Wake interference behind two flat plates normal to the flow: A finite-element study

A finite-element model of the Navier-Stokes equations is used for numerical simulation of flow past two normal flat plates arranged side by side at Reynolds number 80 and 160. The results from this simulation indicate that when the gap between the plates is twice the width of a single plate, the individual wakes of the plates behave independently, with the antiphase vortex shedding being dominant. At smaller gap sizes, the in-phase vortex shedding, with strong wake interaction, is favored. The gap flow in those cases becomes biased, with one of the wakes engulfing the other. The direction of the biased flow was found to be switching at irregular intervals, with the time histories of the indicative flow parameters and their power spectra resembling those of a chaotic system.This research was sponsored by NASA-Johnson Space Center under Grant NAG9-449, by NSF under Grant MSM-8796352, and by the U.S. Army under Contract DAAL03-89-C-0038.     

Drag on a body placed between two parallel plates in a hele-shaw flow

In [1], the drag was found that acts on a circular gas bubble between two parallel plates in a slow viscous flow. In the present paper, the problem considered in [1] is solved for a body of arbitrary shape under the assumption that the conditions of a Hele-Shaw flow are satisfied. An expression is obtained for the drag containing only one coefficient in the expansion of the complex potential in a Laurent series.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–162, September–October, 1979.     

Lock-on characteristics behind two side-by-side cylinders of diameter ratio two at small gap ratio

The lock-on characteristics, the detailed interactions and downstream evolutions of the wakes behind side-by-side cylinders of unequal diameter (D/d?=?2), spaced by a gap ratio 0.75 (G/D?=?0.75), are investigated at Reynolds number 600 by the dye flow visualization, laser Doppler anemometry (LDA) and particle image velocimeter (PIV) velocity measurements. The lock-on frequency bands are studied by LDA and PIV at Reynolds number 2,000. The D, d and G are the diameters of the large, the small cylinders and the net gap between two cylinders, respectively. Periodic excitations, in form of rotary oscillation about the cylinder center, are applied to the large cylinder with the same amplitude. It is found that while the large cylinder is excited, two lock-on frequency bands of the wake behind the large cylinder are detected. These two lock-on frequency bands correspond to the primary and the one-third sub-harmonic lock-on of the wake behind large cylinder, respectively. These two lock-on frequency bands distribute symmetrically about the fundamental and the third superharmonic of the natural shedding frequency behind a single cylinder at the same Reynolds number. The left-shifted frequency band (1.8?≤?f _e /f _os ?≤?2.0) is not considered as a locked-on frequency band because the phase difference between two excitation frequencies across f _e /f _os ?=?2.0 vary significantly. While the wake behind the large cylinder is locked-on at f _e /3 (or f _os ), the gap flow becomes unbiased and the frequency of the wake behind small cylinder remains around the natural shedding frequency. Thus, the frequency band of 3.0?≤?f _e /f _os ?≤?3.22 is also not locked-on because the phase difference in the narrow wake excited at f _e /f _os ?=?2.93 and 3.07 changes significantly. Note f _e and f _os denote the excitation frequency and the natural shedding frequency behind a single large cylinder, respectively.     

Numerical computation of the flow around two square cylinders arranged side-by-side

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A transition phenomenon of ice formation in water flow between two horizontal parallel plates

Experiments have been performed to investigate the icetransition profiles and heat-transfer characteristics for water flows between two horizontal parallel plates. The experiments are carried out under the condition that upper plate is cooled at uniform temperature kept less than freezing temperature of water, while the lower plate is heated at uniform temperature kept higher than the temperature of water flow. The temperatures of the upper and lower plates range from ?8 to ?14°C and from 10 to 60 °C, respectively, with inlet-water temperature varied from 1.5 to 4.5 °C. The cooling and heating temperature ratios, θ_c and θ_h, are ranging from 1.78 to 9.33 and from 1.22 to 39, respectively. By using three kinds of heightH of 16, 30 and 40 mm between the horizontal parallel plates, the Reynolds and Grashof numbers are varied from 3.2 × 10² to 1.5 × 10⁴ and from 3.4 × 10³ to 8.97 × 10⁶, respectively. As a result of this investigation two ice-transition modes are observed. The first ice-transition mode is due to an interruption of upper and lower thermal boundary layers, while the second mode is due to an instability of laminar boundary layer formed on water-ice interface. In order to determine the kind of ice-transition mode, criterion correlation formulas including the Reynolds numberRe _H , Grashof numberGr _H , and heating temperature ratio θ_h are determined and may be written as follows: For thermal icetransition mode (th.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23<1.6×10^?3 and for hydrodynamical ice-transition mode (hy.I.T.M.)Re _H /(Gr _H ·θ _h )^0.23>2.3×10^?3 By introducing the freezing parameterB _f , correlation equations for local and mean Nusselt numbers along the water-ice interface at steady-state condition are determined. From the current experimental results it is found that the local Nusselt number may be described as the following equation:Nu _x =0.835 Re _H ^0.278 · B _f ^0.834 ·x/H)^?0.139     

Large eddy simulations of the flow past two side-by-side circular cylinders

A LES Large Eddy Simulation is performed to study the flow past two side-by-side circular cylinders at a Reynolds number of 5800, based on the free-stream velocity and the cylinders diameter. The centre-to-centre transverse pitch ratio T/D is varied from 1.5 to 3. Both cylinders are slightly heated and the small amount of heat can be treated as a passive scalar. The numerical simulations are in good agreement with experimental observations.     

Flow induced oscillation of two rigid rectangular plates in a side-by-side configuration

The present work is an experimental study of two oscillating rigid plates placed in side-by-side configuration, hinged at their leading edges, subjected to low subsonic flow. This problem is investigated using smoke-wire flow visualization, hot-wire anemometry, and time resolved particle image velocimetry. It is found that beyond a critical Reynolds number, the plates set into oscillatory motion. This critical Reynolds number depends on the gap between the plates. It is also seen that this value of Reynolds number, at lower values of gap to thickness ratio (<7) is significantly higher than that of the single plate configuration value. The frequency and amplitude of the oscillating plates at various gaps and Reynolds numbers have been studied and compared with the characteristics of an oscillating single plate. It is also found that depending on the gap and acceleration of the free-stream, there exist two modes of oscillation - (i) in-phase and (ii) out-of-phase. For gap to thickness ratio less than 10, only in-phase oscillations take place for all values of free-stream velocity considered in the present work, whereas, when this ratio is greater than 10, the mode of oscillation depends on the initial conditions up to a certain free-stream velocity, beyond which the plates switch to in-phase mode. Smoke wire flow visualization technique along with time resolved particle image velocimetry reveal that the vorticity distributions around the plates are responsible for the initiation of the two modes of oscillations.     

Interaction of gap flow with flapping dynamics of two side-by-side elastic foils

Two side-by-side elastic foils placed in an axial flow with the leading edges clamped lose their stability to exhibit in-phase or out-of-phase modes due to the proximity induced effects. Of particular, the passive out-of-phase flapping mode typically represents the clapping mechanism exhibited by biological organisms such as jellyfish and squid for swimming via jet propulsion. An impact of the viscous gap-flow dynamics on such passive flapping modes and vice versa is not well understood for the side-by-side elastic foil system. In the present work, we explore the mutual interaction of two side-by-side elastic foils performing flapping motion with the viscous gap-flow via a high-order finite element based fluid-elastic formulation with an exact tracking of fluid-foil interface. We show that the gap-flow exhibits pulsating flow with higher net drag for the passive out-of-phase coupled mode compared to the in-phase flapping where it exhibits uniform flow rate. Three distinct gap-flow velocity patterns are identified as functions of the coupled flapping modes: (i) unsteady symmetrical gap-flow with variable gap for the out-of-phase, (ii) unsteady alternating biased asymmetrical gap-flow with a uniform gap for the in-phase, and (iii) unsteady alternating biased asymmetrical gap-flow with variable gap for the mixed in-phase and out-of-phase. We examine the role of the gap-flow on the coupled fluid-elastic instability and the passive flapping modes. Two side-by-side elastic foils can experience significantly lower drag compared to their single foil counterpart and the two side-by-side rigid foils by undergoing static outward deformation. We utilize this phenomenon to understand the greater propensity of the flapping instability of the two side-by-side elastic foils in contrast to their single foil counterpart. We show that the coupled system does not exhibit the out-of-phase flapping if there is no gap-flow between the foils. We also find that two elastic foils when placed in proximity to each other always lose their stability to exhibit the out-of-phase coupling irrespective of whether the fully developed flapping exhibits in-phase or the out-of-phase flapping. The transition from the initial out-of-phase to the in-phase flapping is characterized by the loss of symmetry in the jet-like gap flow at the exit area of the side-by-side foils.     

Numerical solution to the shearing flow of granular materials between two plates

We study the shearing flow of granular materials between two horizontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (DOE Report, DOE/PETC/TR-90/3, 1990). The material coefficients such as viscosity and normal stress coefficients are based on the model of Boyle and Massoudi (Int. J. Eng. Sci 28 (1990) 1261). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.     

The flow of incompressible immiscible fluids between two plates

Summary The flow of layers of different heights of n incompressible immiscible fluids between two plates has been considered and it has been shown that whatever be the number of fluids and whatever be their heights, a unique velocity maximum always exists and a formula for finding the layer in which this maximum occurs has been given. For the particular case of two layers it has been shown that the curve of total flux against the ratio of the heights of the fluids has always a point of inflexion. Further this ratio has been determined so that the fluxes of the two fluids are equal.     

Numerical simulation of fluid flow of two rotating side-by-side circular cylinders by Lattice Boltzmann method

A numerical investigation of the two-dimensional laminar flow around side-by-side rotating circular cylinders using Lattice Boltzmann method is conducted. The effects of variation of rotational speed ratio β and different gap spacings g* at Reynolds number of 100 are studied. A various range of rotational speed ratio 0 ≤ β ≤ 2 for four different gap spacings of 3, 1.5, 0.7 and 0.2 are investigated. Flow conditions and its characteristics, such as lift and drag coefficients and Strouhal number, is studied. The results indicated that as β increases, the flow changes its condition from periodic to steady after a critical rotational speed. Results also indicated that variation of the gap spacing and rotational speed has significant effect on wake pattern. Wake pattern in turn has significant effect on the Strouhal number. Finally, the result is compared with experimental and other numerical data.     

Viscoplastic flow between two approaching or parallel circular plates

The problem of the flow of a viscoplastic medium between two parallel circular plates in translatory coaxial relative motion is solved. The Bingham model [1] of a viscoplastic medium is assumed. The problem is solved in the inertialess thin layer approximation [2] for arbitrary values of the viscosity coefficient and yield stress.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 9–17, January–February, 1996.     

Transient free convection flow between two vertical parallel plates

Transient free convection flow between two infinite vertical parallel plates has been investigated and good agreement was found between the results for large values of time and the well known ones for the steady-state problem.