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Critical Reynolds Number (critical + reynold_number)
Selected AbstractsNumerical simulation of turbulent flow through series stenosesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003T. S. Lee Abstract The flow fields in the neighbourhoods of series vascular stenoses are studied numerically for the Reynolds numbers from 100 to 4000, diameter constriction ratios of 0.2,0.6 and spacing ratios of 1, 2, 3, 4 and ,. In this study, it has been further verified that in the laminar flow region, the numerical predictions by k,, turbulence model matched those by the laminar-flow modelling very well. This suggests that the k,, turbulence model is capable of the prediction of the laminar flow as well as the prediction of the turbulent stenotic flow with good accuracy. The extent of the spreading of the recirculation region from the first stenosis and its effects on the flow field downstream of the second stenosis depend on the stenosis spacing ratio, constriction ratio and the Reynolds number. For c1 = 0.5 with c2 , c1, the peak value of wall vorticity generated by the second stenosis is always less than that generated by the first stenosis. However, the maximum centreline velocity and turbulence intensity at the second stenosis are higher than those at the first stenosis. In contrast, for c1 = 0.5 with c2 = 0.6, the maximum values at the second stenosis are much higher than those at the first stenosis whether for centreline velocity and turbulence intensity or for wall vorticity. The peak values of the wall vorticity and the centreline disturbance intensity both grow up with the Reynolds number increasing. The present study shows that the more stenoses can result in a lower critical Reynolds number that means an earlier occurrence of turbulence for the stenotic flows. Copyright © 2003 John Wiley & Sons, Ltd. [source] Linear stability analysis of flow in a periodically grooved channelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003T. Adachi1 Abstract We have conducted the linear stability analysis of flow in a channel with periodically grooved parts by using the spectral element method. The channel is composed of parallel plates with rectangular grooves on one side in a streamwise direction. The flow field is assumed to be two-dimensional and fully developed. At a relatively small Reynolds number, the flow is in a steady-state, whereas a self-sustained oscillatory flow occurs at a critical Reynolds number as a result of Hopf bifurcation due to an oscillatory instability mode. In order to evaluate the critical Reynolds number, the linear stability theory is applied to the complex laminar flow in the periodically grooved channel by constituting the generalized eigenvalue problem of matrix form using a penalty-function method. The critical Reynolds number can be determined by the sign of a linear growth rate of the eigenvalues. It is found that the bifurcation occurs due to the oscillatory instability mode which has a period two times as long as the channel period. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the validity of the perturbation approach for the flow inside weakly modulated channelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002H. Zhou The equations governing the flow of a viscous fluid in a two-dimensional channel with weakly modulated walls have been solved using a perturbation approach, coupled to a variable-step finite-difference scheme. The solution is assumed to be a superposition of a mean and perturbed field. The perturbation results were compared to similar results from a classical finite-volume approach to quantify the error. The influence of the wall geometry and flow Reynolds number have extensively been investigated. It was found that an explicit relation exists between the critical Reynolds number, at which the wall flow separates, and the dimensionless amplitude and wavelength of the wall modulation. Comparison of the flow shows that the perturbation method requires much less computational effort without sacrificing accuracy. The differences in predicted flow is kept well around the order of the square of the dimensionless amplitude, the order to which the regular perturbation expansion of the flow variables is carried out. Copyright © 2002 John Wiley & Sons, Ltd. [source] Results of a modified PROMISE experimentASTRONOMISCHE NACHRICHTEN, Issue 7 2008F. Stefani Abstract The PROMISE experiment relies on the fact that the critical Reynolds number for the appearance of the magnetorotational instability (MRI) in liquid metal flows drastically decreases when the purely axial magnetic field is replaced by a helical one. We report the results of a modified version of this experiments in which the radial electrical boundary conditions are changed. Special focus is laid on the role of the radial jet region where the two Ekman vortices from the top and the bottom meet each other. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Nonlinear simulations of magnetic Taylor-Couette flow with currentfree helical magnetic fieldsASTRONOMISCHE NACHRICHTEN, Issue 9 2006J. Szklarski Abstract Themagnetorotational instability (MRI) in cylindrical Taylor-Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (106) (axial field only) to O (103) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ,50 Gauss and axial current ,4 kA for the toroidal field. It is sufficient that the vertical velocity uz of the flow can be measured with a precision of 0.1 mm/s. We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Linear stability analysis of oscillating Ekman boundary layersPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Martin Withalm The analysed Ekman layer is generated in a fluid layer rotating around an axis normal to its two bounding rigid plates. One of the plates is stationary, the other moving at certain Reynolds numbers. An additional oscillation is added to the moving plate at different amplitudes and frequencies. The linear stability of this system is determined via a Floquet analysis and a Galerkin-approximation of the corresponding Navier-Stokes-Equations. If the frequencies of the oscillations are small the critical Reynolds numbers of the Type I and Type II instabilities do not differ much from steady Ekman layers. Also for a purely oscillating system the critical values of the instabilities are almost consistent with those for a steady system. Interestingly, for higher frequencies the Type II instability does not appear any more. Instead the boundary layer becomes unstable only in terms of a Type I instability. In comparison with findings of other authors these results seem to be quite reasonable. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] The effect of particle shape on pipeline friction for newtonian slurries of fine particlesTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2000Jason Schaan Abstract Experiments have been conducted to assess the effect of particle shape on pipeline friction in turbulent flow, using laboratory pipelines of nominal diameter 50 mm and 150 mm. The experiments were intended to examine the extent to which a fluid model is appropriate for slurries of this type, especially at high solids concentrations. The experiments confirm that fluid friction at low and moderate solids concentrations is proportional to slurry density, with particle shape being of minor importance. At high solids concentrations, additional increases in friction are observed and these depend upon the ratio of the solids concentration to the maximum settled concentration. Although this friction increase is qualitatively similar to that which would result from increased slurry viscosity, the evidence suggests that particle-wall contact is the mechanism. However, the transition from turbulent to laminar flow indicates that an effective viscosity should be used in calculating critical Reynolds numbers. Afin d'évaluer l'effet de la forme des particules sur le frottement dans les pipelines en régime turbulent, des expériences ont été menées avec des pipelines de laboratoire d'un diamétre nominal de 50 mm et de 150 mm. Le but de ces expériences était de voir jusqu'à quel point un fluide modèle est approprié pour ce type de suspensions, en particulier à de fortes concentrations de solides. Les expériences confirment que le frottement du fluide à des concentrations de solides faibles ou moyennes est proportionnel à la masse volumique des suspensions, la forme des particules étant de peu d'importance. À de fortes concentrations de solides, on observe un accroissement supplémentaire du frottement qui est lié au rapport entre la concentration de solides et la concentration sédimentée maximum. Bien que cette augmentation du frottement soit d'un point de vue qualitatif semblable à ce qu'il réulterait d'une viscosité accrue des suspensions, selon toutes les apparences le mécanisme réside dans le contact particules-paroi. Cependant, la transition de l'écoulement turbulent à l'écoulement laminaire indique qu'une viscosité effective devrait ##etre utilisée dans le calcul des nombres de Reynolds critiques. [source] | ||||||||||