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EDITORIAL

J. Fluids Eng. 1976;98(2):141. doi:10.1115/1.3448239.
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Abstract
Commentary by Dr. Valentin Fuster

COMMENTARY

Commentary by Dr. Valentin Fuster

BIBLIOGRAPHIES

J. Fluids Eng. 1976;98(2):151-155. doi:10.1115/1.3448241.
FREE TO VIEW
Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Fluids Eng. 1976;98(2):156-161. doi:10.1115/1.3448242.

The Navier-Stokes equations are examined here for the flow of an incompressible fluid contained between rotating eccentric cylinders of finite length and moderate clearance ratios. Based on a modified form of the Reynolds Equation an analytical solution for short cylinders, and numerical results for finite configurations are given for the range of Reynolds numbers and (C/R) ratios in which inertia forces can be neglected. In a subsequent paper consideration will be given to the range of Taylor numbers in which inertia and transverse effects may become significant.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):163-172. doi:10.1115/1.3448247.

The general objective of the investigation reported in this paper is to obtain a reliable understanding of the three-dimensional inviscid effects in axial flow turbomachinery. The calculation is based on the method of distributed singularities. The baldes are represented by a series of line vortices and line sources which have their axes along the radial direction and are arranged along the blade mean camber surface. The basic perturbed velocity fields due to radial vortex lines of constant strength and radial source lines of variable strength are computed from a modified theory based on Tyson’s and Rossow’s formulation. Examples illustrating the three-dimensional effects due to hub/tip ratio, stagger angle, and number of blades are carried out. The effects of the radial variation of the strength of the radial source line are examined. The three-dimensional effects are found to be appreciable for a low hub/tip configuration with small number of blades.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):173-180. doi:10.1115/1.3448250.

Frictional pressure drop in rectangular ducts is examined. Using correspondence between theory and experiment in laminar flow as a means for acceptance of published data, turbulent flow data for smooth rectangular ducts were compared with smooth circular tube data. Data for ducts having aspect ratios between unity and 39:1 were obtained in the literature and, in conjunction with new experimental data, were examined for deviations from the smooth circular tube line (smooth Moody). It was found that at constant Reynolds number based on hydraulic diameter the friction factor increases monotonically with increasing aspect ratio. It was thus concluded that the hydraulic diameter is not the proper length dimension to use in the Reynolds number to insure similarity between the circular and rectangular ducts. Instead, it was determined that if a modified Reynolds number Re* was obtained so that geometric similarity was provided in laminar flow by the relation f = 64/Re* for all geometries, that this Reynolds number also provided good similarity in fully developed turbulent flow within a ∼ 5 percent scatter band about the smooth tube line. By using this “laminar equivalent” Reynolds number, Re*, it is demonstrated that circular tube methods may be readily applied to rectangular ducts eliminating large errors in estimation of friction factor.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):182-191. doi:10.1115/1.3448255.

Knowledge of the dynamic performance of pumps is essential for the prediction of transient behavior and instabilities in hydraulic systems; the necessary information is in the form of a transfer function which relates the instantaneous or fluctuating pressure and mass flow rate at inlet to the same quantities in the discharge from the pump. The presence of cavitation within the pump can have a major effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous inlet and discharge mass flow rates. The present paper utilizes results from free streamline cascade theory to evaluate the elements in the transfer function for a cavitating inducer and shows that the numerical results are consistent with the characteristics observed in some dynamic tests on rocket engine turbopumps.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):192-198. doi:10.1115/1.3448256.

An analytical study has been made to clarify the details of the flow between a rotating disk and a stationary casing side-wall with and without an axisymmetric inward through-flow. The flow field between the casing side-wall and the surface of the rotating disk is divided into four layers instead of three in earlier analyses. Proceeding from the casing side-wall to the disk, they are a wall boundary layer, an outward-flow layer, a core and a disk boundary layer. The flow field is determined so that the integrated equations of motion as well as the continuity equation are satisfied for each of the four layers. In the present analysis, least empirical informations relative to a rotating disk are used compared with the theories in the literature. The mechanics of the flow field is explained by the flow model without contradiction, and the predicted radial and axial distributions of velocity and the pressure distribution in the casing agree well with experimental results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):199-206. doi:10.1115/1.3448258.

The flow of steam through a safety valve vent pipe system has been analyzed to provide a design basis for sizing the pipe to prevent blowback of steam. The analysis is based upon the application of modern fluid dynamics to the flow in ejectors and free-jet wind tunnels. The resulting vent pipe design procedure is, in the authors’ opinion, based upon a more realistic analysis than has previously been performed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):208-215. doi:10.1115/1.3448261.

A critical review is presented on methods of surface distribution of singularities around multielement arifoils in plane potential flow analysis. The approach of piecewise constant distribution of vorticity, used originally for airfoils, is treated here to develop a numerical method for multielement cascades. The incompressible flow pattern is obtained by superimposing solutions for 3 × N prescribed onset flows around an N-element cascade system. Compressibility effects are treated by an extension of Goethert’s rule involving affine transformation. Emphasis is placed upon a comprehensible description of the problem formualtion and, in particular, on deriving the correct circulation strength around multiply-connected domains. Some results are presented and discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):217-223. doi:10.1115/1.3448264.

The flow between a rotating disk and a stationary disk, with nonaxisymmetric boundary conditions is studied. A flow field of this type exists in the narrow gap between the rotor and side plates of a rotary vane compressor. Fluid is admitted into the gap in the center of the disk for the purpose of sealing against leakage due to the nonaxisymmetric pressure distribution externally imposed on the disk circumference. The flow is solved analytically by a perturbation technique. Flow maps and pressure maps are obtained for various operating conditions. The effectiveness of the fluid seal is evaluated for these conditions by calculating the flow rates that pass through the gap. The flow field is simulated on a test apparatus and experimental verification is given to the analytical results. The results obtained indicate the possibility of appreciably reducing the leakage through the gap by a proper selection of the fluid pressure and the disk geometry.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):224-228. doi:10.1115/1.3448267.

A pneumatic tube system suitable for transportation purposes is simulated in an experimental facility. The vehicle position, velocity and corresponding system pressures were obtained and are presented for representative test runs. An analysis for prediction of these quantities during the transit of a vehicle through a tube under conditions of fixed inlet pressure and discharge volume flow rate is also presented. This analysis is applied to the experimental operating conditions and is shown to predict the experimental results closely and to be applicable to the prediction of the performance of prototype pneumatic tube systems over a significant range of interest.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):229-235. doi:10.1115/1.3448268.

The rate of mixing between parallel fluid streams depends on the turbulence intensity in each stream, and, if these turbulence levels are unequal, on whether the higher intensity occurs in the faster stream or the slower. These dependencies can be well predicted by the finite-difference methods using existing analytical models of turbulent motion. Experimental and predicted results for plane mixing-layer flows are compared for different stream velocity ratios and turbulence levels.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):236-242. doi:10.1115/1.3448272.

An experimental investigation of the flow regime and the performance of straight-core annular diffusers operating immediately downstream of an axial compressor was carried out. Features of the compressor’s discharge including the size of the blade wakes, the streamwise relative turbulence intensity and the periodic streamwise component of velocity induced by the rotor blades were studied. The periodic streamwise velocity component was found to be quite small and it decayed as the flow proceeded through the diffusers. The relative turbulence intensities were comparatively large and increased along the diffusers. The statistical distribution of the stall periods for the diffuser with transitory stall had characteristics similar to those found for two-dimensional diffusers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):244-248. doi:10.1115/1.3448275.

A method is given for determining the transient response approximation for noncircular fluid transmission lines. The results are presented in terms of a characteristic frequency which depends only on the laminar viscous steady flow resistance and inductance of the noncircular line. The components of an equivalent circuit based on standard transmission line theory are analyzed, and approximations of the series impedance, shunt admittance, propagation operator, and characteristic impedance are presented. These circuit parameters are transformed into the time domain to give a simple approximation for the step response of noncircular fluid-filled lines. The solution is expressed as a single complementary error function. Results are shown for air at 27°C. The results are restricted to laminar flow conditions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):249-255. doi:10.1115/1.3448276.

A closed-form solution has been obtained for the potential flow about a circular cylinder situated in an impinging slot jet. Among other results, the potential flow solution yields the free stream velocity for the boundary layer adjacent to the cylinder surface. A basic feature of the solution is the division of the flow field into subdomains, thereby making it possible to employ harmonic functions that are appropriate to each such subdomain. The boundary conditions on the free streamline and the conditions of continuity between the subdomains are satisfied by a combination of least squares and point matching constraints. Numerical evaluation of the solution was carried out for cylinder diameters greater or equal to the nozzle width and for a range of dimensionless separation distances between the nozzle and the impingement surface. Results are presented for the velocity and pressure distributions on the cylinder surface, for the position of the free streamline, and for the velocity gradients at the stagnation point. The latter serve as input information to the Nusselt number and skin friction expressions that are given by boundary layer theory. Comparisons were made with available experimental results for the pressure distribution, velocity gradient, and Nusselt number, and good agreement was found to prevail in the stagnation region.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):256-260. doi:10.1115/1.3448277.

The momentum-flux development from three-dimensional free jets has been investigated. The analysis is presented for free jets from circular, triangular, rectangular and elliptical orifices. The bluff jets, with eccentricity near unity, show the usual potential region and the axisymmetric decay region for the maximum axial velocity decay. The slender jets, with smaller than one eccentricity values, show three zones of flow development. The potential core region is followed by a characteristic decay region where velocity decay is dependent on the shape and eccentricity of the orifice. The maximum axial velocity of all slender jets finally decay axisymmetrically with increasing downstream distances.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):261-268. doi:10.1115/1.3448280.

A Reynolds stress model is proposed for modeling the local turbulence structure in flow along a streamwise corner. Initial discussion centers on present methods of predicting internal and extenal corner flow behavior. An algebraic Reynolds stress model is then developed by operating on a modified form of the Reynolds stress transport equations. Application of the model involves specification of two empirical constants and a global representation for the mixing length. The paper concludes with a discussion of the features and limitations of the model.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):269-276. doi:10.1115/1.3448281.

The applicability of the Reynolds stress model developed in Part I to fully developed rectangular duct flow is investigated. Two sets of experimental data are analyzed in order to prescribe a representative mixing length variation and appropriate values for the constants in the model. Predicted Reynolds stress values are in good agreement with their experimental counterparts for both sets of data. These results are compared with predictions referred to an alternate model in order to explain discrepancies observed in a previous study. Possible extensions of the proposed model to increase its flexibility are discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):278-281. doi:10.1115/1.3448284.

The periodic flow obtained in a wind tunnel test section by means of an upstream pulsator is investigated. The turbulence level in this section is quite small and the direction of the periodic velocity is that of the mean velocity. The measurement of the velocity skewness and flatness factors indicates that true sinusoidal pulsation is achieved only for the resonance frequency which depends little on the length of the test section.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):284-291. doi:10.1115/1.3448288.

Measurements, obtained with hot wire anemometry, are reported in a co-axiol jet flow where the inner and outer initial maximum velocities were the same. The hot-wire signal was processed with a modified, linearized procedure which is described. The downstream results show that the coaxial jet develops more rapidly than a single jet but that, for example, the Reynolds shear stress has not attained a self-preserving condition at a distance of 30 external diameters. Particular attention was paid to the region of the wake of the pipe wall and two dominant frequencies were observed, corresponding to two orthogonal velocity components. The high frequencies of these fluctuations indicate that they must be regarded as turbulent fluctuations and, as might be expected, lead to regions of almost constant Prandtl and Prandtl-Kolmogorov length scales.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):292-296. doi:10.1115/1.3448291.

An approximate method is developed for locally nonsimilar laminar boundary layer flows. This method is applicable to several boundary layer velocity problems where the nonsimilarity stems from the freestream velocity distribution and the transverse curvature. The results are compared with those obtained by other methods and, except in the neighborhood of the point of separation, they are in good agreement.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):297-304. doi:10.1115/1.3448292.

Hot film needle and catheter probes were used to measure the velocity waves in the dog aorta between the aortic valve and the iliac bifurcation. The forms of the waves were found to be of two types, those in which there was a reverse flow, following systole, everywhere along the centerline of the aorta and those for which there was no flow reversal in the regions below the diaphragm. Energy spectra were measured before and after the administration of a cardiac stimulant. Except for a shift to higher frequencies, no significant change in the form of the spectra was observed. Characteristic times developed for the mean flow and the decay of a fully developed turbulence suggest that it is difficult to sustain small scale turbulence which might be initiated during peak systole.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):305-310. doi:10.1115/1.3448293.

Entry flow in curved channels is investigated by an approximate method analogous to that used by Pohlhausen in his treatment of boundary layer flows. Constant total pressure across the channel at the entrance is assumed. Therefore, if the upstream influences of viscosity have been neglected, the initial condition is given by a nonuniform velocity right at the entrance to the curved channel. The boundary layer in the entrance region is estimated by assuming a velocity profile that approaches the near parabolic profile when the flow becomes fully developed. As a result of wall curvature, entrance length becomes longer and the pressure drop along the inner wall is different from that along the outer wall.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):311-317. doi:10.1115/1.3448294.

The mixing of a supersonic with a subsonic stream is treated in a one-dimensional, ideal gas analysis to determine when the mixed flow can be supersonic and to reveal the relationship between certain phenomena described by the terms “forbidden region” of “thermal choking.” A singularity in the equations is shown to divide the mixing process solution curves into two branches: subcritical or supercritical leading, respectively, to subsonic or supersonic mixed states.

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

ERRATA

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Fluids Eng. 1976;98(2):318-320. doi:10.1115/1.3448297.
Abstract
Topics: Wakes , Cylinders
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):320-322. doi:10.1115/1.3448298.
Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):322-323. doi:10.1115/1.3448299.
Abstract
Topics: Vortices
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):326-328. doi:10.1115/1.3448301.
Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(2):328-330. doi:10.1115/1.3448302.

Steady, incompressible two-dimensional laminar boundary layers on curved surfaces with spanwise rotation are investigated using an approximate method. A fourth-degree polynomial is assumed for the velocity profiles and they are found to constitute a three-parameter family of curves characterized by a pressure factor, a curvature parameter and a rotational parameter. The results obtained for constant surface velocity flow with/without rotation on plane/curved surfaces are found to be consistent with those reported in the literature.

Commentary by Dr. Valentin Fuster

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