Turbulent flow in a tube containing an offset rod

A numerical finite volume prediction method for arbitrary-shaped passages has been applied to the case of fully developed axial turbulent flow past a rod eccentrically placed in a circular tube. The numerical method was based on an orthogonal curvilinear mesh and employed an algebraic stress transport model to calculate the full three-dimensional velocity field directly from the governing partial differential equations. This study is one of a series of applications of this prediction method to a range of different non-circular passages that have been made in order to establish the capabilities and usefulness of this type of procedure. The present eccentric rod case was the subject of a comprehensive experimental investigation by Kacker¹ which has enabled a detailed comparison to be made between the present predictions and the measurements. This comparison included local distributions of axial velocity, wall shear stress and secondary velocities; and although found to be satisfactory overall, some differences in detail revealed possible shortcomings in the measurement of secondary flow. This, together with other previously reported cases, indicates, that, although the present method cannot be expected to replace experiment in providing turbulent passage flow data, it has an important role to play in interpreting and supplementing experiments.     

Approximate elongation flow properties utilising the opposed orifice technique – Correction for shear and inertia

Mackay et al. (1995) have presented an approximate technique to determine the elongation viscosity from pressure drop measurements in a simple stagnation flow device. In the present paper we describe experiments using a high viscosity Newtonian oil, aimed at probing some of the assumptions made by Mackay et al. We find that Trouton ratios calculated using the original analysis are well above the value of three expected for Newtonian fluids. Finite element simulations of the flow field show this is due to the net pressure drop having a substantial shear contribution, which should be corrected for before the Trouton ratios are evaluated. Interestingly, most of the shear correction is due to shear on the inside of the orifice near the exit from the central flow region. The shear contribution to the pressure drop occurs for all flow rates, however, at large flow rates there is also an inertial correction to the pressure drop. In this paper we describe an approximate method that corrects for both shear and inertial effects. With these effects recognised and corrected for, the measured Trouton ratios are reduced to around three. Received: 15 December 1997 Accepted: 16 March 1998     

A staggered control volume scheme for unstructured triangular grids

The purpose of this work is to introduce and validate a new staggered control volume method for the simulation of 2D/axisymmetric incompressible flows. The present study introduces a numerical procedure for solving the Navier–Stokes equations using the primitive variable formulation. The proposed method is an extension of the staggered grid methodology to unstructured triangular meshes for a control volume approach which features ease of handling of irregularly shaped domains. Two alternative elements are studied: transported scalars are stored either at the sides of an element or at its vertices, while the pressure is always stored at the centre of an element. Two interpolation functions were investigated for the integration of the momentum equations: a skewed mass-weighted upwind function and a flow-oriented exponential shape function. The momentum equations are solved over the covolume of a side or of a vertex and the pressure–velocity coupling makes use of a localized linear reconstruction of the discontinuous pressure field surrounding an element in order to obtain the pressure gradient terms. The pressure equation is obtained through a discretization of the continuity equation which uses the triangular element itself as the control volume. The method is applied to the simulation of the following test cases: backward-facing step flow, flow over a two-dimensional obstacle and flow in a pipe with sudden contraction of cross-sectional area. All numerical investigations are compared with experimental data from the literature. A grid convergence and error analysis study is also carried out for flow in a driven cavity. Results compared favourably with experimental data and so the new control volume scheme is deemed well suited for the prediction of incompressible flows in complex geometries. © 1997 John Wiley & Sons, Ltd.     

VOLUME-TRACKING METHODS FOR INTERFACIAL FLOW CALCULATIONS

A new algorithm for volume tracking which is based on the concept of flux-corrected transport (FCT) is introduced. It is applicable to incompressible 2D flow simulations on finite volume and difference meshes. The method requires no explicit interface reconstruction, is direction-split and can be extended to 3D and orthogonal curvilinear meshes in a straightforward manner. A comparison of the new scheme against well-known existing 2D finite volume techniques is undertaken. A series of progressively more difficult advection tests is used to test the accuracy of each scheme and it is seen that simple advection tests are inadequate indicators of the performance of volume-tracking methods. A straightforward methodology is presented that allows more rigorous estimates to be made of the error in volume advection and coupled volume and momentum advection in real flow situations. The volume advection schemes are put to a final test in the case of Rayleigh–Taylor instability. © 1997 by CSIRO.     

Deep field noise in holographic particle image velocimetry (HPIV): numerical and experimental particle image field modelling

 Holographic recording overcomes the limits in 2-D particle image velocimetry (PIV) to cover a 3-D flow field volume. Interrogation by focusing on single planes in a reconstructed particle field is disturbed by noise from out-of-focus particles. A numerical simulation models image reconstruction and shows how validation rates depend on aperture and volume depth. An experimental model environment of scattering particles in moveable plastic slices gives support to the numerical results. Simulations and tests are carried out for interrogation by autocorrelation and crosscorrelation techniques and furnish guidelines for system design. Received: 27 December 1996 / Accepted: 14 August 1997     

Two-dimensional subcritical and supercritical open channel flow calculation using a time-marching method

A time-marching method is presented for the calculation of two-dimensional, high-speed channel flow, including the usually neglected terms of slope and bottom friction. Time-marching methods are potentially the most flexible means of calculating flow through geometrically complex channel passages, since they can readily deal with subcritical and supercritical flows. The adopted numerical scheme comes straight from gas flow computations in turbomachines. The flow is assumed to be fully mixed in the vertical direction, so that vertical variations may be neglected. Comparisons with other numerical solutions for various open channel configurations show that the proposed approach is a comparatively accurate, reliable and fast technique. It can be utilized for open channel designs.     

Two-dimensional planar flow of a viscoelastic plastic medium

The present study is concerned with finite element simulation of the planar entry flow of a viscoelastic plastic medium exhibiting yield stress. The numerical scheme is based on the Galerkin formulation. Flow experiments are carried out on a carbon black filled rubber compound. Steady-state pressure drops are measured on two sets of contraction or expansion dies having different lengths and a constant contraction or expansion ratio of 4:1 with entrance angles of 90, 45 and 15 degrees. The predicted and measured pressure drops are compared. The predicted results indicate that expansion flow has always a higher pressure drop than contraction flow. This prediction is in agreement with experimental data only at low flow rates, but not at high flow rates. The latter disagreement is possibly an indication that the assumption of fully-developed flow in the upstream and downstream regions is not realistic at high flow rates, even for the large length-to-thickness ratio channels employed. The evolution of the velocity, shear stress, and normal stress fields in the contraction or expansion flow and the location of pseudo-yield surfaces are also calculated.     

Brownian dynamics simulation for suspensions of oblong-particles under shear flow

Computer simulations of the shear flow for the suspensions of oblong-particles were performed using nonequilibrium Brownian Dynamics (BD). The model particle is a rigid body made up of linearly connected spheres with the interparticle potential of a repulsive Lennard-Jones potential. The length-over-width ratios of the oblong-particles used in the present calculations are 5/3 and 3. In the concentrated suspensions high orientation is easily induced by shear at low shear rates. The systems of the oblong-particles exhibit the structural transition that causes the significant change in the rheological properties at high shear rates. Furthermore, the dependence of the length-over-width ratio of the particle is examined. Received: 16 June 1997 Accepted: 3 February 1998     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

颗粒材料剪切流动状态转变的环剪试验研究

颗粒材料的剪切流动行为广泛地存在于滑坡、泥石流等自然灾害以及矿物原料传输、泵送等工业过程中.颗粒材料在不同体积分数、剪切速率和应力约束下会表现出不同的流动状态并发生相互转化.对颗粒材料在剪切流动过程中力学特性的研究有助于加深理解其发生不同流动状态的内在机理,为解决相应的颗粒材料问题提供理论依据.为此,本文研制了颗粒材料剪切流动的中型环剪仪,并对颗粒材料在不同法向约束应力和剪切速率下的剪切应力和体积膨胀率进行了测试.结果表明,剪切应力和体积膨胀率均随剪切速率的增大而增大,但增长速率在临界剪切速率处发生转变,使其随剪切速率的平方呈分段式线性增长.通过对颗粒材料在不同剪切速率和惯性数下有效摩擦系数变化趋势的分析,讨论了颗粒材料由慢速流向快速流转化的基本规律,以及在临界剪切速率处发生流动状态转化的内在条件.此外,通过对不同法向应力下临界剪切速率以及快速流动下运动规律的测试,发现临界剪切速率随法向应力的增加而减小,即法向应力可促进颗粒材料由慢速流向快速流的转化,但在快速流动状态下的有效摩擦系数对法向应力不敏感.以上对颗粒材料在不同剪切速率、法向应力下流动状态的环剪试验研究有助于揭示其发生不同流动状态转化的内在机理.      

可降解性表面活性剂体系下水平管内气液两相螺旋流实验研究

通过气液两相螺旋流实验仪器,研究具有可降解性的天然椰子油新型添加剂对于气液两相螺旋流流型影响以及流型的转变规律,并与表面活性剂十二烷基苯磺酸钠(SDBS)进行对比研究。实验工况设定为:实验介质为空气和水,含气率10%~90%,气相折算速度0.01~4.0m/s,液相折算速度0.01~4.0m/s,表面活性剂采用从植物提取的可降解性椰子油和SDBS,起旋装置为叶轮。实验观察到天然椰子油对于螺旋轴状流、螺旋团状流、螺旋弥散流转换特性的影响与SDBS的效果相类似,该三种流型发生条件相比于以往都有所提前,且存在范围被拓宽。浓度为500ppm时椰子油体系下的主要流型为螺旋弥散流,而SDBS体系下则以螺旋团状流为主。     

High speed optical tomography system for quantitative measurement and visualization of dynamic features in a round jet

An optical tomography system that is capable of operating at frame rates of up to 5 kHz has been used to obtain spatially resolved cross-sectional temperature images of a heated round jet. These tomographic images show dynamic details in the evolving vortical flow structures found in the near field of the jet that are consistent with previous studies of low speed jet flow. Reconstructions produced by the system are quantitative temperature distributions of a planar cross section of the jet measuring temperature differences with a spatial resolution of 1.4 mm. Received: 31 July 1997/Accepted: 18 December 1997     

Effect of Volume Energy Supply on the Stability of a Subsonic Vortex Flow

Calculations of the stability of an axisymmetric vortex flow of viscous heat-conducting gas with volume energy supply are presented. The unperturbed axisymmetric vortex flow was found numerically using a quasi-cylindrical approximation of the Navier-Stokes equations under the assumption of constant peripheral-velocity circulation in the ambient co-current flow. The volume energy supply in the viscous vortex core was modeled by an additional source term in the energy equation. The stability characteristics of the viscous vortex flow in a longitudinal vortex with respect to both axisymmetric and non-axisymmetric three-dimensional waves traveling along the vortex axis and corresponding to both positive and negative values of the azimuthal wave number were found using the time-dependent formulation of the linear stability theory for compressible three-dimensional plane-parallel flows.     

Numerical investigation of flow structures around a sphere

A numerical investigation of flow around a sphere is performed and compared with previous studies. Here, a second-order accurate, finite volume method is used in order to predict the instantaneous and time-averaged flow characteristics using large eddy simulation (LES) on the multi-block grid system. Namely, the objectives of this article are: (i) the presentation of flow structures in the wake region downstream of the sphere with a wide variety of flow properties such as the distribution of velocity vectors, patterns of streamlines, Reynolds stress correlations, root mean square of velocity components and other time-averaged flow data in order to reveal the vortical flow structures in detail and (ii) to demonstrate the abilities of computational methods in simulation of vortical flow data. Finally, it has been concluded that there are good agreements between the experimental results and numerical predictions.     

Computation of a drastic flow pattern change in an annular swirling jet caused by a small decrease in inlet swirl

This paper investigates the flow pattern change in an annular jet caused by a sudden change in the level of inlet swirl. The jet geometry consists of an annular channel followed by a specially designed stepped‐conical nozzle, which allows the existence of four different flow patterns as a function of the inlet swirl number. This paper reports on the transition between two of them, called the ‘open jet flow high swirl’ and the ‘Coanda jet flow.’ It is shown that a small sudden decrease of 4% in inlet swirl results in a drastic and irreversible change in flow pattern. The objective of this paper is to reveal the underlying physical mechanisms in this transition by means of numerical simulations. The flow is simulated using the unsteady Reynolds‐averaged Navier–Stokes (URANS) approach for incompressible flow with a Reynolds stress turbulence model. The analysis of the numerical results is based on a study of different forces on a control volume, which consists of the jet boundaries. The analysis of these forces shows that the flow pattern change consists of three different regimes: an immediate response regime, a quasi‐static regime and a Coanda regime. The simulation reveals that the pressure–tangential velocity coupling during the quasi‐static regime and the Coanda effect at the nozzle outlet during the Coanda regime are the driving forces behind the flow pattern change. These physical mechanisms are validated with time‐resolved stereo‐PIV measurements, which confirm the numerical simulations. Copyright © 2008 John Wiley & Sons, Ltd.     

Electrical noise generated during capillary flow of aqueous poly(ethylene oxide) solutions

 The relation between the electrical noise generated during flow of aqueous poly(ethylene oxide) PEO solutions in three capillaries of different lengths and entry shape but the same diameter and the flow behaviour was investigated. Flow into the square cut off capillary entry was characterised by a low pressure loss regime followed at higher shear rates by a high pressure loss regime while flow into the trumpet shaped capillary end exhibited only the low pressure loss regime. The high pressure loss flow was associated with strong electrical noise generation. The results suggest that the noise generation mechanism includes a current source supplied by the flow through the capillary volume with an associated streaming potential and a modulation of the current by mixing and turbulence at the capillary entrance. The noise measuring technique can potentionally be used to study disturbances in the entry flow to capillaries. Received: 22 July 1996/Accepted: 9 June 1997     

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.     

Liquid film break-up in a model of a prefilming airblast nozzle

 The paper describes the atomisation process of a liquid in an axissymmetric shear layer formed through the interaction of turbulent coaxial jets (respectively, inner and outer jets), with and without swirl, in a model airblast prefilming atomiser. The atomisation process and spray quality was studied using different visualisation techniques, namely laser shadowgraphy and digital image acquisition. The experiments were conducted for different liquid flow rates, Reynolds numbers ranging from 6600 to 66000 and 27300 to 92900 for the inner and outer air flows, respectively, for different outer flow swirl levels, and two liquid film thicknesses −0.2 and 0.7 mm. All the tests were carried out at atmospheric pressure and using water. The results include the analysis of the film structure at break-up and of the break-up length, and suggest that the deterioration of the liquid film close to the atomising edge exhibits a periodic behaviour and is mainly dependent on the inner air velocity. Film thickness strongly affects the time and length scales of the break-up process for the lower range of air velocities. For higher inner air velocities, the break-up length and time become less dependent on liquid flow rate and initial film thickness. Received: 14 March 1997/Accepted: 27 October 1997     

Measurements and analysis of high-intensity turbulent characteristics in a turbine-agitated tank

Turbulent flow in the impeller zone and the bulk zone in a turbine-agitated tank was measured by constant temperature anemometry. A split-film probe was used which sensed the directionality of the flow. Turbulent characteristics such as intensity and anisotropy were expressed by statistical moments for all three directions of flow. Turbulent kinetic energy and mean Reynolds stresses were also calculated. The convective velocity was estimated from Taylor's hypotheses as well as from other hypothesis and approximations which considered both the mean velocity and the fluctuations of the flow. The local energy dissipation rates were calculated using three different methods. They were based on energy dissipation spectrum. Kolmogorov's hypotheses and dimensional analysis. The method based on Kolmogorov's hypotheses is suggested here. Received: 4 February 1997 / Accepted: 22 May 1998     

On the non-linear instability of fiber suspensions in a Poiseuille flow

The non-linear instability characteristics of fiber suspensions in a plane Poiseuille flow are investigated. The evolution equation of the perturbation amplitude analogous to Landau equation is formulated and solved numerically for different fiber parameters. It is found that the equilibrium amplitude decreases with the increase of the fiber aspect ratio and volume fraction, i.e. the addition of the fibers reduces the amplitude of the perturbation, and leads to the reduction of the flow instability. This phenomenon becomes significant for large volume concentration and aspect ratio. The mechanism of the reduction of the flow instability is also analyzed by taking into account of the modification of the mean flow and the energy transfer from the mean flow to the perturbation flow.