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J. Basic Eng. 1972;94(2):257. doi:10.1115/1.3425400.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Basic Eng. 1972;94(2):258-285. doi:10.1115/1.3425401.

The turbulent frictional resistance of dilute polymer solutions can be as low as one-quarter that of the pure solvent. The reduction of drag can be associated with polymer properties and the hydrodynamics of the flow. This review illustrates the key concepts in hydrodynamics, polymer chemistry, and rheology which apply to polymer drag reduction. The effect of parts-per-million polymer concentrations on laminar-turbulent transition, boundary-layer properties and turbulent frictional resistance in pipe flow and along flat plates is emphasized, using experimental data from current literature. Industrial, fire-fighting, marine, and biological applications are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):286-313. doi:10.1115/1.3425402.

Despite the fact that the world’s need for desalinated water is becoming more urgent, the ability to economically desalinate on a large scale still remains a goal rather than a reality. The present review examines distillation, freezing, electrodialysis, and reverse osmosis which together account for essentially all of the installed desalination capacity. Although distillation is by far the most widely employed system, emphasis is placed on the other three methods because of their potential. It is shown that for each process one or more of the critical technical problems which lead to increased fresh water costs is associated with a fluid mechanical phenomenon. The review attempts to present the critical fluid engineering problems, and where possible the solutions and their consequences in relation to the goal of obtaining desalted water economically.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):314-319. doi:10.1115/1.3425403.

An analysis is made of fully developed turbulent flow in a parallel-plate channel having one porous bounding wall. A velocity slip model is employed to characterize the boundary condition at the porous surface. The turbulent transport processes in the channel are represented via the Prandtl mixing length concept in conjunction with a modified form of the Van Driest damping factor. Numerical results are obtained for Reynolds numbers ranging from 5000 to 200,000 and for a wide range of values of a dimensionless slip grouping. The results show that velocity slip at the porous surface brings about a reduction in the friction factor, the extent of the reduction being accentuated with increasing Reynolds number. The velocity slip also causes a skewing of the velocity profiles, such that the location of the maximum velocity is shifted toward the porous wall.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):321-329. doi:10.1115/1.3425407.

A family of hodograph models for the cross flow velocity component of three-dimensional, turbulent boundary layers is presented. The principal advantage of this family is its flexibility which allows a wide variety of possible shapes for the hodograph. An integral method based on this family is developed and applied to data obtained in curved, rectangular channels. For the cases treated, the method gives acceptable results for cross flow profiles with and without flow reversal. Suggestions for refining the method are given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):333-337. doi:10.1115/1.3425411.

This paper describes a submersible pressure probe, which permits the measurement of the pressure near the surface of a water wave, even in the regions below the crest. The probe is based on the principle that the liquid entry into a cavity through a small hole is impeded by surface tension. Normally, however, there is liquid membrane formed over the hole upon withdrawal from water, and this was solved by selection of proper material. The methods of testing the probe and some measurements obtained with it are also presented in this paper.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):339-344. doi:10.1115/1.3425414.

This paper presents an experimental investigation of mean velocities of turbulent, three-dimensional incompressible air jets from various rectangular orifices issuing tangentially to and flowing along the surface of a curved wall into quiescent ambient air. An experimental study of the jet separation is also presented. The three-dimensional curved wall jet is found to be drastically different in its mean property behavior from its so-called two-dimensional counterpart. Velocity contour plots show the resultant effect on the jet flow of two diverging tendencies—the free jet flow and the Coanda flow. This effect is found to occur earlier with smaller aspect-ratio orifices. Within the range of variables studied, three-dimensional curved wall jets may be characterized by three regions of maximum velocity decay. The rate of maximum velocity decay is dependent on orifice aspect ratio, except in the potential core region. Further, the curved wall jet differs from other three-dimensional jet flows in its growth behavior.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):345-351. doi:10.1115/1.3425417.

A calculation method using a differential equation for the turbulent shear stress has been successfully applied to boundary layers with compressibility, heat transfer, three-dimensionality or unsteady flow, with an empirical input obtained almost entirely from low-speed flow at constant pressure. With numerical changes in the empirical input the method has been extended to duct flows and free shear layers. Running times are typically 5–10 sec on a CDC 6600 or five times this on an IBM 7094; programs are freely available from the authors.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):353-361. doi:10.1115/1.3425420.

Fully developed turbulent flow in both smooth and rough-walled pipes is investigated for Reynolds numbers from 30,000 to 480,000. The values of mean velocity, root-mean-square values of the fluctuating velocity components, and cross-correlation values of the fluctuating velocities are presented for flow in a smooth pipe and two sand-roughened pipes, R/ε = 208 and R/ε = 26.4. The quantity R/ε is the ratio of the actual pipe radius to the average sand particle size. The experimental measurements for flow in smooth pipes are in good agreement with those of previous investigations throughout the Reynolds number range considered. Several of the rough pipe turbulence quantities show substantial deviations from the corresponding smooth pipe quantities. For rough pipes, the measured uv cross-correlation values approach those predicted empirically from the Reynolds equations for fully developed, axisymmetric flow as the flow approaches the hydraulically smooth case. However, as the Reynolds number is increased and the flow proceeds through the transition region from smooth to fully rough flow and to the fully rough flow region, the values of the uv cross correlation in rough pipes are significantly lower than the predicted values. This difference between predicted and measured data becomes more pronounced as the Reynolds number is further increased and the flow becomes fully rough. The difference between measured and predicted uv values, and other differences between smooth and rough pipe results, suggests that the accepted reduction of the Reynolds equations for flow in smooth pipes is not valid for flow in rough pipes. Thus, the Reynolds equations are re-examined for flow in rough pipes, and it is shown that these equations can be satisfied by the experimental data if secondary flows and angular variations in the mean velocity are postulated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):363-367. doi:10.1115/1.3425423.

A review of the two main theories of red cell structure is given. One theory asserts that the cell structure is simply an elastic membrane around liquid contents, while the counter theory contends that there is an internal structure to the cell which supports the membrane shape. An experiment is reported which tests the effect of the structural contents of the red cell on its deformability. A comparison of the force-deformation characteristics of intact red cells and red cell ghosts is made. The deformabilities are compared by measuring the distances which intact red cells and red cell ghosts move down the inside of a tapered glass tube under the same pressure head before they lodge inside the tube. The results of the experiment indicate a negligible difference in the deformabilities of red cells and ghosts. These results do not disprove the existence of an internal structure; they do assert that the contents are structurally insignificant.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):369-372. doi:10.1115/1.3425426.

A basic solution for in-reactor sag of horizontal pressure tubes is proposed in accordance with a nonlinear anisotropic creep theorem. As an example, numerical solutions for in-reactor sag of cold-worked zircaloy-2 pressure tubes supported at the ends only are given for various combinations of anisotropy coefficients. It is shown that an isotropic analysis may overestimate or underestimate the deflection due to sag by about 100 percent if hoop creep rates are about 50 percent smaller or larger than longitudinal creep rates.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):373-376. doi:10.1115/1.3425427.

The low temperature fracture behavior of prestressed notched bars has been studied. The fracture stress was generally below the prestress level due to the influence of reverse plastic flow at the notch tip on unloading. When reverse plastic flow was prevented, low temperature fracture occurred at stress levels in excess of the prestress level. The benefits of prestressing are interpreted in terms of the introduction of plastic zones rather than the influence of residual stresses. The influence of aging and higher strain rates on the fracture behavior of prestressed specimens is also studied.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):377-380. doi:10.1115/1.3425428.

Basic circuits involving the thermocouple as a temperature-sensing device have been described and analyzed in the literature. However, relatively little has been written on the thermocouple as part of an overall instrument circuit wherein external electrical effects are important. After reviewing the more important electrical effects which are extraneous to the basic thermocouple circuit, the problem of multiple grounds in a thermocouple proper is considered in some detail. Experiment and analysis indicate that serious errors in temperature measurement can result from the use of improper grounds in thermocouple circuits.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):381-386. doi:10.1115/1.3425429.

The International Practical Temperature Scale has been redefined recently. It follows that the interpolating equations relating platinum resistance to temperature must be reevaluated for all platinum resistance thermometers which are used as standards for calibration work. After a brief review of the former calibration procedure, the new temperature scale is discussed as it affects resistance thermometry in the temperature range from 0 C to 630.74 C. An example based on new experimental data is given to illustrate the method of determining thermometer constants for the new scale, and to indicate the magnitude of the changes required.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):387-393. doi:10.1115/1.3425432.

A numerical technique for the efficient computation of singular states of stress is developed and applied to several plane strain elastic problems. The method which extracts the effect of the singularity from the field permits the use of relatively coarse nodal meshes with rapid solution times but maintains a high degree of accuracy. Using this technique, stress intensity factors are calculated for the torsion and flexure of solid and hollow cylinders and the internal pressurization of cylinders of varying thicknesses.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):394-400. doi:10.1115/1.3425433.

The influence of projectile strength on cratering was investigated for projectiles of aluminum alloys impacting semi-infinite aluminum targets over the velocity range of 1 km/sec to 5.0 km/sec. The experimental results showed that crater diameters were not significantly influenced by varying projectile strength. The crater depths were found to vary appreciably with strength at lower velocities but to become virtually the same at 3.5 km/sec for the series of projectile alloys investigated. A simple dynamic model for cratering was developed and compared with the experimental results of this study and other experimental results at higher velocities. These comparisons showed that the model provided predictions of crater diameter which were within 8 percent for the experimental results of this study and within 13 percent for the hypervelocity data. Crater depth predictions showed good agreement with the experimental results of this study for projectiles having greater yield strength than the target material. The predictions of depth as a function of velocity showed qualitative agreement with the hypervelocity data.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):401-405. doi:10.1115/1.3425434.

The finite-element technique has been applied in the analysis of a variety of pressure vessel problems. The example problems described in this paper suggest that the finite-element method is perhaps the most suitable means currently available for obtaining quick and accurate solutions for real-life pressure vessel problems. Finite-element programs can be used by the practicing engineer. Companion programs are available that can be used to check the input data and graphically display both the input and output data.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):407-416. doi:10.1115/1.3425436.

An analytical model has been developed to predict the flow behavior within axisymmetric single-nozzle ejectors employing variable-area mixing tubes. The primary flow may be supersonic or subsonic and may have a different stagnation temperature than the subsonic secondary flow. Tests were performed on an ejector with an 800 deg F supersonic (M = 2.72) primary jet to evaluate the analytical model. Measured velocity profiles, temperature profiles, and wall static pressure distributions are presented and compared to the analytical predictions. Agreement is generally good.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):417-421. doi:10.1115/1.3425437.

A simple mathematical analog for determination of the squeeze film behavior between two parallel annular disks, one having a porous facing, from the already available solutions of comparable nonporous disks is presented. A comparison of the analog solution with a Fourier-Bessel solution has been made and the agreement is found to be good for a range of values of the permeability parameter and the porous facing thickness. The results also have been extended to include the rotating inertia effect of the film fluid. The resulting dimensionless pressure distribution and the dimensionless squeeze film load are expressed in terms of a permeability parameter, inertia parameter, squeeze film number, and the disk dimensions. For constant squeeze film load, a relationship between squeeze time and film thickness also has been obtained. Generally, the presence of the porous facing will decrease the squeeze film load and will reduce the total squeeze time to some finite value. The inertia effect will further decrease the squeeze film load and the squeeze time, however, the squeeze time reduction due to the inertia effect will become small if the porous facing has high permeability and is thick.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):422-428. doi:10.1115/1.3425438.

In this paper a new concept of the inertial multiplier is introduced to relax the restriction of the time increment in a computation method for natural gas transient analysis. The range of usefulness of this multiplier and the criteria on the allowable reach length for natural gas transient flow calculation are presented. The validity and the application of the criteria are demonstrated by practical examples. A semianalytical solution with the second-order approximation to the nonlinear difference equations for steady oscillatory flow in natural gas systems is also discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):429-433. doi:10.1115/1.3425439.

A computer-based system utilizing an electro-optical instrument has been developed for generating and processing a signal proportional to the instantaneous sand concentration at a point in a flow field. Herein are described the instrumentation and techniques used in a study of sediment entrainment by periodic waves breaking on sand beaches. The instantaneous sediment concentration has been decomposed as follows:

C(x, y, z, t) = C(x, y, z)
  + C(x, y, z, t) + Cp(x, y, z, t)
where C (x, y, z) is the temporal average concentration, C′ (x, y, z, t) is a random component of the sediment concentration, and Cp (x, y, z, t) is a repetitive component with period equal to the period of the breaking waves. Particular attention has been given to isolating the repetitive component which was so obscured by the signal characteristics that no periodicity was apparent on either an oscilloscope trace or a strip chart recorder. Spectral analysis was not applicable because the shape of the repetitive waveform, Cp (x, y, z, t), over one wave cycle was desired.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):434-440. doi:10.1115/1.3425440.

The flow field resulting from the interaction of a finite amplitude standing acoustic field and a viscous fluid was investigated analytically and experimentally. For an adiabatic wall, an analytical solution was obtained for the velocity field over the entire duct cross section. The solution predicts standing vortices in the duct cross section: their number is proportional to the resonance mode number. Similar secondary flow behavior has been found by Maslen and Moore who considered the case of an isothermal duct. The analysis is strictly valid for a characteristic Reynolds number of the order of magnitude one compared to δ, where δ ≃ 10−3 . Measurements of the resonant pressure field and photographs of the induced secondary motion, using smoke as a tracer, qualitatively substantiated the analysis. Experimental data were obtained at values of the characteristic Reynolds number varying from 4.5 to 15.3.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):441-446. doi:10.1115/1.3425441.

The basic relationships for transient flow in a straight tube are investigated for the case of axial boundary motion. Viscous effects and other small terms are neglected allowing the problem to be described by the wave equation subjected to a moving boundary. Using this equation the case of pressure surge generation due to instantaneous load rejection in a finite straight tube is investigated. The axial boundary motion is due to the internal pressure stretching the pipe wall along the pipe axis. A closed form analytical result is obtained using a differential difference equation and shows that the pressure surge magnitude can be significantly greater than that predicted neglecting the boundary motion. This result is used to obtain a simple expression for estimating the maximum value of the pressure surge following the load rejection. An experiment is conducted which shows the significance of the axial line motion and compares well with the prediction of this effect.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):447-454. doi:10.1115/1.3425442.

Hydraulic mining involves the erosion of a material with a high speed water jet. This technique can be applied to coal mining, tunnelling for high speed ground transportation systems and drilling for deep oil wells. A high speed, unsteady jet of water is known to have a much greater potential for hydraulic mining than a steady jet of water. A comprehensive study of mining with unsteady jets would involve three aspects: (1) the hydraulic and mechanical aspects of producing an unsteady jet, (2) the study of the dispersion of the jet, and (3) the response of the material being eroded. This paper deals with the first aspect and studies three different systems for producing unsteady water jets. A computer program was written to calculate the unsteady jet velocities for each system using the method of characteristics. The unsteady jet velocity was integrated and used in a theoretical model to compare the effectiveness of the three different systems. The effect of varying certain design and operating parameters of the system was also studied. Factors affecting the choice of the appropriate system are discussed.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):455-456. doi:10.1115/1.3425443.

Presently, the only accurate solutions for the step response of a semi-infinite, circular fluid transmission line result from involved, time consuming, numerical finite series or integration techniques [1, 2, 3]. None of these solutions is practically suitable for either a rapid manual prediction for an arbitrary fluid line (liquid or gas), or for extension of the semi-infinite line results to the more meaningful problem of a finite line with arbitrary inputs. In the frequency domain (sinusoidal signals), a complete, verified solution exists [1, 4, 5] and theoretically could be transformed into the time domain. This was the scheme used by Brown and Nelson for liquid lines [2], but it required the numerical techniques referred to above and, in their own words, was a “very complex and tricky business.” However, simpler solutions for most operating regimes also exist in the frequency domain [6, 7]. These simple frequency domain solutions were transformed into the time domain and provided the basis for a simple solution for the step response.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):457-465. doi:10.1115/1.3425444.

A review of methods of handling unsteady flow problems in metal pipes by numerical methods is undertaken. The characteristic method, typifying explicit methods, and the centered implicit method are developed, including the manner various boundary conditions are introduced into the solutions. High velocity flow is briefly reviewed, i.e., flow cases with the velocity of flow of the same order of magnitude as the pulse wave speed. Three complex boundary conditions are examined: turbomachinery, column separation, and the compressed gas accumulator.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):467-472. doi:10.1115/1.3425449.

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):474-482. doi:10.1115/1.3425453.
Abstract
Topics: Fluids , Modeling
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):483-489. doi:10.1115/1.3425456.

It is generally assumed that orifices and valves follow closely their steady-state characteristics during transient operation. However, this assumption of quasisteady behavior may lead to errors in predicting transient flow conditions under certain circumstances. In order to evaluate the transient behavior of an orifice, a differential equation relating the flow through and the pressure drop across an orifice was derived. An extension was made to include an axial dimension for the orifice. The solution of this equation for transient flow through an orifice subjected to a step change in pressure drop across the orifice is significantly different than that obtained using the steady state relationship. An experiment was designed to evaluate the theoretical results in which an orifice on the end of a line was subjected to a sudden pressure change and the resulting transient pressures were observed. It was found that a significant short term transient occurs before the orifice flow reaches the new steady state condition. The observed short term transient agrees well with that predicted by the theory. It is concluded that the behavior of an orifice can deviate considerably from that predicted by steady-state equations during periods of rapid pressure or flow changes. The dynamic description of orifice flow may be combined with a larger system analysis (e.g., using the method of characteristics) to more accurately predict the overall transient performance of flow systems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):492-499. doi:10.1115/1.3425459.

Particle velocity profiles, air velocity profiles, and local particle flux profiles were determined experimentally for suspensions consisting of air and spherical glass particles having average diameters of 62 and 200 microns. Three tube sizes were used: 0.5, 0.75, and 1.0 in. diameter, and the Reynolds number ranged from 5670 to 50,000. Continuum theory of suspension flows predicts a universal velocity profile for the suspension, and the experiments produced suspension velocities which form a family of logarithmic curves with the mass loading ratio as a parameter. Each profile was found to be independent of Reynolds number. Other results are presented and compared to the analytic solutions which are presented in another paper [1].

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

TECHNICAL BRIEFS

J. Basic Eng. 1972;94(2):500-502. doi:10.1115/1.3425460.
Abstract
Topics: Jets , Vortices
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):504-506. doi:10.1115/1.3425462.
Abstract
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):506-508. doi:10.1115/1.3425463.

Solutions are obtained for fully developed laminar flow of a compressible fluid through a rotating vertical cylinder. The results enable the velocity, friction loss, and pressure gradient to be easily calculated from corresponding incompressible flow solutions. It is shown that compressibility effects may be neglected completely over a practical range of operating conditions, such as encountered in centrifugal aerosol separators, enabling the flow analyses in these more complicated configurations to be justifiably simplified.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Basic Eng. 1972;94(2):509-510. doi:10.1115/1.3425465.

A small supersonic resonance tube was constructed and tested utilizing a combustion heated jet. Comparing these results to a cold jet it was found that the combustion jet has an increased frequency and a higher power output level which reflects the increased gas enthalpy.

Commentary by Dr. Valentin Fuster

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