, respectively. As expected, Laurdan fluorescence is highly sensitive to DPPG gel–fluid transition. However, it is shown that Laurdan fluorescence, in DLPC, is also dependent on the temperature, though the bilayer phase does not change. This is in contrast to the rather similar fluorescent emission obtained for the analogous hydrophilic probe, Prodan (2-dimethylamino-6-propionylnaphthalene), when free in aqueous solution, over the same range of temperature. Therefore, Laurdan fluorescence seems to be highly dependent on the lipid bilayer packing, even for fluid membranes. This is supported by Laurdan fluorescence anisotropy and spin labels incorporated at different positions in the fluid lipid bilayer of DLPC. The latter were used both as structural probes for bilayer packing, and as Laurdan fluorescence quenchers. The results confirm the high sensitivity of Laurdan fluorescence emission to membrane packing, and indicate a rather shallow position for Laurdan in the membrane.