瞬态加速液柱的流体力学问题研究

介绍了用激波和压缩气体加速液柱时的流体动力现象的实验研究,实验中采用了高速摄影技术。研究分为两部分:第一部分,液柱在被加速后在管内的气/液两相流的发展以及流出管外后喷雾流的形成,喷雾流自下而上产生;第二部分,气/液界面上的流体力学不稳定性,即Rayleigh Taylor(RT)不稳定性及Richt myer Meshkov(RM)不稳定性,液柱自上而下运动。实验发现,用此方法产生的喷雾具有流量大、射程远、覆盖面积大等特点。液柱在管内的加速过程中,上端面保持平面,下端面在经历了初始的不稳定性之后形成弹状流。在本实验的驱动压力及马赫数的范围内,RT和RM不稳定性的后期的发展过程比较接近,尽管两者的增长率不同。在RT不稳定性的初始阶段,高密度流体的尖钉先伸入低密度流体中;但是,在RM不稳定性的初始阶段,低密度的气泡先伸入高密度流体中。     

Air-cooled gas-turbine discs: a review of recent research

The flow between corotating compressor or turbine discs and the flow between a turbine disc and an adjacent stationary casing can be respectively modelled by a rotating cavity and by a rotor-stator system. This paper reviews some of the recent experimental and theoretical work on flow and heat transfer in these two classes of rotating-disc systems. Comparisons between the theoretical and measured distributions of velocity, pressure, and Nusselt numbers are made for the rotating cavity with a superimposed radial flow of cooling air. For the rotor-stator system, some recent work on the fluid dynamics is outlined, and particular mention is made of the so-called “ingress problem” and of the use of pre-swirl air to improve the blade-cooling effectiveness.     

Modelling of turbulent flow in gas-turbine blading: achievements and prospects

Some of the problems associated with applying currently available viscous flow calculation schemes to turbulent flow in gas-turbine blading and passages are reviewed. These flows pose severe difficulties in both numerics and turbulence modelling, although the main emphasis here is on the latter aspect. Since complex strain fields and strong body forces are an intrinsic part of flow in turbomachinery, it is preferable that the turbulence modelling of these flows be based on an approximation of the Reynolds stress transport equations themselves. Some current views on closure approximations for these equations are discussed. Applications considered include the effects of free stream turbulence and streamline curvature, the mixing of blade wakes, and the three-dimensional flows that arise in a 90° bend and in the corner boundary layer near a blade root     

Exact solutions of a dipolar fluid flow

Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i) The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.     

Hierarchial structure theory for basic equations of fluid mechanics (BEFM) and the simplified Navier-Stokes equations (SNSE)

A hierarchial structure for the basic equations of fluid mechanics (BEFM) is found through the analysis of scales of length and time that proves a measure of the rate of change of the quantities describing the motion of the fluid as well as an estimation of the order of magnitude of various terms included in BEFM. The hierarchial structure theory shows that if (1) the characteristic Reynolds numbersRe is larger than unity and (2) the length scale in one coordinate direction is larger than that in other coordinate directions. BEFM can be classified into some levels according to the estimation of the order of magnitude of various terms included in BEFM. The hierarchial structure of BEFM has two branches: one is from BLE- to BEFM inner hierarchy, the other is from EE- to BEFM outer hierarchy, where BLE and EE are abbreviations of the boundary-layer equations and of Euler equations, respectively. The relationship between the two branches of the hierarchial structure, the characteristics, subcharacteristics and mathematical properties of the hierarchial equations are studied. A comparison between the present hierarchial equations and the Simplified Navier-Stokes equations (SNSE) appeared in literatures is also made. BLE-, EE-and Inner-outer-matched (IOM) equations hierarchies are the most important and useful three levels for solving viscous flow-fields approximately.     

Semi-analytical techniques for investigating thermal non-equilibrium effects in wet steam turbines

This paper describes a semi-analytical solution of the polydispersed wet stream equations, valid in regions where the nucleation rate is negligible. The solution can be used in conjunction with any conventional turbomachinery calculation procedure to obtain estimates of the magnitude of departures from thermal equilibrium. For example, from an initial estimate of the pressure distribution, it is a simple matter to calculate the distribution of supercooling and wetness fraction, together with the thermodynamic losses incurred by the flow.The method differs from the usual numerical approach by providing general results which give considerable physical insight. Computational time and effort is also dramatically reduced. The controlling parameters emerge naturally from the analysis, and information concerning the fundamental fluid mechanics of wet steam is revealed. In particular, the analysis demonstrates the role played by the thermal relaxation time and the rate of expansion in controlling the deviation from equilibrium.The versatility and usefulness of the technique in furnishing results for the turbine designer are demonstrated by a number of applications including one-dimensional nozzle flows and two-dimensional blade-to-blade and hub-to-tip flows. In each case it is shown how the droplet size and expansion rate influence the thermodynamic losses and other flow variables of interest.     

Start-up Flow of a Bingham Fluid in a Pipe

We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian.     

Unsteady flows of a generalized second grade fluid with the fractional derivative model between two parallel plates

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced. Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus. The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions of the shear stresses at the plates are also determined. The project supported by the National Natural Science Foundation of China (10372007, 10002003) and CNPC Innovation Fund     

A Universal Variational Formulation for Two Dimensional Fluid Mechanics

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Convergence of steady and unsteady formulations for inviscid hovering rotor solutions

An upwind Euler solver is presented, and applied to multibladed lifting hovering rotor flow. These flows can be simulated as a steady case, in a blade‐fixed rotating co‐ordinate system. However, forward flight simulation will always require an unsteady solution. Hence, as a stepping stone in the development of a forward flight simulation tool, both explicit steady and implicit unsteady simulations of the same hovering case are presented. Convergence of the two approaches is examined and compared, in terms of residual history, cost, and solution evolution, as a means of both validating the unsteady formulation and considering implications for forward flight simulation. Consideration of the solution evolution and wake capturing shows that for hovering rotor cases, the unsteady and steady solutions are the same, but the unsteady solution is more expensive in terms of CPU time. It is also shown that for hover, the fewer real time‐steps taken per revolution the more efficient the implicit scheme is. However, this is a characteristic of the case, which results in smooth solution variation between time steps. It is also demonstrated that for rotary flow simulation, the global residual is not a useful quantity to assess convergence. The residual reaches a very low (constant in the implicit case) value while the solution is still evolving. Copyright © 2003 John Wiley & Sons, Ltd.     

A variational principle for fluid mechanics

Summary A variational principle for fluid mechanics is derived without calling for any additional postulates in any ad hoc way. In the principle derived here, the Lagrangian is essentially the sum of kinetic and heat energy transferred to the fluid, less the sum of its internal and potential energy, less the work done on its exterior (similar to the enthalpy concept), rather than the difference between only kinetic energy and internal energy, as obtained previously by Seliger and Whitham [1] for a more restricted mode of variation.     

Unsteady Self-Similar Flow of a Viscous Incompressible Fluid in a Plane Divergent Channel

The problem of two-dimensional unsteady flow of a viscous incompressible fluid in a sector-like domain is considered. Initially a strictly radial flow is imposed, which makes it possible to seek solutions within the class of self-similar flows. A numerical method based on mixed finite-difference and spectral spatial discretization is developed, making it possible to find the self-similar solution efficiently. The process of development and establishment of the steady Hamel-Jeffery and Moffatt flows is modeled mathematically.     

An adaptive cut‐cell method for environmental fluid mechanics

In this work we present a numerical method for solving the incompressible Navier–Stokes equations in an environmental fluid mechanics context. The method is designed for the study of environmental flows that are multiscale, incompressible, variable‐density, and within arbitrarily complex and possibly anisotropic domains. The method is new because in this context we couple the embedded‐boundary (or cut‐cell) method for complex geometry with block‐structured adaptive mesh refinement (AMR) while maintaining conservation and second‐order accuracy. The accurate simulation of variable‐density fluids necessitates special care in formulating projection methods. This variable‐density formulation is well known for incompressible flows in unit‐aspect ratio domains, without AMR, and without complex geometry, but here we carefully present a new method that addresses the intersection of these issues. The methodology is based on a second‐order‐accurate projection method with high‐order‐accurate Godunov finite‐differencing, including slope limiting and a stable differencing of the nonlinear convection terms. The finite‐volume AMR discretizations are based on two‐way flux matching at refinement boundaries to obtain a conservative method that is second‐order accurate in solution error. The control volumes are formed by the intersection of the irregular embedded boundary with Cartesian grid cells. Unlike typical discretization methods, these control volumes naturally fit within parallelizable, disjoint‐block data structures, and permit dynamic AMR coarsening and refinement as the simulation progresses. We present two‐ and three‐dimensional numerical examples to illustrate the accuracy of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Laminar/turbulent oscillating flow in circular pipes

A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re_max = 1,920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are here compared with experimental results of previous investigators. Predictions of the flow regime on present oscillating flow conditions are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-ε turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-ε model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.     

Qualitative Questions in Fluid Mechanics

In this paper in honour of Professor Leen van Wijngaarden, some propositions about fluid mechanics are discussed. First, basic fluid mechanics research should be judged as much by its progress in clarifying the essential questions about the phenomena of fluid flow and in establishing general concepts, as by its contribution to the solutions of specific problems. In fact, the latter often contribute to the former. Both aspects attract good students to the subject.Second, researchers make more progress and are likely to impress a journal editor when they relate their problems to general physical and/or mathematical considerations, and when they analyse and present their results in a wide but fluid mechanically relevant context, for example through symmetry considerations, invariants (including dimensionless groups, scaling laws and topological constraints), differential properties (or jumps, wiggles and swirls), and through raising new questions and concepts of general significance from studies of specific flows.Lastly, decisions by organisations and individuals about future research directions also benefit from being considered in a wide conceptual framework.     

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。     

Unsteady Behavior of an Elastic Beam Floating on the Surface of an Infinitely Deep Fluid

The effect of initial disturbances and unsteady external loading on an elastic beam of finite length which floats freely on the surface of an ideal incompressible fluid is studied in a linear treatment. The fluid flow is considered potential. The beam deflection is sought in the form of an expansion in the eigenfunctions of beam vibrations in vacuum with time-dependent amplitudes. The problem reduces to solving an infinite system of integrodifferential equations for unknown amplitudes. The memory functions entering this system are determined by solving the radiation problem. The beam behavior is studied for various loads with and without allowance for the weight of the fluid. The effect of fluid depth on beam deformation was determined by comparing with the previously obtained solutions of the unsteady problem for a beam floating in shallow water. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 85–94, January–February, 2006.     

Computation of unsteady flow past blunt bodies

In accordance with the recent experimental research for flow visualization,theunsteady behavior of the starting period is investigated numerically for flow past bluntbodies.Finite difference methods are employed to solve the unsteady two-dimensionalincompressible Navier-Stokes equations.A short discussion is presented of explicit,implicit and ADI methods.Finally,the explicit and ADI schemes are used to study the flowfield in the starting period for flow past mountain-shaped and rectangular bodies.     

On Plane-Parallel Separated Flows of an Incompressible Fluid near Flat Boundaries

On the basis of Stokes separated flows, examples of separated flows described by the Navier-Stokes equations of a viscous incompressible fluid are constructed. These flows are represented by series convergent in a certain non-zero neighborhood of a flat contour immersed in the flow. In this neighborhood, the series have the same structure as those for the basic Stokes flows. Examples of the regions in which the series segments chosen give only a slight deviation from the numerical solutions of the Navier-Stokes equations are presented. The comparison between inviscid separated flows (without the no-slip condition on the contour) and viscous flows of the same structure (with the no-slip condition) shows that the viscosity does not play a decisive role in the formation of separation or the type of streamline approach to or departure from the contour.     

On Solutions of Some Non-Linear Differential Equations Arising in Newtonian and Non-Newtonian Fluids

Some steady as well as unsteady solutions of the equations of motion for an incompressible Newtonian and non-Newtonian (second-grade) fluids are obtained by applying different methods including the Lie symmetry group method. The flows considered are axially symmetric with the swirling motion, and the governing equations for second-grade fluid flow have been modeled. Expressions for streamlines, velocity and vorticity components are constructed explicitly in each case. Exact analytical solutions in second-grade fluid are obtained and compared with the corresponding viscous solutions.