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RESEARCH PAPERS

J. Fluids Eng. 1990;112(4):376-385. doi:10.1115/1.2909414.

The mean flow field surrounding obstacles attached to a wall under a turbulent boundary layer is analyzed. The analysis concentrates on how major features of the flow are influenced by model geometry and the incident shear flow. Experimental data are analyzed in terms of nondimensionalized variables chosen on the basis that their effect on major flow features can be simply appreciated. The data are restricted to high Reynolds number shear layers thicker than the attached obstacle. The work shows that data from a wide range of flows can be collapsed if appropriate nondimensional scales are used.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):386-392. doi:10.1115/1.2909415.

Vortex shedding from spheres at Reynolds numbers from 3 × 102 to 4 × 104 in a uniform flow was investigated experimentally. Standard hot-wire technique were used to measure the vortex shedding frequency from spheres in a low-speed wind tunnel. Flow-visualization experiments were carried out in a water channel. Important results from the investigation were that (i) the variation of the Strouhal number St (=fD/U0 , U0 : freestream velocity, D: diameter of the sphere, f: vortex shedding frequency) with the Reynolds number (= U0 D/v, v: kinematic viscosity) can be classified into four regions, (ii) the Reynolds number at which the hairpinshaped vortices begin to change from laminar to turbulent vortices so that the wake structure behind the sphere is not shown clearly when a Reynolds number of about 800 is reached, and (vi) at Reynolds numbers ranging from 8X102 to 1.5X104 , the higher and lower frequency modes of the Strouhal number coexist.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):393-401. doi:10.1115/1.2909416.

The flow downstream of the intersection of both a circular and a tapered cylinder with a flat plate was examined at ReD = 1.3 × 105 using surface visualization, five-hole-probe anemometry, and flow visualization. A pair of large, counter-rotating swirls with common flow away from the wall and with centers over one diameter away from the wall was present downstream of both obstacles. It is suggested that the large, swirling pair are formed in the near wake of an obstacle that is exposed to symmetrical channel flow. A pair of smaller counter-rotating vortices with common flow toward the wall was observed embedded in the wall-shear flow eight diameters downstream of the tapered cylinder. This implies that the legs of the horseshoe vortex system only propagate downstream behind the streamlined obstacle shape.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):402-408. doi:10.1115/1.2909417.

Experimental studies on the measurement of pressure fields in the region of separating and reattaching flows behind several two-dimensional fore-bodies and one axisymmetric body are reported. In particular, extensive measurements of mean pressure, surface pressure fluctuation, and pressure fluctuation within the flow were made for a series of two-dimensional fore-body shapes consisting of triangular nose with varying included angle. The measurements from different bodies are compared and one of the important findings is that the maximum values of rms pressure fluctuation levels in the shear layer approaching reattachment are almost equal to the maximum value of the surface fluctuation levels.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):409-415. doi:10.1115/1.2909418.

A computational and experimental study is reported of turbulent flow around a square-sectioned U-bend with a mean bend radius equal to 3.375 times the hydraulic diameter (DH ): the duct Reynolds number is 58,000. The bend geometry is the same as that for which Chang et al. (1983) have reported extensive LDA data except that in the latter experiment the bend was preceded by some thirty hydraulic diameters of straight ducting (thus the boundary layers filled the duct). In the present case, with the inlet section shortened to only 6 DH , the boundary layer thickness at inlet to the bend was only about 0.15 DH . Despite the thinner boundary layers a strong secondary flow is generated which, by 135° around the bend, appears to have broken down into a chaotic pattern. Computations of the flow using a three-dimensional finite-volume solver employing an algebraic second-moment (ASM) turbulence model are in generally close agreement with the experimental data and suggest that the secondary flow, in fact, breaks down into a system of five eddies on either side of the mid-plane, in place of the classical single vortex structure.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):416-424. doi:10.1115/1.2909419.

A new viscous-inviscid interaction procedure of the semi-inverse type has been developed to predict two-dimensional separated flows. The method is applied to incompressible flow over an external backward-facing step, using linearized potential theory for the inviscid region and a simple modification of Pohlhausens’ momentum-integral method in the viscous region. The modified Pohlhausen method, which approximates the reverse flow region with a region of “dead-air,” is first tested without the viscous-inviscid procedure to predict fully developed laminar and turbulent flow in a plane symmetric sudden expansion. Comparisons are made with experimental data, other calculation methods, and finite difference predictions using a modified version of an elliptic code (TEACH-II). Reasonable predictions of the sudden expansion and backward-facing step flows are obtained, provided that the step-height to boundary-layer thickness ratio is large enough for the Pohlhausen type velocity profiles to be effective. The relative simplicity of the zonal equations coupled with the viscous-inviscid interaction procedure makes the present calculation method computationally attractive. The method should also prove useful in more complex separated flow situations, such as bluff-body aerodynamics.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):425-432. doi:10.1115/1.2909420.

The two-layer concept is a framework for interpreting events and constructing mathematical models of turbulent wall layers. In this paper an asymptotic theory is constructed employing the idea that the interaction between the layers is the most important aspect. It is shown that the matching process for the layers can be used to define a characteristic scale, u*, and to produce an equation that relates u* to the known parameters; U∞ , v, h, e, and dp/dx. At infinite Reynolds number the scale u* is equal to uτ , the friction velocity, but they are distinct at moderate Reynolds numbers. The theory produces very simple results. For instance, the overlap velocity laws are logarithmic with an invariant von Kármán constant; at low Reynolds numbers the additive constant changes while the slope remains the same. The effect of low Reynolds numbers on the Reynolds stress in the overlap layer is also analyzed. A composite expansion explains the strong Reynolds number effect on the stress profiles. This occurs because the mixing of outer and inner layer phenomena take place at different locations as the size of the overlap region changes. The location of the maximum Reynolds stress is given by y+ max = (Re/k)1/2 . The overlap region was not found to be a region of constant stress, as put forth in many heuristic arguments.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):433-436. doi:10.1115/1.2909421.

This paper presents the development of a practical one-parameter integral method for transpired turbulent boundary layer flow. The method involves the use of one-parameter polynomial approximations for total stress and the solution of the familiar integral momentum equation. The method is compared with experimental data and numerical solutions for a range of near equilibrium boundary layers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):437-440. doi:10.1115/1.2909422.

Previously established characteristics of steady-state discharge through a valve are employed for the study of quasi-steady discharge from a vessel. Experimental examination of the problem has also been carried out. The data obtained in the laboratory fully supported the validity of the quasi-steady approach to this type of unsteady flow problems.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):441-446. doi:10.1115/1.2909423.

The interference drag identified with the junction of a streamlined cylindrical body and a flat plate was investigated. The junction drag was calculated from a set of detailed, self consistent, high quality data using a control volume approach. The drag for the isolated flat plate and streamlined cylinder making up the junction was calculated using boundary-layer solvers together with surface pressure measurements. For the particular and relatively thick body under consideration, the results show a significant increase in drag due to the junction. These and other available results indicate that the interference drag has a systematic dependence on the thickness to chord ratio. The junction vortex wake increases the downstream flat plate drag significantly. Because of this effect, a unique value for the drag force, drag coefficient, or induced drag coefficient for a junction vortex flow would require that the geometry be specified in detail. The induced drag and the total pressure losses identified with the junction are also reported.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):447-454. doi:10.1115/1.2909424.

The influence upon flow of fan induced inlet swirl is examined for two commonly used sizes of uniformly perforated polyethylene ventilation tubes (polytubes). Swirl is present at the inlet of most polytubes that are directly connected to a supply fan whether or not an antiswirl device is used. Four experimentally obtained inlet swirl angles are examined using swirl modified pressure recovery coefficients, pipe friction factors, and orifice discharge equations. A computational procedure divides the polytube into five equal length segments to obtain a rapid yet acceptably accurate procedure. An iterative microcomputer spreadsheet solves the resulting set of simultaneous equations, providing pressure and flow discharge profiles along the tube that are in very good agreement with the experimental data and with the data of others. An extension of the analysis for uniformly spaced orifices indicates that supply swirl angles greater than 25 deg and large length to diameter ratios should be avoided.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):455-460. doi:10.1115/1.2909425.

A method for treating nonideal gas flows through converging-diverging nozzles is described. The method incorporates the Redlich-Kwong equation of state. The Runge-Kutta method is used to obtain a solution. Numerical results were obtained for methane gas. Typical plots of pressure, temperature, and area ratios as functions of Mach number are given. From the plots, it can be seen that there exists a range of reservoir conditions that require the gas to be treated as nonideal if an accurate solution is to be obtained.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):462-467. doi:10.1115/1.2909428.

The formation mechanism of streamwise vortices in the near field of the three-dimensional wall jet discharging from a circular nozzle along a flat plate is studied experimentally using a conditional sampling technique. Ensemble-averages of the lateral velocity component indicate the presence of large-scale horseshoe-like structures, whose legs are inclined and stretched to form the streamwise vortices in the mixing region of the jet. Based on the present result, a coherent structure model for the near field of the wall jet is proposed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):468-475. doi:10.1115/1.2909429.

Computations and flow visualization experiments have been carried out on 2-D flow in a channel, with an indentation in one wall that can move in and out. There is plane Poiseuille flow upstream and attention is focussed on the flow downstream of the indentation. Four time-courses of indentation motion are examined: I oscillation between a flush and an indented postion; II advance from flush to indented, after which it remains stationary; III retraction to flush from a steady indentation; IV small amplitude oscillation about a substantially indented position. Various values of Reynolds number, Re, and Strouhal number, St, are employed (250≤Re≤911; 0.01≤St≤0.1). The results show that (a) vorticity waves and eddies are generated in cases I and II (as in reference [11]); (b) in case II at higher experimental Re the flow does not become steady because the steady flow is unstable to a Rayleigh wave, on the shear layer bounding the main separation region, whose wavelength is significantly less than that of the vorticity wave; (c) in case III the waves that are generated at each parameter set seem to be Rayleigh waves not vorticity waves; (d) in case IV short waves give way to longer waves whose amplitude is comparable with the mean indentation height not the oscillation amplitude. Although resembling vorticity waves these do not propagate like the forced waves of case I and presumably represent a nonlinear interaction between Rayleigh waves, vorticity waves, and the very long, weak waves present even in steady flow. Further downstream, in many cases, the 2-D waves break down into turbulence via 3-D disturbances.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):476-480. doi:10.1115/1.2909430.

In an extensive experimental investigation (Christodoulou, 1985) the performance of a disk skimmer rotating in the vertical plane and partially immersed in a liquid has been studied. The aim of the study was to examine the physical and hydrodynamic parameters governing the oil collection rate of the disk when used as one element of a rotating disk skimmer, a device commonly employed to recover oil and similar immiscible liquids from a water surface. This paper presents a theoretical solution for the flow field set up by the disk which has led to an improved understanding of the hydrodynamics of the disk drag-out problem at low to moderate speeds. Experimental data are presented and compared with the theoretical solutions: discrepancies are then explained in terms of departures from the original assumptions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):481-486. doi:10.1115/1.2909431.

Interactions and breakup processes of 1.50-mm-diameter ethyl alcohol droplets and 5.14-mm-diameter water bubbles with planar shock waves were observed using double-exposure holographic interferometry. Experiments were conducted in a 60 mm × 150 mm cross-sectional shock tube for shock Mach number 1.56 in air. The Weber numbers of droplets and liquid bubbles were 5.6 × 103 and 2.9 × 103 , respectively, while the corresonding Reynolds numbers were 4.2 × 10 and 1.5 × 105 . It is shown that the resulting holographic interferogram can eliminate the effect of the mists produced by the breakup of the droplets and clearly show the structure of a disintegrating droplet and its wake. This observation was impossible by conventional optical flow visualization. It is demonstrated that the time variation of the diameter of a breaking droplet measured by conventional optical techniques has been overestimated by up to 35 percent.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):487-491. doi:10.1115/1.2909432.

The availability of a single bubble-droplet system is derived from energy conservation and the principle of entropy. The equilibrium and critical conditions are determined by minimizing the availability without any assumption on the volume of the bubble-droplet system. It is found that the compressibility effect of the liquid-gas solution can be neglected in such a small bubble-droplet system and dilute solution condition. The results of the present analyses confirm previous conclusions reached by Cha that a bubble can remain in a state of stable equilibrium provided that the ratio of the total number of moles of gas to the total number of moles of the liquid is not extremely small and the external pressure falls between a dissolution limit and a cavitation limit.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):492-495. doi:10.1115/1.2909433.

The influence of cavitation on vortex shedding behind constrained sharp-edged bluff prisms is studied experimentally. At a given blockage, the length of the vortex formation region is found to increase as the cavitation number of the flow is reduced. The vortex appears to be stabilized from breaking up in the partially cavitating regime of flow. Test results indicate that the separation velocity is the proper velocity scale to reduce or eliminate blockage effects.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):496-500. doi:10.1115/1.2909434.

The classic formula for waterhammer wavespeed is extended to calculate the complex-valued, frequency-dependent wavespeed in a viscoelastic pipe, which takes into account the effect of viscoelasticity of pipe wall material on wave propagation. With the complex wavespeed, the standard impedance or transfer matrix is directly used to analyze resonating conditions in systems including viscoelastic pipes, and the impulse response method presented previously by the authors is applied to compute nonperiodic transients. Numerical results are compared with experimental data and good agreement is observed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):501-509. doi:10.1115/1.2909435.

Transonic strong blade-vortex interaction is numerically analyzed by solving the unsteady 2-D Navier–Stokes equations using an iterative implicit second order scheme. The dominant processes during the interaction are the development of large transverse pressure gradients in the upper leading edge region and the development of disturbances at the root of the lower surface shock wave. As a result of this interaction, high pressure pulses are emitted from the leading edge, and acoustic waves are radiated from the lower surface in a region originally occupied by a supersonic pocket. In addition, severe load variations occur when the vortex is within one chord length of the blade.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):510-520. doi:10.1115/1.2909436.

A numerical procedure is presented for computing time-accurate solutions of flows about two and three-dimensional configurations using the Euler equations in conservative form. A nonlinear Newton method is applied to solve the unfactored implicit equations. Relaxation is performed with a point Gauss-Seidel algorithm ensuring a high degree of vectorization by employing the so-called checkerboard scheme. The fundamental feature of the Euler solver is a characteristic variable splitting scheme (Godunov-type averaging procedure, linear locally one-dimensional Riemann solver) based on an eigenvalue analysis for the calculation of the fluxes. The true Jacobians of the fluxes on the right-hand side are used on the left-hand side of the first order in time-discretized Euler equations. A simple matrix conditioning needing only few operations is employed to evade singular behavior of the coefficient matrix. Numerical results are presented for transonic flows about harmonically pitching airfoils and wings. Comparisons with experiments show good agreement except in regions where viscous effects are evident.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1990;112(4):524-526. doi:10.1115/1.2909438.

Flow through orifices has been investigated thoroughly and a large amount of information on discharge coefficients and losses is available. Almost all of these results presuppose that the approaching flow is symmetrical in respect to the orifice. Very little information, however, is available for flows such as those through an orifice located in the wall of a pipe which itself carries a fluid. The present investigation consists of a set of exploratory experiments to obtain discharge coefficients for this kind of orifice flows and, in particular, to ascertain the effect of the velocity in the pipe on these coefficients.

Commentary by Dr. Valentin Fuster

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