Gas Entrainment from a Ventilated Cavity with a Negative Cavitation Number

The hydrodynamics of a ventilated cavity with a negative cavitation number are studied experimentally. The pressure distributions in the closure region of the cavity, the flow-pressure head characteristics, and the cavitation number (or pressure coefficient) as a function of the gas-injection rate are measured. The two-phase flow pattern near the Taylor-unstable cavity boundary is investigated using spark photography and videophotography. The results are compared with the known theoretical and numerical data. It is shown that in the near-critical flow regime the basic mechanism of gas entrainment from the cavity is connected with the Rayleigh-Taylor instability. On this basis, the gas entrainment coefficient of the cavity is found to be proportional to the curvature of the cavity boundary and the square of the boundary length.     

Cavity detachment on a hydrofoil with the inclusion of surface tension effects

The non-linear problem of cavity flow past a hydrofoil is considered with taking into account fluid viscosity in the cavity closure region and surface tension, which affect the cavity detachment. The theoretical model is based on the concept of viscous–inviscid interaction between the outer inviscid cavity flow and the inner turbulent separated flow downstream of the cavity. The outer inviscid flow is solved by constructing the complex flow potential, and the wake model is based on the method of integral relationships for separated turbulent flows. The obtained numerical results are compared with experimental data.     

Finite Difference Method for the Acoustic Radiation of an Elastic Plate Excited by a Turbulent Boundary Layer: A Spectral Domain Solution

A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic plate, clamped at its boundaries, is excited by a turbulent boundary layer. Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid, baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains. Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very complex and unresolved task. Ducan and Sirkis [1] proposed a model for the two-way interactions between a membrane and a turbulent flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified by the displacement of the membrane. Howe [2] proposed a model for the turbulent wall pressure fluctuations power spectrum over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the plate, but the vibration of the plate does not modify the characteristics of the flow. A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity; (b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior acoustic pressure. A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos model [3] and the Chase model [4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure. In [3], this difference is explained by calculating a wavenumber transfer function of the plate. In [6], coupled beam-cavity modes for similar geometry are calculated by the finite difference method. This revised version was published online in July 2006 with corrections to the Cover Date.     

开放空腔壳体倾斜入水运动特性试验研究

基于高速摄像试验方法,研究了开放空腔壳体的倾斜入水运动特性,重点分析了开放空腔结构引起的空泡流动特征和壳体运动规律. 通过试验数据分析了开放空腔内气体运动将引起独特的空泡流动和阶段性的运动规律,探讨了初始入水速度、入水姿态对入水弹道和空泡形态等运动特征的影响. 结果表明:开放空腔壳体入水空泡出现阶段波动演化现象,并先后经历两次闭合;入水空泡演化改变流体动力分布,直接影响壳体运动方式,进而改变水下弹道特征;空腔内部形成相对独立流场环境和开放端周期性流动,在重力作用下液体对空腔内下侧壁面作用力较大,加剧壳体偏转,从而改变入水运动过程的稳定性;随着入水速度的增大,空泡波动特征逐渐明显,闭合时间延迟,非对称深闭合引起的横向位移减小,但偏转角度与入水速度无关;随着初始姿态倾角减小,空泡波动程度减弱、闭合时间延迟,偏转角速度增大,闭合引起的横向位移增大.      

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das’ nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.     

Jet impingement onto a cylindrical cavity: consideration of annular nozzle cone angles,and cavity diameter

In the present study, gas jet emerging from an annular nozzle and impinging onto a cylindrical cavity is considered. The geometric configuration of the nozzle is varied in the simulations. Air is used as impinging gas while stainless steel is considered as workpiece material. Reynolds turbulence model is accommodated to account for the turbulence. A numerical scheme employing a control volume approach is used to simulate the flow field. Heat transfer characteristic and shear stress distribution around the cavity are computed. It is found that outer cone angle of the annular nozzle influences the heat transfer rates from the cavity wall. The flow structure around the cavity changes significantly with increasing cavity diameter. Moreover, increasing cavity depth results in stagnation zone moving into the cavity.     

Heat transfer in a three-dimensional rectangular cavity oriented at an angle to the free-stream

We consider a flow of a viscous incompressible heat-conducting fluid over a cubic cavity. The heat transfer on the bottom of the cavity rotated at an angle to the free stream is studied numerically. The numerical algorithm includes a finite-difference approximation in the spatial coordinates, a semi-implicit time integration method, and a modified version of an iterative stabilized method of biconjugate gradients with an algebraic multigrid preconditioner for solving the Poisson equation. The algorithm is designed for the use of multiprocessor computers. Two different inlet flow conditions are considered: a steady-state flow and a steady flow with superimposed periodic perturbations. In the first case, it is shown that the integral heat transfer rate increases monotonically with increase in the cavity rotation angle α. For α = 45°, the increase in the heat flux amounts to 20%. The presence of periodic disturbances may result in up to 3-fold increase in the integral heat transfer rate as compared to the case of the steady-state inlet flow. The enhancement of heat transfer occurs when the frequency of the inlet flow disturbances is close to the frequency of unstable modes of the mixing layer formed at the upper boundary of the cavity.     

直角和贴体坐标系下两种格子Boltzmann方法的比较研究

采用格子Boltzmann方法(LBM)和改进的插值格子Boltzmann方法(GILBM)研究了45°斜方腔的顶盖驱动流和Roach通道内的流动特性,并与基准解进行了对比。结果表明,对于45°斜方腔的顶盖驱动流,当雷诺数较小时,两种方法的计算结果与基准解吻合较好;但当雷诺数较大时,采用LBM的计算结果准确性降低,而基于GILBM方法得到的结果准确度升高,且计算稳定性好。对于Roach通道内的流体流动而言,两种方法的计算精度和复杂边界的复杂程度与雷诺数大小有关。根据流场边界形状的复杂程度,网格划分与计算精确度的不同要求,两种方法各有利弊。     

细长体水下运动空化流场及弹道特性实验

为了研究细长体水下高速运动时空泡的产生、闭合及脱落特性,及影响细长体空泡形态及弹道特性的复杂因素等,初步开展了细长体模型水下高速运动的实验研究,分析了不同初始空化数下细长体模型在水中高速运动的一系列流动现象,重点研究了空泡的发展、闭合、尾部回射流和尾部脱落特性,以及轴对称细长体模型弹道特性与空泡形态变化之间的关系和转动特性随时间的变化历程等。结果表明:细长体水下高速运动时形成超空泡,空泡头部光滑透明,尾部凝结有汽水混合物且有交替脱落的含气漩涡;初始空化数对细长体的速度衰减有所影响;受初始扰动影响,细长体水下运动伴随有绕头部的转动且初始扰动影响细长体俯仰角随时间的变化历程。     

Experimental study of ventilated cavity flow over a 3-D wall-mounted fence

Ventilated cavity flow over a fixed height 3-D wall-mounted fence is experimentally investigated in a cavitation tunnel for a range of free-stream conditions. The impact of 3-D effects on cavity topology is examined, along with the dependence of the cavitation number and drag on the volumetric flow rate coefficient, fence height based Froude number and vapour pressure based cavitation number. Three different flow regimes are identified throughout the range of cavitation numbers for a particular free-stream condition. Generally, the cavity has a typical re-entrant jet closure the intensity of which is found to increase linearly with increasing Froude number. This increase in re-entrant jet intensity causes an increase in drag with Froude number for constant volumetric flow rate coefficient. At low Froude numbers the closure mechanism transitions from a single to a split re-entrant jet. The parameters used to characterize the cavity topology show a linear dependence on Froude number irrespective of the closure mode. The cavity topology and drag are found to be independent of vapour pressure based cavitation number.     

A three-dimensional PSME model for rotating flows in an annular cavity

A pseudospectral matrix-element (PSME) numerical model is described for the simulation of rotating flows in a three-dimensional annular cavity. Temporal discretisation is implemented using a second-order semi-implicit scheme. Modified compressibility is invoked to handle the coupling between velocity and pressure while maintaining the incompressibility constraint. The governing continuity and Navier–Stokes momentum equations and boundary conditions are discretised using Chebyshev and Fourier collocation formulae. The model is validated against numerical results from alternative schemes and experimental data on rotating flows in an annular cavity. A base flow regime and instability patterns are observed, in accordance with other previously published investigations. It is demonstrated that the PSME model provides an accurate representation of rotating flows in an annular cavity.     

A boundary element analysis of multiply connected three‐dimensional cavity mixing flow of polymer solutions

The emergence of non‐linear dynamics in cavity mixing is examined using the boundary element method (BEM). The method is implemented for the simulation of three‐dimensional transient creeping flow of Newtonian or linear viscoelastic fluids of the Jeffreys type. A boundary only formulation in the time domain is proposed for viscoelastic flow. Special emphasis is placed on cavity flow involving multiply connected moving domains. The BEM becomes particularly suited for this case, when part of the boundary (stirrer or rotor) is moving, and the remaining outer part (cavity) is at rest. In contrast to conventional volume methods, the BEM is shown to be much easier to implement since the kinematics of the elements bounding the fluid is known (imposed). It is found that, for a simple cavity flow induced by a rotating vane at constant angular velocity, the tractions at the vane tip and cavity face exhibit non‐linear periodic dynamical behaviour with time for fluids obeying linear constitutive equations. Copyright © 1999 John Wiley & Sons, Ltd.     

空泡流非稳态现象的流动控制

处于跨临界阶段的空泡流必然导致强烈的周期性冲击和振动,空泡流的激振来源于空泡云的周期性大规模脱落,空泡云的形成和发展与流动的边界层效应有着强烈的相关性,且空泡末端的局部流动直接影响空泡流的整体稳定性,本试验在NACA16012水翼表面粘附一条展向1mm厚10mm宽的挡流条,尝试以干扰水翼上表面局部流动的方法来影响整个空泡流的形态及其流动稳定性,最终在一定的空泡数范围内抑制了空泡流激振现象,并从试验研究的角度探索了空泡云脱落的机理。     

Heat transfer and supersonic flow structure in surface cavities

The characteristics of the flow and heat transfer in two- and three-dimensional open cavities on plane and cylindrical surfaces in a supersonic stream in the presence of a turbulent boundary layer have been investigated experimentally. The effects of the Mach number, boundary layer thickness, the shape of the cavity, and its angle of inclination to the free-stream direction on the flow parameters in the mixing layer above the cavity and the heat flux and pressure distribution on the surface of the cavity and its bottom are descirbed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 74–80, July–August, 1998.     

交错式扇贝阻尼密封动力特性研究

建立交错式扇贝阻尼密封三维数值分析模型,基于动网格及多频椭圆涡动模型研究密封动力特性沿轴向分布规律,计算分析错开角度(α=0°、11.25°、22.5°、33.75°)与密封腔深度(h=2.8、3.3、3.8和4.3 mm)对密封动力特性的影响. 结果表明:上游腔室(C1~C4)具有较大的正直接刚度和有效阻尼,对抑制转子涡动、提升系统稳定性的贡献相对较大. 相对并列式(α=0°)结构,交错式扇贝阻尼密封流体周向速度较小、湍流耗散增加,系统稳定性提升,同时密封泄漏量降低. 错开角度为33.75°时的有效阻尼约为0°时的111%~121%;错开角度为22.5°时的泄漏量相较于0°时约降低了2.11%. 有效阻尼随密封腔深度减小而增大,密封腔深度为2.8 mm时的有效阻尼约为4.3 mm时的146%~211%;密封泄漏量随密封腔深度增大而降低,密封腔深度为4.3 mm时的泄漏量相较于2.8 mm时降低了约3.73%.      

Perturbation solution to 3-D nonlinear supercavitating flow problems

A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow past cones with various apex-angles at different cavitation numbers. The numerical results are found in good agreement with experimental data. The project supported by the National Natural Science Foundation of China     

Unsteady phenomena of an oscillating turbulent jet flow inside a cavity: Effect of aspect ratio

Self-sustained oscillatory phenomena in confined flow may occur when a turbulent plane jet is discharging into a rectangular cavity. An experimental set-up was developed and the flow analysis has been made using mainly hot-wire measurements, which were complemented by visualisation data. Previous studies confirmed that periodic oscillations may occur, depending on the location of the jet exit nozzle inside the cavity, and also the distance between the side-walls. The present study deals with the symmetrical interaction between a turbulent plane jet and a rectangular cavity and the influence of the geometrical characteristics of the cavity on the oscillatory motion. The size and aspect ratio of the cavity were varied together with the jet width compared to that of the cavity. The study is carried out both numerically and experimentally. The numerical method solves the unsteady Reynolds averaged Navier–Stokes equations (URANS) together with the continuity equation for an incompressible fluid. The closure of the flow equations system is achieved using a two-scale energy-flux model at high Reynolds number in the core flow coupled with a wall function treatment in the vicinity of the wall boundaries. The fundamental frequency of the oscillatory flow was found to be practically independent of the cavity length. Moreover, the oscillations are attenuated as the cavity width increases, until they disappear for a critical value of the cavity width. Contour maps of the instantaneous flow field are drawn to show the flow pattern evolution at the main phases of oscillation. They are given for several aspect ratios of the cavity, keeping constant values for the cavity width and the jet thickness. The proposed approach may help to investigate further the oscillation mechanisms and the entrainment process occurring in pressure driven jet–cavity interactions.     

Solution of the Navier–Stokes equations in velocity–vorticity form using a Eulerian–Lagrangian boundary element method

This paper describes the Eulerian–Lagrangian boundary element model for the solution of incompressible viscous flow problems using velocity–vorticity variables. A Eulerian–Lagrangian boundary element method (ELBEM) is proposed by the combination of the Eulerian–Lagrangian method and the boundary element method (BEM). ELBEM overcomes the limitation of the traditional BEM, which is incapable of dealing with the arbitrary velocity field in advection‐dominated flow problems. The present ELBEM model involves the solution of the vorticity transport equation for vorticity whose solenoidal vorticity components are obtained iteratively by solving velocity Poisson equations involving the velocity and vorticity components. The velocity Poisson equations are solved using a boundary integral scheme and the vorticity transport equation is solved using the ELBEM. Here the results of two‐dimensional Navier–Stokes problems with low–medium Reynolds numbers in a typical cavity flow are presented and compared with a series solution and other numerical models. The ELBEM model has been found to be feasible and satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.     

Analysis of two-dimensional cavity flow by finite elements

The variational principle in terms of stream function ψ for free surface gravity flow is discussed by the formulation of first-order variation in a variable domain. Because of different transversal conditions adopted, there are four forms of variational principle in terms of ψ.A n air-gilled cavity flow with given discharge and total energy is then analysed by finite element method. At the end of the cavity, the free stream line is tangent to a short fictitious plate of given length, which joins the fixed boundary at on angle to be determined. The condition that the free stream line should be tangent to the fixed boundary at the point of separation makes the solution unique.Finally curves giving the cavity length as a function of the Fraude number, cavity pressure and channel bottom slope are presented.     

Effect of an axial throughflow on buoyancy-induced flow in a rotating cavity

In this paper large-eddy simulation is used to study buoyancy-induced flow in a rotating cavity with an axial throughflow of cooling air. This configuration is relevant in the context of secondary air systems of modern gas turbines, where cooling air is used to extract heat from compressor disks. Although global flow features of these flows are well understood, other aspects such as flow statistics, especially in terms of the disk and shroud boundary layers, have not been studied. Here, previous work for a sealed rotating cavity is extended to investigate the effect of an axial throughflow on flow statistics and heat transfer. Time- and circumferentially-averaged results reveal that the thickness of the boundary layers forming near the upstream and downstream disks is consistent with that of a laminar Ekman layer, although it is shown that the boundary layer thickness distribution along the radial direction presents greater variations than in the sealed cavity case. Instantaneous profiles of the radial and azimuthal velocities near the disks show good qualitative agreement with an Ekman-type analytical solution, especially in terms of the boundary layer thickness. The shroud heat transfer is shown to be governed by the local centrifugal acceleration and by a core temperature, which has a weak dependence on the value of the axial Reynolds number. Spectral analyses of time signals obtained at selected locations indicate that, even though the disk boundary layers behave as unsteady laminar Ekman layers, the flow inside the cavity is turbulent and highly intermittent. In comparison with a sealed cavity, cases with an axial throughflow are characterised by a broader range of frequencies, which arise from the interaction between the laminar jet and the buoyant flow inside the cavity.