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REVIEW ARTICLES

J. Fluids Eng. 1985;107(1):6-22. doi:10.1115/1.3242443.

A review is given of current computational methods for analyzing flows in turbomachinery and other related internal propulsion components. The methods are divided primarily into two classes, inviscid and viscous. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, on the other hand, due to the state-of-the-art, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler approaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Fluids Eng. 1985;107(1):23-30. doi:10.1115/1.3242435.

The design of air-to-air, thrust augmenting ejectors having short curved wall diffuses utilizing boundary layer control is discussed. The design is achieved by an inverse method which uses the vorticity at the diffuser inlet as a flow parameter in the analysis. Three diffusers having ejector length-to-mixing chamber diameter ratios of approximately 6:1 and mixing chamber inlet area-to-primary nozzle area ratios of 20:1 and 40:1 were designed and tested. A new high level of performance was analytically predicted and achieved experimentally. Comparisons between predicted and observed performances, velocity distributions and pressure distributions are presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):31-35. doi:10.1115/1.3242436.

A simplified method of using four-hole probes to measure three-dimensional flow-fields is presented. This method is similar to an existing calibration and application procedure used for five-hole probes. The new method is demonstrated for two four-hole probes of different geometry. These four-hole probes and a five-hole probe are used to measure the turbulent boundary layer on a flat plate. The results from the three probes are in good agreement with theoretical predictions. The major discrepancies occur near the surface of the flat plate and are attributed to wall vicinity and velocity gradient effects.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):36-43. doi:10.1115/1.3242437.

The theory for steady flow of an incompressible fluid through an orifice has been semi-empirically established for only certain flow conditions. In this paper, the development of a more rigorous theory for the prediction of the orifice flow contraction effect is presented. This theory is based on the conservation of momentum and mass principles applied to global control volumes for continuum flow. The control volumes are chosen to have a particular geometric construction which is based on certain characteristics of the Navier-Stokes equations for incompressible and, in the limit, inviscid flow. The treatment is restricted to steady incompressible, single phase, single component, inviscid Newtonian flow, but the principles that are developed hold for more general conditions. The resultant equations predict the orifice contraction coefficient as a function of the upstream geometry ratio for both axisymmetric and two-dimensional flow fields. The predicted contraction coefficient values agree with experimental orifice discharge coefficient data without the need for empirical adjustment.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):44-48. doi:10.1115/1.3242438.

In applying the ultrasonic contrapropagation method to the measurement of flow in highly attenuating fluids, or to fluids in conduits having only limited access, it is sometimes necessary to interrogate along a path other than the conventional tilted diameter or midradius chordal paths. The meter factor K, which relates the path average to the area-averaged flow velocity, is derived from Nikuradse profiles for several new paths. The results enable one to locate transducers so that for the chosen type of path, K will be (a) minimally dependent on Re, and/or (b) approximately equal to unity, or (c) represented by a simple function of Re. For smooth-wall steady flow conditions, the error in the calculated K’s is estimated as ±2 percent ± the effect due to the disturbance of Nikuradse profiles by the transducers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):49-54. doi:10.1115/1.3242439.

A finite difference calculation procedure has been developed for the calculations of the three-dimensional fully elliptic flows over irregular boundaries. A simple control volume analysis is introduced to reformulate the momentum equations in the generalized velocity and coordinate system, without resorting to any extensive tensor calculus. The finite difference equations are obtained by discretizing the conservation equations in this generalized system. For a practical application of the present finite difference calculation scheme, calculations are carried out on the three-dimensional separated flow in a converging-diverging rectangular duct. The calculation results reveal an extremely complex nature of the three-dimensional separated flow.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):55-60. doi:10.1115/1.3242440.

The objective of the present study was to examine experimentally the turbulent flow structure in a repeated rib geometry rough wall surface as a function of the ratio of the roughness height to the pipe diameter (K/D), the ratio of the spacing between the elements to the roughness height (P/K), the axial position within a rib cycle, and the Reynolds number. For small P/K values, the turbulent intensities and Reynolds shear stress variations were similar to those found for smooth wall pipe flow. Unique relationships for the u′ and v′ were found that were valid in the outer layer of the flow for all axial positions and all values of P/K and K/D.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):61-66. doi:10.1115/1.3242441.

The present study examines the vortex street wake behavior of a flexible, helically wound, high aspect ratio marine cable in a linear shear flow. Particular attention is paid to the lock-on phenomena associated with uniform and sheared flow past the cable when it is forced to vibrate in the first mode, normal to the flow. An analysis is given of the effects on the vortex shedding and synchronization phenomena that are generated by placing distributions of spherical bluff body shapes along the span of the cable in uniform and sheared flow. The latter geometry is representative of a number of cable system deployments and has special consequencies for strumming in a shear flow. The effectiveness of these attached spheres as strumming-suppression devices is evaluated. Synchronized vibration and/or the presence of the bluff bodies significantly affected the spanwise character of the near wake cellular vortex shedding structure. The spanwise extent of the resonant, vortex-excited oscillations was significantly extended by the presence of the spheres along the cable span. This finding was particularly significant because it meant that the undesirable effects that accompanied synchronization would be extended over a longer portion of the cable span.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):67-72. doi:10.1115/1.3242442.

The dynamics of the thin film established, by oil injection, on the inside wall of the casing in certain rotary compressors are analyzed both experimentally and theoretically. The film may provide an effective pressure seal to prevent leakage of air from one side of a rotor lobe to the other. It is found that Reynolds’ bearing theory, corrected for Reynolds number and surface tension effects, gives reasonable results for the film thickness needed to sustain typical operational pressure differences in the machine. The theoretical predictions have been verified experimentally in a series of tests performed in a specially designed apparatus.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):73-78. doi:10.1115/1.3242444.

Necessary conditions for the stability of a general class of compressible vortex flows are obtained using the method of generalized progressing wave expansion. The vortex motion and the density are assumed to vary in both the radial and axial directions. These conditions, representing a generalized state of statically stable distribution for the steady flow, require that the flow be stable in the centrifugal force field created by the rotation of the fluids, in the gravitational force field arisen from the density variation, and in the pressure field constraining the variation of density and forces in both the radial and axial directions. These results also suggest the likely behavior of Richardson criteria for stability of the flow yet to be derived.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):79-85. doi:10.1115/1.3242445.

When the eddy viscosity is defined by the standard k-ε turbulence model, the equations governing self-similar incompressible plane and radial jets have a solution that is not analytic at the jet edge. A transformation that stretches the similarity variable simplifies the defining set of ordinary differential equations and makes them amenable to efficient numerical integration. Highly resolved solutions for the velocity, turbulent kinetic energy and dissipation rate profiles are tabulated and entrainment, velocity decay rate and growth rate are determined. The growth rate differs by 6 percent from a parabolic marching asymptotic solution to the full partial differential equations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):86-91. doi:10.1115/1.3242446.

Resonant flow-induced oscillations of a flexible cable can occur when the damping of the cable system is sufficiently small. The changes in the flow field that occur in the near wake of the cable during these resonant oscillations are closely related to the changes in the fluid forces that accompany these oscillations. The present wind tunnel experiments were undertaken to examine the effects that forced synchronized vibration and the helically-wound cross section of the cable have on near wake vortex shedding-related parameters; specifically the shedding frequency, vortex formation length Lf , reduced velocity Ur , vortex strength and the wake width Lw . The range of flow speeds over which the vortex shedding was locked on to the vibration frequency varied directly with the vibration amplitude. The helical cross section and the synchronized vibration caused significant changes in the near wake development that could be directly related to the increase in hydrodynamic forces associated with unforced synchronized vibration.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):92-96. doi:10.1115/1.3242447.

Spin-up from rest in a cylinder with top and bottom endwall disks rotating in opposite directions (ΩT and ΩB are the respective rotation rate, but S[≡ ΩT /ΩB ] < 0) is investigated. The sidewall is fixed to the faster-rotating disk. A finite-difference numerical model is adopted to integrate the unsteady Navier-Stokes equations. We consider a cylinder of aspect ratio 0(1) and minute Ekman numbers. Numerical solutions are presented to show the transient azimuthal flow structures, axial vorticity profiles, and meridional flow patterns. An azimuthal velocity front, which separates the rotating from the nonrotating fluid, propagates radially inward from the sidewall. The appearance of the front is similar to the front propagation in spin-up in a rigid cylinder. As S decreases from zero, the direction of rotation in the bulk of the interior fluid becomes the same as that of the faster-rotating disk. The azimuthal velocities are still vertically uniform in the bulk of the interior. The scaled time to reach the steady state decreases. The angular velocities of the interior fluid near the central axis become very small. Under counter-rotation, the meridional circulation forms a two-cell structure. A stagnation point appears on the slower-rotating disk. During spin-up, the stagnation point moves from the sidewall to its steady-state position. As counter-rotation increases, the radial distance traveled by the stagnation point decreases.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):97-104. doi:10.1115/1.3242448.

A finite-difference scheme is developed for solving the boundary layer equations governing the laminar flow about a rotating sphere which is subjected to a uniform stream in the direction of the axis of rotation. Numerical results are presented for the meridional and azimuthal velocities and for the wall-shear-stress components. Also, the angle at which the meridional velocity gradient normal to the wall vanishes is given at values of the parameter Ta/Re2 ranged from zero (the stationary sphere case) to 10000. As compared with the momentum integral technique of Schlichting [8], the present scheme succeeded in obtaining solutions for very considerably larger values of the parameter Ta/Re2 .

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):105-111. doi:10.1115/1.3242423.

An implicit factorization method has been developed for solving numerically the complete two-dimensional Navier-Stokes and continuity equations for pressure transients in a slightly compressible viscous liquid contained in a rigid pipe. Two problems have been analyzed: (1) The stopping of a steady Poiseuille flow by closure of a valve, and (2), the initiation of a nearly rectangular pressure pulse at the end of the pipe. In problem (1), radial as well as axial pressure variations were found; nearly periodic damped waves exist at the centerline and at the wall, and are approximately 180 deg out of phase. Essentially plane waves are found for problem (2), regardless of whether the fluid is flowing or not, provided that the initial pulse magnitude is not too large; the results show that the viscous effects are concentrated in a thin boundary layer.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):112-119. doi:10.1115/1.3242424.

This paper deals with the prediction of propeller cavitation noise from model experiments in a cavitation tunnel. The purpose was to investigate the validity of a simple scaling formula for high frequency cavitation noise, and to get information about the influence of test parameters and analysis methods. The results indicate that the scaling formula normally used at low frequencies can, as a first approximation, be used also at high frequencies. Concerning analysis methods it is demonstrated that the noise signals in model and full scale may have different statistical properties, implying that the simple root-mean-square value of the model signal is not always a sufficient basis for prediction of full scale noise.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):121-125. doi:10.1115/1.3242427.

In order to clarify whether a separation bubble always plays an important role, the desinence of streamer-cavitation, a kind of attached-cavitation, was carefully investigated in typical internal flows through venturies with and without a 40 μm thin backward facing step under a prescribed cavitation nuclei as well as various hydrodynamic conditions. The following facts have been found: (i) the separation bubble can play an important role in the desinence only when the separation bubble thickness H is larger than the diameter of nucleus dnp that may grow up to a critical one [18], (ii) a marked change takes place in the desinent cavitation number σd due to the step, i.e., σd ≅ |Cps | for H > dnp but σd < |Cps | for H ≦ dnp , (iii) for the cavitation there are two geneses, i.e., the nuclei floating within the separation bubble and the bubble-cloud occurring in the reattachment-region.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):127-133. doi:10.1115/1.3242430.

This paper presents a technique for the study of the mechanisms responsible for the generation of noise from cavitating propellers. The experimental method, which involves the cross-correlation of the pressure gradient in the near-field of the propeller with the far-field sound, allows the determination of the spatial distribution of acoustic source strength on and near the cavitating propeller. The paper describes the mathematical basis for the cross-correlation technique, and then presents some of the results from experiments with propellers specifically designed to produce vortex and bubble forms of cavitation. Cross-correlations performed at a number of points along a track parallel to the axis of the propeller indicate that most of the noise from propellers producing vortex cavitation originates from the region of vortex collapse. A bubble cavitation propeller showed a region of relatively constant source strength distribution from the propeller disk region downstream to the point of vortex collapse.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):134-138. doi:10.1115/1.3242431.

Cavitation damage tests in polymer solutions are made with a vibratory cavitation apparatus. It is possible for this device to suppress the degradation of polymer by ultrasonic cavitation. Polymer solutions used are 100 wppm, 500 wppm, and 1000 wppm solutions of Polyox. The weight loss in 100 wppm Polyox solution is larger than that in water, but in 500 wppm and 1000 wppm Polyox solutions the weight losses after 60 min exposure to cavitation are relatively small. It is indicated that the cavitation damage in polymer solutions is subject to the effective influence of elastic properties of liquids.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1985;107(1):139-147. doi:10.1115/1.3242432.

During operational transients or a hypothetical LOCA (loss of coolant accident) condition, the recirculating coolant of PWR (pressurized water reactor) may flash into steam due to a loss of line pressure. Under such two-phase flow conditions, it is well known that the recirculation pump becomes unable to generate the same head as that of the single-phase flow case. Similar situations also exist in oil well submersible pumps where a fair amount of gas is contained in oil. Based on the one dimensional control volume method, an analytical method has been developed to determine the performance of pumps operating under two-phase flow conditions. The analytical method has incorporated pump geometry, void fraction, flow slippage and flow regime into the basic formula, but neglected the compressibility and condensation effects. During the course of model development, it has been found that the head degradation is mainly caused by higher acceleration on liquid phase and deceleration on gas phase than in the case of single-phase flows. The numerical results for head degradations and torques obtained with the model favorably compared with the air/water two-phase flow test data of Babcock and Wilcox (1/3 scale) and Creare (1/20 scale) pumps.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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