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RESEARCH PAPERS

J. Basic Eng. 1962;84(4):415-418. doi:10.1115/1.3658656.

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.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):419-432. doi:10.1115/1.3658657.

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.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):434-445. doi:10.1115/1.3658661.

A venturi designed to operate at critical flow conditions and to provide accurate measurement of flow rates of compressible fluids is described. A theoretical method of determining the discharge coefficients for this venturi is presented, and a comparison of the theoretically and experimentally determined coefficients for one venturi is shown (working fluid—air). The values of discharge coefficient were in the range of 0.992 to 0.994, and the theoretically and experimentally determined coefficients agreed within ±0.06 per cent over the range of conditions investigated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):447-457. doi:10.1115/1.3658664.

Critical flowmeters for accurately measuring the mass flow rates of nonreacting real gases were reviewed. Discussions were presented on theoretical flow functions, on parameters for correlating discharge coefficients, and on the importance of real gas properties. The performance characteristics of critical nozzles and orifices of several designs were reviewed. Approaches were discussed to problems which must be researched before the fullest potential of this type of flow measurement can be realized.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):461-467. doi:10.1115/1.3658669.

A low-loss and low-coefficient metering element has been devised and its operating characteristics determined under various conditions. The design was found to be not unduly sensitive to cavitation. The effects of installation have been evaluated for a short radius elbow and a tee. A partly open butterfly valve could be located 1 1/2 throat diameters downstream from the throat piesometers with an effect not exceeding 1/2 per cent upon the coefficient. Finally, the effects of pipe roughness and converging or diverging pipe can be correlated with the velocity distribution just upstream of the metering element.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):471-479. doi:10.1115/1.3658675.

The general performance of turbine-type or propeller flowmeters operating on liquid hydrocarbons in the range 0.5 to 250 gpm is described. Particular characteristics investigated include the effects of flow rate, viscosity, pressure level, entrance flow pattern, and orientation on the performance of these meters. It is shown that metering precision better than 0.2 per cent can be attained for selected ranges of flow rate and viscosity when entrance conditions and meter orientation are suitably controlled. Other factors briefly reviewed include dynamic response, totalization considerations, and the readout instrumentation.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):491-498. doi:10.1115/1.3658688.

This paper presents a theoretical analysis of the dynamics of a rotor-bearing system. The analysis is quite general but because of space limitations only the symmetrical rotor supported in two plain cylindrical journal bearings is considered. Furthermore, the rotor mass is concentrated at midspan giving the rotor only one degree of freedom. Limiting the analysis to small amplitudes of rotor motion the components of the fluid film force are made linear with respect to journal amplitude and velocity. The resulting 8 coefficients, denoted spring and damping coefficients, are calculated from Reynolds equation and by coupling them with the rotor, the motion and the force transmitted to the bearing pedestal are obtained. Results are presented in dimensionless form for transmitted force and for critical speed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):503-508. doi:10.1115/1.3658691.

Journal bearing whirl is simulated on an electronic-analog computer and typical whirl paths of the journal center are presented as obtained from the computer and recorded on an x-y plotter. Transient and steady-state paths of the journal of a rigid rotor are shown. Families of steady paths indicate the changes in orbital size of whirl from nearly zero to very large as influenced by load, journal speed, journal mass, bearing diameter, bearing length, clearance, and viscosity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):511-518. doi:10.1115/1.3658694.

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.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):521-531. doi:10.1115/1.3658698.

The regions of stability for plain cylindrical journal bearings have been determined analytically here. The linear “variational” equation of motion has been employed to obtain the stability regions bounded by families of load-carrying capacity and operating eccentricity curves. The results were applied to the “quasi-static” equilibrium case for gas lubricated cylindrical journal bearings of L/D = 2. They show that there exists a “minimum” in the stability curves, a prediction supported by experimental evidence. The results of this work seem to bridge together observation on stability at very small clearances and large ones.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):533-537. doi:10.1115/1.3658701.

Experimental data from cyclic strain fatigue tests on twelve structural materials are compared on the basis of a low cycle fatigue equation as suggested by an ASME task group. This equation

S = Ec2N1/2 + Se
where Se is the endurance limit, E the modulus of elasticity, N the cycles to failure, and c a constant derived from reported values of reduction in area, gives the stress amplitude S for comparison with elastically computed stresses. A satisfactory or good correlation with experiments for up to 105 cycles of failure is found.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):542-546. doi:10.1115/1.3658704.

This experimental study was undertaken to investigate the validity of the theory based on the crack tip stress intensity factors to explain the fracture of thin cracked plates subjected to static bending moments. Plexiglas sheets were used as specimens and the loading was pure cylindrical bending. The results indicate that there is in fact a critical value of the stress intensity factor at which the crack starts growing. It was found that, while in static tensile tests the crack growth was unstable, in the case of bending, the external load (here, the bending moment) which starts the crack growing is not sufficient for the complete fracture of the plate if it is maintained constant. That is, when the critical value of the stress intensity factor is reached, the crack starts growing on the tensile side of the plate whereupon the crack tip takes a triangular shape and the system again becomes stable. In order to make the crack grow further, a considerable increase in the load is required.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):547-553. doi:10.1115/1.3658705.

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.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):554-557. doi:10.1115/1.3658706.

This paper presents an extension to the problem discussed in previous papers by Irmgard Flügge-Lotz and Mih Yin.2, 3 In the full third-order problem it was found desirable to modify the iteration procedure used in the periodic approximation method that was developed in solving the optimum problem of the second-order, velocity-controlled system.2 A number of examples illustrate the new method. The examples were first constructed in reverse time by employing the true optimum switching times satisfying the optimum switching function, equation (6), which was developed by the methods of Pontrjagin.2 The final values of error and error derivatives which are obtained give the initial values for testing the approximate method. Periodic approximations of the optimum switching times are then obtained. It was found that for less than three switchings the approximate method leads to identical results. Reasonably small differences occur when three or more switchings are needed to reduce the initial disturbance to zero.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):559-569. doi:10.1115/1.3658710.

This paper presents a technique for predicting the effect of an extra high frequency sinusoidal input on systems with various commonly occurring types of nonlinearities. This input may be thought of as an extra input introduced into a system to improve the performance of nonlinear components. The mathematical analysis is greatly simplified by the introduction of a certain approximation to the input-output relationship of a nonlinear element when the input to the nonlinear element is the sum of the regular sinusoidal input signal and an extra sinusoidal signal of higher frequency. For the approximation to be valid experience and theory indicate that the ratio between the frequencies of the sinusoidal inputs should be on the order of ten or more. The extra sinusoidal input may reduce or remove the hunt (self-oscillation) of some systems, but it may create a hunt in others. In computations, a nonlinear element with an extra sinusoidal input may often be replaced by an equivalent nonlinear element without the extra input. By introducing the extra input a designer may be saved the expense of physically replacing one nonlinear component by another, the input-output characteristics of the first being transformed by the extra input into the characteristics of the second. The introduction of an extra signal may yield much better transient response than is possible by changing open loop gain. Examples are given with analog computer verification.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):571-578. doi:10.1115/1.3658713.

The stability of nonlinear autonomous systems with nonlinearity representable in polynomial form is investigated. For the case of locally stable systems the following theorem is presented: A sufficient condition for local stability of the system ẋ = X (x ) is the existence of a definite function v = φ(x ) such that dv/dt = θ(x )g[ξ(x )], where θ(x ) is a semidefinite function not identically equal to zero on a solution of ẋ = X (x ), g(x ) is such that g(0) = 0 and sign g(u) ≠ sign g(−u), and ξ(x ) = 0 is a closed surface. A procedure for constructing Liapunov functions based upon the use of a generating v-function is developed. Such a generating v-function may have the form:

v(x) = x A (x)x
where A(x ) = {aij (xi , xj )}, and aij = aji . The coefficients aij (xi , xj ) can be computed in order to obtain dv/dt of the wanted form. Particular emphasis is given to the case of systems with limit cycles and, as an example, the limit cycle of the van der Pol equation is identified with good approximation. It is also analytically proved that outside a closed algebraic curve, circumscribing the limit cycle, the system is asymptotically stable.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):579-585. doi:10.1115/1.3658714.

The theory pertaining to the annulus flow problem in axial turbomachinery is reviewed and a simplified analysis which is essentially concerned with the effect of streamline curvature is worked out. Some generalized results are obtained for the case of a single blade row and for the oscillating flow between repeating blade rows of arbitrary spacing. The effect of finite blade width is assessed. The simple radial equilibrium hypothesis which is still attractive to designers is reconsidered and a modified radial equilibrium theory which directly eliminates the oscillatory terms is proposed as being more accurate and simpler than the conventional radial equilibrium theory.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):587-592. doi:10.1115/1.3658718.

The adaption of the schlieren method for the purpose of observing flow in water is a recent development at the Garfield Thomas Water Tunnel. Flow is shown over an opening and over a semicylinder for a range of Reynolds numbers of 2.5 × 104 to 25 × 104 . The relative effects of temperature and pressure as they affect the index of refraction are treated. The relative persistency of a temperature gradient in air and water is considered, and the relative effects in air and water of a chosen density gradient are calculated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):593-600. doi:10.1115/1.3658719.

The use of hydraulic mechanisms in low-energy transfer and information-transmittal devices requires a working understanding of dynamic hydraulic behavior. In this paper the effects of fluid viscosity and wall interference on wave motion in a simple hydraulic device are considered. It is shown that for the applications considered these phenomena may be treated by boundary-layer methods. Calculations are carried out to show their effect on piston displacement, and these effects are compared with the behavior when viscosity is not taken into account.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):602-608. doi:10.1115/1.3658721.

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.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1962;84(4):609-616. doi:10.1115/1.3658722.

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.

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

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