EHD flows at large electric Reynolds numbers

The motion of a medium consisting of neutral particles and charged particles of single sign is studied under the assumption that the electric Reynolds number (R_q=u/bE) is large. We calculate the freezingin integral and the Bernoulli and Cauchy-Lagrange integrals, study the fluid motion in a stream tube, and formulate the boundary layer problem.     

Nearly singular two-dimensional Kolmogorov flows for large Reynolds numbers

We study the convergence of two-dimensional stationary Kolmogorov flows as the Reynolds number increases to infinity. Since the flows considered are stationary solutions of Navier-Stokes equations, they are smooth whatever the Reynolds number may be. However, in the limit of an infinite Reynolds number, they can, at least theoretically, converge to a nonsmooth function. Through numerical experiments, we show that, under a certain condition, some smooth solutions of the Navier-Stokes equations converge to a nonsmooth solution of the Euler equations and develop internal layers. Therefore the Navier-Stokes flows are nearly singular for large Reynolds numbers. In view of this nearly singular solution, we propose a possible scenario of turbulence, which is of an intermediate nature between Leray's and Ruelle-Taken's scenarios.     

Deconvolution‐based nonlinear filtering for incompressible flows at moderately large Reynolds numbers

We consider a Leray model with a deconvolution‐based indicator function for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under‐resolved meshes. For the implementation of the model, we adopt a three‐step algorithm called evolve–filter–relax that requires (i) the solution of a Navier–Stokes problem, (ii) the solution of a Stokes‐like problem to filter the Navier–Stokes velocity field, and (iii) a final relaxation step. We take advantage of a reformulation of the evolve–filter–relax algorithm as an operator‐splitting method to analyze the impact of the filter on the final solution versus a direct simulation of the Navier–Stokes equations. In addition, we provide some direction for tuning the parameters involved in the model based on physical and numerical arguments. Our approach is validated against experimental data for fluid flow in an idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion, as recommended by the U.S. Food and Drug Administration). Numerical results are in good quantitative agreement with the measured axial components of the velocity and pressures for two different flow rates corresponding to turbulent regimes, even for meshes with a mesh size more than 40 times larger than the smallest turbulent scale. After several numerical experiments, we perform a preliminary sensitivity analysis of the computed solution to the parameters involved in the model. Copyright © 2015 John Wiley & Sons, Ltd.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

Okra as a drag reducer for high Reynolds numbers water flows

The capability of a mixture of okra fiber and mucilage as drag reducer in high Reynolds number flows through a pipeline, in which the flux is maintained by a centrifugal pump with controlled rotation, is analyzed. A DR close to the maximum drag reduction asymptote, which is obtained for polymeric additives, was achieved when concentrations around 1600 ppm were used. The loss of efficiency of the solution over the number of passes through the system was almost the same of that observed for rigid materials like Xanthan Gum and Guar Gum, which suggest that the main cause of a decreasing drag reduction is the de-aggregation instead of mechanical degradation, commonly observed in flexible polymers. As expected, the material degrades biologically, but it seems that it is not a great problem for open systems, since such a degradation is perceptible only after 24 h. We strongly believe that this new bio-drag reducer can be an alternative to synthetic polymers or other biopolymers, since it is extremely cheap and easy to be obtained.     

Three-dimensionality of grooved channel flows at intermediate Reynolds numbers

 This paper describes the three-dimensional flow structure in grooved channels with different cavity lengths at intermediate Reynolds numbers. For steady flow, the three-dimensional effects are dominant near the side walls of the channel. However, after the onset of self-sustained oscillatory flow due to Tollmien–Schlichting waves as the primary instability, a secondary instability produces a three-dimensional flow with Taylor–Geortler-like vortical structure, at the bottom of the groove. This trend becomes more significant as the cavity length increases. Furthermore, the reason for three-dimensional flow is discussed using additional numerical analysis, and it is confirmed that the source of three-dimensional instability is the groove vortices due to the presence of side walls, rather than the channel traveling wave. Received: 7 September 1999/Accepted: 11 November 2000     

On the decay process of turbulence at large Reynolds and Peclet numbers

When fluctuating temperature field is considered to be super imposed on a general field of eddy turbulence, the early period decay phenomena in regard to velocity, temperature and velocity-temperature are guided by three dynamical equations that are obtained here in a straightforward manner. The equations so obtained are simplified for the case of homogeneous turbulence and subsequently for the case of homogeneous and isotropic turbulence.     

Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers

It has been observed by researchers in the past that vortex shedding behind circular cylinders can be altered, and in some cases suppressed, over a limited range of Reynolds numbers by proper placement of a second, much smaller, ‘control’ cylinder in the near wake of the main cylinder. Results are presented for numerical computations of some such situations. A stabilized finite element method is employed to solve the incompressible Navier–Stokes equations in the primitive variables formulation. At low Reynolds numbers, for certain relative positions of the main and control cylinder, the vortex shedding from the main cylinder is completely suppressed. Excellent agreement is observed between the present computations and experimental findings of other researchers. In an effort to explain the mechanism of control of vortex shedding, the streamwise variation of the pressure coefficient close to the shear layer of the main cylinder is compared for various cases, with and without the control cylinder. In the cases where the vortex shedding is suppressed, it is observed that the control cylinder provides a local favorable pressure gradient in the wake region, thereby stabilizing the shear layer locally. Copyright © 2001 John Wiley & Sons, Ltd.     

Ion current saturation on electric probes in plasma flows at low Reynolds numbers

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 159–163, January–February, 1990.     

The unsteady drag on a spherical bubble at large Reynolds numbers

The flow past a spherical bubble undergoing a rectilinear motion in the unsteady flow of an unbounded liquid medium is investigated. The liquid velocity field at infinity is assumed to be uniform and the Reynolds number to be large. The Strouhal number is taken to be of order unity. The velocity distribution is sought by superposition of a perturbation field on the potential flow past the bubble so that the flow field is divided into four regions, i.e. the external flow field where the potential flow holds, the boundary layer, the rear stagnation point region and the wake. The flow in the rear stagnation point region and the wake is assumed to be essentially inertial. The unsteady drag experienced by the bubble is calculated from the mechanical energy balance of the liquid.     

Diffusion flux to a distorted gas bubble at large Reynolds numbers

The diffusion flux to a distorted gas bubble situated in a uniform viscous incompressible fluid flow is determined for large Reynolds and Péclet numbers and finite Weber numbers. The bubble has the shape of an ellipsoid of revolution, oblate in the flow direction, making it possible to use the flow field derived by Moore [1] in the form of a two-term expansion with respect to the flow parameter =R^–1/2 (R is the Reynolds number; the zeroth term of the expansion corresponds to potential flow). The dependence of the diffusion flux onto the bubble surface on the Weber and Reynolds numbers is determined. The results of Winnikow [2] and Sy and Lightfoot [3] are thus generalized to the case of finite Weber numbers and a broader range of Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 70–76, July–August, 1976.     

On the stability of plane parallel viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability.     

Diffusion to a particle at large péclet numbers and small Reynolds and Hartmann numbers

A study is made of the influence of a homogeneous magnetic field on the mass transfer for a spherical solid particle and a liquid drop in a flow of a viscous electrically conducting fluid. The previously obtained [1] velocity field of the fluid is used to calculate the concentration distribution in the diffusion boundary layer, the density of the diffusion flux, and the Nusselt number, which characterizes the mass transfer between the particle and the surrounding medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 189–192, January–February, 1980.     

On the breakup of bubbles at high Reynolds numbers and subcritical Weber numbers

In this paper we propose a simplified two-dimensional model to describe some aspects of the turbulent breakage of bubbles at subcritical Weber numbers. In particular we focus on the breakup of bubbles owing to their interaction with an array of successive eddies, modeled by a train of straining flows. Our simulations show that, under certain conditions, a bubble accumulates energy due to its interaction with a sequence of turbulent structures until it eventually breaks, even if none of the eddies is sufficiently energetic to split the particle by itself. It is also shown that the different strain directions of the eddies acting on the surface of the bubble, and the resonance effect between their characteristic frequency and the natural oscillation frequency of the bubble immersed into the straining flow are the two key factors in the bubble deformation, and subsequent breakup mechanism. Moreover, the breakup patterns obtained from our simulations seem to agree qualitatively well with the experimental observations.     

Stability of viscoelastic shear flows in the limit of high Weissenberg and Reynolds numbers

We consider a limit of the upper convected Maxwell model where both the Weissenberg and Reynolds numbers are large. The limiting equations have a status analogous to that of the Euler equations for the high Reynolds number limit. These equations admit parallel shear flows with an arbitrary profile of velocity and normal stress. We consider the stability of these flows. An extension of Howard’s semicircle theorem can be used to show that the flow is stabilized if elastic effects are sufficiently strong. We also show how to analyze the long wave limit in a fashion similar to the inviscid case.     

Spin-down of a fluid in a low cylinder at large Reynolds numbers

The problem of the axisymmetric motion of a fluid between infinite disks is solved by the method of matched asymptotic expansions without introducing model assumptions. For the strongly nonlinear stage of spin-down solutions are found that correspond to initial states different from rigid-body rotation, when the boundary layer is not a Kármán layer. The experimental results obtained are in qualitative and quantitative agreement with the theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–46, May–June, 1986.The authors wish to thank A. M. Obukhov and F. V. Dolzhanskii for formulating the problem and for constructive discussion.