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, Willem Jan van de Berg, Leo R M Maas
Published: 6 March 2005
Fluid Dynamics Research, Volume 36, pp 175-188; https://doi.org/10.1016/j.fluiddyn.2005.01.005

Abstract:
We present results from laboratory experiments in a ‘tidal tank’, demonstrating the resonant response of the Helmholtz mode in an almost-enclosed basin. In particular the dependence of the response curve (amplification of the tide in the basin relative to the tidal signal at sea as a function of forcing frequency) on the tidal amplitude due to the nonlinear influence of dissipation is observed. Although Lorentz’ linearization procedure for coping with this nonlinear effect was already developed at the beginning of the previous century, quantitative experimental validation in this context has not yet been provided. The experimental results presented in this paper show good agreement with theory. Keywords: Wave amplification; Harbor resonance; Quadratic friction; Head loss; Flow separation; Oscillatory flow; Lorentz’/equivalent linearization; Laboratory test
Kazuto Kuzuu, Katsuya Ishii, Kunio Kuwahara
Published: 31 August 1996
Fluid Dynamics Research, Volume 18, pp 165-182; https://doi.org/10.1016/0169-5983(96)00014-7

Abstract:
Premixed flame propagation of methane-air mixture in a closed tube is estimated through a direct numerical simulation of the three-dimensional unsteady Navier-Stokes equations coupled with chemical reaction. In order to deal with a combusting flow, an extended version of the MAC method, which can be applied to a compressible flow with strong density variation, is employed as a numerical method. The chemical reaction is assumed to be an irreversible single step reaction between methane and oxygen. The chemical species are CH4, O2, N2, CO2, and H2O. In this simulation, we reproduce a formation of a tulip flame in a closed tube during the flame propagation. Furthermore we estimate not only a two-dimensional shape but also a three-dimensional structure of the flame and flame-induced vortices, which cannot be observed in the experiments. The agreement between the calculated results and the experimental data is satisfactory, and we compare the phenomenon near the side wall with the one in the corner of the tube.
Knut H Bech, Helge I Andersson
Published: 31 July 1996
Fluid Dynamics Research, Volume 18, pp 65-79; https://doi.org/10.1016/0169-5983(96)00008-1

Abstract:
The structures and mechanisms for maintaining a high Reynolds shear stress throughout the core region of plane turbulent Couette flow were examined by means of databases originating from a direct numerical simulation. At the relatively low Reynolds number considered, the mean shear rate and some one-point statistics exhibited a non-negligible variation in the core region, which conflicted with the postulated homogeneity. The slope of the mean velocity profile was below a theoretically established lower bound for the limit of infinite Re. Analysis of the time-averaged and structural information obtained by conditional sampling showed that mean shear generation and velocity-pressure gradient correlations played a crucial role in the generation and annihilation of the Reynolds shear stress. It was moreover observed that strong, very localized velocity fluctuations in the wall-normal direction were essential in both processes. A simple conceptual model was proposed to explain the physical significance of the pressure field associated with quadrant 2 events.
Peter A Davies, Iftikhar Ahmed
Published: 30 April 1996
Fluid Dynamics Research, Volume 17, pp 237-274; https://doi.org/10.1016/0169-5983(95)00036-4

Abstract:
Results of laboratory experiments are described in which the motion of a round negatively buoyant jet discharged horizontally into a rotating homogeneous fluid has been investigated. Particle streak and dye photographs are presented (i) to demonstrate the complex three-dimensional flow fields generated by the discharge and (ii) to illustrate how the structure and time development of the flow field is controlled by the momentum (M) and buoyancy (B) fluxes of the discharge, the lateral location y* of the discharge source from the container wall and the rotation rate Ω of the system. The effects of background rotation are studied by contrasting flow patterns for rotating and non-rotating cases, with all other parameters being kept fixed. For cases in which the system is rotating, measurements of momentum-dominated and buoyancy-dominated discharges reveal that the downstream position xp and streamwise dimension Lp of the primary anticyclonic eddy corner circulation (formed by the deflection to the right of the descending jet) depend primarily upon the dimensionless distance y*/W (where W is the width of the channel). The influences of the dimensionless time Ωt and the relevant Coriolis parameter MΩ/B on xp and Lp are shown to be relatively weak. The counterpart dimensions Ls and xs of the secondary cyclonic eddy (generated by the shear associated with (i) the primary eddy and (ii) a boundary current formed along the right side wall of the channel) increase with time. Both dimensions are shown to scale satisfactorily with the inertial scale u0/Ω and the buoyancy/Coriolis scale g'/Ω2, where u0 and g' are the source discharge velocity and the modified gravitational acceleration, respectively. The speed uN of the nose of the wall boundary current is shown to be determined primarily by the dimensionless parameter MΩ/B; for values of MΩ/B greater than about 5, the quantity uN is determined primarily by the discharge velocity at the source. For values of MΩ/B less than about 5, the dimensionless nose velocity uNΩ/g' increases monotonically with increasing MΩ/B for all values of y*/W.
Peter A Davies, Yakun Guo, Don L Boyer,
Published: 31 December 1995
Fluid Dynamics Research, Volume 17, pp 27-47; https://doi.org/10.1016/0169-5983(95)00021-5

Abstract:
Results are presented from a series of laboratory experiments in which a flow has been generated in a linearly-stratified fluid (initially at rest in a cylindrical container of radius RT) by the impulsive steady azimuthal rotation of a flat, smooth, horizontal circular disk of radius Rd. Experiments have been conducted for a range of disk sizes Rd, disk rotation rates ω and buoyancy frequencies N0, and the spatial and temporal development of the motion and density fields (and mixing associated therewith) have been shown to be critically dependent on the ratio Rd/RT. For cases in which this ratio is close to unity, the principal mixing mechanisms affecting the flow development are shown to be (i) the localised overturning of fluid forced by the disk Ekman layers and confining sidewalls and (ii) shear-induced billow entrainment along the outer edge of the so-called primary interface between the upper, unmixed fluid and the lower, partially-mixed fluid regions adjacent to the disk. For the large disk case, for sufficiently high values of ω/N0, density gradients develop sequentially with time within the partially-mixed region and the forms of the associated density interfaces also change with time as the primary interface migrates vertically. At the other extreme, for small values of the ratio Rd/RT but otherwise identical external conditions, the container walls play a negligible role in the flow development and the initial mixing is achieved primarily by shear-induced billow overturning at the primary interface. A scaling analysis is advanced to predict the growth rate of the primary interface and the experimental data are shown to be in good agreement with the analysis.
Ruby Krishnamurti
Published: 31 August 1995
Fluid Dynamics Research, Volume 16, pp 87-108; https://doi.org/10.1016/0169-5983(95)00056-j

Abstract:
This is a report on observations of low frequency oscillations in turbulent Rayleigh-Benard convection, in the Rayleigh number (R) range 107–108, with Prandtl number (Pr) equal to 7. It has been known that for convecting layers with large aspect ratio A, a steady large scale flow sets in at R = 2 × 106. Tilted transient plumes embedded in this flow, and maintaining it through Reynolds stresses, drift in one direction along the bottom of the layer, and in the opposite direction along the top. At a fixed point near the bottom or top boundary, there is a variability associated with the passage of these plumes. We call this the high frequency variability. A new kind of organization is observed for 107 < R < 108; clusters of transient tilted plumes travel in a horizontal direction as coherent units. These clusters are separated from each other by quiescent zones with almost no plumes. Now at a fixed point near the bottom boundary, there is a low frequency variability associated with the passage of clusters, as well as the high frequency variability from the passage of plumes within the cluster. Quantitative information on this low frequency oscillation derived from space-time portraits and from temperature time series is presented.Heat flux measurements show a Nusselt number (N)-Rayleigh number relationship for 106 < R < 108 which is hysteretic for A = 12, but when the convecting layer is partitioned into 144 cells each with A = 1, hysteresis is not present and the N-R relationship then agrees with earlier results for single cells with A = 1.
Mitsuaki Funakoshi
Published: 30 April 1995
Fluid Dynamics Research, Volume 15, pp 251-269; https://doi.org/10.1016/0169-5983(94)00057-7

Abstract:
The evolution of uniform or non-uniform circular vorticity regions (of radius R) of Kármán-vortex-street type (with a distance h between the two rows, and a spacing d of the regions of the same sign) is examined numerically and analytically. The domain in the (, ) plane for which the vorticity regions merge to nearly parallel vorticity layers and the domain for which they continue to be localized are obtained using the discrete vortex method. Here = h/R and = d/R. Most of this localized behavior is qualitatively explained by the theory in which each neighboring vorticity region is replaced by a point vortex. Moreover, the increase in / from a small value due to an external transverse flow causes the transition to the nearly parallel vorticity layers if initial value is small. It is suggested that h/d just before the breakdown of the Kármán vortex street in experiments is larger than 0.365.
Christian Karcher, Ulrich Müller
Published: 31 January 1995
Fluid Dynamics Research, Volume 15, pp 25-42; https://doi.org/10.1016/0169-5983(94)00024-t

Abstract:
The coupled effects of thermal convection and solidification of a Single-component liquid in a porous medium are investigated. A rigorous two-parameter perturbation analysis is used to determine the effects on both the stability of the basic state of heat conduction and the stability of finite-amplitude convection. The analysis shows that due to the kinematic conditions at the solid/liquid interface, hexagons having upflow in the center are stable near the onset of convection. For sufficiently supercritical Rayleigh numbers, however, rolls are the only stable mode. The transition from hexagons to rolls is characterized by a hysteresis loop. Moreover, the transition is shown to be controlled by one particular critical value of the convection amplitude. This generic property holds for non-Boussinesq convection in bulk liquid-layers too.
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