bluuebunny/crossref_metadata_2025 huggingface dataset:
Steady Fluid Flow in a Radial Vaneless Diffuser
Authors: Jansen W.
Published: November 2011

The performance of a centrifugal pump or compressor system has often been investigated on an overall basis for a wide range of operations and these investigations have, in the past, resulted in some remarkable technical advances. Detailed and penetrating studies of both the rotor and the components up and downstream are essential to obtain a knowledge of the critical areas and to increase further the efficiency of the system. In this study one problem area, the flow in radial diffusers in the absence of unsteady flow, is isolated and an extensive analytical and experimental study concerning this has been undertaken. In the absence of wakes from the impeller or other unsteady flow phenomena, the formation of a boundary layer on the side walls of the diffuser is the main cause of a loss in diffuser efficiency. The boundary layers which are three dimensional in character are investigated for several inlet conditions, and the theoretical results are compared with those of the experiments; the agreement is good. The analysis is extended for a three-dimensional compressible boundary layer.
Pressure Drop Due to the Entrance Region in Ducts of Arbitrary Cross Section
Authors: Lundgren T. S. , Sparrow E. M. , Starr J. B.
Published: November 2011

A general analytical method has been devised for determining the pressure drop due to flow development in the entrance region of ducts of arbitrary cross section. The essential feature of the analysis is that the pressure drop can be determined without actually solving for the entrance-region velocity development. Instead, the calculation only requires a knowledge of the fully developed velocity profile. Application of the method is made to a variety of cross sections including the circular tube, elliptical ducts, rectangular ducts, isosceles triangular ducts, and annular ducts. Numerical results are presented and comparisons are made with available experiments and with prior analysis.
The Stability of an Annulus of Liquid in a Tube
Authors: Griffith Peter , Lee Kyung Suh
Published: November 2011

An annulus of liquid on the walls of a tube is sometimes found to be unstable under the action of surface forces and to break up, spontaneously, into a series of bubbles. This process is a possible mechanism for the transition from annular to slug flow. The wavelength of the breakup is predictable from potential-flow theory and the essential correctness of the prediction shown from experiment. It is shown that for liquid volume fractions less than about 6 percent no breakup occurs. The time to breakup is not found to be predictable.
On the Axial Rigidity of a Perforated Strip and the Strain Energy Release Rate in a Centrally Notched Strip Subjected to Uniaxial Tension
Authors: Forman R. G. , Kobayashi A. S.
Published: November 2011

This paper presents theoretical studies on the axial rigidities in strips with circular and elliptical perforations and subjected to uniaxial tension. Greenspan’s original derivations on these axial rigidities [2] were improved by using the elasticity solutions by Howland [6] and Ishida [7] for infinite strips with circular and elliptical perforations, respectively. Finally, the correction factors for centrally notched strips subjected to uniaxial tension were rederived from the above results following the energy approach by Irwin and Kies [3].
A Study of the Dynamic Features of a Wall-Reattachment Fluid Amplifier
Authors: Muller H. R.
Published: November 2011

The paper describes the characteristics of a wall-reattachment fluid amplifier. The switching of the jet from the wall to which it is attached to the opposite one is analyzed. It is shown that the control input characteristic that is measured statically can be applied in the dynamic case. This fact is far from being trivial, as the transient flow patterns occurring during the switching process are basically different from the stationary patterns. The variation of the response time (time interval between when a control pulse is applied at the control port and when the output signal is received at the other receiver) with the control supply pressure is given and compared with the results obtained from a simple analytical switching model. For a control supply pressure of 40 percent of the supply pressure, the response time is 5 to 8 times the transport time of a particle traveling 20 times the nozzle distance.
The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts
Authors: Sparrow E. M. , Lin S. H.
Published: November 2011

A new analytical method has been applied for determining the developing laminar flow in the hydrodynamic entrance region of annular ducts. Detailed results are presented for the development of the velocity distribution and the pressure drop over a wide range of annulus radius ratios r1/r2 (r1 = inner radius of annulus, r2 = outer radius of annulus). It is found that the pressure drop and flow development in annular ducts with radius ratios substantially less than unity is quite similar to that in a parallel-plate channel (r1/r2 → 1). On the other hand, the results far an annular duct with radius ratio as small as 0.001 depart significantly from those for a circular tube (r1/r2 = 0). The hydrodynamic entrance length, measured as a multiple of the hydraulic radius, increases as the duct radius ratio decreases at a fixed Reynolds number.
Vorticity Generation of a Body of Revolution at an Angle of Attack
Authors: Rodgers E. J.
Published: November 2011

An experimentally obtained velocity field about a body of revolution at a small angle of attack, and at subsonic velocity, is used to determine the vorticity distribution about the body. Surface-flow visualization and pressure-distribution tests are used to supplement the vorticity-distribution data in attempting to explain the mechanisms of the flow, and thus the differences between the real flow and that predicted by potential theory.
Cumulative Plastic Deformation in Rolling Contact
Authors: Moyar G. J. , Sinclair G. M.
Published: November 2011

Plastic deformation that accumulates with running time may constitute a mode of failure in some rolling element applications, particularly at elevated temperature. This phenomenon is studied in a simple room temperature investigation involving annealed brass toroids and cylinders mated with hard steel rollers. Evidence of sizable accumulation of plastic strain with cycles of rolling, despite subsequent contact stress reduction, leads to a consideration of the effect of a complex combined stress history, such as that induced by the rolling action, on plastic flow in metals.
Turbulent Flow in the Inlet Region of a Smooth Pipe
Authors: Barbin A. R. , Jones J. B.
Published: November 2011

This paper reports measurements of mean velocities, turbulence intensities, and turbulence (Reynolds) stresses in the inlet region of a smooth pipe. Data are presented for the first 40 diameters of pipe length. Fully developed flow is not attained in this length for a Reynolds number (based on pipe diameter and mean velocity) of 388,000, but the wall shear stress and the static pressure gradient attain their fully developed values within the first 15 diameters. Velocity profiles at successive sections in the inlet region are not similar as assumed in some published calculation methods. Longitudinal convection of turbulence energy is appreciable; except very near the pipe entrance, radial convection is negligible.
Plane Turbulent Wall Jet Flow Development and Friction Factor
Authors: Myers G. E. , Schauer J. J. , Eustis R. H.
Published: November 2011

An investigation of the jet development, the velocity profiles, and the wall shearing stress in a two-dimensional, incompressible, turbulent wall jet was undertaken. The maximum velocity decay, jet thickness, and the shearing stress are predicted analytically by momentum-integral methods. Experimental data concerning velocity profiles, velocity decay, and jet thickness agree well with previous investigators. The wall shearing stress was measured by a hot-film technique and the results help to resolve a wide divergence between the experimental values of other investigators.
Capped End, Thin-Wall Tube Creep-Rupture Behavior for Type 316 Stainless Steel
Authors: Rowe G. H. , Stewart J. R. , Burgess K. N.
Published: November 2011

The creep-rupture behavior of 34 capped end, thin-wall tubular specimens was correlated with results for 54 uniaxial tensile specimens in tests at 1350 F, 1500 F, and 1650 F. Basic tests established isotropy in creep-rupture properties as well as metallurgical stability for the material used in the study. Significant correlations of creep rate, rupture life, and rupture ductility were established for the cases of stress ratios 1/0 and 2/1 in the biaxial tension quadrant. Data from tests at 1500 F were evaluated for a statistical argument. This same material was subsequently utilized in a high temperature structures research program to be reported separately.
On a Successive Approximation Technique in Solving Some Control System Optimization Problems
Authors: Aoki Masanao
Published: November 2011

It has been realized for some time that most realistic optimization problems defy analytical solutions in closed forms and that in most cases it is necessary to resort to judicious combinations of analytical and computational procedures to solve problems. For example, in many optimization problems, one is interested in obtaining structural information on optimal and “good” suboptimal policies. Very often, various analytical as well as computational approximation techniques need be employed to obtain clear understandings of structures of policy spaces. The paper discusses a successive approximation technique to construct minimizing sequences for functionals in extremal problems, and the techniques will be applied, to a class of control optimization problems given by: Minv  J(v)=Minv  ∫01g(u.v)dt, where du/dt = h(u, v), h(u, v) linear in u and v, and where u and v are, in general, elements of Banach spaces. In Section 2, the minimizing sequences are constructed by approximating g(u, v) by appropriate quadratic expressions with linear constraining differential equations. It is shown that under the stated conditions the functional values converge to the minimal value monotonically. In Section 3, an example is included to illustrate some of the techniques discussed in the paper.
Analysis, Design, and Testing of a Position Servo Utilizing a Stepper Motor
Authors: Nicklas J. C.
Published: November 2011

The development of a position control system using a stepper or incremental motor is described. The advantages of this type of prime mover are discussed, and a technique of integrating the stepper motor into the system is analyzed. The output signal from the error detector used in the system comes from a sampler and zero-order hold circuit. This signal controls a gate which either allows or inhibits a pulse train to drive the stepper motor. The load on the motor is an underdamped second-order system. The stepper motor output position and the reference input determine the error. The analysis includes a stability investigation using the describing-function method and a computer simulation to determine the dynamic performance of the system. The effects of noise in the system are also investigated on the computer. The equipment used to mechanize the control system is described, and results of experimentol work to determine the actual performance of the system are given.
Static and Dynamic Properties of Partial Journal Bearings
Authors: Warner Paul C.
Published: November 2011

The liquid lubricated partial journal bearing is analyzed in an approximate yet accurate manner in order to obtain its static and dynamic properties. The solution of the governing differential equation is analytical rather than numerical, permitting inexpensive computation of results over a very wide range of the parameters involved.
Analysis of a Rolling-Element Idler Gear Bearing Having a Deformable Outer-Race Structure
Authors: Jones A. B. , Harris T. A.
Published: November 2011

Conventional calculations of ball and roller bearing carrying capacity and fatigue life assume that the raceway bodies are rigid structures and that all elastic deformation occurs at the rolling elements’ contact with the raceways. In many instances, and particularly with aircraft applications, the bearing rings and their supports cannot be considered rigid. One such application is the planet gear in a transmission. This report develops a theory whereby the effects of the elastic distortions of the outer race of a rolling-element bearing on the internal load distribution and fatigue life of the bearing can be considered. The theory has been programmed for a high-speed, digital computer. An example of calculation for a planet gear roller bearing whose outer race is integral with the gear and of relatively thin section is given. The distortions of the flexible outer ring cause a significantly lower bearing fatigue life (L10) than would occur if the outer ring were rigid and considering a practical range of bearing diametral clearances. Mr. Jones developed the theoretical analysis for this paper and Mr. Harris provided the programming and the experimental data.
Correlation of the Coefficient of Adhesion With Various Physical and Mechanical Properties of Metals
Authors: Sikorski M. E.
Published: November 2011

The coefficients of adhesion determined by a modification of the twist-compression bonding method are compared with the following properties of metals: crystal structure, hardness, surface energy, elastic modulus, work-hardening properties, recrystallization temperature, purity, and atomic volume. Conclusions are reached regarding the desirable characteristics of metals, or combinations of metals, for antifriction applications.
The Molecular Transit Time and Its Correlation With the Stability of Externally Pressurized Gas-Lubricated Bearings
Authors: Turnblade R. C.
Published: November 2011

This paper advances the hypothesis that the regimes of unstable operation of externally pressurized gas-lubricated bearings may be defined by certain dimensionless parameters in much the same way as the Reynolds’ number predicts the transition of laminar to turbulent flow. A theoretical discussion of the basic principles of gas bearings indicates that unstable operation is related to the capacity of a bearing to change its contained fluid mass. Some general expressions are developed which suggest the nature of some dimensionless parameters and permit experimental evaluation of the theory.
Observations on Cavitation Damage in a Flowing System
Authors: Hammitt F. G.
Published: November 2011

Cavitation damage to specimens of stainless steel, carbon steel, aluminum, and plexiglas, placed in a cavitating venturi using water and mercury as test fluids is mostly in the form of irregularly shaped pits which do not change with additional exposure to the cavitating field within the limited durations utilized. The rate of damage is very high initially, decreases for a relatively short period of time, then increases again up to the maximum test durations of 150 hours with water and 270 hours with mercury. Observation of damage effects by several independent techniques, using a variety of specimen materials, with two different fluids under various fluid dynamic conditions, leads to a suggested correlating model in terms of the cavitation bubble density and energy and specimen material strength.
Turbulent Flow of Water in Plane Curved Channels of Finite Depth
Authors: Brown O. G. , Marris A. W.
Published: November 2011

An experimental study of turbulent flow in a plane curved channel of depth-to-width ratio 8:1 and mean radius-to-width ratio 1.83:1 by means of measured distributions of mean peripheral velocity and pressure and flow visualization methods using dye. It appears that due to the large depth-to-width ratio, the secondary flow, though appreciable, is apparent mainly in the end plate regions. Even so it has a pronounced effect on the flow near the inner (convex) wall. It appears that the sharp curvature is effective in quenching the turbulence of the entering rectilinear shear flow at the inner wall of the curved channel by causing a mean flow acceleration in this region. The study indicates that localized backflows can occur at the inner wall at the meeting of secondary and main flows under near-laminar conditions.
Half Sommerfeld Approximation for Finite Journal Bearings
Authors: Fedor J. V.
Published: November 2011

An approximate analytical solution is developed for full journal bearings which includes the effects of bearing finiteness and an incomplete oil film. The approximate solution is obtained by modifying the complete oil film solution to Reynolds equation. The developed equations are in finite form and are simple to evaluate. Calculated values agree well with published computer solutions.
The Role of Elastohydrodynamic Lubrication in Rolling-Contact Fatigue
Authors: Zaretsky E. V. , Sibley L. B. , Anderson W. J.
Published: November 2011

The five-ball fatigue tester was used to determine the rolling-contact fatigue life of 1/2-inch-diameter M-1 steel balls with four lubricants at 300 deg F. Film thickness measurements were made with the rolling-contact disk machine under simulated five-ball test conditions. Under certain conditions, elastohydrodynamic lubrication was found to exist at initial maximum Hertz stress levels up to 800,000 psi. There appears to be a correlation among the following variables: Plastically deformed profile radius of the ball specimen at ambient temperature; lubricant type; and rolling-contact fatigue. No correlation was found between contact temperature obtained with different lubricants and fatigue life.
Stability of Unloaded Gas-Lubricated Bearings
Authors: McCann R. A.
Published: November 2011

This paper deals with a perfectly cylindrical, self-acting, gas-lubricated, and unloaded journal bearing. Complete stability criteria for the translational mode of oscillation are formulated and a method is given by which the ultimate stable operating speed may be found for arbitrary ambient pressure, viscosity, and bearing geometry. The nature of the stable motion is indicated. In addition, a simplified criterion and bearing motion are given for low-speed operation. Graphs which show the effect of design parameters on bearing forces are included as an aid in numerical calculations.
Fatigue Characteristics of Open-End Thick-Walled Cylinders Under Cyclic Internal Pressure
Authors: Davidson T. E. , Eisenstadt R. , Reiner A. N.
Published: November 2011

Thick-walled cylinder fatigue data due to cyclic internal pressure for open-end cylinders in the range of 103 to 105 cycles to failure and having a diameter ratio of 1.4 to 2.0 at a nominal yield strength of 160,000 pounds per square inch is presented. Discussed and also presented are the effects of autofrettage on the fatigue characteristics of thick-walled cylinders. Autofrettage substantially enhances fatigue characteristics at stress levels below the corresponding overstrain pressure, the degree of improvement increasing the decreasing stress levels. The rate of improvement in fatigue characteristics increases significantly with diameter ratio in autofrettaged cylinders up to a diameter ratio of 1.8–2.0 and to a much smaller degree in the nonautofrettaged condition. The rate of improvement of fatigue characteristics above 2.0 is the same for both the autofrettaged and nonautofrettaged cases. It is shown that thermal treatment of 675 F for 6 hours after autofrettage does not affect fatigue characteristics and that there is a correlation between the cyclic-stress level and the area and depth of the fatigue crack to the point of ductile rupture. The depth of the fatigue crack decreases with increasing cyclic-stress level. A means for using data from a unidirectional tensile fatigue test to predict the fatigue characteristics of thick-walled cylinders is discussed.
The Viscosity-Temperature-Pressure Relationship of Lubricating Oils and Its Correlation With Chemical Constitution
Authors: Roelands C. J. A. , Vlugter J. C. , Waterman H. I.
Published: November 2011

Viscosities of twenty well-defined, representative mineral-oil fractions have been determined at temperatures from 25 to 90 deg C (77 to 194 deg F) and at pressures up to about 1000 atmospheres (15,000 psi) with the aid of a falling-needle viscometer. An analysis has been made of both the present measurements and reliable data from literature, which chiefly concern mineral oils and pure hydrocarbons, but also include some silicones, fatty oils, and alcohols. Many literature data cover ranges of viscosity, temperature, and pressure that are more extensive than those of the authors. Newly developed empirical formulas are presented for the isobaric viscosity-temperature relationship, the isothermal viscosity-pressure relationship, and the complete viscosity-temperature-pressure relationship. The formulas have been found to be satisfactorily applicable to all the aforementioned liquids in a wide range, that is, generally, from about 20 to 150 deg C (68 to 302 deg F) and up to pressures of at least 3000 atmospheres (44,000 psi). Diagrams derived from these formulas have proved particularly suitable for a systematic study of the correlation between, on the one hand, the temperature and pressure variation of viscosity of the liquids concerned and, on the other hand, their chemical constitution. This is exemplified by the results for the mineral oils investigated. In fact, it proved possible, presumably for the first time, to establish for mineral oils a really satisfactory quantitative correlation between their viscosity-temperature-pressure dependence and their chemical constitution; the latter has been characterized by the carbon distribution according to the “Waterman analysis” in the form of the so-called n-d-M method.
Investigation of Whirl in Externally Pressurized Air-Lubricated Journal Bearings
Authors: Gross W. A.
Published: November 2011

The nature of whirl of a rigid rotor in externally pressurized air-lubricated journal bearings, including self-acting bearings as a special case, is discussed and an experimental investigation described. Rotor unbalance leads to synchronous whirl which can persist through one or more critical speeds. Self-excited whirl is likely when the rotational frequency is about twice the lowest critical frequency. We discuss the effects of supply pressure, number and location of sources, rotational speed, mass, unbalance, and load upon the onset of self-excited whirl, and describe first-order prediction techniques.
On the Translatory Whirl Motion of a Vertical Rotor in Plain Cylindrical Gas-Dynamic Journal Bearings
Authors: Pan C. H. T. , Sternlicht B.
Published: November 2011

For the theoretical prediction of the dynamical characteristics of a rotor system, it is necessary to have an accurate knowledge of the bearing fluid film forces under dynamical conditions. With a small clearance ratio and at a moderate speed, the motion of the lubricant is governed by the generalized Reynolds equation. If the lubricant is a gaseous medium, the Reynolds equation is complicated by the compressibility effects, which include nonlinearity and time-dependence under dynamic conditions [1]. In the case of a vertical rotor operating in plain cylindrical journal bearings, the steady whirl approximation is appropriate and time-dependence in the Reynolds equation can be removed by a co-ordinate transformation. The form of the transformed equation is identical to the static Reynolds equation except that the compressibility number is modified by a factor which depends on the angular speed of the whirl motion [2, 3]. The altitude angle, in the presence of the whirling motion, is quite different from the static attitude angle. On the other hand, the magnitudes of the forces are not very different. The steady whirl analysis may be used to determine the synchronous whirl motion of an unbalanced rotor. The phase angle between the fluid film force and the maximum film thickness plane is the complement of the attitude angle according to the quasi-static analysis. Experimental data are in excellent agreement with the results of the steady whirl analysis. Also, the modified compressibility number is reduced to zero at half-frequency whirl, and the Reynolds equation, for an isothermal gaseous film with the small eccentricity ratio approximation, becomes identical to that of the liquid film. Since it has been established that the threshold of half-frequency whirl for vertical rotors operating in plain cylindrical journal bearings is at zero speed in [4], the same conclusion applies to the corresponding gas-dynamic bearing.
Fluid Lubrication Theory of Roller Bearing—Part I: Fluid Lubrication Theory for Two Rotating Cylinders in Contact
Authors: Sasaki Tokio , Mori Haruo , Okino Norio
Published: November 2011

This paper which consists of Parts I and II presents a general and practical fluid lubrication theory of roller bearings lubricated by Newtonian and non-Newtonian lubricants with considerations to the effect of sliding of roller and the influence of unsteady load. In Part I, the fundamental theory for the lubrication between two rotating cylinders in contact has been investigated. The load capacity and friction of a non-Newtonian lubricant, supposed to be a Bingham plastic, coincide approximately at high speed with those of a Newtonian lubricant with viscosity equivalent to the plastic viscosity of the non-Newtonian lubricant. Under unsteady loads, the squeeze action works effectively so that the load capacity increases. The amount of friction is 4/3 and the load capacity is 2/3 in the case of two rotating cylinders in contact involving sliding, compared with that involving no sliding.
Fluid Lubrication Theory of Roller Bearing—Part II: Fluid Lubrication Theory Applied to Roller Bearing
Authors: Sasaki Tokio , Mori Haruo , Okino Norio
Published: November 2011

Using the theory for two rotating cylinders in contact obtained in Part I, the fluid lubrication theory of roller bearings for Newtonian and non-Newtonian lubricants was developed in Part II with considerations of the influences of unsteady load and sliding of rollers. It is clarified that the load capacity under unsteady load is generally larger than that under constant basic load and the average friction is nearly equal for both cases. The frictional moment and load capacity for roller bearing including sliding of rollers decrease to 2/3 of the amount of those for roller bearing including no sliding.
The Toroid Contact Roller Test as Applied to the Study of Bearing Materials
Authors: Greenert W. J.
Published: November 2011

An understanding of the basic mechanics and statistical variables of the contact roller test as it is applied to surface fatigue phenomena was obtained. One hundred ninety-four contact rollers of AISI 52100 bearing quality steel were tested to establish dispersion limits. No significant fatigue differences were indicated for heats, bars, or test replications among steels of similar quality, composition, and heat-treatment. A statistical evaluation of results points to the contact roller test as a suitable means for studying significant variables that pertain to both the theoretical and material aspects of antifriction bearings. Stresses in the contact surfaces based on the orthogonal shear-stress theories showed good correlation with fatigue life.
The Structure of Optimum Control Systems
Authors: Friedland Bernard
Published: November 2011

A large class of optimum control problems can be formulated as the variational problem of minimizing a known functional subject to isoperimetric and nonholonomic constraints. The (vector) Euler equation for this problem leads directly to the structure of the optimum controller, which turns out to comprise a dynamic portion which is the adjoint of the plant to be controlled and instantaneous nonlinear elements determined by the performance functional and input constraints. Continuous measurement of the state of the plant results in the elimination of the dynamic portion, and the entire optimum controller is instantaneous. An example is given which illustrates the complete design of regulators for a simple plant with constraints on either amplitude or energy of the actuating signal which minimize response time or integrated square error.
Trends and Implications of Data on Notched-Bar Creep Rupture
Authors: Voorhees H. R. , Freeman J. W. , Herzog J. A.
Published: November 2011

Extended research on creep rupture of notched specimens, conducted at the University of Michigan under Air Force sponsorship, is analyzed along with recent publications of others. The combined results suggest that notch strengthening is general for all alloys studied under some test conditions and is not specific to individual materials or to a given ductility level. Quantitative explanation of notch rupture behavior in terms of unnotched-specimen properties is handicapped by present uncertainties in the basic factors controlling creep-rupture life under variable multiaxial stress.
Cavitation in Turbopumps—Part 2
Authors: Stripling L. B.
Published: November 2011

Cavitation performance data of several helical inducers for various flow coefficients are correlated with existing theory. For complete head breakdown conditions, the method employs semiempirical correlation coefficients which supplement the idealized free-streamline solutions obtained by various investigators. Considerations are given to the partial cavitation region utilizing the free-streamline wake solution. The model clearly illustrates the influence of the mixing losses, downstream of the cavity closure, on the inducer’s developed head as the inlet pressure is reduced. With the use of the above semiempirical correlation factors the theory forms a useful basis for design.
Quadrant Edge Orifice Performance-Effect of Upstream Velocity Distribution
Authors: Bogema Marvin , Spring Bradford , Ramamoorthy M. V.
Published: November 2011

Quadrant edge orifices offer constant discharge coefficients to much lower Reynolds numbers than do sharp edge orifices, nozzles, or venturi meters. Published results show different values for the lower limit of constancy. This paper presents experimental results which indicate that at flows below pipe Reynolds number of 4000 the discharge coefficient variation is related to the degree of velocity profile development in the upstream meter run.
Two-Phase Flow Measurement With Orifices
Authors: Murdock J. W.
Published: November 2011

This paper presents a practical method for computing two-phase flow rates through AGA-ASME stamdard orifice meters to a tolerance of 1.5 per cent. A rational equation is developed modifying the present single-phase metering equation by the introduction of one experimentally determined constant and permitting the use of data already contained in the ASME Fluid Meters Research Committee publications. Equations are also given for computing the two-phase flow of natural gas using the American Gas Association Report No. 3. No additional data are needed for the solution of two-phase flow metering problems. The experimental constant is derived from the analysis of 90 test points for two phase flow of steam-water, air-water, natural gas-water, natural gas-salt water, and natural gas-distillate combinations. Three separate test series are described for orifices equipped with radius, flange, and pipe tap locations in 2 1/2, 3, and 4-inch pipe with beta ratios ranging from 0.25 to 0.50. Pressures ranged from atmospheric to 920 psia, differentials from 10 to 500 inches of water, and liquid weight fractions from 2 to 89 per cent. Temperatures were from 50 to 500 F and Reynolds numbers for the liquid from 50 to 50,000 and for the gas from 15,000 to 1,000,000. These data were correlated to a standard deviation of 0.75 per cent. The areas where further research is needed to increase the universality of the two-phase metering equation are delineated.
A Preliminary Study of Whirl Instability for Pressurized Gas Bearings
Authors: Larson R. H. , Richardson H. H.
Published: November 2011

Experimental data are presented for the threshold of whirl instability for a short, rigid rotor supported in externally pressurized compensated gas journal bearings. The effects of supply pressures from zero to 200 psig and of radial clearances from 0.0006 to 0.0032 in. are discussed for one type of bearing configuration. A simple stability criterion is presented which explains qualitatively the observed trends. Whirl instability was observed when the frequency of rotation of the shaft exceeded from two to six times the lowest natural frequency of the shaft-bearing system.
The Transient Response of Fluid Lines
Authors: Brown F. T.
Published: November 2011

Functional operators are derived for the propagation factor and characteristic impedance for small amplitude waves in rigid uniform fluid transmission lines when the effects of varying velocity profile and heat transfer are included. The special case of sinusoidal excitation yields the identical result given by Iberall. The results, however, are used particularly to determine the impulse and step responses of a line, which clearly demonstrate the observed dispersion of fast transients.
An Experimental Study of the Vortex in the Cyclone Separator
Authors: Smith J. L.
Published: November 2011

The symmetric vortex in a cylindrical cyclone with a flat bottom was studied with the aid of smoke, and was probed for the distribution of the velocity. The smoke studies revealed a laminar regime of flow at very low velocities, the normal turbulent regime of operation, and a new periodic regime of flow in which the vortex turned and attached to the cylindrical wall of the cyclone. A curious core region apparently capable of separating tobacco smoke from the air was also found. The velocity distribution measured in the vortex showed how the flow pattern is strongly influenced by the inlet area of the cyclone.
An Analysis of the Vortex Flow in the Cyclone Separator
Authors: Smith J. L.
Published: November 2011

The theory of rotating fluids is applied to the flow in the cyclone. The effects of radial instabilities in the boundary layers on the walls are discussed. The dynamics of the central core in the flow are studied in a simple nonviscous model which exhibits wave propagation and weir flow similar to a free surface flow. A momentum-integral analysis is used to show the effect of friction and to predict the axial distribution of radial inflow.
Crack Propagation in Thin Metal Sheet Under Repeated Loading
Authors: Liu H. W.
Published: November 2011

An experimental and analytical investigation was undertaken to study the fundamental factors of crack propagation in a thin metal sheet under repeated axial loading. Sheet specimens of 2024-T3 aluminum alloy containing a central hole were used in the experimental investigation. Stress range and mean stress were the controlled parameters. An expression for crack length was derived, based on the concept of geometric similarity of crack configuration, for a semi-infinite sheet subjected to repeated loads consisting of a constant stress and mean stress. The expression is in terms of a stress dependent propagation factor and an exponential function of the number of cycles of loading. The expression for a semi-infinite sheet was modified for crack propagation in a specimen of finite width. Accurate predictions of the propagation life was possible using the modified equation. Photomicrographic observations of the crack tips were made.
Solution Space Approach to Optimal Control Problems
Authors: Ho Yu-Chi
Published: November 2011

In this paper, we study the control of the dynamic system governed by the matrix differential equation, x˙ = Fx + Du, x(0) = −c, where the input vector u is constrained in amplitude. It is shown that in the discrete (sampled data) case: (a) The general optimal control problem can be formulated as a nonlinear programming problem amenable to treatment by techniques developed in the operation research field. (b) The specific time optimal control problem originally studied by Kalman is treated here using a different approach which yields well-known as well as new results.
The Optimum Response of Second-Order, Velocity-Controlled Systems With Contactor Control
Authors: Flu¨gge-Lotz Irmgard , Yin Mih
Published: November 2011

This paper is concerned with the optimum control problem for plants described by second-order differential equations with constant coefficients and with velocity control. Emphasis is placed on the case where the characteristic equation of the system has one zero root and two complex conjugate roots. The problem is studied in terms of the motion of the phase point in a three-dimensional phase space. An iteration method is developed to obtain the optimum trajectory, which in turn gives the optimum response.
Pulse-Width Relay Control in Sampling Systems
Authors: Nelson Winston L.
Published: November 2011

The use of pulse-width control for the on-off regulation of systems subject to sampling is investigated in this paper. The inherent inability of simple on-off control to achieve accurate, or dead-beat control in sampling systems is demonstrated, and methods for predicting and minimizing the limit-cycle behavior of these systems are given. It is then shown that if the on-off control is modified by allowing control of the “on” time during each sampling period, it is possible to achieve asymptotically stable dead-beat control. Sufficient conditions for the asymptotic stability in the large of pulse-width control systems are developed, using the “second method” of Lyapunov. Practical design of pulse-width controllers is developed from the theoretical results and experimental evaluation is given for some specific design problems.
Kinetic Lyapunov Function for Stability Analysis of Nonlinear Control Systems
Authors: Chang S. S. L.
Published: November 2011

A kinetic Lyapunov function is a Lyapunov function of the first derivatives of the state variables. Its use leads to a sufficient condition for the asymptotic stability in the large of a general nonlinear system without hysteresis. The foregoing sufficient condition is similar to but more stringent than the local stability condition for linearized systems.
Solution of Reynolds Equation for Arbitrarily Loaded Journal Bearings
Authors: Pinkus O.
Published: November 2011

The Reynolds equation has been solved on a digital computer for the case of 150, 100, and 75-deg bearing arcs subject to loads acting in any arbitrary direction. The results cover the entire range of attitudes and load angles and provide solutions for L/D ratios from 1 1/2 down to 1/4. The application of these basic results to the calculation of the performance of noncentrally loaded partial, grooved, and multilobed bearings is discussed.
Inertia Effects in Hydrostatic Thrust Bearings
Authors: Dowson D.
Published: November 2011

This paper includes the predominant inertia terms in an analysis of hydrostatic thrust bearings. The influence of centripetal accelerations on the distribution of pressure is found to be considerable. For parallel surface bearings of constant film thickness the inertia effects are found to be detrimental to load capacity. In a stepped bearing however correct location of the step can result in an increased load capacity at speed. No increase in load capacity can result from inertia effects if the step radius is less than 0.4508 of the bearing radius. A consequence of the inclusion of inertia terms in the analysis is the existence of a velocity component in the axial direction. Even in the parallel surface bearing considered a fluid element is found to move toward the rotating surface as it spirals through the clearance space.
Expansion Coefficients for Orifice Meters in Pipes Less Than One Inch in Diameter
Authors: Marxman G. A. , Burlage H.
Published: November 2011

A practical technique for using orifices to meter most gases of engineering interest is described. This technique can be employed in pipes less than 1 in. ID, as well as in larger sizes. An analytical expression for the orifice expansion coefficient is developed; this expression includes an empirical factor based on published data for orifice installations in pipes two or more inches in diameter. Experimental verification has shown that the equation gives correct results for the smaller systems and in gases with a specific heat ratio other than 1.3 or 1.4. It is also shown that the empirical equation for orifice-expansion-coefficients which appears in the ASME Fluid Meters Report [1] can be used over a range that includes most gases as well as pipe diameters as small as 1/4 in.
Flow Measurement for Accounting Purposes
Authors: Livingstone D. D.
Published: November 2011

This paper discusses the industrial measurement of gases and liquids by means of thin-plate orifices. Installation and maintenance practices which reduce measurement errors are described. Records of flows for twenty-one streams are analyzed to estimate the accuracy of the metering.
Nonsteady Discharge of Subcritical Flow
Authors: Rudinger George
Published: November 2011

The calculation of a nonsteady flow discharging into the atmosphere, or into a large reservoir, is generally based on the assumption that the effective exit pressure is the same as if the flow were steady. In reality, however, the steady-flow boundary conditions are asymptotically approached after a disturbance produced by an incident wave, and recently published investigations provide a better approximation to these transient boundary conditions. Utilizing these results, one can compute the rate of discharge and compare it with the rate obtained in the conventional manner. The difference between the results of the two calculations is used to define a lag error in the conventional calculations. Examples for discharges through an open end and through a sharp-edged orifice indicate that the actual transient flow rate may deviate considerably from that computed on the basis of steady-flow boundary conditions.
Effects of Inlet Conditions on Performance of Two-Dimensional Subsonic Diffusers
Authors: Waitman B. A. , Reneau L. R. , Kline S. J.
Published: November 2011

Performance data and flow characteristics for subsonic two-dimensional plane-wall diffusers are presented for the following conditions. (a) Wall-length to throat-width ratios of 8.0, 12.0, and 48.0, (b) total divergence angles from 2.5 to 40 deg, (c) extremely thin inlet boundary layers to fully established channel flow, (d) a vaned diffuser with L/W1 = 8.0 and quite thick inlet boundary layers. Flow conditions and variations of flow regimes for L/W1 = 48.0 are compared. No real gain in recovery or pressure effectiveness is achieved by use of very large L/W1. L/W1 = 20 – 25 appears to be maximum useful range in the absence of boundary-layer control. A few data are given where the inlet flow of the diffuser is distributed by obstructions. Recovery and effectiveness are found to be strongly dependent on type and amount of inlet turbulence.
Transport Processes Involving a Moving Rotating Disk in a Low-Density Gas
Authors: Soo S. L.
Published: November 2011

An analytical method is presented for studying the compressible boundary-layer motion over a rotating disk including axial forced flow. Some existing incompressible flow data can be utilized. The range considered includes free-molecule flow, slip flow, and high-density gas flow. A new correlation for treating disk-friction data is suggested. General aspects of friction and heat transfer are discussed. Results suggest the rotating disk as a suitable tool for experimental study of mechanics of a rarefied gas.
Pressure Surges Following Water-Column Separation
Authors: Kephart J. T. , Davis Kenneth
Published: November 2011

Equations have been derived using rigid-water-column theory which permit rapid assessment of pressure surge magnitude owing to rejoinder of water columns in pump-discharge lines subsequent to a water-column separation induced by failure of power to the pump drivers. The method is valid only for systems which are equipped with check valves at the pumps.
Short-Time Tensile Properties of Type 316 Stainless Steel at Very High Temperatures
Authors: Gibbs T. W. , Wyatt H. W.
Published: November 2011

An evaluation program was conducted on Type 316 stainless-steel sheet material to determine the effects of residual cold-work and welding on the room-temperature and elevated-temperature mechanical properties to 1800 deg F. Short-time tensile and tensile-creep elongations tests were run to determine the stresses required to produce elongations up to 10 per cent in 2 min. The effect of welds in tension was to lower the elongation with no loss in strength. The effect of cold-work on the annealed material was to increase appreciably the strength properties, thus allowing for higher design stresses. The results of a few tests indicate that Type 316 stainless steel retains some strength properties up to 2300 deg F. A definite stress-strain relationship exists in which the 0.2 per cent yield stress is very close to the tensile stress.
Effects of Specimen Size and Notch Acuity on the Brittle Fracture Strength of a Heat-Treated Steel
Authors: Yukawa S. , McMullin J. G.
Published: November 2011

Effects of various methods of notch preparation on the notched slow bend fracture strengths of heat-treated alloy steel specimens were studied. The results indicate that several kinds of cracks result in about 35 per cent lower strength than a machined 0.005 in. root radius notch. The importance of testing sufficiently large size specimens to reveal this difference is shown.
A Solution of Reynolds Equation for a Full Finite Journal Bearing
Authors: Ramachandra S.
Published: November 2011

Reynolds equation for the pressure in a full finite journal bearing which is nonhomogeneous has been reduced to a homogeneous equation. By separating the variables the problem is reduced to an eigenvalue problem. The orthogonal functions expansion method is used to determine the eigenvalues and eigenfunctions. First four eigenvalues are calculated. Design charts are prepared for the eccentricity ratios of 0.2, 0.4, 0.6, 0.8 and length to diameter ratios of 0.5, 1.0, 1.5, and 2.0.
A Flow Model for Two-Phase Slug Flow in Horizontal Tubes
Authors: Kordyban E. S.
Published: November 2011

The paper presents a construction of a simplified model approximating the actual observed flow pattern. The resulting expressions for frictional pressure drop are found to agree fairly well with the author’s data for steam and water and the data for air and water of other investigators. The similarity with a portion of the Chenoweth-Martin correlation appears to present a logical explanation for the applicability of that correlation to slug flow.
Adiabatic Flow of Flashing Liquids in Pipes
Authors: Sajben M.
Published: November 2011

The assumption of a homogeneous fluid in thermodynamic equilibrium has frequently been made in describing the behavior of a vapor-liquid mixture flowing in constant area pipes. Although this flow model is acceptable for a range of conditions, its extensive use has been prohibited by the large amount of computational labor involved. In the present paper the equations of this flow model are reviewed, several conventional but unnecessary restrictions are removed, and computed results are presented on working charts suitable for practical purposes. Critical flow rates and the amount of subcooling necessary to avoid flashing in the pipe were given special attention.
Cavitation Tests on Hydrofoils Designed for Accelerating Flow Cascade: Report 1
Authors: Numachi F.
Published: November 2011

In previous reports, theory [1, 2] and experiments [3–7] were discussed on profiles that promised to possess desirable characteristics when incorporated into cascades of given arrangement. These previous studies concerned profiles destined for use in decelerating cascades. The present report is the first of a series on accelerating cascade profiles.