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RESEARCH PAPERS

J. Basic Eng. 1972;94(3):513-519. doi:10.1115/1.3425468.

The vortex, the velocity, and the pressure distribution along the vane surfaces are calculated for two impellers, one having six vanes and the other twelve vanes. The vanes were of logarithmic shape with a blade angle of 30 deg and impeller inlet to exit radius (r1 /r2 ) ratio of 0.6. All the foregoing quantities were calculated for five different flow coefficients from 0.05 to 0.25 in steps of 0.05 for both the impellers. In the case of impellers with twelve vanes, the flow phenomena were also calculated at a flow coefficient of 0.16 so as to compare with the published results.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):521-531. doi:10.1115/1.3425471.

Cavitation damage tests of iron and steel have been carried out using two types of experimental facilities. One is a water tunnel system which presumably simulates the field conditions fairly closely and the other is a magnetostriction vibratory unit commonly used for accelerated cavitation erosion testing of metals. A comparison between water tunnel and vibratory tests shows a difference in mechanism of cavitation damage. Consequently, it has been concluded that the application of the test results obtained in a magnetostriction vibratory apparatus should be limited to provide rough data for the primary selection of proper materials to be used in the construction of hydraulic units and other industrial systems, unless damage is caused under similar conditions to that of the vibratory apparatus.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):533-541. doi:10.1115/1.3425474.

A brief review is given of the literature on damage accumulation during creep and inadequacies in our present understanding are pointed out. By drawing on recent studies of the processes involved in creep-rupture, it is suggested that a new criterion for creep-damage accumulation may be proposed, which is more general than existing approaches. This involves the consideration of both the initiation and propagation phases of fracture, and it is seen that in some cases, strengthening rather than weakening may result from prior loadings. Experimental results are cited in support of these observations.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):544-550. doi:10.1115/1.3425477.

The general nature of the flow separation of a turbulent boundary layer ahead of an inward-projecting normal step is shown to be well predicted by a rotational flow analysis (frozen vorticity theory). The basis of this theory—that in the immediate vicinity of major wall contour changes the diffusive effects of viscosity and turbulence on the vorticity may be neglected and the flow field thus made amenable to rather simple analysis—is demonstrated and its application, via numerical iterative calculation, to prediction of the separation flow occurrence ahead of a step in terms of a given turbulent boundary layer is indicated. Good experimental verification of the predictions is found.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):551-556. doi:10.1115/1.3425480.

A model and procedure for calculating turbulent mixing of a confined jet is presented. The flow consists of a high velocity jet which is directed into a constant diameter duct, where it mixes with a concentric, low velocity stream. The flow model which includes the wall boundary layer covers the entire flow development from the mixing tube entrance to the start of fully developed flow conditions. The calculated results are presented for a range of flow conditions and are compared with the experimental results of a previous paper by the same authors. It was found that including the boundary layer, as part of the model, gave results which were significantly different and in better agreement with experiment for small and moderate velocity ratios.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):559-563. doi:10.1115/1.3425484.

Cavitation damage is studied for several materials over a range of temperatures in the cavitating liquid from 0 C to 90 deg C. The cavitating liquids used were distilled water, distilled water buffered to pII 8, and a 3 percent solution of NaCl in distilled water. The cavitation damage was produced by continuous oscillation of the test specimens with a magnetostrictive transducer so that long term chemical effects tended to be suppressed. It is found that the maximum in the damage rate occurs at temperatures in the range 40 C to 50 deg C. The decrease in the damage observed at the higher temperatures is to be expected as a consequence of the increase in vapor pressure. The rise in damage at the lower temperatures has a less obvious interpretation and may be due to an increase in chemical activity with temperature.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):567-573. doi:10.1115/1.3425489.

Tests performed with a remarkable number of inducers and pumps indicate that there exists a definite pattern of the manner in which the velocity of flow of the liquid and the peripheral velocity of the inlet tips affect the suction characteristics of a pump. Within certain limits, this pattern is unaffected by the shape of the blades, by the type of the pump, and by the flow rate. This consistency of behavior allows one to calculate the NPSH-requirements of a pump along its total working range, provided that the suction conditions are not disturbed by a particularly unfavorable blade geometry or by other effects.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):575-580. doi:10.1115/1.3425492.

A method utilizing high pressure fluid environments is described whereby a three-dimensional subsequent yield surface was determined for 304 stainless steel. Cylindrical parent specimens of this material were prestrained in axial compression under fluid pressure and then small subspecimens were sectioned from these parent specimens. Finite element techniques were used to optimize the parent specimen size so that a zone of uniform axial stress would result during the prestraining. Longitudinal strains in this zone were monitored during the prestraining and the subspecimens were cut from this region in a manner that did not allow the machining to appreciably affect the properties of the specimens. Following this, conventional tension and compression tests were performed on the subspecimens in various fluid pressure environments to determine the yield strengths for the cold-worked material in the direction of the principal axis of prestrain and the two transverse axes. These data are used to construct the three-dimensional subsequent yield surface which clearly illustrates the effects on 304 stainless steel, of cold working under pressure.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):581-585. doi:10.1115/1.3425495.

The turbine hysteresis characteristics in Francis pump-turbines when operated as turbine were reported in the previous paper [1]. In the present report the characteristics of inner flow of runners will be observed and at the same time the effect given by the entrance angle of runner vanes and the sweepback at the entrance of runner vanes to the performance of pump-turbine will be studied. As a result, the enlargement of the sweep-back at the entrance of runner vanes is to be proved as a desirable remedy to hysteresis characteristics of Francis pump-turbines.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):586-588. doi:10.1115/1.3425498.

Metalworking under pressure requires viscosity data for the working fluids. A suitable viscometer is described and data on three typical hydrostatic metal working fluids presented.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):589-594. doi:10.1115/1.3425500.

Bend tests were conducted to determine the effect of changes in ambient pressure on the minimum bend radii of titanium and beryllium sheet. Sheet specimens of commercially pure titanium, Ti-6Al-4V, Ti-8Mo-8V-2Fe-3Al (beta-titanium alloy), Ti-8Al-1Mo-1V, and 1.5 percent BeO beryllium sheet were bent using a series of bend radii in fluid pressurized up to 225,000 psi. All the materials could be bent to radii well below this pressure level except Ti-8Al-1Mo-1V, and beryllium. Extrapolation of the test results indicated that these latter two material would have to be pressurized to about 260,000 psi to accommodate a 1T bend. No relationship was evident between mechanical properties of the sheet and the influence of ambient pressure on minimum bend radii. Strain and reduction in area values experienced by the sheet in bending were calculated as a function of bend radius.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):595-598. doi:10.1115/1.3425503.

Plates of 7075-T6 Aluminum have been folded along a major axis in pressure environments of atmospheric, 20,000 psi, and 40,000 psi. A finite element computer program is used to determine the stress state in the plates at various loads. Tension and compression tests conducted in pressure environments up to 70,000 psi were used to construct models using effective stress, effective strain, and pressure as parameters to predict the behavior of the material under various stress conditions. A prediction of the occurrence of fracture in the folded plate was possible using the computer results and the pressure dependent model. As better finite element stress analysis programs become available, both the forming operation and the test specimen can be analyzed to provide more accurate data that can be coupled with tension and compression data to predict the performance of metalforming operations under pressure.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):599-604. doi:10.1115/1.3425505.

This paper develops a program for closed loop simulation of the transient behavior of a hydroelectric composite. The system modeling is comprehensive, including such factors as governor nonlinearities in mechanical compensation and servomotion. Special emphasis is given to conduit simulation in its elastic and frictional characteristics. The problem of friction is treated by appropriate attenuation of the traveling pressure wave. This point of view accounts for the phenomenon of regained head at decreased flows. The turbine characteristics are represented globally by means of polynomial approximation [1].

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):606-611. doi:10.1115/1.3425508.

Pressure and acceleration-induced distortion of an incompressible, inviscid liquid region is predicted numerically. The liquid is bounded by both fixed and free boundaries, and its motion is irrotational. Normal velocity is prescribed on fixed, though perhaps permeable boundaries, and the starting velocity potential is given on all free surfaces. Distortions of the liquid region are described by the motion of discrete kinematic markers assigned to each free surface. Problems are formulated on a square mesh computation field in terms of velocity potential. The liquid region interior is solved numerically by overrelaxation at every time step, which permits velocity components and potential rates to be calculated at the free surfaces. Marker positions and potentials are advanced each time step, thus preparing the computation field for further overrelaxation, and the process is repeated until finished. This technique was formulated as a Fortran IV computer program, FREESURF, for studying free surface motions. The technique can solve two-dimension rectangular or axisymmetric problems with fixed boundaries and up to three free surfaces. Bubble expansion and collapse near a free surface, dam break flows, draining of a tank, and other similar problems can be predicted with the method.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):613-621. doi:10.1115/1.3425512.

A solution has been obtained for a stator-rotor pair operating in an annulus with constant hub and tip radii. The stator and rotor are represented as actuator discs, and perfect fluid flow is assumed. The solutions are exact within these limitations, no linearization being required. The forms of blade loadings considered allow the introduction of large vorticity by either the rotor or stator. As a result, the rotor may be a “nonconstant-work” row. The solutions obtained are of summational form, but many of the summations are obtained in closed form, the resultant formulas allowing rapid calculation of desired examples. An example numerical result is included.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):622-628. doi:10.1115/1.3425514.

A means of increasing the useful range of pressure sensing diaphragms is developed. This is done by considering certain variable thickness plates as potential diaphragms and attempting to maximize deflection without causing other performance characteristics to differ appreciably from those of a uniform thickness plate. A thickness variation which is simple to manufacture is found and optimum geometric parameters are determined. Results are presented in the form of a series of equations which are convenient for use by the instrument designer.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):629-635. doi:10.1115/1.3425517.

A series of experiments was carried out to investigate transient axial thrust caused by pump starting. Conditions of discharge piping pressure distribution around the impellers and the relation between steady and transient operating conditions were studied. Transient pump operating conditions were calculated and compared with test data. The maximum axial thrust at starting was calculated from the measurement of axial thrust under steady operating conditions and the calculation of transient operating conditions.

Topics: Thrust , Pumps , Pressure , Impellers , Pipes
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):636-642. doi:10.1115/1.3425519.

A new approach is proposed for analyzing the compressible turbulent boundary layer with arbitrary pressure gradient. Utilizing a compressible law-of-the-wall and a Crocco energy approximation, the new theory integrates the momentum equation across the boundary layer in terms of inner variables only. The result is a single first-order ordinary differential equation for skin friction, devoid of integral thicknesses and shape factors. When analyzed for flat plate flow, this new equation has an exact solution apparently superior in accuracy to any other flat plate theory (Table 1). The new equation also agrees well with supersonic skin friction data in both favorable and adverse pressure gradients. The new theory contains an explicit separation criterion and is the simplest and possibly most accurate existing analysis for compressible turbulent flow.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):643-648. doi:10.1115/1.3425520.

This paper investigates the effects of different boundary conditions in calculating pressure fields corresponding to incipient cavitation. We have utilized a technique which allows us to obtain a numerical solution of this problem for various frequencies and geometrical configurations. Our results provide evidence that determination of the pressure field is not only a function of depth but also a strong function of radius and whether or not the end conditions involve the use of a baffle. We have found that, particularly at the higher frequencies, the changing of the boundary conditions will cause large variations and differences in the pressure field. The numerical technique provides a method which allows the calculation of mixed boundary value problems associated with the reduced wave equation in finite domains. The technique specifies known error bounds. However, the distribution of errors over the domain is unknown.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):649-654. doi:10.1115/1.3425521.

Solutions of the second order longitudinal curvature boundary layer equations near the stagnation point of a two-dimensional circular cylinder are presented. Four cases corresponding to 1 first order locally similar solutions, 2 first order nonsimilar solutions, 3 second order locally similar solutions, and 4 second order nonsimilar solutions are considered. For each of the four cases, results for four different altitudes are given. The only second order effect considered is longitudinal curvature. Based on the numerical results, it is concluded that similarity and curvature assumptions can alter the skin friction calculations significantly. The heat transfer calculations are much less sensitive to the various assumptions, at least for the cases studied in this paper.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):655-665. doi:10.1115/1.3425522.

This study consists of three parts: the effects of heat and mass transfer on the motion of nearly spherical bubbles; the effects of compressibility of the liquid on the motion of nearly spherical bubbles; and the variational methods for dynamics of nonspherical bubbles. The programs of the linear stability of spherical bubbles become more complete with the former two parts, while the latter not only offers an alternate exact method to deal with the problem but also opens new avenues for approximate treatments. Analyses are limited entirely on the theoretical level in this study.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):666-674. doi:10.1115/1.3425523.

The influence of tangential fluid injection on the performance of inherently stalled, two-dimensional diffusers is examined both analytically and experimentally. In particular, the effects of injection flow rate, slot size, and blowing system efficiency on pressure recovery characteristics are investigated. A finite-difference method of analysis based on a model suggested by Patankar and Spalding is used to predict diffuser performance with jet blowing for purposes of comparison with the experimental results. The analysis is also utilized to predict the influence of variations in injection slot location and jet velocity profile shape on overall performance. The results show that significant increases in diffuser performance can occur with fluid injection, even when jet blowing power requirements are taken into account.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):675-681. doi:10.1115/1.3425524.

The fundamental transverse oscillations of a liquid jet which impinged upon a flow splitter were examined for a wide range of dimensionless splitter distance, nozzle exit Reynolds number, and dimensionless frequency. The results are presented in the form of a design map. The data, taken at low nozzle aspect ratio, reveal that fundamental (stage 1) oscillations can exist for Reynolds numbers up to at least 7000. Up to Reynolds numbers of about 3000, the jet behavior is Reynolds number dependent for all values of splitter distance. Beyond Reynolds number of 3000 the jet behavior is independent of Reynolds number. In general, the Strouhal number, based on nozzle exit-splitter distance, decreases with increasing values of splitter distance. Jets issuing from nozzles with no parallel development sections were considered. Jet nozzle shape influences the dimensionless frequency of oscillation in that the effect of a vena contracta formation outside the nozzle exit is to yield a higher value of dimensionless frequency relative to nozzles which produce parallel flow with small boundary layer thickness at the exit. Similar decreases have been found for two-dimensional jets. Of the above findings, the only comparable results for two-dimensional jets are variations in Strouhal number with nozzle exit-splitter distance.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):682-688. doi:10.1115/1.3425525.

The paper describes an experimental investigation of the characteristics of low-Mach number flow of air from four planar nozzles. The nozzles had rectangular (rounded) inlets from a circular duct and aspect ratio of 3 at the exit. In general, two types of spiraling secondary flows were observed at nozzle exits. One type was observed in the vicinity of the midplane of the nozzles near the upper and lower walls, and the other type in the vicinity of the side walls in the corners. Experiments have shown that the secondary flows located in the vicinity of the midplane are produced by the contraction from the circular duct to the rectangular inlet, while the secondary flows located in the vicinity of the side walls are produced by the boundary layer migration toward the convex inner wall sections of the nozzles. The secondary flows have low total pressure associated with them. A comparison of discharge coefficient is made for the nozzles examined. The experiments were performed at the Reynolds numbers, based on the average flow speed at the nozzle exit and nozzle throat width, in the range of 3.4 × 103 to 2.5 × 104 .

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):689-696. doi:10.1115/1.3425526.

The swirling, incompressible flow within a short vortex chamber of aspect ratio 1/9, defined by the ratio of chamber height to chamber diameter, has been investigated analytically. The theoretical analysis consists of the adaptation of Wormley’s analytical technique and the extension of the method to include the apparent viscosity factor. The Runge-Kutta method is used to solve numerically the set of differential equations. The analytical results are compared with those of the experimental investigations conducted by Savino and Keshock. The analytical results prove that the values of apparent viscosity seriously affect the velocity profiles within the vortex chamber. The results also show that the apparent viscosity varies from 7000μ at the vortex chamber periphery to 4500μ at the orifice exit plane, where μ is the operating fluid viscosity. An empirical expression for the apparent viscosity is found in the form μa = K1 νδn + K2 , where n, K1 , and K2 are constants and νδ is the tangential velocity. The constants n, K1 , and K2 are found to be −1/3, 0.01, and 0.0005, respectively, for this investigation.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Basic Eng. 1972;94(3):697-698. doi:10.1115/1.3425527.
Abstract
Topics: Flow (Dynamics)
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(3):700-703. doi:10.1115/1.3425529.
Abstract
Commentary by Dr. Valentin Fuster

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