Theoretical and Numerical Investigation of Flow Transition in Rotating Curved Annular Pipes

Flows in rotating curved annular pipes are investigated by employing a theoretical and numerical method. The numerical results and the perturbation solutions confirm each other. The variations of the flow structure, including the secondary flow and the axial flow, with the force ratio (the ratio of the Coriolis force to the centrifugal force), the curvature and the radius ratio (the ratio of the radius of the inner circle to the radius of the outer circle of the annular pipe) are discussed in detail. The nature of the wall shear stress and the friction factor ratio are also shown. This study is the first to shows the flow transition of the flow in a rotating curved annular pipe and covers large ranges of parameters. Many interesting and previously unreported flow characteristics are obtained. Received 4 February 2002 and accepted 21 May 2002 Published online 30 October 2002 RID="*" ID="*" This research was supported by the Department of Energy under Contact Number W-7405-ENG-36. Communicated by H.J.S. Fernando     

Convective heat transfer for viscoelastic fluid in a curved pipe

In this paper, fully developed convective heat transfer of viscoelastic flow in a curved pipe under the constant heat flux at the wall is investigated analytically using a perturbation method. Here, the curvature ratio is used as the perturbation parameter and the Oldroyd-B model is applied as the constitutive equation. In the previous studies, the Dirichlet boundary condition for the temperature at the wall has been used to simplify the solution, but here exactly the non-homogenous Neumann boundary condition is considered to solve the problem. Based on this solution, the non-axisymmetric temperature distribution of Dean flow is obtained analytically and the effect of flow parameters on the flow field is investigated in detail. The current analytical results indicate that increasing the Weissenberg number, viscosity ratio, curvature ratio, and Prandtl number lead to the increase of the heat transfer in the Oldroyd-B fluid flow.     

Local nonsimilarity solution for the impact of the buoyancy force on heat and mass transfer in a flow over a porous wedge with a heat source in the presence of suction/injection

Combined heat and mass transfer in free, forced and mixed convection flows along a porous wedge with internal heat generation in the presence of uniform suction or injection is investigated. The boundary-layer analysis is formulated in terms of the combined thermal and solute buoyancy effect. The flow field characteristics are analyzed using the Runge-Kutta-Gill method, the shooting method, and the local nonsimilarity method. Due to the effect of the buoyancy force, power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters as a special case. The effects of the buoyancy force, suction, heat generation, and variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are studied. The results obtained are found to be in good agreement with previously published works.     

Turbulent boundary layer on a mildly curved convex surface

Extensive single point turbulence measurements made in the boundary layer on a mildly curved heated convex wall show that the turbulence heat fluxes and Stanton number are more sensitive to a change in wall curvature than the Reynolds stresses and skinfriction coefficient, and that downstream, as the flow adjusts to new curved conditions, the St/c _f ratio of Reynolds analogy is appreciably lower than in plane wall flow for the same conditions. Details of the turbulence structure in unheated flow have been documented in an earlier paper; temperature field measurements now described comprise mean temperature distributions, the streamwise variation of wall heat flux, profiles of the temperature variance, transverse and streamwise heat fluxes, and triple correlations. Turbulent diffusion of heat flux is drastically reduced even by mild curvature; changes in the heat fluxes are of the same order as changes in the shear stress, that is, an order of magnitude greater than the ratio of boundary layer thickness to wall radius of curvature. The data include plane flow measurements taken in a developed boundary layer upstream of a change in wall curvature.     

Combined heat and mass transfer by laminar natural convection from a vertical plate

Simultaneous heat and mass transfer in buoyancy-induced laminar boundary-layer flow along a vertical plate is studied for any ratio of the solutal buoyancy force to the thermal buoyancy force by using a new similarity transformation. The effects of the buoyancy ratio and Lewis number on the rates of heat and mass transfer are presented explicitly for most practical gaseous solutions (Pr=0.7, 0.21≤Sc≤2.1) and aqueous solutions (Pr=7, 140≤Sc≤1400). Very accurate correlations of the mass transfer and heat transfer rates are developed for the cases of single and combined buoyancy forces.     

Streamline flow through a curved annulus

Summary Theoretical calculations are carried out for the steady laminar incompressible flow of an ordinary viscous fluid in a curved annulus. At first the flow parameters are evaluated for the general case and then a particular example is solved numerically. The graphical representations of the flowline in the plane of symmetry and the projection of the stream-lines on a normal section are given. Only the case of large radius of curvature of the annulus is considered; more precisely this means that the ratio of the radius of the outer curved pipe to that of the circle in which the common axis of the two curved pipes is coiled is sufficiently small.     

Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties

The aim of the present study is to understand the problem of buoyancy and thermocapillary induced convection of cold water near its density maximum in an open cavity with temperature dependent properties in the presence of uniform external magnetic field. The governing equations are solved by the finite volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, Rayleigh, Hartmann and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. Convection heat transfer is enhanced by thermocapillary force when buoyancy force is weakened.     

Stability Analysis of a Vertical Curved Channel Flow with a Radial Temperature Gradient

The linear stability analysis of a Newtonian incompressible fluid in a vertical curved channel formed by two coaxial cylindrical surfaces with a radial temperature gradient and an azimuthal pressure gradient shows that critical modes are oscillatory and non-axisymmetric. We have derived a generalized Rayleigh discriminant which includes both the curvature and buoyancy effects. Centrifugal buoyancy induces weak asymmetry of the dependence of the control parameter critical values on the sign of the temperature gradient. The critical parameters depend on the temperature gradient, the radius ratio and the nature of the fluid. For a wide curvature channel flow, there are two critical modes: oscillatory Dean modes for small temperature gradients and oscillatory centrifugal-thermal modes for relatively large temperature gradients. Received 14 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 Communicated by H.J.S. Fernando     

Combined heat and mass transfer by laminar natural convection from a vertical plate with uniform heat flux and concentration

This paper studies combined heat and mass transfer by laminar natural convection from a vertical plate maintained with uniform surface heat flux and species concentration. Very accurate finite-difference solutions of a set of nonsimilarity equations have been obtained for most practical gaseous solutions (Pr?=?0.7, 0.21 ≤ Sc ≤ 2.1) and aqueous solutions (Pr?=?7, 140 ≤ Sc ≤ 1400). Variations of heat and mass transfer rates with buoyancy ratio and Lewis number are presented. Precise correlations have been developed for predicting heat and mass transfer rates of natural convection arising from single (solutal or thermal) buoyancy force and dual buoyancy forces.     

Fluid flow in a rotating curved rectangular duct

The fluid flowing in a rotating curved duct is subjected to both the Coriolis force due to a rotation and the centrifugal force due to a curvature. In this paper, the combined effects of the two forces on the flows in rotating curved rectangular ducts are examined numerically. According to the aspect ratio of the cross-section, the rectangular ducts are divided into three types: η>1, η=1, η<1, where η is the aspect ratio. The variations of the flow structures with the force ratio F (the ratio of the Corislis force to the centrifugal force) are studied in detail and many hitherto unknown flow patterns are found. The effects of the force ratio and the aspect ratio of the cross-section on the friction factor are also examined. Present results show both the characteristics of the secondary flow, axial flow and the natures of the friction factor.     

Entropy generation analysis of fully developed laminar forced convection in a helical tube with uniform wall temperature

In the present study, fully developed laminar flow and heat transfer in a helically coiled tube with uniform wall temperature have been investigated analytically. Expressions involving relevant variables for entropy generation rate contributed to heat transfer and friction loss, and total entropy generation rate have been derived. The effect of various flow and coil parameters like Reynolds number, curvature ratio, coil pitch, etc. on the entropy generation rate has been studied for two fluids- air and water. The results of the present study have been compared to the corresponding entropy generation values of straight pipe. Investigating the results, some optimum values for Reynolds number have been proposed and compared with the optimum Reynolds numbers of laminar flow inside a coiled tube subjected to constant heat flux boundary condition.     

Turbulence measurements from a plane air jet with buoyancy induced curvature

An experimental investigation of the turbulence structure of a heated plane air jet discharged at various angles into quiescent surroundings is described. Hot-wire anemometry was used to obtain the profiles of mean and turbulent velocities and temperature normal and tangential to the curved path of the flow. Measurements in the buoyancy induced curved region of the jet show the relative influence of the stability induced by both buoyancy and jet curvature on the turbulence structure.     

Wave propagation in a fluid flowing through a curved thin-walled elastic tube

The pulsatile flow in a curved elastic pipe of circular cross section is investigated. The unsteady flow of a viscous fluid and the wall motion equations are written in a toroidal coordinate system, superimposed and linearized over a steady state solution. Being the main application relative to the vascular system, the radius of the pipe is assumed small compared with the radius of curvature. This allows an asymptotic analysis over the curvature parameter. The model results an extension of the Womersley's model for the straight elastic tube. A numerical solution is found for the first order approximation and computational results are finally presented, demonstrating the role of curvature in the wave propagation and in the development of a secondary flow.     

Electrokinetic flow and energy conversion in a curved microtube

Curved channels are ubiquitous in microfluidic systems. The pressuredriven electrokinetic flow and energy conversion in a curved microtube are investigated analytically by using a perturbation analysis method under the assumptions of the small curvature ratio and the Reynolds number. The results indicate that the curvature of the microtube leads to a skewed pattern in the distribution of the electrical double layer (EDL) potential. The EDL potential at the outer side of the bend is larger than that at the inner side of the bend. The curvature shows an inhibitory effect on the magnitude of the streaming potential field induced by the pressure-driven flow. Since the spanwise pressure gradient is dominant over the inertial force, the resulting axial velocity profile is skewed into the inner region of the curved channel. Furthermore, the flow rate in a curved microtube could be larger than that in a straight one with the same pressure gradient and shape of cross section. The asymptotic solutions of the axial velocity and flow rate in the absence of the electrokinetic effect are in agreement with the classical results for low Reynolds number flows. Remarkably, the curved geometry could be beneficial to improving the electrokinetic energy conversion (EKEC) efficiency.     

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.     

A numerical study of fully developed laminar flows in pipes with two planar curvatures

The spectral element method is applied on unstructured tetrahedral elements to solve the Navier–Stokes equations for fully developed laminar flow in pipes with two planar curvatures. Specific implementations of the spectral element method to double curved pipes and parallelization are described. Previous studies on flows in pipes focused on constant curvature or torsion geometries, as well as pipes with varying curvature. This study focuses on the periodic variation of both the curvature as well as torsion by analysing a pipe having two planar curvatures. The effects of the three parameters defining the pipe are studied to isolate the curvature and torsion effect on the magnitude and angle of the secondary flow. Furthermore, the geometric effects on the wall shear stress are studied, as it is an important fluid flow property, especially in blood flows. Copyright © 2006 John Wiley & Sons, Ltd.     

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number.     

Effect of temperature gradient within a solid particle on the rotation and oscillation modes in solid-dispersed two-phase flows

Liquid–solid two-phase flow with heat transfer is simulated, and the effect of temperature gradient within a solid particle on the particle behaviour and heat transfer is studied. The interaction between fluid and particles is considered with our original immersed solid approach on a rectangular grid system. The local heat flux at the fluid–solid interface is described with an anisotropic heat conductivity matrix, and the governing equation of temperature is time-updated with an implicit treatment for the diffusion term. The method is applied to a 2-D natural convection flow of a relatively low Rayleigh number including multiple particles. Heat transfer and particle behaviours are studied for different solid heat conductivities (ratio to the fluid conductivity ranging between 10⁻³ and 10³) and solid volume fractions. Under a condition of relatively low heat conductivity ratio, the particles show a simple circulating flow. By increasing the heat conductivity ratio, a transition of the particulate flow is observed to oscillation mode around the domain centre due to the buoyancy force as a restitution force. The oscillation period is found to vary with the heat conductivity ratio, and it is related to the time scales for the heat transfer via fluid and solid.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

Steady laminar flow of viscoelastic fluid in a curved pipe of circular cross-section with varying curvature

The steady laminar flow of viscoelastic fluid through pipes of circular cross-section, whose center-line curvature varies locally, is analyzed theoretically. The flows in three kinds of pipes whose center-lines are specified by

as the examples of once, twice, and periodically curved pipes, respectively, are discussed in comparison with purely viscous flow. The analysis is valid for any other two-dimensionally curved pipes, when the center-line curvature is small. In addition, the reason why the secondary flow of a viscoelastic fluid in a curved pipe of circular cross-section is stronger than that of a purely viscous fluid is explained. In the present paper, the White—Metzner model is employed as the constitutive equation.