Some Viscous and Other Real Fluid Effects in Fully Developed Cavity Flows

Some significant differences between fully developed cavity flows and their corresponding potential flow models are described and an attempt is made to interpret the results in terms of the real fluid properties. The phenomenon of cavity separation from a smooth surface and the nature and appearance of the cavity interface are given particular attention

A Linear Dynamic Analysis of Vent Condensation Stability

Pressure suppression systems in boiling water reactors are designed to condense a large amount of steam very rapidly by injecting it into a pool of water. It transpires that such condensing flows are unstable and can lead to large oscillatory pressures on the walls of the containment system. This paper presents a theoretical model whose purpose is to attempt to understand why these flows are unstable and to extract the important parameters and frequencies pertaining to the instability. A simple linear dynamic model is constructed comprising linear transfer function for (i) the unsteady steam flow in the vent (ii) the condensation interface and (iii) the pool hydrodynamics. The analysis demonstrates the existence of both stable and unstable regions of operation defined by several non-dimensional parameters including the ratio of the steam flow rate to the effective thermal diffusivity in the water just downstream of the condensation interface and the frictional losses in the vent. Instability frequencies are in the vicinity of the vent acoustic frequencies or the pool manometer frequency depending on the conditions. Though the qualitative dynamic behavior of the model is consistent with the experimental observations, quantitative comparison is hindered by difficulties in accurately assessing the effective thermal diffusivity in the water. Nevertheless the model provides insight into the nature of the instability

Wave Patterns on the Surface of Hydrodynamic Cavities

In experiments on cavities behind various axisymmetric headforms, a pattern of waves or ripples with crests parallel to the separation line was observed on the cavity surface just downstream of separation. A theoretical analysis suggests that this pattern results from amplified instabilities in the separated laminar boundary layer on the cavity surface

Channel flows of granular materials and their rheological implications

While the flow of a dry granular material down an inclined channel may seem at first sight to be a relatively simple flow, the experiments which have been conducted up to now suggest sufficient complexity which may be present in all but the very simplest granular material flows; consequently it is important to our general understanding of granular material rheology that these experimental observations be fully understood. This review of the current knowledge of channel flows will focus on the basic mechanics of these flows and the contributions the observations have made to an understanding of the rheology. In order to make progress in this objective, it is necessary to avoid some of the complications which can occur in practice. Thus we shall focus only on those flows in which the interstitial fluid plays very little role in determining the rheology. In his classic paper, Bagnold (1954) was able to show that the regime in which the rheology was dominated by particle/particle or particle/wall interactions and in which the viscous stresses in the interstitial fluid played a negligible role could be defined by a single, Reynolds-number-like parameter. It transpires that the important component in this parameter is a number which we shall call the Bagnold number, Ba, defined by Ba = p₈d²δ/µF where p₈,µF are the particle density and interstitial fluid viscosity, d is the particle diameter and δ is the principal velocity gradient in the flow. In the shear flows explored by Bagnold δ is the shear rate. Bagnold (1954) found that when Ba was greater than about 450 the rheology was dominated by particle/particle and particle/wall collisions. On the other hand, for Ba < 40, the viscosity of the interstitial fluid played the dominant role. More recently Zeininger and Brennen (1985) showed that the same criteria were applicable to the extensional flows in hoppers provided the extensional velocity gradient was used for δ. This review will focus on the simpler flows at large Ba where the interstitial fluid effects are small. Other important ancillary effects can be caused by electrical charge separation between the particles or between the particles and the boundary walls. Such effects can be essential in some flows such as those in electrostatic copying machines. Most experimenters have observed electrical effects in granular material flows, particularly when metal components of the structure are not properly grounded. The effect of such electrical forces on the rheology of the flow is a largely unexplored area of research. The lack of discussion of these effects in this review should not be interpreted as a dismissal of their importance. Apart from electrical and interstitial fluid effects, this review will also neglect the effects caused by non-uniformities in the size and shape of the particles. Thus, for the most part, we focus on flows of particles of spherical shape and uniform size. It is clear that while an understanding of all of these effects will be necessary in the long term, there remain some important issues which need to be resolved for even the simplest granular material flows

Shock Waves and Noise in the Collapse of a Cloud of Cavitation Bubbles

Calculations of the collapse dynamics of a cloud of cavitation bubbles confirm the speculations of Morch and his co-workers and demonstrate that collapse occurs as a result of the inward propagation of a shock wave which grows rapidly in magnitude. Results are presented showing the evolving dynamics of the cloud and the resulting far-field acoustic noise

On the Acoustical Dynamics of Bubble Clouds

Recently, Morch [1,2,3,4] Chahine [5,6] and others have focused attention on the dynamics of a cloud or cluster of cavitating bubbles and have expanded on the work of van Wijngaarden [7,8] and others. Unfortunately, there appear to be a number of inconsistencies in this recent work which will require further study before a coherent body of knowledge on the dynamics of clouds of bubbles is established. For example, Morch and his co-workers [1,2,3] have visualized the collapse of a cloud of cavitating bubbles as involving the inward propagation of a shock wave; it is assumed that the bubbles collapse virtually completely when they encounter the shock. This implies the virtual absense of non-condensable gas in the bubbles and the predominance of vapor. Yet in these circumstances the mixture in the the cloud will not have any real sonic speed. As implied by a negative L.H.S. of equation (9), the fluid motion equations for the mixture would be elliptic not hyperbolic and hence shock wave solutions are inappropriate

Nonlinear Effects in Cavitation Cloud Dynamics

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a fourier series analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillations of a single bubble. This is used in the approximate solution of the oscillating wall problem and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. The frequency content of the bubble radius and pressure oscillations near the wall is examined. Nonlinear effects are seen to increase with increased amplitude of wall oscillation, reduced void fraction and viscous and surface tension effects

The Noise Generated by the Collapse of a Cloud of Cavitation Bubbles

The focus of this paper is the numerical simulation of the dynamics and acoustics of a cloud of cavitating bubbles. The prototypical problem solved considers a finite cloud of nuclei that is exposed to a decrease in the ambient pressure which causes the cloud to cavitate. A subsequent pressure recovery then causes the cloud to collapse. This is typical of the perturbation experienced by a bubble cloud as it passes a headform or the blade of a ship propeller. The simulations employ the fully non-linear, non-barotropic, homogeneous flow equations coupled with the Rayleigh-Plesset dynamics for individual bubbles. This set of equations is solved numerically by an integral method. The computational results confirm the early speculation of Morch and his co-workers (Morch 1980 & 1981, Hanson et al. 1981) that an inwardly propagating shock wave may be formed in the collapse of a cavitating cloud. The structure of the shock is found to be similar to that of the steady planar shocks analyzed by Noordij and van Wijngaarden (1974). The shock wave grows rapidly not only because of the geometric effect of an inwardly propagating spherical shock but also because of the coupling of the single bubble dynamics with the global dynamics of the flow through the pressure and velocity fields (see also Wang and Brennen 1994). The specific circumstances which lead to the formation of such a shock are explored. Moreover, the calculations demonstrate that the acoustic impulse produced by the cloud is significantly enhanced by this shock-focusing process. Major parameters which affect the dynamics and acoustics of the cloud are found to be the cavitation number, [sigma], the initial void fraction, [alpha-zero], the minimum pressure coefficient of the flow, [C Pmin], the natural frequencies of the cloud, and the ratio of the length scale of low pressure perturbation to the initial radius of the cloud, [D/A-zero], where D can be, for example, the radius of the headform or chord length of the propeller blade. We examine how some of these parameters affect the far field acoustic noise produced by the volumetric acceleration of the cloud. The non-dimensional far-field acoustic impulse produced by the cloud collapse is shown to depend, primarily, on the maximum total volume of the bubbles in the cloud normalized by the length scale of the low pressure perturbation. Also, this maximum total volume decreases quasi-linearly with the increase of the cavitation number. However, the slope of the dependence, in turn, changes with the initial void fraction and other parameters. Non-dimensional power density spectra for the far-field noise are presented and exhibit the [equation] behavior, where n is between 0.5 and 2. After several collapse cycles, the cloud begins to oscillate at its natural frequency and contributes harmonic peaks in its spectrum

Computer Simulation of Chute Flows of Granular Materials

The purpose of the present paper is to present results from computer simulations of the flow of granular materials down inclined chutes or channels and to compare the results of these calculations with existing experimental measurements of velocity, solid fraction and mass flow rate profiles