Dynamics of a flat cavity in a low-viscosity liquid

The problem of the motion of a cavity in a plane-parallel flow of an ideal liquid, taking account of surface tension, was first discussed in [1], in which an exact equation was obtained describing the equilibrium form of the cavity. In [2] an analysis was made of this equation, and, in a particular case, the existence of an analytical solution was demonstrated. Articles [3, 4] give the results of numerical solutions. In the present article, the cavity is defined by an infinite set of generalized coordinates, and Lagrange equations determining the dynamics of the cavity are given in explicit form. The problem discussed in [1–4] is reduced to the problem of seeking a minimum of a function of an infinite number of variables. The explicit form of this function is found. In distinction from [1–4], on the basis of the Lagrauge equations, a study is also made of the unsteady-state motion of the cavity. The dynamic equations are generalized for the case of a cavity moving in a heavy viscous liquid with surface tension at large Reynolds numbers. Under these circumstances, the steady-state motion of the cavity is determined from an infinite system of algebraic equations written in explicit form. An exact solution of the dynamic equations is obtained for an elliptical cavity in the case of an ideal liquid. An approximation of the cavity by an ellipse is used to find the approximate analytical dependence of the Weber number on the deformation, and a comparison is made with numerical calculations [3, 4]. The problem of the motion of an elliptical cavity is considered in a manner analogous to the problem of an ellipsoidal cavity for an axisymmetric flow [5, 6]. In distinction from [6], the equilibrium form of a flat cavity in a heavy viscous liquid becomes unstable if the ratio of the axes of the cavity is greater than 2.06.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 15–23, September–October, 1973.The author thanks G. Yu. Stepanov for his useful observations.     

Slender axisymmetric cavities in a supersonic flow

Slender axisymmetric cavities in a subsonic flow of compressible fluid were investigated in [1–4]. In [5] a finite-difference method was used to calculate the drag coefficient of a circular cone, near which the shape of the cavity was determined for subsonic, transonic, and supersonic water flows; however, in the supersonic case the entire shape of the cavity was not determined. Here, on the basis of slender body theory an integrodifferential equation is obtained for the profile of the cavity in a supersonic flow. The dependence of the cavity elongation on the cavitation number and the Mach number is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–181, January–February, 1989.     

Effect of density extremum on the solidification of water on a vertical wall of a rectangular cavity

Experiments were performed in a two-dimensional rectangular cavity to study the transient flow in an initially isothermal and motionless fluid due to a step decrease in temperature on one of the two vertical end walls. In the experiments water was used as the phase-change medium, with the cold-wall temperature maintained below the freezing temperature. The opposite vertical wall was kept at the initial temperature, greater than the temperature where the density extremum occurs. The growth of ice and the transient flow in the cavity were visualized with the aid of a tracer technique to examine the effect of density inversion. The temperature field was continuously recorded by an array of thermocouples. It was found that the density inversion of water strongly influences both the growth of ice and the convective flow in the liquid region of the test cavity.     

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.     

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.     

Conjugate heat exchange and hydrodynamics for a viscous incompressible fluid moving in a rectangular cavity

Numerical simulation was performed of the motion of a viscous incompressible nonisothermal fluid in an open rectangular cavity under conditions of forced convection and conjugate heat exchange. The effect of the jet dynamic parameter (Reynolds number) and fluid flow conditions on the character of motion and heat exchange of viscous incompressible nonisothermal fluids in rectangular cavities is studied. A hydrodynamic pattern of viscous flow in an open cavity under forced convection conditions (in the conjugate and nonconjugate formulations of the problem) is obtained. The effect of parameters of the model on the character of motion is studied. Temperature profiles for the solid and fluid phases are obtained. The effect of parameters of the model on the character of temperature distribution in both phases is studied.     

Experimental Study of Flow in a Cavity on an Axisymmetric Body

The flow past a cylindrical cavity on an axisymmetric body in the range of Mach numbers from 0.6 to 1.18 and the effect of the Mach number in the transition from subsonic to supersonic flow velocities are studied experimentally. In addition, a broad, 5.3—11.3 range of relative elongations of the cavity which permits one to determine the influence of the elongation on flow regimes including flows with closed and open separation zones is studied.     

Three-dimensional viscoelastic flows through a rectangular channel with a cavity

Three-dimensional viscoelastic flows in a rectangular channel with a cavity were studied both numerically and experimentally. In the numerical study, computations were carried out using the Phan-Thien–Tanner (PTT) model as a constitutive equation. A finite volume method (FVM) using colocated grids was applied. A three-dimensional structure in the cavity was observed even when three-dimensional behavior was not remarkable in main flows. At high Weissenberg number, the flow in the cavity spirals to move towards the center plane of the channel. In the experiments, the flow of polymer solutions was visualized to observe three-dimensional flow behavior near the cavity part. It was confirmed that the spiraling flow moving towards the center plane emerged in the cavity.     

Self-aeration and turbulence in a stepped channel: Influence of cavity surface roughness

The strong interactions between free-surface flows and atmospheric surroundings may lead to substantial air–water mixing with void fractions ranging from zero in clear-water to 100%. In this study, the air–water flow properties were studied in a large stepped water channel operating at large Reynolds numbers. Interactions between free-surface and cavity recirculation were systematically investigated in the skimming flow regime. Some surface roughness was introduced on the cavity walls and identical experiments were performed with several configurations. Basic results demonstrated some influence of step surface roughness on the flow properties leading to some counter-intuitive finding. The presence of cavity roughness was associated with higher flow velocities and comparatively lower turbulence levels. Distributions of bubble/droplet chords spanned over several orders of magnitude without significant influence of the cavity roughness. The distributions of turbulence levels and bubble count rates showed some correlation and highlighted strong interactions between entrained particles (bubbles, drops) and the flow turbulence.     

A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity

This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.     

Self-sustained oscillations of shear flow past a slotted plate coupled with cavity resonance

Shear flow past a slotted plate configuration can give rise to highly coherent, self-sustained oscillations when coupling occurs with a resonant mode of an adjacent cavity. The distinctive feature of these oscillations is that the wavelength of the coherent instability along the plate is of the order of the plate length. This observation is in contrast to previous investigations of flow past perforated or slotted surfaces, where the instability scales on the diameter of the perforation or the gap length of a slot. The present oscillations occur even when the inflow boundary layer is turbulent and an inflectional form of the shear flow cannot develop along the cavity opening, due to the presence of the slotted plate. Instigation of a resonant mode of the cavity, in conjunction with an inherent instability of the shear flow along the plate, gives rise to ordered clusters of instantaneous vorticity and instantaneous velocity correlation. During the oscillation, ejection of flow occurs from the cavity to the region of the shear flow; this ejection is in accord with the convection of the large-scale cluster of vorticity along the slotted plate. This oscillation can be effectively detuned by adjusting the inflow velocity, such that the inherent instability of the shear flow past the slotted plate is no longer coincident with the resonant frequency of the cavity. Certain features of this self-sustained oscillation are directly analogous to recent findings of oscillations due to shear flow past a perforated plate bounded by a cavity, but in the absence of cavity resonance effects.     

Instabilities in viscoelastic flow past a square cavity

Elastic flow transitions in viscoelastic flow past a square cavity adjacent to a channel are reported. The critical conditions for the onset of flow transitions and the qualitative and quantitative characterization of the secondary flows generated by the instability have been examined using streakline photography and instantaneous pressure measurements. Cellular type of instabilities inside the cavity is observed for flow rates beyond a critical value. Small and large scale eddies are observed at high flow rates. The flow inside the cavity and in the channel upstream and downstream of the cavity becomes weakly time-dependent for high flow rates.     

Effects of dual jets distance on mixing characteristics and flow path within a cavity in supersonic crossflow

A rectangular open cavity with upstream dual injectors at a freestream Mach number of 1.9 was investigated experimentally. To evaluate the effect of the distance between the jets, the flow characteristics were investigated using the high-speed schlieren photography, particle image velocimetry, and surface oil flow techniques. The dual jet distances of 18 and 54 mm were used. Unstable flow occurs over the cavity in all cases and is not improved by changing the distance between the dual jets. Although the distance between the dual jets does not influence the flow stability, the flow field varies decidedly depending on the dual jets distance. The enhancement of air mixing depends on the distance between the jets. A long dual jets distance was found to yield better mixing characteristics within the cavity than a short one. When the jets are further apart, the mainstream between two counter-rotating vortex pairs behind the jets flows strongly into the cavity because of the increased blow-down occurring between the vortex pairs. Additionally, a counterflow with a low velocity magnitude occurs behind the jets. Hence, mixing is enhanced within the cavity by effects of the opposed flow. When the jet pairs are closer to each other, the counter-rotating vortex pairs are in contact; as a result, the blow-down effect does not occur between them. The flow drawn into the cavity from the mainstream is supplied from the sides of the test section into the cavity.     

Flow and heat transfer in a rotating cavity with a radial inflow of fluid Part 1: The flow structure

Flow visualization has been conducted in a rotating cavity, comprising two steel discs and a peripheral polycarbonate shroud, for dimensionless flow rates of air up to |C_w|8000 and rotational Reynolds number up to Re_φ10⁶. For all the experiments, the ratio of the inner to outer radii of the discs was 0.1 and the ratio of the axial clearance between the discs to their outer radii was 0.133; five different shroud geometries were tested. The flow visualization has confirmed that the flow structure comprises a source region near the shroud, laminar or turbulent Ekman layers on the discs, a sink layer near the centre of the cavity, and an interior core of rotating fluid. Above a certain flow rate, this structure was found to be unstable; heating one disc tended to stabilize the flow. For isothermal flow, measurements of the size of the source region were in good agreement with values predicted from a simple theoretical model.     

侧加热腔内的自然对流

开展侧加热腔内自然对流的研究具有重大的环境及工业应用背景. 总结侧加热腔内水平温差驱动的自然对流的最新研究进展, 并概述相应的流动性质、动力机制和传热特性以及对不同无量纲控制参数的依赖也有重要的科学价值. 已取得的研究结果显示突然侧加热的腔内自然对流的发展可包括初始阶段、过渡阶段和定常或准定常阶段. 不同发展阶段的流动依赖于瑞利数、普朗特数及腔体的高宽比, 且定常或准定常阶段的流态可以是定常层流流动、非定常周期性流动或者湍流流动. 此外, 回顾了对流流动失稳机制的研究成果以及湍流自然对流方面的新进展. 最后, 展望了侧加热腔内的自然对流研究的前景.      

Transient removal of a contaminated fluid from a cavity

A numerical and experimental study of the time-dependent hydrodynamic removal of a contaminated fluid from a cavity on the floor of a duct is presented. The duct flow has a parabolic inlet velocity profile and laminar flows are considered in a Reynolds number range between 50 and 1600 based on the duct height. The properties of the contaminated cavity fluid are assumed to be the same as for the fluid flowing in the duct. Attention is focussed on the convective transport of contaminated fluid out from the cavity and the effect of duct flow acceleration on the cleaning process. Passive markers which are convected with the flow are used in the numerical simulation for the purpose of identifying the contaminated cavity fluid. It is shown that the cleansing of the cavity is more pronounced during the unsteady start-up of the duct flow and the rate of cleaning decreases as the flow reaches a steady state. The cleaning process is enhanced as the cavity aspect ratio is increased and as the duct Reynolds number increases. A ‘volumetric’ approach based on the spread of markers is shown to be useful in determining the fraction of the cavity that remains contaminated after steady conditions have been reached. The distribution of the contaminant in a cavity during the unsteady stage and after steady conditions are reached are identified using passive markers.     

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.     

Stokes waves on a cavity surface in a rotating fluid

The axisymmetric flow of an inviscid incompressible fluid rotating about a cavity with constant pressure is considered. Due to the centrifugal force, on the cavity surface waves may exist, in particular, waves with a break in the wave base where the cavity meridional sections form the angle 2/3, i.e. Stokes waves. A method of finding these waves from the boundary-value problem for the fluid velocity potential is described. For an infinite cavity, the dependence of the wave parameters on the cavitation number, calculated using the pressure in the cavity, is given.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 105–110, November–December, 1996.     

Tip leakage aerodynamics over stepped squealer tips in a turbine cascade

Tip gap flow physics and aerodynamic loss generations for two stepped squealer tips of a “Higher Pressure-side rim and Lower Suction-side rim” (HPLS) tip and a “Lower Pressure-side rim and Higher Suction-side rim” (LPHS) tip have been investigated in a turbine cascade. For a fixed tip gap height-to-chord ratio of h/c = 2.0%, oil film flow visualizations are performed on the casing wall as well as on the cavity floor, and three-dimensional flow fields downstream of the cascade are measured with a five-hole probe. For the HPLS tip, the leakage inflow over the pressure-side rim cannot reach the suction-side rim in the upstream region due to the presence of an inlet flow intrusion, and there exists a strong near-wall flow heading toward the trailing edge all over the cavity floor. On the other hand, the LPHS tip has a mid-chord leakage flow penetration into the blade flow passage, and also provides a downstream leakage flow penetration deeper than that for the HPLS tip. Its cavity floor can be divided into a backward flow region and a wide separation bubble. Aerodynamic loss for the HPLS tip, which is nearly identical to that for the cavity squealer tip, is lower than those for the LPHS and plane tips in a considerable degree.     

Unsteady flow and heat transfer adjacent to the sidewall wall of a differentially heated cavity with a conducting and an adiabatic fin

The unsteady natural convection flow adjacent to the finned sidewall of a differentially heated cavity is numerically investigated through comparisons between the cases with a conducting fin and an adiabatic fin. The results show that the flow and temperature structures in the transition to a periodic flow induced by a conducting fin are considerably different from those by an adiabatic fin. Based on the present numerical results, the temporal development and spatial structures of the flow adjacent to the finned sidewall are described, and instabilities are characterized. It is found that the conducting fin improves the transient convective flows in the cavity and enhances heat transfer across the cavity (by up to 52% in comparison with the case without a fin).