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IN MEMORIAM

J. Fluids Eng. 1975;97(4):397. doi:10.1115/1.3448037.
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Abstract
Commentary by Dr. Valentin Fuster

REPORTS

J. Fluids Eng. 1975;97(4):398. doi:10.1115/1.3448038.
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Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):399. doi:10.1115/1.3448039.
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Abstract
Commentary by Dr. Valentin Fuster

COMMENTARY

J. Fluids Eng. 1975;97(4):400. doi:10.1115/1.3448040.
Abstract
Commentary by Dr. Valentin Fuster

FOREWORD

J. Fluids Eng. 1975;97(4):401. doi:10.1115/1.3448041.
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Abstract
Topics: Cavity flows
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):412-417. doi:10.1115/1.3448047.

Unsteady flow in a cavitating axial inducer pump is analyzed with the help of a simple two-dimensional cascade model. This problem was motivated by a desire to study the effect of unsteady cavitation on the so-called POGO instability in the operation of liquid rocket engines. Here, an important feature is a closed loop coupling between several different modes of oscillation, one of which is due to the basic unsteady characteristics of the cavitation itself. The approaching and leaving flow velocities up- and downstream of the inducer oscillate, and the cavity-blade system participates dynamically with the basic pulsating flow. In the present work, attention is focused on finding a transfer matrix that relates the set of upstream variables to those downstream. This quantity, which is essentially equivalent to cavitation compliance in the quasi-static analyses, is found to be complex and frequency dependent. It represents the primary effect of the fluctuating cavity in the system. The analysis is based on a linearized free streamline theory.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):419-428. doi:10.1115/1.3448051.

A nonlinear exact theory to investigate a steady two-dimensional supercavitating flow past a cascade of arbitrarily shaped blades is presented. The solutions obtained by numerically solving a system of nonlinear, functional equations are compared with the available experimental data for flat-plate cascades and with linearized theories for both flat-plate and circular arc cascades. The force coefficients calculated with the present method show considerably smaller values than those of the linearized theories, as is expected.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):430-437. doi:10.1115/1.3448057.

A nonlinear method of finding two-dimensional supercavitating sections in a cascade is developed. The load distribution is taken from linear theory for low drag super-cavitating foils in a cascade. The double spiral vortex model is used for the cavity termination. Linear and nonlinear theories are compared with special emphasis put on analyzing the blunt leading edge. The foil-cavity shape, the cavity drag and the cavitation number can be obtained by a computer program from the given cavity length and geometrical parameters of the cascade.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):439-449. doi:10.1115/1.3448061.

Theoretical developments on cavity flow studies are briefly reviewed. Physical and mathematical difficulties involved in cavity flow problems are discussed. Particular attention, with regard to practical applications, is given to the development of linearized theories. Based on the existing analyses, efforts to develop simple approximate expressions for the force coefficients of supercavitating hydrofoils (including the effects of free surface, cascade, aspect ratio, and finite disturbance) are made. Numerical results calculated from these expressions are compared with existing experimental data. Special problems involving unsteady cavity flows, such as pulsation of the finite cavities, are also discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):453-462. doi:10.1115/1.3448069.

Measurements were made of lift, drag, and moment coefficients, and cavity length for aspect ratio 3 and 5 supercavitating hydrofoils of elliptical planform. These measurements are compared with theoretical predictions obtained from matching asymptotic expansions for large aspect ratio. Good agreement was obtained for lift and drag coefficients for angles of attack from 10 deg to 15 deg and for a wide range of cavity lengths. Theoretical moment coefficients were too large indicating the need for lifting surface corrections.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):465-473. doi:10.1115/1.3448076.

The method of matched asymptotic expansions is used to analyze the flow around a base-vented lifting foil with rounded nose beneath a free surface. The foil is defined numerically. Results concerning the lift and drag coefficients and the limiting values of incidences without cavitation are compared with experiments. The relation between the cavity length and the ventilation number at several depths of submergence is given in the case of a symmetrical wedge: it agrees with the experimental one except by a nearly constant coefficient.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):475-481. doi:10.1115/1.3448080.

The flow around an arbitrary supercavitating, jet-flapped hydrofoil operating at an arbitrary submergence is analyzed by a second order theory and the following results are obtained; (i) The hydrofoil performance data are shown for various submergences and jet operating conditions. (ii) The flap effects are highly dependent on the submergence as well as the hydrofoil shape. (iii) Operation of the jet flap results in an increase in the cavity thickness so that the hydrofoil thickness can be increased. (iv) Especially at the shallower submergences, the performance, as well as the flow pattern, changes strikingly with changes in submergence.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):482-491. doi:10.1115/1.3448081.

The wall effects for fully and partially cavitating flows are investigated for both compressible and incompressible two-dimensional jets. The exact solution for Roshko’s model in a channel with a wedge shaped body is obtained and some particular models are studied. The hodograph method as developed by S. V. Falkovitch [19] is used and the solutions are given as infinite series of Chaplygin’s functions. The exact expressions of the drag coefficients for the aforementioned configurations are also given. Numerical computations are carried out for wedges of all angles. Tables and diagrams are included.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):492-499. doi:10.1115/1.3448085.

Two-dimensional open channel flow with a steady and fully developed cavity forming at a step on the bottom of the channel was analyzed according to potential flow theory using a re-entrant-jet model. The effects of gravity and the free water surface were fully considered. Cavity profiles and other flow characteristics were found to be significantly different depending upon whether the flow was subcritical or supercritical with a discontinuity at the critical point. The classic solution for an infinite fluid in a nongravitational field was shown to be the limiting case of the subcritical regime. The theory compares favorably with a limited number of existing data in the supercritical regime.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):501-505. doi:10.1115/1.3448090.

The results of an experimental investigation into the effect of gas diffusion on the volume flow-rate of gas needed to sustain a ventilated cavity are presented. Gas diffusion was found to have a significant effect on the ventilated flow rate required to sustain a cavity of a given size. An analysis for the gas diffusion effect was conducted based on a mathematical model of diffusion proposed by Brennen. The results compare favorably with experimental data. Also, an empirical scaling relationship is proposed for ventilated cavity flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):507-513. doi:10.1115/1.3448095.

The results of an investigation of thermodynamic effects are presented. Distributions of temperature and pressure in a developed cavity were measured for zero- and quarter-caliber ogives. A semiempirical entrainment theory was developed to correlate the measured temperature depression, ΔT, in the cavity. This theory correlates ΔTmax expressed in dimensionless form as the Jakob number in terms of the dimensionless numbers of Nusselt, Reynolds, Froude, and Péclét, and dimensionless cavity length, L/D. The results show that in general ΔT increases with L/D and temperature and the cavitation number based on measured cavity pressure is a function of L/D for a given model contour, independent of the thermodynamic effect.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):515-521. doi:10.1115/1.3448098.

Theoretical and experimental studies have been made of the growth and collapse of fixed cavities in a two-dimensional convergent-divergent nozzle. In this particular configuration an important feature was a re-entrant liquid jet which invaded the growing cavity from the downstream end, travelling upstream along the wall and interrupting the cavity when it reached the nozzle throat. A simple two-dimensional unsteady potential flow theory, developed to model the cycle, gave reasonable agreement with cinephotography and predicted the jet behavior. Because vaporization was neglected the theory overestimated the speed of the cycle.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):523-531. doi:10.1115/1.3448102.

Cavitation testing in a free surface tunnel presents specific problems in terms of low content of undissolved micro air bubbles in the water owing to the high de-aerating capacity of the tunnel. Such air nuclei are necessary to provide realistic conditions for the inception and extension of cavitation, in particular bubble cavitation at intermediate propeller loading. This paper gives a brief discussion of the problem in relation to some test results obtained in the new free surface tunnel at the KMW Marine Laboratory. A special device built into the tunnel circuit to produce the necessary amount of micro bubbles and its effect on cavitation and propeller forces is described.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):550-555. doi:10.1115/1.3448112.

A new integral method is proposed for the analysis of three-dimensional incompressible turbulent boundary layers. The method utilizes velocity profile expressions in wall-law form to derive two coupled partial differential equations for the two components of surface skin friction. No shape factors or empirical shear stress correlations are needed in the method. The only requirements are a knowledge of the external velocity and streamline distribution and initial values of skin friction along a starting crossflow line of the flow. The method is insensitive to sidewall conditions and may be continued downstream until the complete three-dimensional separation line of the flow has been computed. Two comparisons with experiment are shown: a curved-duct unseparated flow and a T-shaped-box separated flow. The calculations are very straightforward and agree reasonably well with the data for friction, crossflow angle, and separation line.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):558-564. doi:10.1115/1.3448117.

Some existing turbulence models for the round jet in coflowing and quiescent ambients are compared to experimental data, and some modifications are suggested and examined. A new model is proposed which results in consistently good predictions for a wide range of velocity ratios, including the important case of a jet discharging into an ambient at rest. The conservation equations of mass, momentum, and energy in differential form for the jet flow are solved numerically in the physical plane using an explicit difference scheme of the DuFort-Frankel type.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):568-578. doi:10.1115/1.3448125.

Measurements in a turbulent channel flow of air are presented for three Reynolds numbers. The design features of the present system suggest that the flow is a closer approximation to fully developed, two-dimensional turbulent flow between two parallel plates than those documented by previous investigators. Comparison of the new data with previous data reveal distinct differences, some of which can be attributed to differences in apparatus design. Interest in these data stems from the fact that channel flow serves as a reference flow for testing various theoretical models and experimental techniques involving turbulent shear flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):581-591. doi:10.1115/1.3448130.

A method of calculating a two-dimensional incompressible and inviscid flow within a centrifugal impeller where the flow separates from the suction side has been developed. Based on experimental observation it has been assumed that mixing of the throughflow with the separated region is suppressed. After a description of the calculation method, which is rather unusual, some results are presented and the implications discussed. The possibility of extending the method to handle compressible flow is outlined.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):598-605. doi:10.1115/1.3448139.

An analytical/numerical method for calculating blade-to-blade transonic flow fields around blade elements of an axial compressor rotor of a turbomachine is presented. Radius variation and stream sheet convergence are included. The analysis considers the time-dependent Navier-Stokes equations in conservation-law form which allows for viscous shock wave formation. A discretized method of characteristics is used to determine the boundary conditions along the blade surface and exit plane. An explicit, time-dependent, second-order, finite difference technique is utilized to numerically solve these partial differential equations in a transformed computational plane. Comparison of numerical results with cascade and rotor data indicate good agreement for blade surface pressure distributions and mixed-out exit conditions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):608-614. doi:10.1115/1.3448143.

Complex turbulent mixing and reacting flows must be characterized in greater detail than is currently possible if analyses are to yield meaningful guidance in the design of practical hardware. An assessment is made of the relative importance of turbulent mass, momentum, and energy transport, and mass transport (mass mixing) demonstrated to be more significant than either energy or momentum transport for a coaxial hydrogen jet reacting with an external high-temperature air stream. A technique is presented for developing and evaluating mixing models, applicable to both reacting and nonreacting flows, in which experimental mean concentration, velocity, and density profiles are differentiated directly, and local transport coefficient distributions obtained.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):615-617. doi:10.1115/1.3448144.

The purpose of the present work is to establish experimentally the nature of the phenomena and the rate of fire spread through explosive media involving concentration gradients in a fuel-air mixture. Most of the work reported has been limited to upward flame propagation using methane as a fuel. Wide deviations from the quasi-steady approach were observed when a flame propagates along a negative concentration gradient in lean methane-air mixtures. It appears that the observed rate of fire spread in stratified lean mixtures can be correlated directly in terms of local concentration gradients and the corresponding propagation rates under homogeneous conditions.

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

ERRATA

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

REVIEW ARTICLES

J. Fluids Eng. 1975;97(4):534-549. doi:10.1115/1.3448111.

Literature on transition in oscillating boundary layers is relatively recent and confusing. The paper first reviews the current thinking on transition in steady boundary layers and on the role of stability theory. The reader is then provided with a background on oscillating boundary layers. The various reports of transition in such boundary layers are analyzed and clarified. The concept of excited wave packets, moving downstream through the “pulsating” boundary layer and cumulatively growing or decaying, largely in response to the transient vorticity distribution, appears to unify much of the data. Recent experiments, designed to test the ingredients of the concept, are reported. Other forms of transition are discussed and their probable occurrence in the domains of interest to practical engineers is mapped out.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):620-621. doi:10.1115/1.3448146.

It is shown that an equation arising in a study of the asymptotic expansions in radial jets is limited to one meaningful coefficient value.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):621-624. doi:10.1115/1.3448147.

A stepped lands piston enclosed within a tight circular cylinder of uniform bore and subjected to unequal upstream and down-stream boundary pressures is analysed for the case of incompressible fluid. Performance characteristics are given for small eccentricity ratios as a function of the step height and location, and a design parameter which relates the leakage and the centering force is defined. It is shown that piston performance can bo optimized by selecting a proper step design.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1975;97(4):624-625. doi:10.1115/1.3448148.

During the study of two axially opposed choked air jets, an unusual effect has been noticed with respect to the impingement plane of the jets. In spite of the fact that both jets were operating at the same pressure ratio, the impingement plane was not necessarily centered between the two nozzle exits. Under certain conditions, the impingement plane had several stable locations along the axis between the two nozzles.

Topics: Air jets , Jets , Nozzles , Pressure
Commentary by Dr. Valentin Fuster

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