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EDITORIAL

J. Fluids Eng. 1977;99(4):614. doi:10.1115/1.3448870.
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Abstract
Commentary by Dr. Valentin Fuster

REVIEW ARTICLES

J. Fluids Eng. 1977;99(4):618-633. doi:10.1115/1.3448871.

There are infinite numbers of possible arrangements of two parallel cylinders positioned at right angles to the approaching flow direction. Of the infinite arrangements, two distinct groups may be identified: in one group, the cylinders are in a tandem arrangement, one behind the other at any longitudinal spacing; and in the second group, the cylinders face the flow side by side at any transverse spacing. All other combinations of longitudinal and transverse spacings represent staggered arrangements. The tandem arrangement will be treated first. A critical survey of previous research revealed some “odd” features which had been observed and overlooked by various authors. The discontinuity of vortex shedding implies that a similar discontinuity should be expected for the drag force on both cylinders. The measurements of the front (gap) pressures of the downstream cylinder and the base pressures of both cylinders at various spacings reveal a discontinuous “jump” at some critical spacing. The discontinuity is caused by the abrupt change from one stable flow pattern to another at the critical spacing. A new interpretation is given for the existing data on the drag force for both cylinders. The effects of Reynolds number and surface roughness are treated in some detail. Following this, two cylinders arranged side by side to the approaching flow are considered. All the available data on measured forces are compiled together with additional measurements in the range of intermittent changes of drag and lift forces. The bistable nature of the asymmetric flow pattern around each cylinder produces two alternative values of the drag force coupled with two alternative values of the lift force. The introduction of the interference force coefficient exposes the physical origin of two different forces experienced by the cylinders when arranged side by side. Finally, the least reported arrangement of two staggered cylinders is reviewed. The various arrangements are grouped into classes according to the sign of the lift force, or whether the drag force is greater or less than that for a single cylinder. The measurements of drag and lift forces for various arrangements reveal two different regimes for the lift force. In one regime, the lift force directed toward the wake of the upstream cylinder is due to the entrainment of the flow into the fully developed wake of the upstream cylinder. The lift force in this regime reaches a maximum value when the downstream cylinder is near to the upstream wake boundary. In the second regime, at very small spacings, the lift force becomes very large due to an intense gap flow which displaces the wake of the upstream cylinder. The maximum lift force occurs with the downstream cylinder near to the horizontal axis of the upstream cylinder. A discontinuity in the lift force for some staggered arrangements is found and attributed to the bistable nature of the gap flow.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Papers From Symposium on Numerical/Diagonal/Laboratory Computer Methods in Fluid Mechanics

J. Fluids Eng. 1977;99(4):634-638. doi:10.1115/1.3448872.

A numerical algorithm is presented for solving laminar, steady, supersonic interacting boundary-layer flows for quasi-three-dimensional configurations. The interaction problem is treated as a boundary-value problem and a salient feature of the scheme is the direct implementation of the downstream boundary condition. Solutions are presented for axisymmetric and swept (yawed) compression ramps for both adiabatic and heat transfer conditions over a Mach number range of 2–6. The results are in good agreement with experimental data and existing theories for axisymmetric cases. For the swept (yawed) configurations, lack of experimental data makes a direct comparison impossible, but the present solutions are found to be in qualitative agreement with earlier studies. In addition, it is shown that the trends obtained for the sweep effects are well predicted by a simple extension of a two-dimensional asymptotic theory.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):640-648. doi:10.1115/1.3448875.

The laminar three-dimensional flow in curved ducts has been analyzed for an incompressible viscous fluid. The mathematical model is formulated using three-dimensional parabolized Navier-Stokes equations. The equations are generalized using two indices which permit the choice of Cartesian or cylindrical coordinate systems and straight or curved ducts. The solutions are obtained numerically using an ADI method for a number of duct geometries and flow parameters. The study presents detailed results for developing laminar flow in rectangular curved ducts; also, the effect of longitudinal curvature on secondary flow is fully analyzed. An investigation is made of the occurrence of Dean’s instability and, for curved square ducts, it is found to first appear at Dean number ≃ 143.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):649-656. doi:10.1115/1.3448876.

Numerical solutions have been obtained for two-dimensional free convective flow in rectangular and annular cavities by the strongly implicit procedure (SIP) and the cyclic reduction-fast Fourier transform (CR-FFT) technique. Rayleigh numbers range from 104 to 106 , Prandtl numbers from 0.713 to 103 , radius ratios from 1 to 3 (annular cavities), and aspect ratios (height/width) from 1 to 15. Motion is generated by either uniformly heating the bottom wall or heating a vertical wall and cooling the opposite wall. Both time-dependent and steady-state solutions confirm results previously obtained by others. Because SIP uses a common set of matrix algorithms, the governing equations of motion can be solved simultaneously without major modification to the method for each equation.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):657-665. doi:10.1115/1.3448877.

Numerical solutions of the equations governing the laminar flow of an incompressible fluid through a two-dimensional sudden expansion are discussed. The fluid motion is started impulsively from rest and is examined in detail during the transient phase to the steady-state condition. Solutions are obtained by two independent finite-difference methods which are discussed. The development of the flow in the zone of separation is investigated, and, during the earliest phases of motion, the generation of vorticity at the solid boundaries and its spatial diffusion is studied in the region of uniform flow. The numerical treatment of the boundary conditions is discussed. Characteristics of the transient solution for two different Reynolds numbers in the laminar range are presented. Included with the results is the temporal development of the streamline dividing the zone of separation from the main flow.

Commentary by Dr. Valentin Fuster

RESEARCH PAPERS: Additional Technical Papers

J. Fluids Eng. 1977;99(4):666-673. doi:10.1115/1.3448878.

The slender channel equations for laminar flow are solved downstream of the entrance of curved channels of variable height. The singularities at the entrance are removed with coordinate transformations which stretch the boundary layer and shrink the core flow. Initial conditions at the entrance are obtained from the governing equations with only the streamwise velocity specified. A modified box scheme is used to develop a finite-difference method which allows the derivatives of the dependent variables across the channel to be discontinuous at the interface between the boundary layer and core flow. Numerical results are presented for several channel geometries and entry conditions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):675-680. doi:10.1115/1.3448882.

Hydrodynamic effects are analyzed for a stepped piston moving within a tight clearance tube filled with an incompressible fluid. Together with the hydrostatic effects that were analyzed in an earlier paper, a complete solution is obtained and an optimum step design for centering of the piston is suggested. The axial speed resulting from an axial driving force is calculated, and some experimental results for pistons falling in a water filled tube are presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):681-686. doi:10.1115/1.3448883.

Experiments have been performed in a low turbulence wind tunnel to investigate the effect of tube pitch to diameter ratios, depth of bank, and Reynolds number on the parameters associated with resonant acoustic vibration in in-line tube banks. Results indicate that the depth of a bank is a significant factor in acoustic response characteristics and both the vortex shedding hypothesis and the turbulent buffeting hypothesis are shown to be inadequate for certain configurations. A combination of both hypotheses together with energy levels in the turbulence spectrum is suggested, although no definitive proof is offered.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):687-692. doi:10.1115/1.3448884.

A quasi two-dimensional method of singularities is developed for the analysis of flow through a centrifugal pump impeller of varying width. The theory is applied to a double suction centrifugal pump impeller and the results are compared with those obtained by existing two-dimensional and empirical methods. The suggested analysis gives satisfactory results at regimes close to the best efficiency point.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):693-698. doi:10.1115/1.3448885.

This paper complements an earlier paper by Karnitz, Potter, and Smith [1] (1974) in which the mechanism of the transition of a plane Poiseuille flow between parallel plates was examined. In the present investigation an experimental critical Reynolds number of 7500 (based on average velocity and channel height) was achieved at which the flow became unstable and transition to turbulence occurred. The linear theoretical Reynolds number of 7700 for instability appears to be a simple extrapolation of the present data as the disturbance intensity is allowed to shrink to zero. Bursting (an alternating turbulent to laminar flow) was observed at transition. The transient changes in the velocity profile when the flow is intermittent between a turbulent burst and a laminar flow were observed. The major portion of the burst profile is characteristic of the one-seventh power law profile common to fully turbulent flow. Disturbances were observed to amplify to turbulent bursts in the wall boundary layers in the entrance region of the channel in high Reynolds number flows (the Reynolds number must exceed the critical Reynolds number by a sufficient amount). Thus, the wall boundary layer becomes unstable, resulting in a transition to turbulence before the flow becomes fully developed at sufficiently high Reynolds numbers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):699-708. doi:10.1115/1.3448888.

In this study, it is theoretically shown that an elastically suspended Tainter-gate system with damping effects possesses the property of a self-excited oscillation, provided that the center of the curved weir plate is not in agreement with the location of the trunnion pin. Moreover, the theoretically obtained characteristics for the self-excited oscillation are confirmed with experiments, and it is shown that the theoretical results are in good agreement with experiments. It is concluded that when designing a dam system with Tainter-gates or other similar devices, more interest and attention to the dynamical behavior of Tainter-gates should be taken in order to prevent disasters such as that which occurred in Japan.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):709-716. doi:10.1115/1.3448889.

Interaction between a collapsing bubble and a free surface is investigated theoretically and experimentally using high speed photography. A limit value for the distance from the free surface to the center of the bubble reported to its radius is found. Under this limit the free surface is not disturbed before the end of the collapse in the first approximation. Only in this case, the method of images can be used and the free surface be replaced by an image-source, symmetrical with respect to the free surface, to the sink representing the bubble. Above this limit, precise measurements of bubble deformation and motion are given. Just after the collapse of the bubble begins, observations show a singular perturbation on the free surface, with the formation of a thin spike directed towards the air. In all cases, buoyancy has no time to take effect, and the bubble is repelled from the free surface while the re-entering jet, formed during collapse, is oriented away from it.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):717-726. doi:10.1115/1.3448892.

An experimental program has been carried out to determine the effects of wall interference on the drag and vortex shedding characteristics of cavitating two-dimensional triangular prisms and circular cylinders. The former shapes were chosen to eliminate effects of Reynolds number in interpreting the results. Direct pressure measurements were made to estimate the drag force. The vortex shedding frequency of the cavitating bodies was recorded with the help of a pressure transducer. The gap velocity u1 and the jet contraction velocity uj are shown to be the proper velocity scales to form the drag coefficients and Strouhal numbers for the bluff shapes tested. The drag coefficient was found to increase due to wall interference effects when partial cavitation conditions prevailed. The trend of the drag coefficient data indicated that wall interference effects are relatively small at very low cavitation numbers (σ → σch ) which correspond to choking conditions. As choking conditions are reached, the vortex shedding from the cavitating source becomes intermittent and finally vortex shedding ceases.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):727-730. doi:10.1115/1.3448893.

The quasi-steady, displacement dependent, whirling instability model of Connors [1] and Blevins [2] is re-examined to clarify the phase relationships involved. In particular, conditions required for the oscillations to occur at a given frequency are clearly established.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):732-736. doi:10.1115/1.3448896.

A survey of experimental work on mass, momentum, and energy transport at the axis of pipes relates the ratio of turbulent diffusivity to kinematic viscosity, ε/ν, to the flow Reynolds number. A single relationship is applicable for all three transport processes. Measurements of turbulent parameters also are surveyed and related to the flow Reynolds number. From a combination of the two sets of results a correlation is obtained between ε/ν and the turbulent Reynolds number, Rl , which is possibly of general validity for isotropic turbulence. The results are based upon transport transverse to the flow (“y” direction) and yield εy /ν = 11 Rly 0.65 for Rly > 100.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):737-743. doi:10.1115/1.3448897.

The three dimensional static density field was measured for transonic flow from a square nozzle using holographic interferometry. These measurements are presented in order to show the efficiency of this method for obtaining accurate experimental data of transonic flows. The accuracy of the measurement was estimated by operating the nozzle at a pressure ratio of 1.89 where the flow should expand to the ambient pressure with no afterexpansion effects. The standard deviation in the static density was approximately 1 percent over the isentropic (potential core) part of the flow. Data are also presented for a pressure ratio of 2.14 where afterexpansion effects are important. The method described represents a significant technical improvement in practical interferometry.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):745-752. doi:10.1115/1.3448900.
Abstract
Topics: Wakes , Propellers
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):753-757. doi:10.1115/1.3448901.

Two-dimensional flow past a rotating circular cylinder with uniform suction at the surface is considered. The method of solution follows closely that used by Glauert [1] and the problem is solved for the case in which there is no viscous flow separation from the cylinder surface. Expressions in terms of the ratio of the cylinder peripheral velocity and a suction parameter are obtained for the lift and torque. The results show that uniform suction has a limited effect on the lift; however, the torque increases with suction. Possible application of these results to wind power generation is briefly discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):758-762. doi:10.1115/1.3448902.

The paper describes the results of a finite-difference solution for the three-dimensional flow field generated by a round turbulent jet deflected by a main stream normal to the jet axis. The Reynolds stresses in the time-averaged momentum equations are calculated by a “two-equation turbulence model” in which differential equations are solved for the kinetic energy of turbulence and for the rate of its dissipation. The solution procedure employs an elliptic finite-difference scheme with the three velocity components and the pressure as the main dependent variables. Results are presented for the cases in which the ratio of the jet velocity to the main-stream velocity ranges from 2 to 10. The numerical predictions are shown to agree well with available experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):763-771. doi:10.1115/1.3448903.

This paper provides an improvement over the earlier theoretical analysis for a rigid, frictionless, cylindrical capsule moving parallel to the horizontal pipe wall (Garg and Round [1]) by taking into account the effects of friction between the capsule and pipe surfaces and of nonuniform clearance over the capsule length. It is found that these effects markedly affect the energy requirements suggesting, thereby, an optimum operation of the capsule-pipeline system. The theoretical results are also compared with the available experimental data.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

J. Fluids Eng. 1977;99(4):772-774. doi:10.1115/1.3448904.

A method is described for forming a flow nozzle whose cross section varies smoothly from one shape to another. The flow passage consists of fiber glass cloth saturated with epoxy resin cast in place about an elastic water filled rubber diaphragm. An example of such a nozzle, with a circular inlet section and a rectangular exit section was constructed and incorporated in a wind-tunnel design. The flow distribution, excluding the exit boundary layer, is uniform to within 0.5 percent. The exit boundary layer is laminar and steady and the discharge coefficient is 0.989.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):774-777. doi:10.1115/1.3448905.

The driven flow in a polar cavity has been analyzed using the complete Navier-Stokes equations formulated in terms of a stream function and vorticity. An alternating-direction implicit method, with careful treatment of the convective terms in the equations, is used to obtain the numerical solutions. Results are obtained for the stream function, vorticity, velocities and pressure for various values of the two characteristic parameters of the problem, namely, the flow Reynolds number Re and the aspect ratio of the cavity. The formulation is general and produces results for the driven rectangular cavity-flow problem as a special case. Good agreement is obtained between the present solutions for this case and available corresponding results. The overall features of the driven polar-cavity flow are found to be generally similar to those for the rectangular cavity.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):778-779. doi:10.1115/1.3448906.
Abstract
Topics: Creeping flow
Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1977;99(4):779-781. doi:10.1115/1.3448907.
Abstract
Topics: Gas flow
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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