The prediction of spatially periodic flows using a finite‐volume model

A periodic boundary condition has been developed that can be used in conjunction with a specified flow rate to produce accurate results in spatially periodic geometries. This condition is useful in situations where the flow rate is known, or more importantly, in cases where the pressure gradient is not known a priori, such as in countercurrent flows. Using the present condition, the flow rate is imposed at the inlet in terms of a bulk velocity, but the velocity field evolves as part of the solution. The condition is formulated to be suitable for both fixed and moving periodic domains. For the case of a moving domain, a correction is introduced to account for changes in the instantaneous velocity through the periodic edges. Under periodic conditions, these corrections integrate to zero over a complete (temporal) period. The new periodic condition is shown to produce accurate results for flat and wavy‐walled channels under both induced flow and countercurrent conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical solution of steady free‐surface flows by the adjoint optimal shape design method

Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. Free‐boundary problems can be reformulated into optimal shape design problems, which can in principle be solved efficiently by the adjoint method. In this work we investigate the suitability of the adjoint shape optimization method for solving steady free‐surface flows. The asymptotic convergence behaviour of the method is determined for free‐surface flows in 2D and 3D. It is shown that the convergence behaviour depends sensitively on the occurrence of critical modes. The convergence behaviour is moreover shown to be mesh‐width independent, provided that proper preconditioning is applied. Numerical results are presented for 2D flow over an obstacle in a channel. The observed convergence behaviour is indeed mesh‐width independent and conform the derived asymptotic estimates. Copyright © 2003 John Wiley & Sons, Ltd.     

Energy spectra of the stable boundary layer: A theoretical model

Summary A derivation of spectral energy functions for stable atmospheric boundary layers is presented for a local similarity regime. Previous studies of this nocturnal atmospheric conditions were usually carried through purely kinematic modellizations. In this study, the atmospheric turbulence energy content is derived from a dynamical viewpoint. This is achieved through the use of the energy balance relation obtained by Rotta from Navier-Stokes equations. The result is an appropriate physical rooting of the spectral energy curves known as Kaimal’s Isopleths. The authors of this paper have agreed to not receive the proofs for correction.     

Hyperviscous diblock copolymer vesicles

Giant vesicles prepared from the diblock copolymer polybutadien-b-polyethyleneoxide (PB-PEO) exhibit a shear surface viscosity, which is about 500 times higher than those found in common phospholipid bilayers. Our result constitutes the first direct measurement of the shear surface viscosity of such polymersomes. At the same time, we measure bending and stretching elastic constants, which fall in the range of values typical for lipid membranes. Pulling out a tether from an immobilized polymersome and following its relaxation back to the vesicle body provides an estimate of the viscous coupling between the two monolayers composing the polymer membrane. The detected intermonolayer friction is about an order of magnitude higher than the characteristic one for phospholipid membranes. Polymersomes are tough vesicles with a high lysis tension. This, together with their robust rheological properties, makes them interesting candidates for a number of technological applications. Received 2 March 2001 and Received in final form 15 February 2002     

Experiments in the mixed convection regime in an isothermal open cubic cavity

A detailed experimental study of the heat transfer in an open isothermal cubic cavity for mixed natural and forced convection is reported. First the experimental model with a temperature control system, the experimental procedure, and the method for determination of the convective heat losses from the experimental data are presented. After presentation of the experimental conditions for the three models of different sizes that were tested, dimensionless parameters (Gr, Re, and Nu numbers) are introduced to generalize the results. In this way, the main influence of natural convection can be separated, and, using regressional analysis, a general interdependence among Nusselt, Reynolds, and Grashof numbers can be obtained.

The local heat transfer effects are indicated by maps of local heat transfer coefficient distributions in the cavity for different orientations of the model. To reduce the effects of convective heat transfer, the influence of different types of front masks were analyzed. The usefulness of the experimental results obtained is shown by estimating the convective heat losses for the central solar receiver of the French solar power plant THEMIS.     

Thermocapillary Vortices Induced by a Light Beam near a Bubble Surface in a Hele-Shaw Cell

This paper studies thermocapillary vortices induced by local heating of a bubble surface in a Hele-Shaw cell by a light beam. It is found that the vortex rotation frequency and its depth depend on the distance from the light-beam projection onto the layer to the bubble boundary. The surface velocity of the thermocapillary flow is calculated using the balance of the near-surface and return flows of the thermocapillary vortex and the equality of capillary and dynamic pressures. It is shown that a decrease in the surface velocity and the vortex rotation frequency with increase in the distance from the light beam to the bubble surface is due to a decrease in the temperature gradient between the illuminated and cold poles of the bubble.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 93–99, September–October, 2005.     

An algorithm for rotating axisymmetric flows: model,validation and industrial applications

The study of axisymmetric flows is of interest not only from an academic point of view, due to the existence of exact solutions of Navier–Stokes equations, but also from an industrial point of view, since these kind of flows are frequently found in several applications. In the present work the development and implementation of a finite element algorithm to solve Navier–Stokes equations with axisymmetric geometry and boundary conditions is presented. Such algorithm allows the simulation of flows with tangential velocity, including free surface flows, for both laminar and turbulent conditions. Pseudo‐concentration technique is used to model the free surface (or the interface between two fluids) and the k–ε model is employed to take into account turbulent effects. The finite element model is validated by comparisons with analytical solutions of Navier–Stokes equations and experimental measurements. Two different industrial applications are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

Corner flow of a suspension of rigid rods

Stress singularities in the neighbourhood of sharp corners can be a source of severe problems in the numerical simulation of non-Newtonian flows leading to loss of convergence with grid refinement (G.G. Lipscombe, R. Kennings and M.M. Denn, J. Non-Newtonian Fluid Mech., 24 (1987) 85 [1]). For Newtonian flows the nature of this singularity is given by the analysis of Dean and Montagnon (W.R. Dean and P.E. Montagnon, Phil. Trans. R. Soc. London, Ser. A., 308 (1949) 199 [2]) in terms of similarity solutions. In this paper we extend this similarity analysis to a suspension of rigid rods. In the limit of nearly full extension the FENE constitutive model has the same behaviour as such a suspension. Our analysis predicts the possibility of lip vortices but their behaviour is somewhat inconsistent with those observed experimentally.     

A note on nonlinear stability of plane parallel shear flows

We present a generalized energy functional E for plane parallel shear flows which provides conditional nonlinear stability for Reynolds numbers Re below some value ReE depending on the shear profile. In the case of the experimentally important profiles, viz. combinations of laminar Couette and Poiseuille flow, ReE is shown to be at least 174.