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RESEARCH PAPERS

J. Basic Eng. 1970;92(4):671-678. doi:10.1115/1.3425101.

Utilizing an ultrasonic vibratory cavitation facility, the onset of cavitation was observed in liquid sodium for different liquid sodium temperatures and at various sinusoidal pressure field frequencies. It was observed that the pressure oscillation required to initiate cavitation decreases linearly as the temperature of the sodium is increased from 500 to 1500 deg F. For frequencies below 20 kHz the cavitation threshold pressure amplitude is essentially independent of frequency. For frequencies above 20 kHz the cavitation threshold begins to increase sharply. Using the onset of cavitation data and the saturation temperature-pressure data for liquid sodium, the superheat required to produce nucleate boiling in liquid sodium was calculated. As the saturation temperature of liquid sodium is increased the calculated superheat decreases. For frequencies below 20 kHz the calculated sodium superheat requirements, which are independent of frequency, are in good agreement with steady-state sodium superheat data reported in the literature.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):681-688. doi:10.1115/1.3425105.

This paper is a review of existing knowledge on cavitation nuclei. The lack of significant tensions in ordinary liquids is due to so-called weak spots or cavitation nuclei. The various forms which have been proposed for nuclei are gas bubbles, gas in a crevice, gas bubble with organic skin, and a hydrophobic solid. The stability argument leading to the postulation of the Harvey model is reviewed. Aspects of bubble growth are considered and it is shown that bubbles having different initial sizes will undergo vaporous cavitation at different liquid tensions. The three modes of growth, namely vaporous, pseudo, and gaseous are presented and implications concerning the interpretation of data are considered. The question of the source of nuclei and implications concerning scale effects are made. The measurement of nuclei is considered together with experiments on the effect of gas content on incipient cavitation.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):689-694. doi:10.1115/1.3425106.

Condensation initiated by heterogeneous nucleation, which is surface dependent, is examined experimentally for the case of rapid nozzle expansions of water vapor. In contrast to previous de Laval nozzle steam experiments for vapor condensation initiated by homogeneous nucleation, the present results are for flows seeded with inorganic smoke and metallic ions. The influence of heterogeneous seeding materials on the condensation process is readily observable by comparison of seeded and unseeded experiments which are otherwise identical. Quantitative results for temperature and other properties, as well as condensation rates, follow based on pressure distribution. The results indicate that the prolonged isentropic expansion of a seeded flow gives a substantial decrease in entropy production for 1/10 micron and below particle sizes determined by electron microscopy. An attempt is made at determining the relative influence of ions and smokes. The competitive nature between heterogeneous and homogeneous processes is clearly evident.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):695-701. doi:10.1115/1.3425107.

Gas-vapor nucleation in liquid solutions is considered. It is shown that for nucleation to occur in a multicomponent solution a nucleus must be created of at least a certain radius. Consideration is then restricted to weak solutions of gas dissolved in liquids with the gas allowed to behave nonideally. A generalized Kelvin equation is derived which relates the partial pressure of the solvent vapor inside a nucleus to the properties of the surrounding solution. It is shown how, for a given temperature, the pressure at which nucleation occurs in a gas-liquid solution is increased as the gas concentration is increased.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):705-711. doi:10.1115/1.3425114.

The case of bubble formation in both quiescent and moving streams due to the injection of a constant gas flow through a small tube is considered. Relationships predicting the expected size and quantity of bubbles generated are proposed. These are compared with measurements taken with stream velocities up to 9 ft/sec, while generating gas bubbles from 40 to 700 microns in diameter. For the case of generation in a quiescent stream the forces due to the virtual mass, surface tension, viscous drag, buoyancy, and the wake formed by the preceding bubble are accounted for. There still remains some question (only partly answered by a comparison with measurements) as to the proper added mass coefficient and the geometry of the bubble previous to detachment, as well as an adequate estimate of the interaction with a preceding bubble’s wake. The proposed model for generation in a moving stream is in good agreement with actual measurements for co-flowing velocities between 1 and 9 fps and capillary tubes in the order of 10−3 cm in dia.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):712-722. doi:10.1115/1.3425117.

A theoretical model of a turbine meter operating in the high Reynolds number regime has been formulated to study the effects of retarding torques, inlet velocity profile, blade interference effects, meter geometry, and other factors. A computer program predicts actual rotor speed by numerical integration of the lift and drag forces on the rotor blade. Numerical sample calculations indicated substantial effects due to velocity profile and blade interference. Retarding torques were relatively unimportant in the high Reynolds number range.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):724-731. doi:10.1115/1.3425121.

The need for a simple and inexpensive method for field checking gas turbine meters exists. One such method called the “spin test” is described in this paper. The relationship between the change of “rotor coast time” of the spin test and the change of meter accuracy due to change of mechanical friction is formulated. Experimental results on two different 6-in. gas turbine meters are presented and show good agreement with analytical results.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):732-739. doi:10.1115/1.3425124.

Results of an experimental investigation of the laminar flow of air over a downstream-facing step are presented. The experiments include visual observations of smoke filaments (in the viscous layer), qualitative velocity fluctuation measurements, and mean velocity profiles. Results are reported over a range of 0.36 – 1.02 cm in step height, 0.61 – 2.44 m/sec in free stream velocity at the step, and 0.16 – 0.51 cm in boundary layer displacement thickness at the step. Laminar flow to reattachment of a free shear layer is observed for subsonic flow and two criteria for which transition to turbulence at reattachment exists are presented. The laminar reattachment length is not a constant number of step heights as for turbulent flow, but varies with Reynolds number and boundary layer thickness at the step. The shape of the velocity profile at reattachment is found to be similar to the shape of a laminar boundary layer profile at separation and the boundary layer profiles downstream of reattachment are similar to those in a laminar boundary layer developing toward separation except that they are traversed in the reverse sense.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):742-751. doi:10.1115/1.3425127.

When flow calibrating a head class meter to establish its discharge coefficient, measurement of the fluctuating differential pressure has caused the largest uncertainty. With conventional techniques, the reported precision of determining discharge coefficients may range from ±0.1 percent to ±0.3 percent. Improved precision and accuracy in the measurement of differential pressure can be achieved by the Null Balance Integration (NBI) instrumentation system reported in this paper. Using this system the obtainable precision ranges from ±0.02 percent to ±0.04 percent. The system provides accurate determination of the average value of the fluctuating differential pressure signal by establishing a constant, predetermined reference differential. The fluctuating differential pressure, developed by the primary element, is continuously compared to this reference differential pressure. The difference is a secondary analog signal, which includes the fluctuation of the measurement signal plus whatever average difference exists between the measured and reference signals. This secondary difference signal is integrated electronically for the calibrating period. The total is divided by the calibrating time and the resultant average difference is algebraically added to the value of the reference signal. The result is an accurate average value of the measured signal during the calibration period. Orifice coefficient data is presented using the NBI System combined with a high accuracy static-weigh/time system. The spread in coefficients was ±.022 percent.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):752-762. doi:10.1115/1.3425130.

New equations are developed which predict the coefficients of discharge for concentric orifice plates as functions of line size, diameter ratio, and Reynolds number. These are developed using modern statistical techniques and an IBM 360 computer. Standard deviations are calculated which show the tolerance with which these new formulas predict the coefficients. The effect of the line size and the diameter ratio on the standard deviation are also presented for the case of flange taps. These equations should be used for predicting the coefficients only in the ranges of Reynolds number, diameter ratio, and line size covered by the data from which they were deduced.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):766-781. doi:10.1115/1.3425134.

The asymptotic analysis of the gaseous squeeze-film bearing has been extended to obtain 0 {σ−1/2 } effects in accordance with the isothermal gas lubrication theory and the method of singular perturbation. 0 {σ−1/2 } corrections are identified to contain not only edge effects (inner problem) but also edge-interior interactions which are analogous to the boundary layer displacement effects in aerodynamics. The latter features can further be recognized to be related to mean-gap taper, squeeze taper, and cross-edge sliding. These results are discussed from the point of view of “global bearing properties” including the temporal mean as well as the in-phase and quadrature synchronous components of the fluid film force and moment. The edge effects are presented in terms of universal functions which can be used directly as corrections in the global properties. The edge-interior interactions must be determined by solving the asymptotic p.d.e. with boundary condition also expressed in terms of universal functions. Formulations applicable to cylindrical, conical, and spherical bearing geometries are outlined. Illustrative numerical examples are provided. Conditions affecting the validity of the isothermal gas lubrication theory (neglecting inertia effects) as related to the magnitude of the squeeze number are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):782-788. doi:10.1115/1.3425135.

Wear on the upstream side of small metal orifices subject to large pressure drops (3000 psi) in phosphate ester base hydraulic fluids has been found to be the result of an electrochemical corrosion driven by a streaming current. A calculation for the current produced by the flowing fluid is described. Results of the calculation and of experimental work are given as evidence in support of the proposed wear mechanism. A large variation of wall shear stress along the metal surface is found to be necessary for the wear.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):792-795. doi:10.1115/1.3425139.

An air metering system has been constructed using an array of critical flow venturis. By plugging individual venturis, the total metering area is varied to provide an airflow range from 25 lb per sec to 1200 lb per sec. A unique flow control valve and air straightening section provides low air velocity distortion at the entrance to the meter.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):797-806. doi:10.1115/1.3425142.

The performance characteristics of supercavitating flapped foils in cascade, (such as the lift coefficient, the drag-lift ratio, and the limiting inlet flow speed) are calculated, for various cascade arrangements and flap angles, as well as flap-chord ratios, e. The extreme case when e = 1.0 corresponds simply to adjusting the cascade angle, such as in the Kaplan-turbine runner. It is found that the poor supercavitating cascade performance characteristics at conditions other than the designed condition, that is, the off-design performance characteristics, are noticeably improved with the use of flapped foils. The characteristics of cascaded foils without flaps, especially where there are no adjustments in cascade angle, make their use impractical in the off-design condition.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):807-813. doi:10.1115/1.3425145.

Cavitation erosion rates in the organic liquids formamide, ethanol, acetone, and glycerol are compared with the rate in distilled water. As is to be expected, these non-ionizing liquids, which are chemically less reactive with metals than water, show lower damage rates. The cavitation damage rates have also been measured for solutions of these organic liquids in water and all these solutions show a monotonic decrease in going from pure water to the pure organic liquid except glycerol. The water-glycerol solutions go through a minimum damage rate for a solution with molecular ratio of glycerol to water of approximately 1 to 1. Solutions of ethanol in glycerol show a maximum in damage rate for a solution with molecular ratio, glycerol/ethanol, of about 2 to 1. Qualitative differences in the cavitation bubble cloud in the various liquids studied are indicated by short-exposure photographs.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):815-818. doi:10.1115/1.3425149.

The growth of a spherical bubble in a viscous, incompressible fluid due to a transient tension is analyzed. The maximum attainable radius of the bubble is derived. The problem is closely related to the experimental study of cavitation inception by the stress wave technique. The analysis reveals clearly the role played by the viscosity and shows that for liquids of high viscosity the stress wave technique can be employed advantageously to determine the average sizes of the nuclei of cavitation.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):819-826. doi:10.1115/1.3425152.

A structural analysis program (Axibody) using conforming triangular finite elements is developed and applied to the study of composite axi-symmetric structures. Two types of elements are used: a novel axi-symmetric ring element and a two-dimensional plain stress element of varying thickness. The displacements in both cases are represented by a complete third-degree polynomial. The derivation of the stiffness and the consistent equivalent load matrices of the elements are described as well as a brief note on the program. Several examples are treated and the results are compared with the theoretical solution. A direct comparison with the results of a strain gauge test performed on a large stay ring—spiral case assembly is also made. Excellent agreement is obtained in all cases.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):827-835. doi:10.1115/1.3425153.

Data on the gross performance of conical diffusers subjected to annular secondary injection at inlet are reported. Tests indicate that the improvement in diffuser performance is significant even at moderate rates of injection. The effects of injection rate and diffuser geometry on the pressure recovery and stall are discussed. An analytical method based on the solution of the boundary layer equations by the Patankar-Spalding finite difference method has been used to obtain predictions of pressure recovery with inlet injection. The predictions compare well with the experimental results.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):836-842. doi:10.1115/1.3425154.

The development of the normalized Reynolds stress tensor, ui uj /q2 , in the region upstream of a fully developed, turbulent shear flow is investigated. An inviscid, linear model is used to predict values of the normalized Reynolds stress tensor as a function of position. The theoretical predictions are then compared with experimental results.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):843-848. doi:10.1115/1.3425155.

Experiments were performed to study the laminar flow characteristics and the laminar-turbulent transition in a parallel-plate channel, one of whose bounding walls is a porous medium. The flow regime investigated herein is characterized by parallel, unidirectional, fully developed flows in the channel and the porous medium. The experimental results for the laminar regime were found to be in excellent accord with theoretical predictions based on a model which admits a slip velocity at the surface of the porous material. The effect of the presence of the porous wall is to increase the mass flow and decrease the friction factor relative to the corresponding quantities for a solid-walled channel. In addition, transition to turbulence occurs at a lower Reynolds number owing to the presence of the porous wall.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):849-856. doi:10.1115/1.3425156.

The complete linear two-port admittance parameters of a short uniform pneumatic line are experimentally determined as functions of driving frequency and the steady through-flow in the line. The measured through-flow influence (c.f. the driving point admittance increase) is found to be much greater than that predicted by known one-dimensional acoustic models (frequency dependent phase velocity and attenuation factor) with mean velocity Doppler shift correction. More satisfactory agreement is found with a model which considers the first-order effects of the through-flow velocity profile. High-frequency (up to 2500 Hz) laminar dynamic flow and pressure data is presented for lines on the order of 6 in. long and 1/8 in. ID, with Mach numbers from zero to 0.16. The experimental aspects of quantitative dynamic flow measurement with a hot-wire anemometer are discussed in detail. Details and calibration of the high-frequency line flow and pressure probes, and the low Reynolds number—high Mach number flow test setup are presented.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):857-864. doi:10.1115/1.3425157.

It is proposed in this work that the transition to slug flow occurs due to Kelvin-Helmholtz instability, which, in this case, is enhanced by the proximity of the upper wall and becomes wave-amplitude dependent. Since the surface waves possess a limiting amplitude, the transition can be predicted by examining whether the highest possible waves are unstable. The theoretical prediction is in good agreement with the authors’ experimental results. It also agrees reasonably well with Baker’s and Schicht’s flow pattern charts for strictly horizontal channels, but it exhibits large differences when the channels deviate somewhat from the horizontal.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):865-873. doi:10.1115/1.3425158.

A laminar boundary-layer model is proposed to account for viscous losses during the transient turbulent flow of a liquid in a tube. In this model, inviscid slug flow is assumed for the core and all viscous effects are assumed to occur in the boundary layer. The transient boundary-layer velocity distribution is determined as a function of a prescribed variation in core velocity and the associated pressure gradient. Both analytical and numerical solutions are presented. This transient flow information is used to calculate local and integrated energy dissipation rates which are then combined, with one-dimensional energy analyses. The result is a prediction of the decrease in pressure-wave magnitude due to viscous dissipation, and a comparison is made with experimental data for rapid flow extinction. Good agreement between the observed and predicted results is obtained.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):874-882. doi:10.1115/1.3425159.

It is the objective of this paper to investigate the dynamic response of fluid and heat flows in screw viscosity pumps so that their performance may be correctly and easily predicted, the design of the pumps may be improved, and appropriate automatic control devices may be installed on them if necessary. These pumps consist essentially of a spindle threaded with screws working within a closely fitting sleeve. The analytical model consists of a viscous fluid in a stationary groove induced to flow by the sliding of a cover plate. The groove is of rectangular form or a semicircle. The effects of fluid viscosity and compressibility are included to derive transfer functions relating the pressure and velocity variables at the two cross sections of a line and the velocity of the sliding cover. The response of the fluid temperature to a deviation in the plate temperature or heat flux is also investigated. Numerical results are obtained for the frequency responses of the fluid velocity, pressure, and temperature for a screw viscosity pump with large-width rectangular groove. A phenomenon of resonance in the amplitude ratio and phase shift is disclosed. Screw viscosity pumps to which the analytical results apply include the screw pressure machine and the screw extrusion machine.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):883-888. doi:10.1115/1.3425160.

The kinetic energy correction factor for the flow at the vena contracta is calculated using experimental data and a modified Bernoulli equation. Based on an assumption of similarity of the profiles upstream and downstream of an orifice, two other nonuniformity factors, the momentum correction factor and the ratio of average velocity to center-line velocity, are also determined.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):889-900. doi:10.1115/1.3425161.

A pump which operates by setting up a vortex in a chamber in front of the impeller is often called a vortex pump. Vortex pumps by virtue of this design have a large free and open flow passage which permits the pumping of solid materials without danger of obstruction. They are thus in common use as materials handling pumps. A one-dimensional analytical model of such a pump is created, handling a Newtonian single-phase fluid. Calculated performance parameters are compared with those measured on a laboratory model. Overall pump characteristics are also computed and compared to those of a number of test pumps of various geometries. Finally, an examination is made of the similitude parameters governing this style of pump.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):901-907. doi:10.1115/1.3425162.

Experiments were conducted in a 1-in. × 3-in. supersonic wind tunnel on two-dimensional secondary fluid injection into a uniform primary supersonic stream. Both primary and secondary fluids were air at the same stagnation temperature, but the secondary stagnation pressure was varied from about 0.2 to 2 times the primary value; injection was sonic and the jet issued into the primary stream through a slit of constant width at 0 deg, 8 deg, 23 deg, and 50 deg upstream (the angle being measured from the normal to the primary flow). Primary stream Mach number covered the range from 1.64 to 2.96 in the tests. The shape of the leading shock shows similarity in modified blast variables at all angles of injection. It is also found that the separation shock in front of the main shock corresponds to a nearly constant flow deflection of about 10 deg. Estimates of the interaction force obtained from the measured pressure field show rough agreement with the calculations of Broadwell and of Spaid and Zukoski, and while supplementing the experimental data given by the latter, they bring out the dependence of the amplification factor on injection angle.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):908-914. doi:10.1115/1.3425163.

A two-dimensional incompressible isothermal laminar separation of a Newtonian fluid in steady flow was investigated. The geometry chosen for this study was a constant-width channel with a sharp 90-deg turn. It was found that an adaptation of a numerical solution for the Navier-Stokes equations first proposed by Allen gave convergence for all Reynolds numbers in the laminar range. The analytical results were compared with measured velocity profiles from a very low-speed wind tunnel.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):915-922. doi:10.1115/1.3425164.

The impinging jet problem is solved by an iterative finite-difference technique. Reynolds stresses are assumed to be related to the mean strain by a scalar eddy viscosity. The eddy viscosity is assumed to depend on the level of energy fluctuations and a length scale. The level of energy fluctuations is obtained from a second-order differential equation, while the length scale of turbulence is prescribed on the basis of experimental information. The solutions show reasonable agreement with experiment.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):923-929. doi:10.1115/1.3425165.

Analysis and tests were made to investigate the hydrodynamic mass and damping effects of a liquid in a thin annulus surrounding a vibrating rotor. The analytical results are described in this report and the test results in Part 2. The analysis determines the fluid forces for the general case of a vibrating rotor. Vibrational amplitudes and the limits of dynamic stability are then determined for a constant-speed rotor excited by unbalance. Fluid flow was assumed incompressible and tangential and to be in the Taylor vortex regime or in the turbulent regime. The Taylor vortex regime is considered a natural convection process resulting from centrifugal force gradients, while the turbulent regime is a forced convection process. As a result, annular flow around a rotor is considered an inherent combination of forced and natural convection. Fluid damping is estimated for each process separately and for the case where the vortex and turbulent process are predicted to occur simultaneously.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(4):930-937. doi:10.1115/1.3425166.

Analyses and tests were made to investigate the hydrodynamic mass and damping of a fluid in a thin annulus surrounding a rotor which is vibrating due to unbalance forces. The analysis is described in Part 1. This report describes the tests. Vibrational amplitudes were measured of a constant-speed rotor with various fluids and radius-to-clearance ratios. Axial flow was restricted by limited-leakage end seals. The fluid flow was considered to be either vortex or turbulent, based on the Taylor or Reynolds number. The presence of the fluid was found to lower the critical speed. This effect was ascribed to a hydrodynamic mass which was evaluated from the tests. Hydrodynamic masses were also determined for the rotor vibrating without rotation and were found to be in agreement with the results of Stokes [1]. All results were in reasonable agreement with the predictions of Part 1.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

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