层状两相流动的基本方程式

本文将两相流动的雷诺方程沿深度方向进行平均,出求了平均后的运动方程、连续方程和能量方程式,在适当的物理假定下,简化得到可适用于考虑固-液流动及气-液流动两种情况下的两相层状流动基本方程.     

Numerical solution of the turbulent flow of an incompressible fluid in curved planar and axially symmetrical channels

The governing equations for axially symmetric flow, where the Reynolds stresses are expressed by scalar turbulent viscosity, are the Reynolds equations. The turbulence model k, ? is used in the well-known form for fully developed turbulent flow.The numerical method, a continuation of the MAC system¹, is adapted so that even for high Reynolds cell numbers precision (δx²) can be achieved for the steady flow. Irregular cells join the rectangular network on the curved surface. Von Neumann's stability condition of the linearised numerical system is investigated. Special problems concerning the numerical solution of the turbulence model equations are stated and a special procedure is worked out to ensure that the fields k, ? do not converge to physically meaningless values. The program for the computer is universal in that the boundary problems can be assigned by input data.As an example, an axially symmetrical diffuser with an area ratio of widening 1.40 is computed. Fields of velocity and pressure at the wall as well as fields v_T and k are assessed. The results are compared with an experiment. The conclusion is that this method is suitable for the problems mentioned in this study as well as for unsteady flow.     

雷诺数对三角翼绕流的影响

应用染色液流动显示技术研究了雷诺数对６０°尖前缘三角翼前缘涡破裂位置、背风面流动结构等的影响，并详细分析了背风面流动随攻角的变化．     

Three‐dimensional transient free‐surface flow of viscous fluids inside cavities of arbitrary shape

The three‐dimensional transient free‐surface flow inside cavities of arbitrary shape is examined in this study. An adaptive (Lagrangian) boundary‐element approach is proposed for the general three‐dimensional simulation of confined free‐surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free‐surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free‐surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. The method is used to determine the flow field and free‐surface evolution inside cubic, rectangular and cylindrical containers. These problems illustrate the transient nature of the flow during the mixing process. Surface tension effects are also explored. Copyright © 2003 John Wiley & Sons, Ltd.     

Theoretical analysis of using airflow to purge residual water in an inclined pipe

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Simultaneous measurement of transient stress and flow birefringence in one-sided compression (biaxial extension) of a polymer melt

Summary Investigation of time dependent behaviour of a polystyrene melt is carried out with the aid of a new apparatus for biaxial extension. Use is made of the method of two impinging fluid streams guided by lubricated trumpet shaped metal walls. The flow birefringence is measured in the plane of symmetry and, at the same time, the force is measured which tends to separate the trumpets. The linear stress-optical relation turns out to be valid in this new flow geometry. An accurate value for the stress-optical coefficient can be determined from the relaxation experiments. The stress build-up as calculated from the optical measurements, is compared with the pertinent result of the theory of linear viscoelasticity. For the desired interconversion of dynamic moduli use is made of the approximation by Schwarzl and Struik. The steady state measurements are checked by the results of the non-linear model of Acierno et al.With 16 figures and 2 tables     

高超声速层流尾迹的数值模拟

本文利用无波动、无自由参数、耗散的差分格式(NND格式),通过求解NS方程,数值模拟了高超声速层流尾迹的流动,清晰地给出了主激波、拐角膨胀波、迹激波及自由剪切层,所得流场物理量的分布与实验结果甚为一致。计算发现了底部迴流区由起始向定常的发展中,在瞬时流线图上经历了极限环形成、胀大、缩小、再胀大最后消失的演变过程。     

Gas-particle two-phase turbulent flow in a vertical duct

Two-phase gas-phase turbulent flows at various loadings between the two vertical parallel plates are analyzed. A thermodynamically consistent turbulent two-phase flow model that accounts for the phase fluctuation energy transport and interaction is used. The governing equation of the gas-phase is upgraded to a two-equation low Reynolds number turbulence closure model that can be integrated directly to the wall. A no-slip boundary condition for the gas-phase and slip-boundary condition for the particulate phase are used. The computational model is first applied to dilute gas-particle turbulent flow between two parallel vertical walls. The predicted mean velocity and turbulence intensity profiles are compared with the experimental data of Tsuji et al. (1984) for vertical pipe flows, and good agreement is observed. Examples of additional flow properties such as the phasic fluctuation energy, phasic fluctuation energy production and dissipation, as well as interaction momentum and energy supply terms are also presented and discussed.

Applications to the relatively dense gas-particle turbulent flows in a vertical channel are also studied. The model predictions are compared with the experimental data of Miller & Gidaspow and reasonable agreement is observed. It is shown that flow behavior is strongly affected by the phasic fluctuation energy, and the momentum and energy transfer between the particulate and the fluid constituents.     

Boundary layer development of pulsatile blood flow in a tapered vessel

Assuming that the tapered angle is small,the problems of developing flow under unsteady oscillatory condition are studied in this paper.The formula of velocity distribution is obtained.The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length,and the effects of tapered angle on the developing flow are increased with the increment of the tapered angle.     

Transient effects of orthogonal pipe oscillations on laminar developing incompressible flow

This paper presents a numerical study of the transient developing laminar flow of a Newtonian incompressible fluid in a straight horizontal pipe oscillating around the vertical diameter at its entrance. The flow field is influenced by the tangential and Coriolis forces, which depend on the through‐flow Reynolds number, the oscillation Reynolds number and the angular amplitude of the pipe oscillation. The impulsive start of the latter generates a transient pulsating flow, whose duration increases with axial distance. In any cross‐section, this flow consists of a pair of symmetrical counter‐rotating vortices, which are alternatively clockwise and anti‐clockwise. The circumferentially averaged friction factor and the axial pressure gradient fluctuate with time and are always larger than the corresponding values for a stationary pipe. On the other hand, local axial velocities and local wall shear stress can be smaller than the corresponding stationary pipe values during some part of the pipe oscillation. The fluctuation amplitude of these local variables increases with axial distance and can be as high as 50% of the corresponding stationary pipe value, even at short distances from the pipe entrance. Eventually, the flow field reaches a periodic regime that depends only on the axial position. The results show that the transient flow field depends on the pipe oscillation pattern (initial position and/or direction of initial movement). Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of two-phase flow of compressible immiscible fluids through nondeformable porous media using moving finite elements

A system of evolutionary partial differential equations (PDEs) describing the two-phase flow of immiscible fluids in one dimension is developed. In this formulation, the wetting and nonwetting phases are treated to be incompressible and compressible, respectively. This treatment is indeed necessary when a compressible nonwetting phase is subjected to compression during confinement. The system of PDEs consists of an evolution equation for the wetting-phase saturation and an evolution equation for the pressure in the nonwetting phase. This system is applied to the problem of unsaturated flows to assess the importance of air-phase compressibility. For those situations where air can move freely within the medium and ultimately escape through the boundaries without experiencing any compression, it is then reasonable to treat air as an incompressible phase so that the total volumetric flux becomes spatially invariant. As shown by Morel-Seytoux and Billica, this leads to a coupled evolution equation for water saturation and an integral expression for total volumetric flux. In the event that an air phase is subjected to confinement in some manner, the total volumetric flux cannot be assumed to be spatially invariant as did Morel-Seytouxet al.The system of evolutionary PDEs developed in the present paper are precise and uniformly valid in time and space and, more importantly, smoothly accommodate a nonwetting phase whose state may change from unconfined to confined during the course of the flow process and vice-versa. Consequently, the complete system of PDEs may be used to analyze unsaturated flows in a straightforward manner.Depending on the initial and boundary conditions, the solutions to the system of PDEs may develop steep gradients near the wetting front. For this reason, the moving finite element (MFE) method introduced by Miller and Miller in conjunction with Gear's implicit stiff temporal solver provides an automatic and powerful scheme suitable for the initial-boundary value-problem (IBVP) developed herein.     

应用小干扰柱体控制角区马蹄涡结构的实验研究

本文提出一种简单的抑制和控制角区马蹄涡的被动控制方法.即在角区平板上游放置一个远小于主柱体的小干扰柱体,用其产生的弱马蹄涡来抑制和控制角区的马蹄涡结构.目的是使角区原来的马蹄涡结构由强变为弱、由大变为小、由多变为少、由非定常变为定常,以获得减小冲刷、抑制湍流、降低噪声、避免振动的工程效果.作者在风洞中采用烟线法和激光片光流动显示的方法开展研究,实验表明,在平板上游适当位置放置小干扰柱体的确可以有效抑制和控制角区马蹄涡结构.实验发现,当小干扰柱体放置在原角区马蹄涡生成区时,其抑制和控制效果最佳;当小干扰柱体放置在上游区或下游区时,控制效果不好.本文讨论了小干扰柱体控制角区马蹄涡的机理.此外,实验还研究了小干扰柱体相对尺度和截面形状对角区马蹄涡结构抑制和控制的影响.     

An investigation of adiabatic spiral vortex flow by means of cross-wire probes

Flow transitions occurring with increase in the Taylor number in an annular gap of radius ratio 0.8, having an imposed axial flow of air of Reynolds number 500 have been studies using the output from a cross-wire probe in a complex digital analysis. Cross and phase spectra, together with auto and cross correlograms, are presented for four Taylor numbers from 10 620 to 12.2 × 10⁶, covering the onset of vortex flow, chaotic flow and turbulent vortex flow. As the Taylor number increases, there is little alteration in the spiral vortex flow in the axial and tangential directions, which oscillates in phase in these two directions. The tangential velocity gradient was seen to become increasingly dominant, with increase in the Taylor number     

双圆诱导不可压缩势流的几个精确解

Lagally(1929)给出了两个静止圆在均匀来流中的扰动速度势精确解。本文通过使用 Apollonius 保角变换,将两圆外部区域变为圆环内部区域,并在变换平面上用 Fo-urier 级数方法求解 Laplace 方程,从而得出双圆扰动势流的另外三个精确解。它们分别对应于静止流体中两圆膨胀(收缩)、沿连心线相向(相背)运动和垂直连心线反向运动(错动)所诱导的速势场。     

Numerical simulation of the onset of slug initiation in laminar horizontal channel flow

Results are presented for the initiation of slug-type structures from stratified 2D, two-layer pressure-driven channel flow. Good agreement is obtained with an Orr–Sommerfeld-type stability analysis for the growth rate and wave speed of very small disturbances. The numerical results elucidate the non-linear evolution of the interface shape once small disturbances have grown substantially. It is shown that relatively short waves (which are the most unstable according to linear theory) saturate when the length of the periodic domain is equally short. In longer domains, coalescence of short waves of small-amplitude is shown to lead to large-amplitude long waves, which subsequently exhibit a tendency towards slug formation. The non-uniform distribution of the interfacial shear stress is shown to be a significant mechanism for wave growth in the non-linear regime.     

Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.     

A formulation of PANS capable of mimicking IDDES

The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes $f_k$ which denotes the ratio of modeled to total kinetic energy. In RANS, $f_k=1$ while in DNS it tends to zero. In the present study we propose an improved formulation for $f_k$ based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of $f_k$ is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) “detect” laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.     

An analytic solution of dense two-phase flow in a vertical pipeline

According to a mathematical model for dense two-phase flows presented in theprevious paper,a dense two-phase flow in a vertical pipeline is analytically solved,and theanalytic expressions of velocity of each continuous phase and dispersed phase arerespectively derived The results show that when the drag force between two phases dependslinearly on their relative velocity,the relative velocity profile in the pipeline coincides withDarcy’s law except for the thin layer region near the pipeline wall,and that the theoreticalassumptions in the dense two-phase flow theory mentioned are reasonable.     

空间模式下可压缩气固两相混合层流动特性研究

采用Euler-Lagrange颗粒-轨道双向耦合模型对空间模式下含有固粒的二维可压缩混合层流场进行了研究。气相流场采用具有空间三阶精度的WNND格式进行数值模拟,固相方程采用单边三点差分离散。在考虑流场对固粒作用的同时,也计及了固粒对流场的反作用。在对流马赫数为0.5时,研究了颗粒相对密度、颗粒尺寸、Stokes数等因素对粒子运动和流场结构的影响。研究结果表明:在可压缩空间模式混合层中,固粒的Stokes数仍然是主要影响参数之一;相同Stokes数下不同密度的固粒对流场的干扰不同,轻固粒对流场的干扰明显要小。