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GUEST EDITORIAL

J. Fluids Eng. 1977;99(1):2. doi:10.1115/1.3448545.
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Abstract
Commentary by Dr. Valentin Fuster

LETTERS TO THE EDITOR

J. Fluids Eng. 1977;99(1):3. doi:10.1115/1.3448546.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Fluids Eng. 1977;99(1):8-39. doi:10.1115/1.3448570.

Important unsteady fluid dynamic effects occur in a wide range of modern engineering problems. A review and critical appraisal has been made of the current research activities on topics that contain essential and unique unsteady features, especially those which cannot be approximated by quasi-steady analyses. A synopsis of the main areas covered in this paper is given below. Linear potential theory is well advanced and most of the fundamental concepts are well understood. The theory has been specially adapted for engineering purposes to many complex geometries and flow environments, but its limitations are not well established in most cases. Transonic flows have received considerable attention in recent years, and the profusion of numerical analyses of nonlinear unsteady flows has outstripped measurements. However, new experimental investigations are underway. Numerical codes are becoming much more efficient, and efforts are being made to incorporate viscous effects into them. Unsteady boundary layers have been computed with almost no complementary experimental guidance, and this deficiency is particularly acute in the turbulent case. A major conceptual difference between steady and unsteady separation has been identified and is continuing to be studied. Unsteady stall is currently under detailed examination, and recent experiments have shed considerable new insight on the fundamental mechanisms of dynamic stall on oscillating airfoils. New attempts to treat unsteady stall as a strong viscous-inviscid interaction problem are needed. Vortex shedding from bluff bodies is difficult to predict, especially in cases where body oscillations are self-induced by the fluctuating fluid dynamic forces. Nonlinear oscillator models are limited by a lack of understanding of the basic fluid dynamic phenomena. The trailing edge condition of Kutta and Joukowski for thin airfoils has been called into question recently for unsteady flows at high frequencies or with trailing-edge separation. The correct modeling of this condition is important in predicting the fluid dynamic forces on all thin lifting surfaces that fluctuate. Considerable progress has been made in each of these subjects, but none of them has been mastered. The questions that remain unanswered pose intriguing challenges to the fluid dynamics community.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Papers From Symposium on Prediction of Centrifugal Compressor and Pump Stability and Surge

J. Fluids Eng. 1977;99(1):45-50. doi:10.1115/1.3448548.

A vortex nozzle facility for testing radial vaned diffusers independently of any rotor has been developed [1, 2]. This paper describes a comparative experiment designed to evaluate the applicability of results obtained on this facility to actual rotating compressors. Geometrically scaled diffusers were tested in the vortex nozzle facility and in an actual rotating compressor rig, and the results are compared and shown to be very similar in terms of both performance and stability limits. The implications of these results are that blade wake mixing and unsteadiness do not significantly affect diffuser performance.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):53-59. doi:10.1115/1.3448553.

New evidence about the time domain operation of centrifugal compressors and pumps in compliant systems is presented. Data from Toyama [1,2] plus unpublished data from another compressor indicate that the flow rate oscillates continuously, at large amplitudes, when a compressor is operating in its supposedly stable regime. A tentative flow model predicts similar oscillations. The model assumes that the compressor operation at all times is described by its quasi-steady characteristic; no hysteresis or complex aerodynamic phenomena have been invoked.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):64-74. doi:10.1115/1.3448560.

The aerodynamic characteristics of centrifugal compressors are examined with special attention given to the range of flows normally in the unstable region. They are examined for the intended purpose of extending the compressor’s useful stable range. Two such means are investigated, but a close coupled aerodynamic resistance designed to achieve negative combined slope showed the greater promise. A number of experiments are performed in which the geometry and location of the close coupled control devices are varied. It is shown that with adequate design, stable operation is possible down to 40 percent of the normal surge flow. This can be done with hardware the configuration of which is practical and with attendant additional losses which are not prohibitive. The rationale and the empirical work are devoted to the single stage case but an examination is made of the stability considerations for the case of multi-stage machines.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):76-81. doi:10.1115/1.3448563.

A method has been developed by which centrifugal compressor flow range and the nature of the pressure ratio characteristic approaching surge can be predicted by use of fundamental impeller exit conditions and diffuser entrance geometry in a system where minimum to maximum flow range is determined by the diffuser. Experimental results from compressor tests demonstrate the influence of these basic variables on flow range. Data from pipe type diffuser configurations designed under the assumptions of the loss-range method verify the capability to estimate flow range. Results of tests confirm the use of the method to predict the shape of the pressure ratio/weight flow characteristic and the location of maximum efficiency at constant speed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):84-93. doi:10.1115/1.3448569.

Relatively small stable flow ranges experienced on some high Mach number centrifugal compressors, triggered by the inability of stationary vaned diffusers to operate at flows below their maximum recovery point, have focused considerable research effort on the diffuser component. With improved impeller stability, vaned diffusers can be assisted to operate to lower flows where impeller stalling becomes predominant. The results of tests on a small high Mach number centrifugal compressor are presented to suggest that in certain applications the primary factor affecting compressor surge could be the impeller inlet-to-exit velocity diffusion ratio, with specific diffuser types, Mach numbers, and incidence considerations becoming secondary in importance.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):98-102. doi:10.1115/1.3448577.

The authors’ preceding analysis on centrifugal vaneless diffusers is used to examine the influences of diffuser geometries and of flow inlet conditions on the critical flow angle for reverse flow, and the results are presented in graphs. The diffuser width to radius ratio, the inlet Mach number, and the distortion of the inlet velocity distribution have significant influences on the critical flow angle, while the Reynolds number and the boundary layer thickness at the inlet have minor influences.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):104-111. doi:10.1115/1.3448501.

An analytical method is proposed to evaluate the flow behavior in vaneless diffusers assuming that the flow is not symmetric between the walls. In the analysis momentum integral equations are used together with some special relations for the main flow or for the maximum velocity flow. According to the authors’ experiment, for the case of a small flow rate a reverse flow is observed on one wall near the inlet of the diffuser but at a larger radius the reverse flow disappears and another reverse flow is observed on the other wall. The predictions quantitatively agree well with experiments not only in the case of large flow rates but also in the case of small flow rates where the flow pattern is very complicated.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):115-124. doi:10.1115/1.3448506.

Results of high-response measurements in a high-pressure-ratio centrifugal compressor during surge operation are presented. The interpretation of the data provides improved understanding of the flow mechanism of surge and the phenomena which apparently trigger surge. The mass flow throughout the compressor was observed to oscillate in synchronism during supposedly “stable” operation. Surge of the test compressor occurred when a flow perturbation, during “stable” operation, exceeded an apparent limit. When the instantaneous value of diffuser-inlet pressure recovery factor, Cp2*–4 , reached approximately 0.40–0.45, the diffuser inlet flow was badly deteriorated and surge occurred. However, gross separation of the diffuser inlet boundary layer was not observed before surge commencement. It is concluded that instantaneous operating states must be recognized for competent surge prediction. Further, doing so will probably require analysis of the entire compressor system including piping, vessels, flow resistances, etc.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Papers From Symposium on Three-Dimensional Flow in Turbomachines

J. Fluids Eng. 1977;99(1):132-140. doi:10.1115/1.3448514.

The paper demonstrates the operational feasibility of obtaining flow detail through turbomachine blade passages by working iteratively with existing two-dimensional computer programs which solve alternately for S1 and S2 streamsheets. The resulting solution is regarded as “quasi-three-dimensional” because of the constraints implied by the use of S1 streamsurfaces which are surfaces of revolution and of a single, mass averaged S2 streamsurface. Since the S1 streamsheet thickness distributions are determined by the mean S2 solution and the mean S2 streamsurface shape is determined from the set of S1 solutions, the results obtained are anticipated to be better than could have been obtained by either program individually, since the latter application would necessarily have required the user to assume arbitrary variations for these factors. Comparisons of two and quasi-three dimensional results for a centrifugal compressor and a radial inflow turbine are presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):141-147. doi:10.1115/1.3448515.

The streamline curvature through-flow analysis of a centrifugal impeller passage flow has been modified to include a flow model with a wake on the suction surface. With this model, empirically determined or measured impeller conditions can be matched without requiring a distributed stagnation pressure loss within the passage. Its use in impeller design is presented and comparison with experimental measurements from two impellers illustrate the utility of this approach. A brief discussion of experience with the associated forms of curve fitting and streamline smoothing required for the analysis solution is included.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):148-153. doi:10.1115/1.3448516.

A finite-difference procedure is employed to predict the turbulent flow in ducts of rectangular cross-section, rotating about an axis normal to the longitudinal direction. The flows were treated as “parabolic” and the turbulence model used involved the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. Agreement with experimental data is good for a constant-area duct at low rotation, but less satisfactory for a divergent duct at larger rotation. It is argued that a “partially-parabolic” procedure will be needed to predict the latter flow correctly.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):154-166. doi:10.1115/1.3448517.

The structure of a computing system for bladed or unbladed turbomachinery passages is described and discussed. The system, in an overall sense, is modeled after the work of Wu, and is comprised of two coordinated computer programs, one providing solutions on rotationally symmetric blade-to-blade surfaces and the second on streamsheets roughly parallel to the blades. Both approaches utilize streamline curvature techniques.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):167-175. doi:10.1115/1.3448520.

A relatively simple and rapid method for predicting the three-dimensional flow effects in axial flow turbomachinery was investigated. Although the two-dimensional cascade is a satisfactory approximation for the design and analysis of some types of turbo-machines, the flow through devices, such as propeller pumps and inducers, may deviate significantly. A three-dimensional lifting surface theory was used to predict the potential flow around blades, represented by line vortices and sources, spanning an annulus. A rotor was designed, built, and tested (with air as the test medium) for comparison with the theory. Static pressure distributions on a rotating blade were measured. The effect of blade dihedral on these pressures was also measured. Deviation from cascade predictions caused by the three-dimensional flow effects is found to be appreciable for propeller pumps. No theory was developed, but variation of the experimental blade pressure distributions caused by dihedral was found to be considerable.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Additional Technical Papers

J. Fluids Eng. 1977;99(1):176-186. doi:10.1115/1.3448521.

This paper reports the measurement and prediction of the three-dimensional flow field in an axial flow inducer operating at a flow coefficient of 0.065 with air as the test medium. The experimental investigations included measurement of the blade static pressure and blade limiting streamline angle, and measurement of the three components of mean velocity, turbulence intensities and turbulence stresses at locations inside the inducer blade passage utilizing a rotating three-sensor hot-wire probe. Analytical investigations were conducted to predict the three-dimensional inviscid flow and to approximately predict the three-dimensional viscid flow by incorporating the dominant viscous terms into the exact equations of motion in rotating coordinate system. Radial velocities are found to be of the same order as axial velocities and total relative velocity distributions indicate a substantial velocity deficiency near the tip at mid-passage. High turbulence intensities and turbulence stresses are concentrated within this core region. Evidence of boundary layer interactions, blade blockage effects, radially inward flows, annulus wall effects and back-flows are all found to exist within the long, narrow passages of the inducer, emphasizing the complex nature of inducer flow which makes accurate prediction of the flow behavior extremely difficult.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):187-196. doi:10.1115/1.3448522.

This study deals with the calculation of the three-dimensional steady flow of a compressible and viscous fluid through a turbomachine. Using the potential theory, a quasi three-dimensional method is developed, which reduces the simplifying assumptions and yields high numerical accuracy. The method includes all main effects induced by the primary vortex system, in particular the influence of the casing and blade boundary layers on the cascade circulation. The use of two vortex sheets, representing the boundary surface, makes the calculation of flows having strong developed or separated boundary layers possible and allows a direct calculation of the secondary vorticity. Computed divergent and rotational flows are presented and compared with exact solutions or experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):197-204. doi:10.1115/1.3448523.

An experimental study has been performed to determine potential error sources in skin-friction balance measurements. A floating-element balance, large enough to contain the instrumentation needed to systematically investigate these error sources has been constructed and tested in the thick turbulent boundary layer on the sidewall of a large supersonic wind tunnel. Test variables include element-to-case misalignment, gap size, and Reynolds number. The effects of these variables on the friction, lip, and normal forces have been analyzed. Results indicate that some of the intuitive assumptions generally held by designers and users of skin-friction balances may not be valid. For example, it was found that larger gap sizes were preferable to smaller ones; that small element recession below the surrounding test surface produced errors comparable to the same amount of protrusion above the test surface; and that normal forces on the element were, in some cases, large compared to the friction force. The principle contributions of this paper are (1) that users of skin-friction balances can use the data contained in this paper to estimate the errors involved in their measurements, and to make corrections if necessary, and (2) that the results of this study may lead to the development of new and improved devices for direct skin-friction measurement.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):205-212. doi:10.1115/1.3448524.

An economical, “parabolic/hyperbolic hybrid,” numerical prediction procedure, employing marching integration, is presented for the computation of supersonic flows of the boundary layer class in which embedded pressure waves are present. The hyperbolic component is based on the method of characteristics, while the computational procedure of Patankar and Spalding constitutes the parabolic component. The method is evaluated against analytic solutions for inviscid flows and against experiment for laminar and turbulent near-wall flows. Calculations for laminar and turbulent free shear flows are also presented. The method performs well when the viscous/wave interaction is not strong enough to induce significant “upstream influence.”

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):213-216. doi:10.1115/1.3448525.

The effect of a gust parallel to the main stream on a nonlifting airfoil of finite thickness is studied for incompressible flow. General expressions are developed for the resultant unsteady flow field using thin airfoil theory. The pressure perturbation induced on an elliptic airfoil by such a convected “streamwise” gust is examined in detail, and is compared with that involved in the unsteady lift response of a flat plate at incidence in the same gust.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):217-225. doi:10.1115/1.3448526.

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):226-230. doi:10.1115/1.3448527.

The behavior of recirculating flows typical of advanced air-breathing and rocket injectors has been experimentally investigated. The configuration used consisted of a circular duct having a sudden increase of its diameter. Step size and flow velocity were chosen to be of a magnitude representative of “sudden-dump” combustion chambers. The recirculation, which occurred in the separation region behind the sudden expansion, was investigated using a laser-Doppler velocimeter. Detailed measurements of mean axial velocities were made. Sets of partial differential equations—including continuity, axial and transverse momentum, turbulence energy, and turbulence dissipation—were simultaneously solved using finite differencing techniques. Predictions made using these equations were brought into good agreement with the data taken from the recirculating flows under investigation by selection of appropriate “constants” in the models.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):231-239. doi:10.1115/1.3448528.

The development of turbulent shear layers on rotating or curved surfaces is usually characterized by strong effects of streamline curvature on the turbulence structure. The present contribution deals with the calculation of these effects with a model of turbulence which solves transport equations for the turbulence kinetic energy and its local rate of dissipation. The direct effect of curvature in the model is limited to a single empirical coefficient whose magnitude is directly proportional to a Richardson number based on a time scale of the energy-containing eddies. (In the absence of significant streamline curvature the model reduces to a form that has earlier been extensively tested in various thin shear flows.) Finite difference computations are reported of the following turbulent flows: the boundary layer on concave and convex surfaces; fully developed flow in a curved channel; axisymmetric flow over a spinning cylinder; and heat and mass transfer due to spinning cones of various vertex angles. Agreement with experiment is satisfactorily close in all these cases.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):240-243. doi:10.1115/1.3448529.
Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):245-248. doi:10.1115/1.3448532.

A generalized equation is derived which describes the loss coefficient for any differential pressure type fluid meter. This loss coefficient is given in terms of dimensionless factors including: meter geometry, discharge coefficient, contraction coefficient, and diffuser efficiency. The equation applies equally well for venturis, nozzles, and orifices, installed in pipes or with plenum inlets. Another equation is derived which relates the previously published ASME loss parameter for fluid meters to this new generalized loss coefficient.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):249-255. doi:10.1115/1.3448533.

First steps have been taken to demonstrate the feasibility of reducing uncertainties in the use of differential producers. Given a suitable flow conditioner, discharge coefficients are shown to be a highly reproducible function of approach length L/D. In the case of venturis and throat-tap flow nozzles, large effects of excessively small pressure tap diameter ratio δ/d are demonstrated and correlated, and much of the scatter and the premature roll-off of the coefficient with decreasing Reynolds number are thus accounted for. Some influence of throat length ratio x/d upstream of a throat tap is shown.

Commentary by Dr. Valentin Fuster

REVIEW ARTICLES

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

TECHNICAL BRIEFS

J. Fluids Eng. 1977;99(1):256-258. doi:10.1115/1.3448534.

In asymptotic analysis of the hydrodynamic stability of shear flows, the viscous effects enter through the modified Tietjens Function, which is used in the graphical determination of the eigenvalues. For neutral normal modes the argument of this function is real, and values of the function have been calculated previously. For non-neutral normal modes the argument is complex; the present note gives the modified Tietjens Function for complex arguments. This function is particularly useful in investigating the behavior of lightly damped eigenmodes for shear flows of arbitrary velocity profile.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):258-259. doi:10.1115/1.3448535.
Abstract
Topics: Cycles , Surges
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(1):259-261. doi:10.1115/1.3448536.
Abstract
Topics: Flow (Dynamics)
Commentary by Dr. Valentin Fuster

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