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RESEARCH PAPERS

J. Fluids Eng. 1984;106(3):251-256. doi:10.1115/1.3243112.

Particle trajectory calculations provide the essential information required for predicting the pattern and intensity of turbomachinery erosion. Consequently, accurate flow field and blade geometry representation in the trajectory computational model are required to evaluate machine performance deterioration due to erosion. A model is presented that is simple and efficient yet versatile and general, applicable to axial, radial and mixed flow machines, and to inlets, nozzles, return passages and separators. Computations are presented for particle trajectories through a row of twisted vanes in the inlet flow field. The effect of the particle size on trajectory blade impacts, and on particle redistribution and separation are discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):257-261. doi:10.1115/1.3243113.

By applying a new optical technique, moire deflectometry, we have observed complex density patterns in apparently homogeneous solutions, under ambient conditions. The density patterns of the liquids are attributed to cooling due to evaporation, precipitation caused by gravity, or dissolution.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):262-269. doi:10.1115/1.3243114.

A calculation procedure for two-dimensional separated flows over curved boundaries, e.g., flow in constricted tubes, is described. The method is based on the numerical solution with finite differences of the governing equations in orthogonal curvilinear coordinates. A body fitted curvilinear orthogonal numerical grid is generated first which is then employed for the solution of partial differential equations governing fluid flow. Results of calculations are presented for laminar and turbulent flows in constricted tubes. For turbulent flow calculations the k-ε turbulence model has been employed. Comparison between computed and measured values of flow quantities is also presented and is discussed in some detail. Although the present paper deals only with constricted pipes, the method developed is general and can be used without difficulty for two-dimensional flows over other curved boundaries.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):270-278. doi:10.1115/1.3243115.

Experimental and analytical studies are reported for a Newtonian fluid in a partially-filled cylinder rotating about its centerline axis at constant angular speeds. Two fluids, glycerin and water, are used in this study. The analytical results are in good agreement with the experimental data. This comparison is based on the profiles of the free surfaces and the streamlines experimentally obtained using a flow visualization technique and as predicted by the analytical model. When the rotational speed is not high enough to cause solid body rotation of the fluid, due to excessive centrifugal force, a recirculation region forms at the lower portion of the cylinder. The profile of the free surface in this region depends on the relative magnitude of the body force and the viscous force. In general, two distinct flow regions can be recognized for a cylinder of infinite extent; a recirculating flow and a boundary-layer-type flow along the cylindrical wall. In addition to the volume of the fluid in the cylinder, there are two other parameters governing this problem; the Reynolds number and the ratio, G, of the Reynolds number to the Froude number.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):279-284. doi:10.1115/1.3243116.

When an oil tank collapses or ruptures any contained hazardous substance flows outwards and can damage nearby plant or people as well as lead to pollution of the local environment. In recent years, this and similar subjects have given rise to a new kind of engineering—spill prevention and control. However, theoretical background, backed by experiment, is lacking to work out reliable regulations. An intermediate-asymptotic analysis for late-stage spreading is carried out in this paper. This analysis reveals several characteristic features of the spill wave such as transition period and linear relationships between spreading area and time, and wave front velocity and the inverse of zone radius. Most of the latter results have been verified by model experiment. This paper also discusses the discrepancies between observations and the theory suggested in a recent UK Health and Safety Executive report. Finally, the present paper puts forward proper modeling rules for future work.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):285-291. doi:10.1115/1.3243117.

A finite-difference calculation method based on the boundary-layer equations is described for the prediction of laminar, developed channel flow undergoing a symmetric sudden expansion. The scheme requires only a fraction of the computational effort required for the numerical solution of the full Navier-Stokes equations that are usually employed for this flow. Predictions of the method compare very favorably with experimental data and solutions of the full Navier-Stokes equations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):292-297. doi:10.1115/1.3243118.

An experimental program, to determine the magnitude of the force on the impact disk for the radial out-flow between parallel disks, has been carried out for moderate Reynolds numbers. The present results are compared with a previously published, ad hoc, analytical formulation whose coefficients were established for low Reynolds numbers. Acceptable agreement exists for the low Reynolds number range of the present study; progressively significant disagreement is observed as the Reynolds number is increased. The present force data, when combined with previous observations and interpreted via appropriate theoretical considerations, reveal a complex blending of flow phenomena for the Reynolds number, diameter ratio, and plate separation values of the present study.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):298-306. doi:10.1115/1.3243119.

This paper documents some of the effects of free stream turbulence on the mean flow properties of turbulent boundary layers in zero pressure gradients. Attention is concentrated on flows for which the momentum thickness Reynolds number is less than about 2000. Direct Reynolds number effects are therefore significant and it is shown that such effects reduce as the level of free stream turbulence rises. A modification to Hancock’s [1] empirical correlation relating the fractional increase in skin friction at constant Reynolds number to a free stream turbulence parameter containing a dependence on both intensity and length scale is proposed. While this modification has the necessary characteristic of being a function of the free stream turbulence parameters as well as the Reynolds number, it is argued that the relative importance of intensity and length scale changes at low Reynolds numbers; the data are not inconsistent with this idea. The experiments cover the range 500 ⪝ Reθ ⪝ 2500, u′ /Ue ⪝ 0.07, 0.8 ⪝ Le /δ ⪝ 2.9, where u′ /Ue is the free stream turbulence intensity and Le /δ is the ratio of the dissipation length scale of the free stream turbulence to the 99 percent thickness of the boundary layer.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):307-311. doi:10.1115/1.3243120.

A discrete free gas model is presented for numerical simulation of transients in liquids containing free gas. The model is also able to simulate vapor column separation during liquid transient flows in pipelines. The latter application may be the most significant attribute of the model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):312-318. doi:10.1115/1.3243121.

A method for analysis by singularity representations is presented for dynamic responses of partially cavitated hydrofoil cascade to axial gust in bubbly water. Conservation laws of mass and momentum are applied to take account of the unsteady parts of cavity area, cavity termination thickness, and cavity pressure for unsteady partial cavity model. Also, the cavitation compliance and mass flow gain factor obtained from the cavity model determined are considered in relations to cavity length, reduced frequency, and air volume ratio. Comparisons of the mean unsteady pressure rise and unsteady discharge difference are also made with the available former results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):319-326. doi:10.1115/1.3243122.

A survey of the main mechanisms of air entrainment in largely developed cavity flow is given, with paticular attention being given to plane, almost horizontal flows. Specific characteristics of dimensional analysis in this case are exhibited. The evolution of flow configuration when the airflow rate changes is described. Special emphasis is placed on cavity pulsation and its physical characteristics. Some aspects of the pulsation mechanisms are discussed, from a qualitative point of view, with a more detailed examination of the phase relations between the quantities involved.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):327-335. doi:10.1115/1.3243123.

Experimental results are given concerning the behavior of the so called “half-cavity” which is formed by a plane water jet, initially horizontal, projected over a small step at the bottom of a channel. The relation between the air flow rate and the cavity pressure is given particular consideration: the influence of geometrical or dynamic parameters on this relation is studied and it is found that the dominant role is played by the Froude number and the cavitation number. Other results concern cavity pulsation frequency and cavity length. Some theoretical considerations concerning the flow geometry are necessary to identify the gravity effect for the case where the cavity is long compared to the height of the step.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):336-341. doi:10.1115/1.3243124.

Measurements are reported of the pressure fluctuations in the near field of a submerged jet. The mechanisms by which the pressure fluctuations may be generated are discussed and estimates are presented of two of these, namely the transient oscillations of micro-bubbles of air excited by the pressure drop in the nozzle, and the cavitation of micro-bubbles by the turbulent pressure fluctuations in the jet mixing region.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):342-346. doi:10.1115/1.3243125.

The diagnostic facilities of the cross power spectrum and the coherence function have been employed to enhance the identification of not only the inception of cavitation, but also its level. Two piezoelectric pressure transducers placed in the downstream chamber of a model spool valve undergoing various levels of cavitation allowed for the use of both functions—the phase angle of the complex cross spectrum and the dimensionless coherence function—to sense clearly the difference between noise levels associated with a noncavitating jet from those once cavitation inception is attained. The cavitation noise within the chamber exhibited quite a regular character in terms of the phase difference between instruments for limited cavitation. Varying cavitation levels clearly illustrated the effect of bubble size on the attendant frequency range for which there was an extremely high coherence or nearly perfect causality.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):347-351. doi:10.1115/1.3243126.

The purpose of this paper is to investigate the existence of a correlation between the cavitation erosion rate of 99 percent pure aluminium and the sound pressure level of the cavitation noise. The data used were obtained recently for a variety of cavitation inducers and specimen locations at both the University of Southampton, Southampton, U.K. and the Admiralty Marine Technology Establishment, Holton Heath. A regression analysis of the logarithm of erosion rate on sound pressure level, expressed in decibels, shows that for each configuration there is a significant correlation, which is independent of fluid velocity and cavitation number, although the likely error is quite large. It is concluded that an absolute relation between erosion and sound pressure cannot be ruled out and that in any case it would be possible to define a relation for a given configuration provided that calibration could be done in advance.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1984;106(3):352-358. doi:10.1115/1.3243127.

The hydrodynamic stability of a rapidly evaporating liquid surface is examined. The problem is modeled to mimic the case of a superheated liquid in equilibrium with its vapor in which, the pressure above the liquid surface is dropped suddenly. Both the liquid and its vapor are assumed to be inviscid, incompressible and semi-infinite in extent. In addition, the temperature dependence of fluid properties is neglected. A linear stability analysis is applied to this model. This study differs from previous work in that time dependent base states are used. As a result, a system of linear homogeneous differential equations must be integrated in time. This system consists of a partial differential equation for the liquid temperature field and two other linked ordinary differential equations in time. Various types of thermal boundary conditions yielding different base state temperature profiles are considered. The results of this experimentation are contrasted. An attempt is made to compare results of the transient method to experimental data.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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