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COMMENTARY

J. Fluids Eng. 1976;98(3):337-339. doi:10.1115/1.3448309.
Commentary by Dr. Valentin Fuster

LETTERS TO THE EDITOR

Commentary by Dr. Valentin Fuster

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

J. Fluids Eng. 1976;98(3):342-351. doi:10.1115/1.3448313.

The effects of honeycomb of different lengths on free-stream turbulence are studied in air with hot-wire anemometry and in water using hydrogen bubbles visualization. The honeycombs are viewed as operators which suppress the level of the incoming turbulence and generate, primarily through documented instabilities, new turbulence with scales characteristic of the shear layers present in their near wake. The suppression of the incoming turbulence appears to be mostly due to the inhibition of lateral components of the fluctuating velocity. The level, structure and decay of the generated turbulence depends, in part, on the instabilities of the shear layers and therefore can be modified by passive devices acting on the flow field immediately downstream of the honeycomb. Thus, fixing a fine mesh screen to the back of the honeycombs leads to substantially different characteristics of the generated turbulence. While in all cases a net suppression of the free-stream turbulence was achieved by the honeycombs, the positioning of the chopper screen in the near wake of the honeycomb led to a much reduced turbulence level far downstream.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):354-363. doi:10.1115/1.3448319.

Measurements were obtained of the mean velocity, Reynolds stress tensor components and spectral distribution of turbulent energy in a boundary layer that was adjusting spatially from a collateral to a three-dimensional state because of transverse motion of the bounding wall. The results indicate that changes to the turbulent structure lead to a strong coupling between the axial and transverse components of mean velocity. The influence of the imposed motion was found to be confined to a discrete region near the wall over the first ten initial boundary layer thicknesses, after which it became more global in nature.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):364-371. doi:10.1115/1.3448323.

A study was conducted to determine experimentally and theoretically the losses in radial inflow turbine nozzles. Extensive experimental data were obtained to investigate the flow behavior in a full-scale radial turbine stator annulus. A theoretical model to predict the losses in both the vaned and vaneless regions of the nozzle was developed. In this analysis, the interaction effects between the stator and the rotor are not considered. It was found that the losses incurred due to the end wall boundary layers can be significant, especially if they are characterized by a strong crossflow. The losses estimated using the analytical study are compared with the experimentally determined values.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):374-381. doi:10.1115/1.3448327.

A method for calculation of turbulent boundary layers on curved, rotating surfaces is presented, and the applicability of the method to the prediction of attached flow over compressor rotor blades is indicated. Calculated results are compared to existing data sets. Additional sample calculations to study the effects of rotation are also presented. Correlations of these calculated results provide a simple method for estimation of the effects of rotation on skin friction, cf , and boundary-layer shape factor, H.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):382-388. doi:10.1115/1.3448330.

An integral method is used to obtain a solution for laminar flow of a compressible Newtonian fluid between rotating disks. The solution method is based on a Galerkin approach to the solution of the Navier-Stokes (radial, tangential, and axial momentum) equations, continuity, and on approximation of the energy equations. Four parameters are necessary to specify the flow: tangential inlet velocity, Reynolds number, a flowrate parameter, and Mach number of the disk tip. The solution is developed for turbine flow with uniform admission of the fluid at the outer boundary. The method can easily be extended to consider pump flow. Velocity profiles as well as turbine efficiencies are presented. Good agreement with published results for the incompressible regime is demonstrated. Short computational time and acceptable accuracy were obtained with a small number of terms in the velocity expansions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):390-399. doi:10.1115/1.3448334.

Detailed accurate measurements of velocities, directions, and fluctuation intensities were performed with a newly developed laser velocimeter in the internal flow field of a radial discharge impeller, running at tip speeds up to 400 m/s. Relative flow distributions are presented in five measurement areas from inducer inlet to impeller discharge. The impeller flow pattern, which coincides largely with potential-theory calculations in the axial inducer, becomes more and more reversed when the flow separates from the blade suction side, developing a rapidly increasing wake in the radial impeller. The observed secondary flow pattern and effects of channel curvature and system rotation on turbulence structure are discussed with respect to separation onset and jet/wake interaction.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):403-414. doi:10.1115/1.3448341.

A new method for the numerical solution of the meridional through-flow equations in an axial flow machine is presented based on the finite-element method. A rigorous derivation of the pitch-averaged flow equations is presented and the assumption of axisymmetric flow leads, with the introduction of a stream function, to the equation to be solved. A description is given of the finite-element technique which is applied in this problem. The method of solution allows the calculation of transonic stages. Numerical results are compared with experimental data and show very satisfactory agreement. This method appears, therefore, to compare very favorably with the other methods used up to now. Although the present results pertain to axial flow machines, the method is easily applicable to radial flow machines as well and the way of solution for this case is indicated.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):422-429. doi:10.1115/1.3448347.

Experiments with incompressible flow are reported concerning the effects of Coriolis acceleration on flow separation and on separated flow in plane-wall diffusers of rectangular cross section. The diffusers were rotated about an axis perpendicular to the plane of the nearly two-dimensional flow in order to simulate some features of the blade-to-blade flow distribution in the radial portion of the centrifugal impeller. Various stall regimes are mapped on coordinates of rotation number and diffuser area ratio (at fixed wall length). Diffuser pressure-recovery coefficient is reported as a function of area ratio and rotation number. These data demonstrate that, by suppressing turbulent mixing and shear stress in the suction-side boundary layers, the Coriolis acceleration field greatly enhances the tendency for stall to appear in a diffuser. This effect causes a corresponding reduction in the throat-to-exit pressure recovery as compared to that of nonrotating diffusers of the same geometry and inlet flow blockage.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):431-441. doi:10.1115/1.3448352.

An integral entrainment computation technique is presented for the three-dimensional boundary-layer growth on the stationary end-walls of centrifugal turbomachinery. The analytical model assumes axisymmetric inviscid core flow and viscous flow in the wall region, and the interaction between the two layers is considered. A novel form of the three-dimensional boundary-layer equations is presented. The form is physically appealing for this axisymmetric application and provides distinct advantages in the prediction of boundary-layer growth. It is demonstrated that it is essential to use the meridional boundary-layer profile to compute the Head entrainment function for this type of flow, as opposed to the streamwise velocity profile, as is more commonly done. Comparison with experimental measurements shows good agreement in the integral parameters. In addition, good agreement with experimental velocity profiles was achieved for a separating and reattaching flow.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Additional Technical Papers

J. Fluids Eng. 1976;98(3):443-446. doi:10.1115/1.3448357.

A turbulent jet is perturbed transverse to the flow direction by periodic pressure gradients near the nozzle exit. Transit velocities are defined in terms of the measured signal time delay for stations 8, 12, 16 nozzle widths downstream of the nozzle exit. Excitation frequencies to 800 cps are considered. Transit velocities are found to be much less than the jet centerline velocity. The results are related to the convection velocity of turbulence.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):447-452. doi:10.1115/1.3448358.

The performance of many fluid flow devices is limited by the separation of the turbulent boundary layer. This separation may be suppressed or delayed by use of wall jets, raising questions of jet location and strength. A numerical analysis of a single wall jet gave results in close agreement with experiment. The same analysis of a single wall jet gave results in close agreement with experiment. The same calculation procedure indicated that two sequential wall jets, with the same total kinetic energy flux as the single jet, would suppress separation under conditions where the single jet would not. The best two-jet arrangement would be achieved with 63 percent of the total kinetic energy flux in the first jet. It is possible that three-jet arrangements could provide some further improvement.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):455-459. doi:10.1115/1.3448364.

This paper discusses the propagation of pressure surge phenomena in liquids contained in thick-walled pipes and ducts of rectangular cross section. It is shown that the effects of shear forces and side wall elongation should be considered in calculating the velocity of surge propagation in such conduits. Experimental data from three pipelines are included and compared with the theoretical predictions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):461-466. doi:10.1115/1.3448368.

The characteristic dimensions of the steady cavity and the shedding frequency of vortices behind six circular cylinders in a two-dimensional venturi have been studied. The normalized length and maximum width of cavity for cavitation sources of different sizes indicated unified trends with a modified cavitation number km . The angles of detachment θ increased with cavitation number k and decreased with increasing Reynolds number R. The Strouhal number Sd reached minimum values for all cavitation sources at small values of k. The possible role of wall effects on the investigations are discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):469-474. doi:10.1115/1.3448373.

Entrance region solutions of the two-dimensional boundary layer equations are presented in terms of a convergent power series for steady, laminar, incompressible channel flow with uniform mass suction at the walls. The entrance solutions obtained using both uniform and parabolic velocity profiles at the inlet to the channel are compared to the solutions obtained from the similarity equations for a wide range of non-dimensional suction velocities (0 ≤ Rew ≤ 30). With a parabolic inlet velocity profile, the flow does not become fully developed for Rew > 7, except right at the downstream end of the channel (x = L). The similarity solutions are in good agreement with the entrance solutions over a reasonable length of the channel only for very small values of Rew . With a uniform inlet velocity profile, the flow does not become fully developed in the range 7 < Rew < 13, except right at x = L. In this case, the similarity equations should not be used to predict overall axial pressure variations except for very large values of Rew .

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):476-482. doi:10.1115/1.3448376.

The static characteristics of shrouded, acoustically controlled turbulence amplifiers are investigated. The main variables are control sound pressure level and frequency, shroud diameter, gap length and supply flow conditions. Existing analytical and empirical relationships are evaluated. It is found that Bell’s analytical procedure [1] for unshrouded, flow controlled turbulence amplifiers reasonably describes the laminar jet pressure recovery of the amplifiers used in this investigation. The turbulent recovery pressure given by Bell’s procedure is not in agreement with the experimental results of this investigation. A “jump” in the characteristic frequency (defined as the control sound frequency to which the device is most sensitive) occurs as the Reynolds number of the emitter tube is increased. The lower characteristic frequency can be predicted by an advanced Helmholtz resonator theory. Further, the acoustically controlled, unlike the flow controlled, turbulence amplifier can be operated in the proportional mode over a limited range of experimental variables.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):483-486. doi:10.1115/1.3448377.

The force acting on a particle and a bubble in a spherically oscillating inviscid liquid is computed and proved to be directed toward the center of the spherical motion. The theoretical solution is analytic for rigid particles and partly numerical for gas bubbles. Results show that under appropriate conditions this force is of the order of magnitude or greater than the gravity force, and it is greater for bubbles than for rigid particles. The use of this phenomenon as a means of separation and controlling particle motion in both gravitational and nongravitational fields is suggested.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):488-493. doi:10.1115/1.3448381.

The effect of high wall shear rates on the uptake of 131 I-albumin by the arterial wall has been studied in vitro using common carotid arteries excised from anesthetized dogs and perfused with a steady state flow of homologous serum. Wall uptake was found to depend nearly linearly upon wall shear rate. The overall transport of 131 I-albumin from the perfusing fluid to the vessel wall appears to be rate controlled by a shear dependent fluid-wall interface process. This study was carried out at high shear rates for flows which were transitional and turbulent. Because of the complexity of such flows, direct measurements of pressure drop were used to determine the shear rate at the vessel wall. Simultaneous pressure drop and flow measurements allowed the determination of the friction factor as a function of Reynolds number; results obtained at the higher Reynolds numbers correspond to those for a rigid pipe with a relative roughness of 0.05.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):494-498. doi:10.1115/1.3448382.

A stepped piston, enclosed within a tight circular cylinder of uniform bore and subjected to unequal upstream and downstream boundary pressures, is analyzed for the case of a compressible fluid. Performance characteristics are given for small eccentricity and high boundary pressure ratio as a function of step size and location, and a design parameter that relates the leakage and the centering force is defined. It is shown that piston performance can be optimized by suitable step design.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):499-503. doi:10.1115/1.3448383.

The in-line and transverse forces acting on circular cylinders placed near a plane boundary in a sinusoidally oscillating fluid in a U-shaped vertical water tunnel have been measured. The period parameter Um T/D was varied from about 2 to 40, the Reynolds number from 4000 to 25,000, and the gap between the cylinder and the plane boundary from 0.01 D to 1.0D. The drag and inertia coefficients for the in-line force have been determined through the use of the Morison’s equation and the Fourier analysis, least squares method, and a modified least squares method. The transverse force coefficients have been obtained for the forces toward the wall and away from the wall. The results show that the in-line and transverse forces could acquire very large magnitudes and give rise to serious oscillations. For very small values of the period parameter, effects of flow separation become negligible and the inertia coefficient for the in-line force and the lift coefficient for the transverse force approach those predicted by the potential theory.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):506-515. doi:10.1115/1.3448386.

The effect of axisymmetric contractions of a given shape and of contraction ratios c = 11, 22, 44.5, 64, and 100 on the free-stream turbulence of an incompressible flow has been studied experimentally with hot-wires. It is found that the longitudinal and lateral kinetic energies of turbulence increase along the contraction. The monotonic increase of the longitudinal turbulent kinetic energy with increasing c is in contrast with the linear (Batchelor-Proudman-Ribner-Tucker) theory. The variation of the lateral turbulent kinetic energy with c is in qualitative agreement with the theory; however, the increase is much lower than that predicted by the theory. The linear theory overpredicts the decrease in the longitudinal turbulence intensity with increasing c and under-predicts the decrease in the lateral turbulence intensity with increasing c. For the given flow tunnel, it is found that a contraction ratio c greater than about 45 is not greatly effective in reducing longitudinal turbulence levels further; the lateral turbulent intensity continues to decrease with increasing c. In the design of a low turbulence-level tunnel, the panacea for the reduction of the turbulence level does not lie in an indefinite increase of the contraction ratio alone. Studies with various upstream screens and a given contraction of c = 11 suggest that the exit turbulence intensities are essentially independent of the Reynolds number based on the screen-mesh size or screen-wire diameter of the upstream screen.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):516-520. doi:10.1115/1.3448387.

The flow field of a small nitrogen jet (5 mm diameter) injected into a cross flow of air at a momentum-flux ratio of 16 was explored in the plane of the trajectory by means of a laser-Doppler technique. Several traverses were made at right angles to the jet center line obtained from schlieren photographs of light and heavy gases. Velocities were measured in the direction of the traverse and at right angles to it. The locus of the maximum velocity in the direction of the jet trajectory is close to the photographic center line. The vortex center line was derived from the measurements by iteration, and results are in good agreement with those obtained by other investigators with different techniques on a much larger scale. The excess of the center line velocity over the parallel cross stream component decreases faster than for a jet without cross flow, and jet width increases linearly with distance from an effective origin about one jet diameter upstream of the injection point if distances are measured along the trajectory. Velocity profiles exhibit the same similarity as jets injected into stagnant gas.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):521-530. doi:10.1115/1.3448388.

Incompressible flow through an unstaggered cascade in general, unsteady, in-phase motion is considered. By methods of thin-airfoil theory, using the assumptions of wakes trailing back at the through-flow velocity, and the Kutta condition, exact analytical expressions are derived for loading, lift and moment. As application, harmonic motion is considered for plunging, pitching, and sinusoidal gusts. Numerical values of lift and moment for these three cases are given graphically (tables are available from the authors). The results show strong analogies with isolated unsteady thin-airfoil theory. They should prove useful as simple examples of unsteady effects in cascades, and as check cases for other approximate or purely numerical analyses.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):531-537. doi:10.1115/1.3448389.

An iterative procedure for the calculation of the thick attached turbulent boundary layer near the tail of a body of revolution is presented. The procedure consists of the potential-flow calculation by a method of integral equation of the first kind and the calculation of the development of the boundary layer and the wake using an integral method with the condition that the velocity remains continuous across the edge of the boundary layer and the wake. The additional terms that appear in the momentum integral equation for the thick boundary layer and the near wake are taken into account and the pressure difference between the body surface and the edge of the boundary layer and the wake can be determined. The results obtained by the present method are in good agreement with the experimental data. Part 1 of this paper deals with the potential flow, while Part 2 [1] describes the boundary layer and wake calculations, and the overall iterative procedure and results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):538-546. doi:10.1115/1.3448390.

This part deals with the calculation of the flow within the attached boundary layer and the wake of a body of revolution and its interaction with the external potential flow which was treated in Part 1. The iterative technique described in Part 1 is used to obtain a complete solution to the flow in the neighborhood of the tail of the body. The results of the calculations are compared with two sets of experimental data and reasonable agreement is demonstrated.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):550-557. doi:10.1115/1.3448393.

The effect of surface curvature on the development of a two-dimensional wall jet is investigated experimentally by direct comparison between a wall jet flowing around the convex surface of a circular cylinder, and its plane flow equivalent. Centrifugal force instabilities introduce rapid mixing of the curved wall jet with its surroundings, and cause significant increases in turbulence intensity and Reynolds shear stress in the jet. Large departures from self-preservation of the turbulence velocity field in the curved jet are observed, while the streamwise mean velocity profiles retain similar shapes for downstream development. Models for curvature effects on eddy viscosity are compared with experimentally measured values, and indicate that a simple correction for the effects of curvature is possible.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

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

ERRATA

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):560-562. doi:10.1115/1.3448395.

Previously published inception data for cavitation in the wake of sharp-edged disks are reanalyzed. The boundary layer characteristics at the face of the disk are found to play a major role. Good correlation between theory and experiment is achieved when the boundary layer is laminar.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):562-563. doi:10.1115/1.3448396.
Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):563-566. doi:10.1115/1.3448397.

A calculation procedure for predicting mean velocity profiles in drag-reducing flows is presented. The procedure is based upon the eddy diffusivity model of Cess and it requires only pressure drop, flow rate and geometry information. The predictions show excellent agreement with experimentally measured profiles in both Newtonian and drag-reducing flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):567-568. doi:10.1115/1.3448398.
Abstract
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):573-577. doi:10.1115/1.3448403.

In a series of experiments aimed at the visualization of the wet steam flow in the exhaust part of a 200 MW condensing steam turbine a set of periscopes and light sources was used. The aim of the experiment was: 1 – The investigation of the liquid-phase flow over the last stage stator blading of the turbine mentioned. 2 – The investigation of the gaseous-phase flow through the last stage blading at full and part load. The first part of the program partially failed due to the opaqueness of the wet steam atmosphere for the turbine load higher than 10–20 MW. The detailed experimental conditions will be described. An assessment of the primary droplet size will also be given. The preliminary results of the second part of the program will be outlined. The advantages and disadvantages of the equipment used will be discussed.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):578-580. doi:10.1115/1.3448405.
Abstract
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1976;98(3):580-582. doi:10.1115/1.3448406.

Nonsimilarity solutions in closed-form, for a sufficiently energetic line-explosion, in the presence of a constant axial current, are obtained. The gaseous medium is of constant pressure and its density varies as some inverse power of the distance from the line of explosion; ω is the power index, lying in the interval 0≤ω<2. The disturbance is headed by cylindrical shock surface of variable strength. The total energy of the wave is non-constant, but can be made to vary slowly with time.

Commentary by Dr. Valentin Fuster

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