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LETTERS TO THE EDITOR

J. Fluids Eng. 1976;98(1):1. doi:10.1115/1.3448197.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Fluids Eng. 1976;98(1):2-9. doi:10.1115/1.3448202.

The selection of pumps in an hydraulic network (such as those found in plant firewater systems or hydraulic control systems) is formulated as a mixed integer nonlinear program. The design objective is to minimize the total relative pump first cost. The piping network is assumed to exist and hence is not modified during the optimization process. A method is given for the transformation of the mixed integer nonlinear program into a mixed integer separable program. This formulation allows the use of efficient algorithms for the design of hydraulic networks. It also offers an alternative for the analysis of hydraulic networks. This technique may also be used for the analysis and design of general networks with nonlinear elements subject to convexity conditions. Two examples are given which consider an analysis problem and a design problem.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):10-18. doi:10.1115/1.3448158.

The von Karman vortex streets formed in the wakes of vibrating, flexible cables were studied using hot wire anemometers. The experiments took place in or at the boundaries of the flow regime where the vibration and vortex-shedding frequencies lock together, or synchronize, to control the wake formation. Spacial cross-correlations of the wake velocity signals were made for Reynolds numbers between 400 and 1300. Within the synchronized region, the magnitude of the measured spanwise cross-correlation coefficient is seen to approach unity, being limited by turbulence but apparently independent of frequency, amplitude, and Reynolds number. The bounds of the lock-in regime are determined and compare remarkably well with previous vibrating, rigid cylinder results. Further, the downstream longitudinal vortex spacing and induced street velocity are also found to compare well with vibrating cylinder results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):19-24. doi:10.1115/1.3448196.

A semi-empirical, dynamic model for investigating the fluid forces induced on a bluff cylinder by vortex shedding is developed using random vibration theory. The model includes both spanwise correlation effects and the amplitude dependence of the correlated vortex forces. Model parameters are determined by experimental data. The results are then applied to determine the forces exerted on elastic cylinders at resonance with vortex shedding. The predictions are in good agreement with experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):27-32. doi:10.1115/1.3448201.

Attention is focused in this study upon the development of a surface renewal-based analysis of transitional turbulent pulsatile flow and upon the experimental measurement of the instantaneous wall region turbulent periodicity. The resulting theoretical predictions and experimental measurements for periodicity provide a direct test of the validity of the model. The theory and experiment taken together provide further physical insight into the mechanism associated with this complex problem.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):33-40. doi:10.1115/1.3448204.

An experimental investigation of a low-speed turbulent swirling flow in a stationary, concentric, annular duct was made. The experiment involved isothermal air as the working fluid in an annulus with a diameter ratio di /d0 = 0.4, an average axial Reynolds number of 72,000, and an average axial velocity of 15 m/s. The swirl profile initially induced at the inlet was of the forced-vortex type. The rate of swirl, or the magnitude of the tangential velocity relative to the axial component, decayed axially from the inlet. Three different swirl rates were considered, one being straight flow. Extensive measurements were made of the velocity field with a cylindrical pressure probe at seven stations located 1.7 to 32.7 equivalent diameters from the entrance. The specific goals were experimental data on the axial decay of angular momentum and inferred values of the effective turbulent tangential viscosity. Results show a uniform axial decay of angular momentum and a profile shape independent of axial location. An empirical model using tangential eddy diffusivities that vary over the cross-section gave the best description of experimental data. The tangential profile shape and tangential viscosity distribution and magnitude did not depend on the initial rate of swirl.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):41-48. doi:10.1115/1.3448205.

The Navier-Stokes equations are solved by a numerical method for steady, fully developed, incompressible, laminar flow in curved rectangular channels considering the curvature ratio effect in the formulation. Solutions are obtained for aspect ratios 1, 2, 5 and 0.5 and Dean number ranges from 5 to 715, for example, for the case of square channel. It is found that an additional counter-rotating pair of vortices appears near the central outer region of the channel in addition to the familiar secondary flow at a certain higher Dean number depending on the aspect ratio. This phenomenon is consistent with Dean’s centrifugal instability problem and the secondary flow patterns with two pairs of counter-rotating vortices have not been reported in the past. The correlation equations for the friction factor are developed. The friction factor results are compared with the available theoretical and experimental results for the case of curved square channel and the agreement is found to be good.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):49-56. doi:10.1115/1.3448206.

From observations of a stream of gas bubbles rising through a liquid, a two-phase mathematical model is proposed for calculating the induced turbulent vertical liquid flow. The bubbles provide a large buoyancy force and the associated drag on the liquid moves the liquid upward. The liquid pumped upward consists of the bubble wakes and the liquid brought into the jet region by turbulent entrainment. The expansion of the gas bubbles as they rise through the liquid is taken into account. The continuity and momentum equations are solved numerically for an axisymmetric air jet submerged in water. Water pumping rates are obtained as a function of air flow rate and depth of submergence. Comparisons are made with limited experimental information in the literature.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):58-68. doi:10.1115/1.3448210.

The performance characteristics of four different axisymmetric contraction shapes with the same contraction ratio are experimentally investigated for incompressible flow. The pre- and postcontraction mean and turbulent velocity profiles and spectra, and the variation of the mean and turbulent velocities along the axis as a function of local contraction ratio and axial length are presented in this paper. The results show that all the nozzles are of essentially equal effectiveness as far as the core flow in the exit plane is concerned. But the mean and turbulence characteristics of the exit boundary layer, the upstream influence of the contraction, and the departure from equipartition within the nozzle vary significantly with the contraction shape. The data demonstrate the inadequacy of the Batchelor-Proudman-Ribner-Tucker theory in predicting the effect of a contraction on the turbulence structure. These data are of interest in wind tunnel and nozzle design, and in boundary layer prediction.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):70-78. doi:10.1115/1.3448215.

Phase velocities and attenuation factors for the propagation of small amplitude long wavelength sinusoidal disturbances, measured in a tube with turbulent liquid flow, are reported. Three frequency bands are delineated. A quasi-steady-flow model, based primarily on friction-factor data, is corroborated at low frequencies. An eddy-viscosity model, in which the energy of turbulence fails to respond in quasi-steady fashion to the sinusoidal disturbances, is corroborated at higher frequencies. In a predicted transition band unexpected and dramatic peaks in attenuation and phase velocity were found. A discussion suggests that the phenomenon may be related to deterministic aspects of turbulence production.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):79-84. doi:10.1115/1.3448218.

Velocity, pressure, and turbulence measurements were made in the separated, reattached, and redeveloped regions of a two-dimensional incompressible flow over a flat plate with finite thickness and blunt leading edge. Flow characteristics, such as the reattachment length and the flow pattern in the separated region, were determined. The boundary layer characteristics of the flow downstream of the reattachment point are presented through various experimental results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):87-94. doi:10.1115/1.3448223.

The microbubble spectrum in a sample of tap water was measured by the Coulter counter technique under various conditions, and at the same time the tensile strength (i.e., “superheat” capacity) of the tap water was measured by the ultrasonic cavitation technique. It was observed in this experiment that the microbubble population and size increased and the superheat decreased for increasing temperature and under fast neutron irradiation. Finally the generalized Noltingk-Neppiras equation was solved numerically for selected initial microbubble radii, and the suppression pressure (or superheat) determined by this numerical solution was compared with the experimental result. Apparent inconsistencies in experimental results may be primarily due to the neglect of the rectified diffusion effect in the present analysis.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):98-103. doi:10.1115/1.3448229.

The onset of droplet formation from contained oil slicks is interpreted to be due to the breaking of finite amplitude interfacial waves. These waves result from the equilibration of amplifying Kelvin-Helmholtz waves. Experimental evidence is shown to be consistent with this view. From this model, conditions for droplet shedding from the headwave alone and from the entire slick are derived. Also, an earlier result in the stability of thin slicks is shown to be in error.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):106-111. doi:10.1115/1.3448157.

Cavitation in a fluid jet discharged under the surface of a similar fluid was studied using water and dilute solutions of poly(ethylene oxide), a drag-reducing polymer. The addition of a few parts-per-million of poly(ethylene oxide) to the fluid reduced the cavitation-inception index to about one-half the pure-water value. Upstream turbulence increased the cavitation inception index with water but had little effect on cavitation inception with polymer solutions. The viscosity, air content, nuclei number, and tensile strength of the polymer fluid was found to be essentially the same as water, and the surface tension lowered; hence an explanation of the reduced cavitation-inception index observed in polymer solutions must be sought in the changed fluid dynamics of the polymer jet. Photographs of polymer jets discharging in air are presented to aid in the explanation.

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

TECHNICAL BRIEFS

J. Fluids Eng. 1976;98(1):113-116. doi:10.1115/1.3448162.

Friction factors were determined for fully developed turbulent flow of mercury in smooth concentric annuli under conditions where either both walls were unwetted, or both were wetted, or the inner wall was wetted and the outer one unwetted. Three radius ratios (r2 /r1 ) were used, i.e., 2.09, 2.78, and 4.00. Unwetted walls gave the lowest friction factors, which were practically independent of the r2 /r1 ratio over the limited range tested. The factors were 10 ± 1 percent higher than the commonly accepted values for smooth pipes (at the same Reynolds number). The highest friction factors were obtained with the inner wall wetted and the outer wall unwetted, and the greater the r2 /r1 ratio the greater was the effect. For example, at r2 /r1 = 4.00, the friction factors were 9.9% greater than for the situation when both walls were unwetted. The wetting conditions affected the location of the radius of maximum velocity (rm ); and it was found that the nearer rm approached r2 , the higher was the friction factor.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(1):116-119. doi:10.1115/1.3448163.
Abstract
Topics: Flow (Dynamics)
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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