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RESEARCH PAPERS

J. Fluids Eng. 1991;113(2):163-175. doi:10.1115/1.2909476.

A review is made of progress in research during the period 1979–1989 on the fundamental physical mechanisms of hydrodynamic cavitation inception. During that decade identification of the physical phenomena has been made, and techniques have been developed to reproduce on laboratory scale selected forms of full scale cavitation inception. Understanding of the mechanisms remains shallow, and analytical/numerical prediction methods are nonexistent except for the restricted case of travelling bubble cavitation inception in a passive pressure field. The control of inception is seen to be related in part to control of the underlying viscous flow features. A growing body of experimental evidence points to microscale vortex cavitation as a primal inception event.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):176-182. doi:10.1115/1.2909477.

A validated computer simulation model has been developed for the analysis and design of colinear porous sphere systems in a convective stream. Using a modified and extended finite element software package, the steady-state Navier-Stokes equations have been solved describing laminar axisymmetric flow past closely spaced monodisperse spheres with fluid injection. Of interest are the coupled nonlinear interaction effects on the fluid flow patterns and ultimately on the drag coefficient of each sphere for different free stream Reynolds numbers (20 ≤ Re ≤ 200) and intersphere spacings (1.5 ≤ dij ≤ 6.0) in the presence of fluid injection (0 ≤ vb ≤ 0.1). At small spacings and low Reynolds numbers, fluid injection causes earlier flow separation while for Re ≥ 100 surface blowing is more influential in altering the recirculation zones between spheres and thickening the boundary layers. As a result, the total drag of each sphere decreases with increasing blowing intensity although the pressure or form drag of the first sphere may increase at small spacings.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):183-189. doi:10.1115/1.2909478.

This paper deals with the suppression of the fluid forces by controlling a shear layer on one side separated from a square prism. The control of the separated shear layer was established by setting up a small circular cylinder (the control cylinder) in it on one side. Experimental data were collected to examine the effects on the fluid forces and vortex shedding frequency due to variation of the position and diameter of the control cylinder. The results show that (i) the maximum reduction of the time-mean drag and fluctuating lift and drag occurred when the control cylinder was located near what would ordinarily be considered the outer boundary of the shear layer; (ii) the control of the separated shear layer by means of a small cylinder appeared to be effective in suppressing the fluctuating lift and drag rather than the time-mean drag; (iii) in the case of the control cylinder of 6 mm in diameter, the time-mean drag was reduced to about 30 percent, and the fluctuating lift and drag were reduced to approximately 95 and 75 percent, respectively; (iv) the fluid forces and the frequency of vortex shedding of the square prism were mainly dependent on the characteristics of a very thin region near the outer boundary of the shear layer.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):190-198. doi:10.1115/1.2909479.

Numerical results are presented concerning the fluid characteristics of steady-state laminar flow over surface mounted ribs. Computations are carried out using a false transient stream function-vorticity form. The effects of the aspect ratios (width-to-depth) of the ribs and Reynolds numbers as well as initial boundary-layer thickness on entire flow field, separated region, and reattachment length are presented and discussed. The computed reattachment distance compares reasonably well with those data reported by previous studies. A correlation is provided in terms of the rib aspect ratio, Reynolds number, and the ratio of boundary-layer thickness and rib height. The pressure drop is excessive along the upstream vertical step face and it recovers thereafter, which agrees qualitatively with those of the previous studies for the flow over backward-facing steps.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):199-205. doi:10.1115/1.2909480.

A study of laminar pulsating flow through a 45 degree bevel pipe orifice was performed using finite-difference approximations to the governing stream function and vorticity transport equations. The distance from (−∞) to (+∞) was transformed into the region from (−1) to (+1) for the streamwise coordinate. Solutions were obtained for orifice bore/pipe diameter ratios of 0.2 and 0.5 for bore Reynolds numbers in the range from 0.8 to 64 and Strouhal numbers from 10−5 to 102 . Stream and vorticity function plots were generated for all cases and the time-dependent discharge coefficient waws computed and averaged over a cycle of pulsation. The numerical solutions agree closely with available experimental data for steady flow discharge coefficients. The results show that the effects of pulsation on the discharge coefficient can be correlated by using the product of the orifice bore Reynolds and Strouhal numbers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):206-209. doi:10.1115/1.2909481.

Laser Doppler anemometry has been used to make measurements of a small recirculation bubble in a turbulent water flow over a rib roughened surface. The bubble occurs near the leading edge of a transverse rib which is a model of the ribbed surface used to enhance cooling on nuclear reactor fuel pins. The bubble is transient, and spectral and correlation measurements were made to investigate any periodicity. It was found that the bubble itself did not show any periodicity but there was evidence for fluctuations in the main stream with a Strouhal number of 0.1.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):210-215. doi:10.1115/1.2909482.

By solving weakly compressible flow equations with application of Smogrinsky’s subgrid-scale turbulent model and partial-slip condition at the wall, a two-dimensional analysis is made on the flow of Re = 1.2 × 106 in a nonsymmetric planewall diffuser. The calculated velocity profiles are compared with the measured data, and the effect of inlet and outlet conditions on diffuser performance is evaluated. Comparison is also made between the symmetric and non-symmetric plane-wall diffusers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):216-222. doi:10.1115/1.2909483.

The turbulent flow field generated by a stationary cube at Reynolds numbers 2000 and 14,000 is investigated numerically. A vorticity-vector potential formulation of the equations of motion is employed. Turbulence effects are accounted for through the use of a vorticity transport closure scheme in which dynamical equations for vorticity mean and covariance are supplemented by a kinematic equation for turbulent kinetic energy. Semi-implicit finite difference approximations to the equations of motion are solved iteratively by a vectorizable 8-color SOR algorithm. The numerical mesh is designed so that the turbulent flow field can be computed down to solid surfaces without the use of wall functions. The properties of the computed flow field, including drag, axial velocity, separation points, and three-dimensional flow structure show good agreement with experimental observations of similar bluff body flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):223-227. doi:10.1115/1.2909484.

A second series of experiments was conducted to extend and validate recently reported data by the present authors on transition to turbulence in pipe flows started from rest under constant acceleration. The test section diameter was increased from the 5 cm of the previous experiment to 9 cm for the present study. The low end of the acceleration range was also extended by an order of magnitude from 1.8 m/s2 down to 0.2 m/s2 . The highest acceleration was 11.2 m/s2 . Pipe Reynolds number at transition was observed to be as high as 1.1 × 106 . The present results are shown to validate the previously suggested transition correlation parameters. An analysis based on an empirical equation for transition in convectively accelerated flows is extended and applied to the current experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):228-239. doi:10.1115/1.2909485.

Recent interest in unsteady separation and separated flows brings up the need of an accurate and efficient computational scheme for general unsteady three-dimensional boundary-layer flows. Resolution of the singular behavior at separation is a delicate problem. The task is further complicated by the geometrical singularity and the nonstationary stagnation point. The present paper proposes a numerical scheme to sidestep these difficulties. At the first stage of development, the simpler problem of the symmetry-plane solution of the laminar boundary-layer over an impulsively-started prolate spheroid is calculated. Results show that the present Eulerian calculation satisfactorily captures the singular behavior of the boundary layer when separation is approached. Comparison with Xu and Wang’s recent results and those for the two-dimensional elliptic cylinder calculated by the Lagrangian method are also made. Discussions of the results for unsteady separation at zero, small and large incidences are presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):240-244. doi:10.1115/1.2909486.

Measurements of the casing boundary layers were obtained in a four-stage, low speed axial flow compressor, to verify the ‘law of the wall’ applicability to these complex flows. Some of the available shear stress models of the two-dimensional flows have been examined towards the quantitative assessment of skin friction. The shear stress prediction obtained from the Ludwieg-Tillmann relation applied to the streamwise or untwisted profile agreed closely with the measured shear stress by the hot wire. The skin friction was fairly constant for rotor and stator flows and was close to the flat plate values. The boundary layer profiles exhibited a well pronounced semi-logarithmic region with the universal constants of the law of the wall far removed from the standard two dimensional values, especially for rotor flows. Stator flows showed signs of similarity to two dimensional flows.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):245-249. doi:10.1115/1.2909487.

An experimental investigation was made of the impulsive spin-up from rest of a liquid in a partially filled cylindrical container. The main impetus was placed on delineating the effects of the presence of a free surface on the transient development of flow. Of particular interest were the situations in which the free surface intersected either or both of the endwall disks during the course of spin-up. Extensive flow visualizations were carried out by using suspended metal particles. An image processing technique was utilized to determine accurately the propagating velocity shear front as well as the time-dependent free surface contour. Precise measurements of the fluids velocities were obtained by using a laser Doppler velocimeter. The transient velocity profiles were mapped out, and they were found to be in satisfactory agreement with the predictions based on the simplified analysis. The radial location, Rs(t), of the propagating shear front was measured by applying the image processing technique to the visualized azimuthal flow field. The experimental data were found to be consistent with the numerical predictions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):250-255. doi:10.1115/1.2909488.

The controlled processor has been proposed as a means of avoiding velocity bias in laser Doppler anemometry. A theoretical model is presented to show that results free of bias can be obtained if both the ratio of integral time scale to measurement time scale (integral scale data density) and the ratio of sampling time to the measurement time scale (normalized sample interval) are greater than five. Further, by separation of the integral scale data density and normalized sample interval parameters, it is shown that at any integral scale data density the controlled processor will not produce any less bias than a sample and hold processor and no more bias than the free running (unweighted) processor. In some situations it may be considered superior to the sample and hold processor as the data processing and hardware requirements are reduced without any loss of measurement accuracy. Experimental data confirming the theoretical results are also shown. Some of these data are contrary to at least one model available in the literature.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):256-260. doi:10.1115/1.2909489.

A theoretical and experimental investigation has been made of the static pressure hole problem in subsonic flow. Thanks to a linearization, the effects of the boundary layer, of the velocity gradient and of the wall curvature could be separated so that a formula of correction containing three influence functions has been obtained. These functions were determined in the case of practical requirements by means of experiments made on appropriate models for two values of the depth-to-diameter ratio and for at least three values of the Mach number. Then, the method of correction has been applied to the flow around an airfoil at zero angle of attack.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):261-269. doi:10.1115/1.2909490.

This work is concerned with the design of a Cavitation Susceptibility Meter based on the use of a venturi tube for the measurement of the active cavitation nuclei concentration in water samples as a function of the applied tension. The operation of the Cavitation Susceptibility Meter is analyzed and the main considerations leading to the proposed design are illustrated and critically discussed. The results of this analysis indicate that the operational range is mainly limited by nuclei interference, flow separation and saturation (choking), and suggest to develop a Cavitation Susceptibility Meter where: (a) the flow possesses a laminar potential core throughout the venturi throat section in all operational conditions; (b) the pressure at the venturi throat is determined from the upstream pressure and the local flow velocity; (c) the detection of cavitation and the measurement of the flow velocity are carried out optically by means of a Laser Doppler Velocimeter; (d) a custom-made electronic Signal Processor incorporating a frequency counter is used for real time data generation and temporary storage; (e) a computerized system performs the final acquisition and reduction of the data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):270-277. doi:10.1115/1.2909491.

This work is concerned with the development and operation of a Cavitation Susceptibility Meter based on the use of a venturi tube for the measurement of the active cavitation nuclei concentration in water samples as a function of the applied tension. The pressure at the venturi throat is determined from the upstream pressure and the local flow velocity without corrections for viscous effects because the flow possesses a laminar potential core in all operational conditions. The detection of cavitation and the measurement of the flow velocity are carried out optically by means of a Laser Doppler Velocimeter. A custom-made electronic Signal Processor is used for real time data generation and temporary storage and a computerized system for final data acquisition and reduction. The implementation of the whole system is described and the results of the application of the Cavitation Susceptibility Meter to the measurement of the water quality of tap water samples are presented and critically discussed with reference to the current state of knowledge on cavitation inception.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):278-284. doi:10.1115/1.2909492.

Backward facing steps were used to study experimentally the effects of expansion ratio and Reynolds numbers on the incipient cavitation indices. For small changes in the expansion ratio, significant changes in incipient cavitation index were observed. The effect of cavitation and expansion ratio on the frequency of vortex shedding and pressure distribution downstream of flow separation were also obtained. The dependence of the flow characteristics like the reattachment length, the frequency of vortex shedding and the pressure distribution downstream of the step were obtained under noncavitating conditions. In the present study, the range of Reynolds numbers has been extended to values which are normally encountered in prototype installations.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):285-289. doi:10.1115/1.2909493.

Theoretical results on gaseous convective turbulent diffusion in steady axisymmetric flows are found to compare well with experimental results already in the literature. The investigation starts with the formulation of a highly idealized “slug-flow” model of the process for a quick estimate of the importance of turbulent boundary layer convection and for a comparison of previously published experimental and analytical results which had revealed order-of-magnitude discrepancies between calculated and measured air diffusion rates. Next, an existing two-dimensional convective diffusion model is adapted to axisymmetric cavity flow. Good agreement between experimental and calculated mass flow rates is found with a proper choice of turbulent diffusively from a Launder-Spaulding mixing-length model. The adapted “wrap around” model predicts a concentration boundary-layer thickness of the order of the cavity radius at the cavity terminus. Consequently, an axisymeetric analysis is also presented. From this it is found that the important part of the gaseous mass flow into the cavity occurs near the very front of the cavity where the concentration gradients are most severe. Downstream flow regions near the cavity are thereby depleted of dissolved air and the resulting concentration gradients are greatly reduced. Therefore the mass flow rate through downstream cavity surfaces are relatively unimportant and the simpler wrap around calculation can give useful engineering estimates of total mass flow rates.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):290-294. doi:10.1115/1.2909494.

This paper gives an analysis of convective gaseous diffusion into a full cavity behind an oscillating flat-plate hydrofoil in a turbulent flow. The unsteady diffusion theory accounts for fluctuations of cavity gas pressure and length which are assumed to be harmonic oscillations but are not necessarily in phase with the hydrofoil motion. A diffusive lag function is found which, for a given reduced frequency, determines the instantaneous diffusion rate as a product of the lag function and the quasisteady mass diffusion. The present results can be used to study the rate of gas entrainment from the cavity into the wake behind the oscillating cavity.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):295-300. doi:10.1115/1.2909495.

The present study is devoted to the interaction between a swarm of bubbles and a turbulent field in a linear shear flow. The transversal and longitudinal evolutions of the void fraction and of the Reynolds stress tensor have been measured. When the air bubbles are blown uniformly into the shear, the void fraction profiles exhibit a strong gradient which can be explained by kinematical effects. No void migration has been observed. The behavior of the Reynolds tensor indicates that the nonisotropy induced by the mean velocity gradient decreases when the void fraction increases. A simple mechanism is proposed to interpret this fact, and a turbulence model based on one-point closures is compared to the experimental data.

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Fluids Eng. 1991;113(2):301-304. doi:10.1115/1.2909496.

A method for treating nonideal gas flows through a venturi meter is described. The method is an extension of a previous study reported in an earlier paper. The method involves the determination of the expansion factor which may then be used to determine the mass flow rate through the venturi meter. The method also provides the means for determining the critical pressure ratio as well as the maximum flow rate per unit throat area. The Redlich-Kwong equation of state is used, which allows for closed form expressions for the specific heat at constant volume and the change in entropy. The Newton-Raphson method is used to determine the temperature and specific volume at the throat. It is assumed that the following items are known: the upstream temperature and pressure and the ratio of the throat pressure to the upstream pressure. Results were obtained for methane gas. These results indicate that for the cases considered, the use of the ideal gas expression for the expansion factor would lead to an error in the determination of the mass flow rate; the error increases as the throat to inlet pressure ratio decreases. For the example reported in this study, the maximum percent difference in the critical pressure ratio between the ideal and nonideal gases was 5.81 percent, while the maximum percent difference in the maximum flow rate per unit throat area was 7.62 percent.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(2):304-307. doi:10.1115/1.2909497.

The results of an earlier investigation that demonstrated the significance of the particle diameter/fluid length scale ratio in determining whether or not the addition of a dispersed phase would cause an increase or decrease in the carrier phase turbulent intensity are extended to radial locations other than the centerline. Presently, it is shown that similar trends are valid except the results become less correlated approacthing the wall for the case of pipe flows. The results for jets are independent of radial location. It is also shown that other possible non-dimensional parameters do not correlate the data as well.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

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