Mie-Grneisen状态方程可压缩多流体流动的PPM方法

采用流体体积分数的混合型多流体数值模型，将piecewise parabolic method (PPM)方法应用于可压缩多流体流动的数值模拟，拓展了以前提出的模型和数值方法，使它能够处理一般的Mie-Grneisen状态方程。采用双波近似和两层迭代算法求解一般状态方程的Riemann问题；并根据多流体接触界面无振荡原则设计高精度计算格式，对典型的纯界面平移问题可以从理论上证明本算法在接触间断附近压力和速度没有振荡，而且数值模拟结果表明界面数值耗散也被控制在2~3个网格之内。模拟了多种复杂的可压缩多流体流动，算例结果表明本文方法可以有效地处理接触间断、激波等物理问题，且具有耗散小精度高的特点。     

The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions

We study shear banding flows in models of wormlike micelles or polymer solutions, and explore the effects of different boundary conditions for the viscoelastic stress. These are needed because the equations of motion are inherently non-local and include “diffusive” or square-gradient terms. Using the diffusive Johnson–Segalman model and a variant of the Rolie-Poly model for entangled micelles or polymer solutions, we study the interplay between different boundary conditions and the intrinsic stress gradient imposed by the flow geometry. We consider prescribed gradient (Neumann) or value (Dirichlet) of the viscoelastic stress tensor at the boundary, as well as mixed boundary conditions in which an anchoring strength competes with the gradient contribution to the stress dynamics. We find that hysteresis during shear rate sweeps is suppressed if the boundary conditions favor the state that is induced by the sweep. For example, if the boundaries favor the high shear rate phase then hysteresis is suppressed at the low shear rate edges of the stress plateau. If the boundaries favor the low shear rate state, then the high shear rate band can lie in the center of the flow cell, leading to a three-band configuration. Sufficiently strong stress gradients due to curved flow geometries, such as that of cylindrical Couette flow, can convert this to a two-band state by forcing the high shear rate phase against the wall of higher stress, and can suppress the hysteresis loop observed during a shear rate sweep.     

Steady flow of a maxwell fluid in a porous cylindrical annulus with circular cross-section

Summary When a fluid with memory is injected into any flow region some assumptions regarding the initial state of stress have to be made in order to determine the state of stress at any subsequent instant. For a Maxwell fluid, it is assumed that the fluid near the surface of injection is suddenly stressed and responds by starting flow in accordance with the mechanical model chosen. The flow of a Maxwell fluid with a single relaxation time has been determined under the above assumption in the following two cases: (i) annulus between two porous concentric circular cylinders, and (ii) space between two porous and infinitely extending parallel plates. The nature of flow in the present case is similar to that of the Reiner-Rivlin fluids obtained by Narasimhan²).     

A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders

The behavior of vortices induced by a pair of side-by-side square cylinders in an oscillating flow is investigated using an in-house numerical model. The study is carried out for various Keulegan–Carpenter numbers, Reynolds numbers, and cylinder gap spacings. For an oscillating flow past a pair of side-by-side cylinders, the gap ratio plays a vital role in the flow pattern. A jet-like structure is observed when fluid flows through the gap. Moreover, the gap promotes the earlier appearance of asymmetric vortex shedding. In-line force and lift force coefficients of two square cylinders are analyzed using spectral analysis. An autocorrelation function is used to determine the relation between flow patterns around two cylinders. These results demonstrate the transition of the flow field from the periodic state to the chaotic state.     

Macroscopic Two-phase Flow in Porous Media Assuming the Diffuse-interface Model at Pore Level

The paper presents a model for two-phase flow, where liquid and gas are treated as one fluid with variable density. A one-component fluid and the diffuse-interface model for two-phase flow are assumed at pore level. The wetting properties of the fluid are described by the Cahn theory. Macroscopic equations are deduced in the framework of the Marle formalism. It is shown that two-phase flow in porous media can be described by the Cahn–Hilliard equation for the mass density. The concept of relative permeability is not needed. For non-neutral wetting, it is shown that a capillary pressure exists but that it is not a function of state. Two numerical illustrations are presented, one of them showing that the model is, at least in a simple steady-state situation, compatible with the generalized two-continuum model.     

Probability model of solid to liquid-like transition of a fluid suspension after a shear flow onset

The complexity of interactions of different origin between particles in dense fluid suspensions limits application of the concepts of classical mechanics for finding a relation between individual particles dynamics, and the macroscopic dynamic response. For this reason, the probability model of suspension flow after a shear flow onset is proposed that incorporates our certain lack of understanding of environments effects. These effects are identified in the model with the random rate of particles arrival to flow. The multiplication rule is used to sweep from the individual particles to the entire system. The resulting probability of the system shift to flow represents well the measured boundary position, separating the flowing suspension from its solid-like state, and proves thus the appropriate choice of representation of the particle interaction effects.     

Transient solution for flow of evaporating fluid in parallel pipes using analysis based on flow patterns

Flow with evaporation in parallel lines with common inlet and outlet headers may result in an uneven flow distribution among the parallel pipes. The prediction of the flow rate distribution in steady state as well as under transient conditions was based on simplified models. In this paper a more accurate time dependent model based on the temporal-local flow pattern in the pipe is presented. The pipe is subdivided into numerical sections and the calculation of the pressure drop in each cell is based on mechanistic models that are specific for the flow pattern in the cell.     

A multi-mechanism model for cutting simulations combining visco-plastic asymmetry and phase transformation

We develop a multi-mechanism model for strainrate- and temperature-dependent asymmetric plastic material behavior accompanied by phase transformations, which are important phenomena in steel production processes. To this end the well-known Johnson–Cook model is extended by the concept of weighting functions, and it is combined with a model of transformation-induced plasticity (TRIP) based on Leblond’s approach. The bulk model is formulated within a thermodynamic framework at large strains, and it will be specialized and applied to cutting processes in steel production. In this prototype situation we have: Transformation of the martensitic initial state into austenite, then retransformation of martensite. For incorporation of visco-plastic asymmetry two variations of the classical Johnson–Cook model are presented: In “Model A” we introduce a rate dependent flow factor with a rate independent yield function. In “Model B” we introduce a rate independent flow factor with a rate dependent yield function. In the examples parameters are identified for the material DIN 100Cr6, and we illustrate the characteristic effects of our multimechanism model, such as strain softening due to temperature, rate dependence and temperature dependence as well as the SD-effect. A finite-element simulation illustrates the different mechanisms for a cutting process.     

Lattice modelling of nematodynamics

The microstructures of textured nematics under shear are investigated by means of a director lattice model incorporating linear shear response as well as elastic interactions between neighbouring directors. The model can be understood as a lattice implementation of the so-called nematodynamics equation for a constant uniaxial order parameter. The dimensionless number governing the model is found to be a mesoscale Ericksen number, which scales with the square of the lattice cell size. It is shown that the predicted microstructure depends strongly on the scale of that number. In particular, disclination loops are found to grow for a range of mesoscale Ericksen numbers, while below or above that they disappear. We apply the model to investigate the director profiles of tumbling nematics. If the orientations are restricted to lying in the vorticity plane, we reproduce the director wind-up layers and distortion saturation predicted theoretically. In the full three-dimensional case an initially polydomain director field evolves to a vorticity-aligned state up to a critical Ericksen number, above which in-plane orientations with distortion saturation are found. The simulations hence reproduce the transition from log-rolling to flow aligning with increasing shear rate observed experimentally. Received: 9 March 1999 /Accepted: 26 July 1999     

非均匀颗粒材料的类固-液相变行为及本构方程

以非均匀颗粒介质为研究对象,采用三维离散元方法对其在不同密集度和剪切速率下的动 力过程进行了数值模拟,分析了其在由瞬时接触的快速流动向持续接触的准静态流动的转变 过程及其行为特点. 通过对不同材料性质下相变过渡区内颗粒材料的宏观应力、接触时间数、 配位数、团聚颗粒数量、有效摩擦系数等参量的计算,更加全面地描述了非均匀颗粒材料在 类固-液相变过程中的基本特征. 基于以上数值计算结果,建立了一个适用于颗粒材料 类固态、类液态以及其相变过程的本构方程,并通过剪切室实验结果验证了它的合理性.     

Unsteady-state development of plane couette flow for viscoelastic fluids

Unsteady-state development of plane Couette flow for viscoelastic fluids is analyzed using a constitutive equation that can be obtained from molecular theory, in which the molecules are regarded as finitely extensible dumbbells. Typical features of the flow situation are as follows: (i) For a fluid with moderate elasticity, not only stress overshoot but also velocity overshoot are predicted. (ii) For suitable combinations of elasticity and gap width, and for some time intervals stress propagation and reflection phenomena are predicted. (iii) After a sufficient time has elapsed, the stress state behaves similarly to that corresponding to the start-up of a steady simple shear flow.     

The effects of forced boundary conditions on flow within a cubic cavity using digital particle image thermometry and velocimetry (DPITV)

Buoyancy-driven convection within a cavity, whose sidewalls are heated and cooled, is a problem of great interest, because it has applications in heat transfer and mixing. Most studies to date have studied one of two cases: the steady-state case or the development of the transient flow as it approaches steady state. Our main concern was to study the response of the cavity to time-varying thermal boundary conditions. We therefore decided to observe the flow phenomena within a convection cavity under sinusoidal thermal forcing of the sidewalls. To map the flow properly, it is necessary to have simultaneous kinematic and thermal information. Therefore, the digital particle image thermometry and velocimetry (DPITV) is used to acquire data. Implementing this technique requires seeding the flow with encapsulated liquid crystal particles and illuminating a cross section of the flow with a sheet of white light. Extraction of the thermal and kinematic content is in two parts. For the first, the liquid crystals will reflect different colors of the visible spectrum, depending on the temperatures to which they are subjected. Therefore, calibrating their color reflection with temperature allows for the extraction of the thermal content. For the second part, the kinematic information is obtained through the use of a digital cross-correlation particle image velocimetry technique. With the use of DPITV, the flow within a convection cavity is mapped and studied under steady forcing and sinusoidally forced boundary conditions at the Brunt-Väisälä frequency. For the sinusoidally forced case, three cases are studied. In the first, the heating between the two walls is in phase. In the second, the heating between the two walls is 180° out of phase. In the third, the heating between the two walls is 90° out of phase. For steady forcing, the thermal plots show that the flow develops a linearly stratified profile within the center of the cell. At the sidewalls, however, owing to forcing, hot/cold thermal boundary layers develop at the left/right walls. These hot/cold thermal boundary layers then turn around the upper-left/lower-right corners and develop into intrusion layers that extend across the top and bottom walls. The vorticity and streamlines show that the bulk of the fluid motion is concentrated around the walls, whereas the fluid within the center of the cell remains stationary. For the sinusoidally forced cases, the thermal plots show the existence of many thermal “islands,” or pockets of fluid where the temperature is different with respect to its surroundings. The vorticity plots show that the center of the cell is mostly devoid of vorticity and that the vorticity is mainly confined to the sidewalls, with some vorticity at the top and bottom walls. For the 0° forcing, the streamlines show the development of two counterrotating rollers. For the 180° forcing, the streamlines show the development of only one roller. Finally, for the 90° forcing, the streamlines show the development of both a two-roller and a one-roller system, depending on the position within the forcing cycle.     

Viscoelastic properties of durum wheat and common wheat dough of different strengths

Linear viscoelastic properties (LVP) were determined for five durum wheat doughs and five common wheat doughs (representing four different classes of Canadian common wheat) of different strength using creep testing. A creep time of 10,000 s was sufficient to reach a state of steady state flow for all of the doughs. Creep compliances were analyzed in terms of a Burgers model. For the durum doughs, the entire elastic compliance curve was shifted to higher values as the strength of the dough (as measured by extensigraph) decreased, while the steady state viscosity increased with strength. For common wheat doughs, the elastic compliance curves were steeper and the steady state viscosities were lower than for durum doughs of comparable extensigraph strength. The retardation strengths associated with a maximum in the retardation spectra were lower for the stronger durum doughs than for common wheat doughs of comparable strength. Differences in the LVP between durum and common wheat doughs of similar extensigraph strength were interpreted in the context of physical gels with crosslinks and entanglements, whose contributions to material properties are difficult to distinguish in short-time creep or dynamic measurements. The increased extensibility of common wheat doughs relative to durum doughs of comparable extensigraph strength was attributed to a higher molecular weight fraction in the polypeptide chains, similar in some respects to end-linked bimodal polymer networks. The idea of considering these doughs as physical gels was supported by their stress relaxation behavior. Received: 6 February 2000 Accepted: 22 August 2000     

考虑微观结构特征长度演化的内变量黏塑性本构模型

在金属晶体材料高应变率大应变变形过程中,存在强烈的位错胞尺寸等微观结构特征长度细化现象,势必对材料加工硬化、宏观塑性流动应力产生重要影响。基于宏观塑性流动应力与位错胞尺寸成反比关系,提出了一种新型的BCJ本构模型。利用位错胞尺寸参数,修正了BCJ模型的流动法则、内变量演化方程,引入了考虑应变率和温度相关性的位错胞尺寸演化方程,建立了综合考虑微观结构特征长度演化、位错累积与湮灭的内变量黏塑性本构模型。应用本文模型,对OFHC铜应变率在10-4~103 s-1、温度在298~542 K、应变在0~1的实验应力-应变数据进行了预测。结果表明:在较宽应变率、温度和应变范围内,本文模型的预测数据与实验吻合很好;与BCJ模型相比,对不同加载条件下实验数据的预测精度均有较大程度的提高,最大平均相对误差从9.939%减小为5.525%。     

Applications of a higher‐order bounded numerical scheme to turbulent flows

This paper applies the higher‐order bounded numerical scheme Weighted Average Coefficients Ensuring Boundedness (WACEB) to simulate two‐ and three‐dimensional turbulent flows. In the scheme, a weighted average formulation is used for interpolating the variables at cell faces and the weighted average coefficients are determined from a normalized variable formulation and total variation diminishing (TVD) constraints to ensure the boundedness of the solution. The scheme is applied to two turbulent flow problems: (1) two‐dimensional turbulent flow around a blunt plate; and (2) three‐dimensional turbulent flow inside a mildly curved U‐bend. In the present study, turbulence is evaluated by using a low‐Reynolds number version of the k–ω model. For the flow simulation, the QUICK scheme is applied to the momentum equations while either the WACEB scheme (Method 1) or the UPWIND scheme (Method 2) is used for the turbulence equations. The present study shows that the WACEB scheme has at least second‐order accuracy while ensuring boundedness of the solutions. The present numerical study for a pure convection problem shows that the ‘TVD’ slope ranges from 2 to 4. For the turbulent recirculating flow, two different mixed procedures (Method 1 and Method 2) produce a substantial difference for the mean velocities as well as for the turbulence kinetic energy. Method 1 predicts better results than Method 2 does, comparing the analytical solution and the experimental data. For the turbulent flow inside the mildly curved U‐bend, although the predictions of velocity distributions with two procedures are very close, a noticeable difference of turbulence kinetic energy is exhibited. It is noticed that the discrepancy exists between numerical results and the experimental data. The reason is the limit of the two‐equation turbulence model to such complex turbulent flows with extra strain‐rates. Copyright © 2001 John Wiley & Sons, Ltd.     

Three‐dimensional numerical simulation of red blood cell motion in Poiseuille flows

An immersed boundary method based on an FEM has been successfully combined with an elastic spring network model for simulating the dynamical behavior of a red blood cell (RBC) in Poiseuille flows. This elastic spring network preserves the biconcave shape of the RBC in the sense that after the removal of the body force for driving the Poiseuille flow, the RBC with its typical parachute shape in a tube does restore its biconcave resting shape. As a benchmark test, the relationship between the deformation index and the capillary number of the RBCs flowing through a narrow cylindrical tube has been validated. For the migration properties of a single cell in a slit Poiseuille flow, a slipper shape accompanied by a cell membrane tank‐treading motion is obtained for Re , and the cell mass center is away from the center line of the channel due to its asymmetric slipper shape. For the lower Re ?0.0137, an RBC with almost undeformed biconcave shape has a tumbling motion. A transition from tumbling to tank‐treading happens at the Reynolds number between 0.0137 and 0.03. In slit Poiseuille flow, the RBC can also exhibit a rolling motion like a wheel during the migration when the cell is released in the fluid flow with φ = π/2 and θ = π/2 (see Figure 12 for the definition of φ and θ). The lower the Reynolds number, the longer the rolling motion lasts; but the equilibrium shape and position are independent from the cell initial position in the channel. Copyright © 2014 John Wiley & Sons, Ltd.     

1‐D numerical modelling of shallow flows with variable horizontal density

A1‐D numerical model is presented for vertically homogeneous shallow flows with variable horizontal density. The governing equations represent depth‐averaged mass and momentum conservation of a liquid–species mixture, and mass conservation of the species in the horizontal direction. Here, the term ‘species’ refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealized simulation of hyper‐concentrated sediment‐laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to modify the flow structure. A Godunov‐type finite volume scheme is implemented to solve the conservation laws written in a deviatoric, hyperbolic form. The model is verified for variable‐density flows, where analytical steady‐state solutions are derived. The agreement between the numerical predictions and benchmark test solutions illustrates the ability of the model to capture rapidly varying flow features over uniform and non‐uniform bed topography. A parameter study examines the effects of varying the initial density and depth in different regions. Copyright © 2009 John Wiley & Sons, Ltd.     

A calculation method for blood flow velocity distribution in smallep elocd vessels

The calculative method presented in this paper is based on an improvement of boundary conditions for a micro-continuum fluid model with blood flow assuming that the blood cell velocity at blood vessel wall is unequal to zero. As for steady state flood flow equation (flow in vitre—a rigid circular tube) presented by Eringen, the magnitude of the blood cell gyroscopic velocity at blood vessel wall and the slope of the blood cell gyroscopic velocity distribution curve at the axis of the blood vessel are assumed. From the above mentioned assumptions the calculating method of velocity distribution curve in blood vessel is derived. The curve calculated by this method is compared with the test curve measured by Bugliarello and Hayden. The results obtained by Turk, Sylvester and Ariman as well as with this method are compared with each other, too.     

镜像对称顶盖驱动方腔内流过渡流临界特性研究

流场过渡流临界特性是指流场因流动状态改变而引起的流场物理特性变化. 如流动从定常演化为非定常周期性时, 流动处于过渡状态的物理性质. 它从根本上决定了流动演化模式和流场特性等物理规律, 对认清流动现象的形成机理有重要意义. 本文在之前腔体内流流场过渡流临界特性研究的基础上, 针对镜像对称顶盖驱动方腔内流开展数值模拟和流场稳定性分析研究, 捕捉各流动分岔点, 如Hopf流动分岔点和Neimark-Sacker流动分岔点等, 并揭示其对流场特性的影响; 分析流场演化模式, 随着雷诺数增大从定常状态依次演化为非定常周期性流动、准周期性流动和湍流; 揭示各种流动现象的形成机理, 如流动滞后、对称性破坏、能量级串等; 分析流场拓扑结构, 阐明流场镜像对称性和流场稳定性的关系. 本文研究成果有助于揭示该流场的物理特性, 进一步完善了内流流场特性的研究. 研究发现, 针对本文镜像对称方腔顶盖驱动内流, 流场稳定性的破坏总是以Hopf流动分岔点的出现而发生并且伴随着流场对称性的破坏; 流场演化模式符合经典的Ruelle-Takens模式; 流动从定常状态演化至非定常周期性流动时存在流动滞后现象.