The bulk electroviscous effect

Electroviscous stresses arise as hydrodynamic flows disturb the ionic (Debye) clouds that screen charged surfaces in electrolyte solutions. The contribution thereof to the effective bulk viscosity (also known as the second or volume viscosity) of two-phase suspensions is quantified here. Specifically, the bulk viscosity of two model suspensions is calculated: (1) a dilute dispersion of rigid charged spherical particles immersed in a compressible electrolyte that undergoes uniform dilatation and (2) a dilute suspension of charged gas bubbles expanding uniformly in an incompressible electrolyte. In both cases, it is assumed that the fluid flow only slightly drives the Debye cloud out of equilibrium, which formally requires that the ratio of the ion diffusion to flow time scales—a Péclet number—is small. For a suspension of rigid particles, the electroviscous contribution to the effective bulk viscosity is proportional to the particle volume fraction and decreases monotonically as the ratio of the particle radius to the Debye length increases. Similar behavior is well known for the electroviscous contribution to the effective shear viscosity of a dilute hard-sphere suspension; a quantitative comparison between the bulk and shear viscosities is made. In contrast, the electroviscous contribution to the bulk viscosity of a dilute suspension of bubbles is independent of the bubble volume fraction and attains a finite value in the limit of vanishing Debye length.     

On the impedance of the pipe in laminar and turbulent pulsating flows

The response of a facility, consisting of a valveless reciprocating pump, a large settling chamber and a long straight smooth pipe, to a periodic change in the volume was analysed. The impedance of the pipe was estimated in both laminar and turbulent flow regimes under otherwise identical flow conditions. A good agreement with theory was obtained for the laminar flow. The estimate of the pipe impedance from the experimental data in turbulent flow was based on the momentum equation as well as on the measured resonant frequency of the system. These independent methods show that the inertance of the pipe has a qualitatively different behavior in laminar and turbulent flow regimes.     

Further understanding of twisted tape effects as tube insert for heat transfer enhancement

Tube inserts are used as heat transfer enhancement tool for both retrofit and new design of shell and tube heat exchangers. This paper discusses and reviews the characteristics and performance of twisted tapes. The theory and application are also addressed. Industrial case study was selected to illustrate the behaviour effect that the twisted tapes impose at various laminar, transition and turbulent flow regions. This effect was demonstrated by changing the inside tube diameter and twist ratio through evaluating selected exchanger design parameters such as: local heat transfer coefficient, friction factor and pressure drop. Testing the exponent powers for Re and Pr at both laminar and turbulent regions were carried out. General design considerations are outlined for the use of twisted tapes in shell and tube heat exchangers.     

Analytical solutions of the helical flow of non newtonian fluid in eccentric annular space

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Laminar/turbulent oscillating flow in circular pipes

A two-dimensional oscillating flow analysis was conducted simulating the gas flow inside Stirling engine heat exchangers. Both laminar and turbulent oscillating pipe flow were investigated numerically for Re_max = 1,920 (Va = 80), 10,800 (Va = 272), 19,300 (Va = 272), and 60,800 (Va = 126). The results are here compared with experimental results of previous investigators. Predictions of the flow regime on present oscillating flow conditions are also checked by comparing velocity amplitudes and phase difference with those from laminar theory and quasi-steady profile. A high Reynolds number k-ε turbulence model was used for turbulent oscillating pipe flow. Finally, the performance of the k-ε model was evaluated to explore the applicability of quasi-steady turbulent models to unsteady oscillating flow analysis.     

FINITE ELEMENT SOLUTIONS OF LAMINAR AND TURBULENT MIXED CONVECTION IN A DRIVEN CAVITY

This paper presents laminar and turbulent mixed convection solutions of a driven cavity flow using the finite element method. For the laminar flow, distributions of velocity and temperature with and without the effect of buoyancy force are presented and compared. For the turbulent flow, governing partial differential equations of the thermal turbulence two-equati on model and kinetic turbulence two-equation model are used. Corresponding results such as kinetic eddy diffusivity, kinetic eddy energy, thermal eddy energy and their dissipations are presented.     

Asymmetry in transitional pipe flow of drag-reducing polymer solutions

New experimental data are presented and discussed for fully developed pipe flow of shear-thinning, viscoelastic polymer solutions in the transitional regime between laminar and turbulent flow. The data confirm that such transitional flows exhibit significant departures from axisymmetry in contrast to the fully developed pipe flow of Newtonian fluids or both laminar and turbulent flows of such drag-reducing liquids. The azimuthal structure of the asymmetry is investigated together with its axial development and also the velocity fluctuation levels. These data do not lead to an explanation for the asymmetry but do suggest that the influence of the flow geometry both upstream and downstream can be ruled out.     

Influence of vent positions on smoke clearance from a room

Results of solutions to the equations governing the clearance of smoke in laminar and in turbulent flow from a single rectilinear room are presented fof five different vent arrangements. These results show that the average smoke concentration in the room decreases in an approximately exponential manner with time at a rate that depdends much more on room geometry (vent positions in the present case) than on whether the flow is laminar or turbulent. The benefit of this observation is that, provided the clearance air jet is disrupted by impingement on a solid surface within the room, the analysis of smoke movement can for many practical purposes be limited to consideration of laminar flow only. An exceptional case is when the jet is allowed to take a straight line path between the inlet and outlet vents. Here in the absence of the large scale eddies caused by jet impingement, the smaller scale eddies of turbulent flow become relatively important as a mixing mechanism and give higher clearance rates than in laminar flow. Even so, this type of geometry is best avoided. The appearance of the jet is shown in a graphic presentation of the numerical results for laminar flow.     

An analysis of turbulent free convection about bodies of arbitrary geometrical configurations

A general solution method is suggested for the prediction of the turbulent free convection heat transfer from curved surfaces. The method which may be viewed as a generalized version of the Eckert-Jackson method for the isothermal plate, is designed to deal with bodies of arbitrary geometrical configurations. The surface wall temperature is also allowed to vary in the streamwise direction in an arbitrary fashion. For the illustrative purpose, the calculations are carried out for the turbulent free convection about the horizontal circular cylinder, and the results are compared with the existing empirical formula. The flow transition from laminar to turbulent is also predicted by matching the laminar and turbulent solutions.     

Nichtisotherme ebene Freistrahlen unter Schwerkrafteinfluß

Higher-order boundary layer theory is used to study the behaviour of nonisothermal laminar and turbulent free jet flows. In addition to the Prandtl boundary layer equations, an equation is used to describe the equilibrium of forces normal to the flow direction. This equilibrium exists between the buoyancy forces caused by gravity and the centrifugal forces resulting from the curvature in the flow. The proper selection of reference values permits the characteristics of the jet flow to be expressed as universal functions in which only the initial jet orientation and the Prandtl number in the case of laminar flow are input parameters. When the volume flow is given in addition to the momentum and thermal energy, the characteristic parameter are the Archimedes number for turbulent flow and the modified Archimedes number for laminar flow. The jet flow is calculated using an integral method in which the eddy viscosity and the turbulent Prandtl number are given as functions of the local Archimedes number. Comparison of experimental data from the literature and from our laboratory on nonisothermal free jets with the theoretical results, show satisfactory agreement. The universal diagrams given in the paper are valid forall plane laminar (Pr=0.7) and turbulent nonisothermal jets.     

Prediction of periodic boundary layers

A relatively simple, yet efficient and accurate finite difference method is developed for the solution of the unsteady boundary layer equations for both laminar and turbulent flows. The numerical procedure is subjected to rigorous validation tests in the laminar case, comparing its predictions with exact analytical solutions, asymptotic solutions, and/or experimental results. Calculations of periodic laminar boundary layers are performed from low to very high oscillation frequencies, for small and large amplitudes, for zero as well as adverse time-mean pressure gradients, and even in the presence of significant flow reversal. The numerical method is then applied to predict a relatively simple experimental periodic turbulent boundary layer, using two well-known quasi-steady closure models. The predictions are shown to be in good agreement with the measurements, thereby demonstrating the suitability of the present numerical scheme for handling periodic turbulent boundary layers. The method is thus a useful tool for the further development of turbulence models for more complex unsteady flows.     

The rheology of Hydroxy-propylguar (HPG) solutions and its influence on the flow through a porous medium and turbulent tube flow,respectively (Part 1)

The rheology of aqueous HPG solutions in the range 100 wppm to 5000 wppm is investigated. The flow through a porous medium and turbulent tube flow, respectively, of these solutions is studied as well. Especially with respect to the higher concentrations, the data correlate nicely only after the effect of shear is extracted, i.e., after the variable viscosity is taken into account. This is accomplished by working with an apparent viscosity _c , defined such that, the Hagen Poiseuille law (with _c ) holds in laminar tube flow.     

基于滑移理论的超疏水表面减阻性能分析

采用滑移理论计算和数值模拟方法研究超疏水表面的减阻性能.层流流动状态的数值模拟和理论计算结果的一致性较好,并可证明滑移速度与通道内流体速度之比与无量纲压降比的数量级相当;湍流状态的数值仿真结果表明,在目前可实现的滑移速度范围内,超疏水表面对水下航行器的流体阻力影响不显著.     

Method of Lines for Transient Flow Fields

A computational fluid dynamics (CFD) code based on the method of lines (MOL) approach was developed for the solution of transient, two-dimensional Navier-Stokes equations for incompressible separated internal flows in complex rectangular geometries. The predictive accuracy of the code was tested by applying it to the prediction of flow fields in both laminar and turbulent channel flows with and without sudden expansion, and comparing its predictions with either measured data or numerical results available in the literature. The predicted flow fields were found to be in favorable agreement with those available in the literature for laminar channel flow with sudden expansion and turbulent channel flow with Re=6600. The code was then applied to the prediction of the highly turbulent flow field in the inlet flue of a heat recovery steam generator (HRSG). The predicted flow field was found to display the same trend with the experimental findings and numerical solutions reported previously for a turbulent diverging duct. As the code uses the MOL approach in conjunction with (i) an intelligent higher-order spatial discretization scheme, (ii) a parabolic algorithm for pressure, and (iii) an elliptic grid generator using a body-fitted coordinate system for complex geometries, it provides an efficient algorithm for future direct numerical simulation (DNS) applications in complex rectangular geometries.     

Numerical predictions of flows over backward-facing steps

Predictions are reported for two-dimensional, steady, incompressible flows over rearward-facing steps for both laminar and turbulent conditions. The standard k-? turbulence model was used for the turbulent flow. Attention was focused on obtaining accurate solutions to the differential equations. It is concluded that some of the serious discrepancies that have occurred between prediction and observation, and attributed in earlier studies to the inadequacy of the turbulence model, may have been due to the inaccuracy of the solution.     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.     

Similarity solutions of Prandtl mixing length modelled two dimensional turbulent boundary layer equations

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no Blasius type similarity solutions (special exact solutions) have ever been found. In the light of Blasius’ pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and for a special case of flow modelled by Prandtl mixing-length, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. The ordinary differential equation is numerically solved and some useful quantities are produced. For numerical calculations, a complete Maple code is provided.     

Pressure drop for flow in channels subjected to strong system rotation

A disc stack centrifuge is an industrial example of a fluid machine in which all the internal flow takes place in a rapidly rotating frame. The present report gives a survey of the experimental and theoretical work performed at Alfa-Laval in order to estimate the pressure drops in the different internal passages in the centrifuge, including both laminar and turbulent flow.For the laminar flow between the discs, a theory has been developed using the concept of a rotating Hele Shaw cell and conformal mapping. The theory is valid in the limit of very small Rossby numbers. For moderately large Rossby numbers, this model overestimates the pressure drop. The linear theory was extended by introducing advecting vortices in a computer model. The vortices cause vertical fluid transport between the Ekman and geostrophic layers by Ekman pumping, an effect which decreases the pressure drop in the disc stack. The linear model and the enhanced model have both been confirmed by experiments.The flow is turbulent in most parts of the centrifuge, except in the disc stack. The theoretical or numerical modelling for rotating turbulent flows is very difficult and no reliable models exist so far. We therefore have to rely on measurements, which show that the pressure is significantly influenced by rotation for Rossby numbers below unity.     

Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence

We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.     

Drag reduction in the turbulent pipe flow of polymers

The paper concerns an experimental study of the fully developed turbulent pipe flow of several different aqueous polymer solutions: 0.25%, 0.3% and 0.4% carboxymethylcellulose (CMC), 0.2% xanthan gum (XG), a 0.09%/0.09% CMC/XG blend, 0.125% and 0.2% polyacrylamide (PAA). The flow data include friction factor vs. Reynolds number, mean velocity and near-wall shear rate distributions, and axial velocity fluctuation intensity u′ at a fixed radial location as a laminar/turbulent transition indicator. For each fluid we also include measurements of shear viscosity, first normal-stress difference and extensional viscosity. At high shear rates we find that the degree of viscoelasticity increases with concentration (0.3% CMC is an exception) for a given polymer, and in the sequence XG, CMC/XG, CMC, PAA, whilst at low shear rates the ranking changes to CMC, CMC/XG, XG, PAA. The extensional viscosity ranking is XG/CMC, XG, CMC, PAA at high strain rates and the same as that for the viscoelasticity at low shear rates. We find that the observed drag-reduction behaviour is consistent for most part with the viscoelastic and extensional-viscosity behaviour at the low shear and strain rates typical of those occurring in the outer zone of the buffer region.Although laminar/turbulent transition is practically indiscernible from the friction factor vs. Reynolds number plots, particularly for PAA and XG, the u′ level provides a very clear indicator and it is found that the transition delay follows much the same trend with elasticity/extensional viscosity as the drag reduction.