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RESEARCH PAPERS

J. Basic Eng. 1969;91(3):331-338. doi:10.1115/1.3571107.

In this paper the method of characteristics is used to provide a solution of the equations governing unsteady flow in natural gas pipelines. The validity of this approach is confirmed by comparison with experimental transients. The basic working equations are then adapted to a computation scheme which results in a transient control calculation procedure. The main emphasis is given to its use on gas piping networks.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):341-351. doi:10.1115/1.3571110.

An investigation has been made of the pressure attenuation that can be obtained through the application of a rigid tapered section located immediately upstream of a quick-closing valve or other surge-generating device. The model taken was that of an inviscid liquid flowing through the rigid tapered tube terminated by either a very long uniform line or a finite-length line and reservoir. This paper presents an outline of a theoretical method for solving the given problem, along with some practical solutions. A description and the results of experimental work performed to substantiate the theory are also included.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):353-358. doi:10.1115/1.3571115.

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):361-368. doi:10.1115/1.3571118.

Tests are reported which were carried out to establish the performance of pressure-exchanger dividers and equalizers using air as the working fluid. The effects of varying rotor speed, port geometry, and port pressure ratios were explored. It was concluded that, at low pressure ratios, pressure-exchanger dividers and equalizers are comparable in performance with their turbomachine counterparts.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):371-376. doi:10.1115/1.3571122.

For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):379-382. doi:10.1115/1.3571126.

A finite-element computational method is employed to determine the spatial distribution of stress and strain in a notched-plate fatigue specimen fabricated of mild steel. Because of cyclic strain softening of the material, there is a redistribution of stress and strain in the specimen as a function of the number of load cycles. This phenomenon is considered in the analysis by using cyclic stress-strain diagrams as effective stress-strain curves. The numerical results are found to correlate well with measured strain distributions reported in the literature.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):383-385. doi:10.1115/1.3571127.

The one-way air chamber for suppressing water-column separation is described. Operation of the one-way air chamber during a power failure transient is explained. A typical problem solution is shown. The one-way air chamber is compared with the one-way surge tank and the normal air chamber.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):387-395. doi:10.1115/1.3571131.

Many problems were encountered during the startup and trial operation at Yards Creek. This paper describes the major problems and how they were resolved. There are many questions about pump-turbine operation that remain unanswered. Exchange of information and experience is needed. The authors hope that this article will help to stimulate this exchange of information.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):397-412. doi:10.1115/1.3571134.

Measurements have been made of the pressure recovery of straight wall, single plane divergence diffusers with inlet Mach numbers between 0.2 and choking (0.2 ≤ Mt < 1.0). In contrast to the widely held assertion in the literature, there is no “critical” inlet subsonic Mach number above which pressure recovery decreases drastically. Two aspect ratios, AS = 0.25 and 1.0, have been studied for a range of length-to-throat-width ratios L/W1 and divergence angles 2θ around the regions of peak recovery. Diffuser performance maps are given showing pressure recovery Cp as a function of diffuser geometry for fixed values of throat Mach number Mt , throat blockage B, and aspect ratio AS. Significant changes in the location and magnitude of pressure recovery do occur with variations in Mt , B, and AS. The importance to the designer of a knowledge of how diffuser performance depends upon geometric and diffuser inlet parameters is discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):423-432. doi:10.1115/1.3571141.

In pursuit of the studies previously reported [1–3], three profiles suited for application in the main blade elements of high head Kaplan turbines—two intended for sections near boss and one for sections around midway or two thirds along the blade arm—have been produced, and an account is given of the blade characteristics and performance in cavitation tunnel tests.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):434-438. doi:10.1115/1.3571144.

The author demonstrates that significant basic errors are introduced into the Gibson method of measuring water flow rates, even in uniform straight pipes, by failure to take account of velocity distribution in calculating results. Dr. Thoma’s 1926 analysis of the method is quoted extensively, including his conclusion that long straight lengths of pipe upstream and downstream from straight differential-diagram test sections would eliminate the effects of accessory motions and his recommendations for establishing an experimental installation to determine the effects of various disturbed flow conditions. The need for these correction factors or “meter coefficients” in order to avoid consistent errors of approximately 2 percent is emphasized.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):453-460. doi:10.1115/1.3571152.

Equations of motion for a cylindrical tube containing a fluid are developed from a consideration of the forces and moments in the tube wall. These equations are solved for boundary conditions representing the situation where the fluid is flowing steadily through a horizontal pipe and a valve at the downstream end is closed instantaneously. The solution gives theoretical results for the usual water-hammer wave but also predicts the existence of a precursor wave. Expressions are derived for the velocities of propagation of both transients and their associated pressure changes. A comprehensive series of experiments has been carried out. Some interesting and probably unique results were obtained, which demonstrate the behavior of both transients. Measurements of velocity and pressure change have been made. The effect of axial restraint on the pipe is demonstrated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):462-474. doi:10.1115/1.3571155.

An analytical and experimental study on the effects of large distortions of inlet velocity profiles on flow regimes and performance in diffusers is reported. Experiments are restricted to flow in straight, two-dimensional diffusers with turbulent boundary layers. Systematic data are obtained for two general types of inlet flows: (1) simple, uniform shear flows in the core, and (2) severely nonuniform shear flows of the wake, jet, and step-shear type. For uniform shear flows a first order prediction method based on inviscid rotational flow and the boundary layer blockage concept is developed and verified for diffusers operating in the unstalled flow regime. For nonuniform shear flows the inviscid rotational model is shown to predict performance trends better than the irrotational model; however, the inviscid rotational model is inadequate as a precise prediction method because no account is taken of mixing in the core region. Geometry and performance correlations for peak pressure recovery (at constant N/W1 ) are also established.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):475-478. doi:10.1115/1.3571158.

The response of the back pressure signal resulting from nozzle flow suddenly restricted by a downstream surface is described. Experimental results are presented for the periodic signal from a small nozzle in close proximity to a rotating gear. A simplified analysis for the back pressure as a function of time is developed and the calculated signal amplitude versus frequency is compared with the experimental results.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):479-488. doi:10.1115/1.3571160.

A theory is formulated for predicting the variation in average pressure and the rise in average temperature in molten plastic along the axis of a screw extruder. The mathematical model is for a wide, shallow channel of negligible curvature and includes both down and cross channel components of the shearing stress which are related to strain rates by a generalized Rabinowitsch constitutive equation for a non-Newtonian Liquid. Twenty experiments were performed in a commercial screw extruder in which pressures and temperature changes in the plastic were measured. Experimental correlation with theory is very good for pressure distribution along the screw axis and fair for temperature rises of at least 50 deg F.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):493-502. doi:10.1115/1.3571165.

This paper reports on velocity, pressure, and correlation measurements in the turbulent wake and the adjacent unsteady potential flow of a circular cylinder. Particular attention is given to the effects that attend oscillation of the cylinder in the plane of the lift force. The study was undertaken for four reasons. First was the need to generalize measurement results on the lift force of an oscillating cylinder placed in a flow [1]. Second was the desire to clarify the fluidelastic nature of such forces. Third was the wish to compare gross features of real and computer generated flows. And fourth was the presumed possibility to create unsteady flow of controlled characteristics by using vibrating cylinders. The data presented here pertain to the velocity field close to the cylinder. Actually the records for locations further downstream suggest that prospects for control of flow characteristics using vibrating bluff cylinders do not look promising beyond, say, 15 dia. Measurements made close to the cylinder permit more definite conclusions. The fluidelastic nature of the flow associated with vortex-induced vibrations of cylinders has been demonstrated conclusively. Various existing notions about this question can now be segregated. Reynolds numbers of up to 105 were attained; this is sufficiently high to give results in the range of practical application. Revealing records about the flow field structure were acquired. They permit many conclusions by mere visual inspection because of the special attention given to the unsteady or potential flow region.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):506-511. doi:10.1115/1.3571171.

An investigation was conducted to determine the effects of the variables; temperature, strain rate, and precracking fatigue-stress level, on plane-strain crack toughness values of a rate and temperature-sensitive steel. The crack toughness behavior of a 3/4 -in-thick structural steel plate, which had a static room-temperature yield stress of 45,000 psi, was examined over the temperature range from −280 to 0 deg F for strain rates of 8 × 10−5 /sec, 3 × 103 /sec, and 1.5/sec. Crack toughness data, which were obtained from notched bend and single-edge-notched specimens, are presented for precracking conditions obtained at a maximum nominal fatigue stress of 25 percent and 50 percent of the room-temperature yield stress. The plane-strain crack toughness, KIc -values showed only a small sensitivity to changes in temperature and no effect due to changes in strain rate. The beginning of the transition from plane-strain to plane-stress conditions occurred at successive increases in temperature for increasing strain rate. The requirement of B > 2.5 × (KIc /σys )2 for plane-strain behavior of high-strength steels was also valid for this material when the yield stress was evaluated at the test temperature and strain rate. Increasing the fatigue-cracking stress level from 25 to 50 percent of the room-temperature nominal yield stress increased the apparent KIc -values. The data showed that a necessary condition for obtaining valid KIc -values is that the plastic-zone size which develops during fatigue cracking at room temperature must be less than that which occurs at the low temperatures and elevated strain rates of the KIc tests.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):512-518. doi:10.1115/1.3571172.

To determine the crack-toughness behavior of steels subjected to high strain rates, a study was undertaken to establish the effects of strain rate and temperature on the KIc -values of steels. As an initial step, a procedure was developed to obtain dynamic KIc -values of steels by impact loading a fatigue-cracked bend specimen in a drop-weight machine. Steel plates having widely different yield strengths (40, 140, and 250 ksi) were studied initially to establish testing techniques. The results indicate that the procedures and analysis developed were satisfactory for determining static and dynamic KIc -values. For the 250 ksi yield strength steel [18Ni(250) maraging] the KIc linearly increased with increased temperature over a 400 F temperature range with no significant effect of strain rate. The strain rate had no effect on the KIc -values of the 140 ksi yield strength steel [HY-130(T)] between −320 and −150 F. However, in the 1-in-thick specimens the increase in strain rate which occurred in the dynamic test increased the temperature range for which plane-strain crack extension occurred. The KIc behavior of the 40 ksi yield strength steel (ABS-C) showed a marked sensitivity to strain rate with the same crack toughness being measured dynamically at a temperature 190 F higher than for the static test. Correlations of ABS-C steel KIc -values with its yield strength and a rate parameter, T In A/ε demonstrated the equivalency between decreasing temperature and increasing strain rate as influencing the crack toughness. The agreement of an estimate of KId from the dynamic yield strength at the NDT with the measured dynamic KIc -value showed that the six orders of magnitude increase in strain rate for this dynamic test appears sufficient to give KIc -values within 10 percent of the crack-toughness value estimates for a running crack in rate and temperature-sensitive steels. In general, the results of this investigation showed that a dynamic KIc test has been developed which can be used to establish the strain-rate sensitivity of the crack toughness of steels as well as corresponding design information.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):519-524. doi:10.1115/1.3571173.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):525-534. doi:10.1115/1.3571174.

The fracture toughness of A533 steel at room temperature, 0 deg and −70 deg F, was evaluated with 1 and 2-in-thick contoured double cantilever beam (DCB) specimens. To establish the effect of rate on thickness requirements, and to assess the strain rate sensitivity of KIc both initiation and arrest toughnesses were measured in tests covering a wide range of loading rates. The effect of thickness on the measured toughness, Kc , is discussed with reference to the parameter βc = 1/B (Kc /σY )2 where B is specimen thickness and σY is the yield stress at the temperature and strain rate of the test. Measurements at each temperature defined a single level of Kc for initiation, independent of loading rate and thickness, when the criterion βc ≤ 1.0 was satisfied. The values were 85–90 ksi in. at room temperature and 55–60 ksi in. at 0 deg and −70 deg F. As an alternative to identifying these numbers as KIc , an extrapolation function which associates KIc with an infinite plate thickness was applied to the data. The extrapolation defined KIc = 70 ksi in. at room temperature and KIc = 55 ksi in. at the 0 deg and −70 deg which values are consistent with the measured lower bound of arrest toughness. There was essentially no strain rate sensitivity of KIc . The difference between initiation and arrest toughness was small, and the dependence of Kc on loading rate could be attributed to the rate dependence of σY .

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):535-543. doi:10.1115/1.3571175.

The impact forces and specimen bending moments generated during the NRL dynamic tear test are interpreted in terms of the dynamics of the system and the fracture characteristics of the material. It is shown that the impact forces and bending moments up to the time of crack initiation can be predicted using a simple analysis based on Timoshenko’s treatment of transverse beam impact problems. This implies the possibility of using this analysis for dynamic KIc determinations.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

TECHNICAL BRIEFS

J. Basic Eng. 1969;91(3):544-545. doi:10.1115/1.3571176.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):545-546. doi:10.1115/1.3571177.

This Note is concerned with velocity and pressure distributions in the entrance of a right circular tube with slip at the wall for incompressible flow. The method used by Campbell and Slattery [1] for continuum flow is extended to slip flow. The result is then compared with existing work.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):546-548. doi:10.1115/1.3571178.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):549-551. doi:10.1115/1.3571179.

The cause of the white-etching regions outlining certain subsurface cracks in rail-heads was investigated. These cracks known as shells may propagate into “shelly spots,” i.e., deep spalls, usually in the gage corner in rail-heads. Samples containing these regions were metallographically compared to samples with scribed scratches. The white etching regions were found to be stress-induced microstructural changes resulting from the rolling contact fatigue in rail heads.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):551-553. doi:10.1115/1.3571180.
Abstract
Topics: Diffusers
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):553-555. doi:10.1115/1.3571181.
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1969;91(3):555-558. doi:10.1115/1.3571182.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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