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RESEARCH PAPERS

J. Basic Eng. 1964;86(2):169-173. doi:10.1115/1.3653020.

A method of computing the critical flow function, critical pressure ratio, and critical temperature ratio is presented. Use is made of the NBS Circular 564 tabulated data of the speed of sound, enthalpy, and compressibility. Computations are made for dry real air at stagnation temperature from 60 to 100 F and stagnation pressure from zero to 300 psia. The change in the flow function and ratios is 0.9, 0.5, and 0.4 percent, respectively, over this range. Calculations are also performed at elevated pressure and temperature.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):175-182. doi:10.1115/1.3653023.

An approach to the development of “pressure-controlled” fluid-jet relays and amplifiers is proposed. The technique, based on experiments of a jet attaching to a flat wall, combines theoretical reasoning, experimental data, and graphical source-load matching. Single-control and symmetrical double-control amplifiers of a particular “knife-edge” design are used in the illustrations of the approach; typical data are given. Static and dynamic stability of the jet is emphasized including the criteria for oscillators.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):185-193. doi:10.1115/1.3653027.

A survey is presented of recent experimental and theoretical researches on the problem of periodic wakes behind a cylinder in a stream. A synopsis is given of the present knowledge on the mechanics of wake formation and of the associated hydrodynamic forces for the full Reynolds number range from the first appearance of a stationary vortex pair behind the cylinder up to transition of the boundary layer on the cylinder. Experimental data are viewed in the light of the theoretical results of Birkhoff, which, it appears, may replace the classical theory based on the first order stability of a potential flow street of vortex filaments. The paper closes with a discussion of the problem of the induced vibration of a spring mounted cylinder in a stream.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):197-204. doi:10.1115/1.3653033.

Linearized airfoil theory—in conjunction with a mapping technique—is applied to the calculation of the forces and moments acting on supercavitating hydrofoils operating near a free surface at very large Froude numbers and zero cavitation number. Only the effects of angle of attack and flap deflection are considered. The results—intended for engineering use—are presented primarily in the form of curves of flap effectiveness, lift curve slope, pitching and hinge moment coefficient, and flap loading versus flap-chord ratio, depth being introduced as a parameter. Lift-drag ratio and hinge moment coefficient as functions of lift coefficient are presented for typical operating conditions.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):207-212. doi:10.1115/1.3653036.

The analysis presented in this paper shows that poppet valve instability can be caused by interaction of the fluid delivery line dynamics with those of the spring-mass of the valve. The critical frequency in the system is the first harmonic of the delivery line higher than the natural frequency of the valve spring-mass. A stability criterion is derived which relates the design parameters of the valve to those of the system in which it must operate and methods of stabilizing the operation are suggested.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):213-217. doi:10.1115/1.3653038.

The time-varying flow of a boiling liquid through a series of ducts and heaters is considered for the case where the flow rate is controlled by a downstream orifice. It is shown that oscillatory flow will exist for a variety of configurations, provided that the density ratio across the system exceeds a critical value which depends on the geometry and the heat-transfer relationship.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):218-220. doi:10.1115/1.3653039.

An analysis is performed, similar to the classical one for screens, of the effect of a honeycomb on a turbulent stream, when the cell length is large enough to permit the flow to become fully developed. The results indicate that a honeycomb should reduce the turbulence level of a stream passing through it more effectively than a screen, due to two effects: (a) The annihilation of the transverse fluctuation, dependent on the assumption of fully developed flow; (b) the effect of the mass of fluid in each cell, which must be accelerated to permit the passage of a fluctuation. The latter suggests that the honeycomb may be viewed as an inductive filter, if the screen is regarded as the fluid mechanical analogy of a resistive one. A small number of measurements in water are presented which lend quantitative support to the argument. Finally, design charts are presented, which permit calculation of the reduction to be expected from the placing of a given honeycomb in a given flow.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):221-225. doi:10.1115/1.3653040.

An experimental and theoretical investigation is presented which describes the character of the mean motion and the structure of turbulence for the separation, reattachment, and redevelopment of the incompressible turbulent shear flow downstream of a single step-type roughness element. For the redeveloping turbulent boundary layer downstream of reattachment, it is shown that the mean velocity profiles constitute a one-parameter family and that as far as the shape parameters are concerned, this one-parameter family is essentially the same as for a boundary layer developing toward separation. This similarity between developing (toward separation) and redeveloping (after reattachment) turbulent shear layers is utilized to establish an integral method for calculating the redeveloping turbulent boundary layer at essentially zero pressure gradient.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):227-233. doi:10.1115/1.3653044.

Momentum integral equations for the turbulent flow at the plane of symmetry of a three-dimensional boundary layer are rigorously derived. The use of orthogonol curvilinear coordinates allows a simple physical interpretation to be given to the terms of the resulting equations. Evaluation and comparison are made between the derived results and earlier works in Cartesian sets and ambiguities are discussed. Results of an experimental program are reported for the case of a plane of symmetry flow in a collateral three-dimensional turbulent boundary layer wherein four different momentum integral equations are examined in predicting boundary-layer growth. As an aside, two common variations of shape parameter equations were also tested to determine their adequacy in application to this case.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):234-240. doi:10.1115/1.3653045.

An analytical and experimental investigation of the steady-state isothermal flow in a series system, comprised of a constant-diameter tube with reduced size unions located at the tube extremities, is reported herein. The pressure drop across the system has been determined experimentally as a function of the system geometry. The parameters chosen for investigation were the tube length to diameter ratio L/D, the union diameter to tube diameter ratio Df /D, and the Reynolds number. The ranges of the parameters investigated consisted of 159 ≤ L/D ≤ 1475, 0.7 ≤ Df /D ≤ 1.0, and 200 ≤ Reynolds number ≤ 100,000. All tests were conducted at room temperature. The theory is derived considering each geometric element of the system, such as inlet, development length, exit, and so on, and a set of five simultaneous algebraic flow equations results. Solutions to these were obtained by use of a digital computer. A pseudo-friction factor, for fully developed laminar or turbulent flow, is defined. The result indicates that the correlation of theory with experiment is quantitative over the range of parameters investigated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):241-246. doi:10.1115/1.3653046.

The results of the steady-state analysis presented in Part 1 are applied to a quasi-steady analysis isothermal flow in constant diameter tubes (with straight-through unions at the extremities) connected to a closed sensing volume. The ranges of transient pressure inputs and geometric variables were chosen to simulate typical missile pressure sensing systems. The effect of high inlet temperature during descent was not studied, all tests being at room temperature. The correlation of theory with experiment for three types of input (impulse, continuous, and shock) is shown to be quantitative over the range of variables studied. It is concluded that the empirical analysis presented herein provides an adequate working theory for pressure lag during transient flight.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):247-254. doi:10.1115/1.3653047.

Flow in de Laval nozzles of high pressure, low-quality steam-water mixtures was investigated to determine the resulting mass flow rates and to acquire design criteria information. Qualities ranged from 0 to 20 percent and pressures up to 1000 psia. Comparisons of the experimental data to three simple models: (a) isentropic expansion; (b) frozen composition; and (c) slip flow, showed satisfactory correspondence at all conditions except for qualities very close to saturated liquid. Observation was made that a condition similar to shock resulted when the nozzles were overexpanded.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):257-261. doi:10.1115/1.3653052.

Data and observations obtained during the study of two-phase flow phenomena for refrigerants flowing in small bore copper and glass tubes have been examined for their significance to the cavitation. Visual and photographic observations have been made of the inception of vaporization and of the movement of the point of inception as operating conditions are varied. Liquid tension has been deduced as occurring in these tests. Liquid tension and cavitation index data are presented. The experimental method is recommended as a means for studying many aspects of the phenomenon of cavitation.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):265-274. doi:10.1115/1.3653058.

A method is described for obtaining precise measurements of local density (or void fraction) in an axially symmetrical cavitating flow regime wherein a heavy fluid as mercury, molten lead, and so on, is used. The method can be adapted to light fluids by substituting a softer radiation source. Significant information regarding the cavitating flow regime in a particular venturi operating with mercury has been obtained. Among other things it has been shown that regions where substantial damage to test specimens has previously been noted [7] have void fractions of the order of only five percent.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):275-281. doi:10.1115/1.3653059.

Experiments with water in a high speed recirculating water tunnel were undertaken to measure the pressures at which incipient and desinent cavitation occurred. Incipient cavitation is defined as the onset of cavitation; desinent cavitation is defined as the cessation of cavitation. The two lucite test sections used formed the minimum area region of the nozzle in the water tunnel. One test section had a smoothly changing internal contour and the other had an abrupt contour change at the entrance to the cylindrical throat region. Cavitation in the abrupt contour occurred at the throat entrance at higher pressures than the cavitation pressures in the smooth contour. The cavitation in the smooth contour occurred at the entrance to the diffuser part of the nozzle. It was concluded that the cavitation pressures and cavitation numbers increased with velocity, the increase being greater for the abrupt contour with the exception of minimums indicated at incipient conditions in the abrupt contour at throat velocities near 88 ft/sec. A notable difference between the incipient and desinent cavitation numbers and pressures occurred for the abrupt contour, but not for the smooth contour using the techniques described for identifying the incipient and desinent cavitation regimes.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):285-290. doi:10.1115/1.3653063.

An accurate theory which included the following two methods was developed concerning the flow through an arbitrary form supercavitating hydrofoil: (i) A method by which to obtain the hydrofoil form for a given pressure distribution; (ii) a method by which to estimate hydrofoil characteristics. The accuracy of the previously reported linearized solution was checked on, and then a very simple effective correcting method for the linearized solution was found out.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):291-305. doi:10.1115/1.3653066.

The mechanism of head breakdown in cavitating inducers, as affected by thermodynamic properties of the pump fluid and scale effects, is discussed. The approach taken by other investigators is presented, and the limitations to cavitation scaling are examined in relation to experimental data. Because of the incomplete correlation with test data observed, a hypothesis is introduced which relates the head breakdown process to an acoustic shock phenomenon at the point of the leading-edge blade cavity collapse. Also, an integrated model for the cavitating cascade blade is developed, which makes it possible to correlate the potential flow cavity cascade model with the influence of thermodynamic properties, the thermostatic approach, and application of bubble dynamic studies to understand how suction performance is limited by inlet pressure.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):306-310. doi:10.1115/1.3653067.

It was previously shown that the size of loose wear particles formed during the sliding of two materials is equal to 60,000 Wab /P, where Wab is the surface energy of adhesion and p the penetration hardness. Experimental results are presented which show that the experimental particle sizes obtained with a few materials do indeed obey the theoretical relationship, and that the particle size is, as predicted, almost independent of such external variables as speed, time, geometry, and load, provided the load is not too great. Indeed, if particles of the wrong size are fed into the system, then they tend to be broken down or built up until the correct size is reached. However, changes of atmosphere and the use of lubricants, which alter the energy of adhesion, do have a marked influence on wear-particle size, and this fact suggests a possible use of wear-particle measurement to rate boundary lubricants. Other surface interaction phenomena which are governed by the W/p ratio are discussed, and it is suggested that the surface roughness generated during sliding is a function of this ratio.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):313-320. doi:10.1115/1.3653071.

It has been shown that half-frequency whirl is influenced by orifice location, number of grooves, groove location, and so on. This paper presents test results which show the effect of geometry on the threshold of half-frequency whirl. The following bearing configurations were tested: (a) Plain journal bearings with one orifice centrally located; (b) grooved journal bearings with two axial grooves; (c) grooved journal bearings with three axial grooves; (d) grooved journal bearings with three axial grooves and six orifices. In addition, load-carrying capacity and attitude angle for the plain cylindrical and the two and three axial-groove bearings with two groove positions are given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):321-327. doi:10.1115/1.3653072.

The threshold of half-frequency whirl for a rigid rotor in self-acting, plain-cylindrical journal bearings is analyzed by several methods, and the results are compared. The correlation among the various approaches appears to be good. The simplest method of analysis is, therefore, used for comparison with experimental data. Experimental results showing the effect of bearing length and bearing load are compared with theory. The influence of bearing length on the threshold speed follows closely the trend of the calculated results; however, the experimental threshold speeds are always a little higher. In comparing the effect of bearing load it is seen that the calculated threshold speed is consistently somewhat over-pessimistic, but the influence of rotor inclination is in very good agreement with experimental data. The methods presented in this paper can be used readily in design to insure stable operation with plain-cylindrical journal bearings.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):328-336. doi:10.1115/1.3653073.

This paper analyzes the load-carrying capacity of the externally pressurized gas journal bearing, including the effect of journal rotation and vibration. The analysis assumes small eccentricity ratio and small vibration amplitude such that a first-order perturbation solution is obtained. The gas is fed to the bearing through orifice-restricted feeding holes around the circumference in one or two feeding planes. The number of feeding holes is sufficiently large to permit treating the feeding planes as line sources. Results are given for the load-carrying capacity and the attitude angle.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):337-345. doi:10.1115/1.3653074.

The effect of a centrally loaded 150-deg partial bearing on the transmission of unbalance force is determined for a simple, symmetrical rotor-bearing system considering both static and dynamic unbalance. Design curves giving force transmission, mass and journal vibration, and oil-whip stability limits are included.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):348-353. doi:10.1115/1.3653077.

The development of the Reynolds equation for the general case of dynamically loaded journal bearings is extended to include the concept of an effective speed that combines in one term the angular velocities of the journal, bearing, and load. Numerical solutions for the short-bearing approximation are presented for the case of an oscillating effective speed and a load that is constant or varying sinusoidally. Results are compared with available experimental data. The major conclusion is that for those cases involving an oscillating effective speed and a reversing load, the only significant contribution to load capacity comes from the squeeze film and the wedge film can safely be ignored when designing such bearings.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):355-364. doi:10.1115/1.3653080.

Experimental agreement with a finite-difference solution of the isothermal squeeze film equation was obtained for steady-state sinusoidal squeeze motion of parallel, coaxial disks. At low squeeze number, the film force is in phase with the velocity; at high squeeze number, with the displacement. Compressibility effects at high squeeze number introduce a superambient mean film pressure, so that it is possible to operate a gas bearing on squeeze effects alone. Thrust bearings, spherical bearings, and journal bearings have been successfully operated as squeeze bearings, using both electromagnetic and piezoelectric devices to generate the squeeze motion.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):367-386. doi:10.1115/1.3653082.

This 1961–1962 lubrication digest reviews developments in fluid-film and rolling-element bearings, lubrication for bearings, gears, and automobiles; and covers basic work done in the general areas of friction and wear; elastohydrodynamic, boundary, and full film lubrication; and lubricant properties. The authors cover specific areas of lubrication literature and it is recommended that the reader, even the specialist, peruse related areas since the years of effort in this field have exposed more of the fundamentals; and the conclusious drawn, and the basic laws formulated in one area are important to all areas. It is wistfully hoped that the digest will disclose disproportionate effort because of funding and imbalance between empirical and theoretical work and spur corrective action.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):387-394. doi:10.1115/1.3653083.

This paper presents a simplified steady-state analysis of turbulent lubrication. Load-carrying capacity, attitude angle, and fluid film stiffness for plain cylindrical journal bearings operating in the turbulent regime are presented. Simple, easy to use relations for the calculation of load-carrying capacity were generated. Fluid film stiffnesses are included so that they can be used to calculate system critical speeds. In the analysis presented here, side leakage is neglected; however, existing published data on a 360 deg plain circular bearing were used to establish a correlation factor between laminar and turbulent leakage factors.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):396-403. doi:10.1115/1.3653086.

The ability of an externally-pressurized slider to follow faithfully the runout, or waviness of a rotating disk, or drum are investigated. The response and the stability of the slider are considered in terms of small displacements from the equilibrium gap width. The first part of the analysis treats the case of an incompressible lubricant. The dynamic Reynolds equation is integrated with respect to the space coordinate and the relative displacement of the slider is described by a nonlinear, second-order differential equation. Peturbation solutions are obtained, which permit successive approximations of small deviations from the equilibrium gap width. The second part of the analysis treats the case of a gaseous lubricant. A quasi-static variation of the pressure field is assumed and the problem is stated in terms of lumped parameters. The continuity equation and the equation of motion are linearized, yielding a third-order differential equation for small displacements of the slider from the equilibrium gap width. Results are discussed, with particular reference to the effect of the squeeze number, σ, on the response of the slider.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):405-413. doi:10.1115/1.3653089.

The Reynolds equation applicable to a self-acting partial-arc gas journal bearing is perturbed in terms of the compressibility number Λ. The resulting set of equations is then put into a standard form and Galerkin’s method is used to obtain bearing loads and stability derivatives. These results are expressed in a power series in Λ.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1964;86(2):212. doi:10.1115/1.3653037.
FREE TO VIEW
Abstract
Topics: Stability , Valves
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. 1964;86(2):414-416. doi:10.1115/1.3653090.
Abstract
Topics: Fluid dynamics , Water
Commentary by Dr. Valentin Fuster

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