Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length. In this paper, the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic(EMHD)flow through a curved rectangular microchannel is investigated theoretically. The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflo...     

基于无网格Galerkin法求解矩形绝缘管道内的磁流体流动

无量纲磁流体流动控制方程中的哈特曼数较大将导致数值计算发散或误差过大。将无网格Galerkin法引入绝缘管道内的稳定磁流体流动计算中,针对磁流体控制方程中大哈特曼数导致计算误差大的情况,对无网格Galerkin法添加了稳定项。计算结果表明,同等条件下,添加了稳定项的无网格Galerkin法总体相对误差远小于标准无网格Galerkin法的结果,且可以计算哈特曼数最大达50000绝缘管道内的磁流体流动。     

Theoretical study on the bifurcation of vortexes structure for flow in curved tube

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Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.     

Development of secondary flows in viscoelastic curved ducts and the influence of outlet region

This paper presents numerical simulations of Newtonian and viscoelastic flows through a 180° curved duct of square cross section with a long straight outlet region. A particular attention is paid to the development of the flow in the output rectangular region after the curved part. The viscoelastic fluid is modeled using the constitutive equation proposed by Phan–Thien–Tanner (PTT). The numerical results, obtained with a finite-volume method, are shown for three different Dean numbers (125,137,150)$(125,137,150)$ and for three Deborah numbers (0.1,0.2,0.3)$(0.1,0.2,0.3)$. The necessary outlet length to impose boundary conditions is presented and discussed for these cases. Streamlines and vortex formation are shown to illustrate and analyze the evolution of the secondary flow in this region.     

A survey of works on the theory of toroidal shells and curved tubes

This paper gives a survey of works on the theory of toroidal shells which were done by our two universities in recent years. This paper was supported by DAAD Germany     

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.     

Fully developed flow in a curved pipe of arbitrary curvature ratio

It is generally assumed in curved pipe flow analyses that the curvature ratio, δ, of the pipe is very small, in which case the flow depends on a single parameter, the Dean number. This is not the case if δ is not very small. To determine the importance of this effect we have numerically solved the full Navier-Stokes equations, in primitive variable form, for arbitrary values of δ. A factored ADI finite-difference scheme has been used, employing Chorin's artificial compressibility technique. The results show that the central-difference calculation on a staggered grid is stable, without adding artificial damping terms, due to coupling between pressure and velocity. A spatially variable time step is used with a fixed Courant number.     

A multigrid method for predicting periodically fully developed flow

The use of multigrid methods in complex fluid flow problems is still under development. In this paper a full multigrid procedure has been incorporated in a finite volume solution for predicting fully developed fluid flow in a streamwise periodic geometry. Steady computations in two-dimensional body fitted co-ordinates have shown considerable savings in computation time by this multigrid method.     

A moving discontinuous Galerkin finite element method for flows with interfaces

A moving discontinuous Galerkin finite element method with interface condition enforcement is formulated for flows with discontinuous interfaces. The underlying weak formulation enforces the interface condition separately from the conservation law, so that the residual only vanishes upon satisfaction of both. In this formulation, the discrete grid geometry is treated as a variable, so that, in contrast to the standard discontinuous Galerkin method, this method has both the means to detect interfaces, via interface condition enforcement, and to satisfy, via grid movement, the conservation law and its associated interface condition. The method therefore directly fits interfaces, including shocks, preserving a high-order representation up to the interface without requiring shock capturing or an upwind numerical flux to achieve stability. It can be generalized to flows with a priori unknown interfaces with nontrivial topology and curved interface geometry as well as to an arbitrary number of spatial dimensions. Unsteady flows are represented in a manner similar to steady flows using a space-time formulation. In addition to computing flows with interfaces, the method can represent point singularities in a flow field by degenerating cuboid elements. In general, the method works in conjunction with standard local grid operations, including edge collapse, to ensure that degenerate cells are removed. Test cases are presented for up to three-dimensional flows that provide an initial assessment of the stability and accuracy of the method.     

A high‐order accurate discontinuous Galerkin finite element method for laminar low Mach number flows

In this paper we present a discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of laminar flow simulations at low Mach numbers using an implicit scheme. The algorithm is based on the flux preconditioning approach, which modifies only the dissipative terms of the numerical flux. This formulation is quite simple to implement in existing implicit DG codes, it overcomes the time‐stepping restrictions of explicit multistage algorithms, is consistent in time and thus applicable to unsteady flows. The performance of the method is demonstrated by solving the flow around a NACA0012 airfoil and on a flat plate, at different low Mach numbers using various degrees of polynomial approximations. Computations with and without flux preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers. The time accurate solution of unsteady flow is also demonstrated by solving the vortex shedding behind a circular cylinder at the Reynolds number of 100. Copyright © 2012 John Wiley & Sons, Ltd.     

Analytical solutions for laminar fully developed flows in double-sine shaped ducts

Fully developed, constant property, laminar flows in double-sine shaped ducts are considered. This cross section represents a limiting inter-plate channel geometry in plate heat exchangers. Accurate analytical solutions based on the Galerkin integral method are presented. Heat transfer with both T and H1 thermal boundary conditions is analyzed; they simulate the most fundamental practical heating/cooling applications. Velocity and temperature distributions, along withfRe, Nu _T , andNu _H1 results for flows in double-sine ducts of different aspect ratios (1/8 ≤γ ≤ 8) are presented. Effects of the relative cross-sectional geometry and thermal boundary conditions are delineated. A comparison of the thermal-hydraulic performance with that of other compact channel geometries is made. The results suggest an optimum (Nu/fRe) performance in a double-sine duct of aspect ratio near unity.     

曲线桥分析的精细传递矩阵法

将精细积分与传递矩阵法相结合,提出一种新的精细传递矩阵格式,应用于曲线桥的分析中。与传统的传递矩阵法相比,无需对微分方程组进行求解,只需迭代即可得到所需要的传递矩阵。根据边界条件,得到结构的内力及变形。算例表明,该方法正确有效。     

Non-isothermal flow of polymer melts in a curved tube

The results of a numerical study (using finite differences) of heat transfer in polymer melt flow is presented. The rheological behaviour of the melt is described by a temperature-dependent power-law model. The curved tube wall is assumed to be at constant temperature. Convective and viscous dissipation terms are included in the energy equation. Velocity, temperature and viscosity profiles, Nusselt numbers, bulk temperatures, etc. are presented for a variety of flow conditions. Br — Brinkman number - c specific heat, J/kg K - De — Dean number - E dimensionless apparent viscosity, eq. (14d) - G dimensionless shear rate, eq. (19) - k parameter of the power-law model, °C^–1, eq. (7) - mass flow rate, kg/s - m ₀ parameter of the power-law model, Pa · s ⁿ , eq. (7) - n parameter of the power-law model, eq. (7) - Nu 2r _p/ — Nusselt number, eqs. (28,31) - p pressure, Pa - Pe — Péclet number - P —(p/)/r _c — pressure gradient, Pa/m - dissipated energy, W, eq. (29) - total energy, W, eq. (30) - r radial coordinate, m - r _c radius of tube-curvature, m, fig. 1 - r _p radius of tube, m, fig. 1 - r _t variable, m, eq. (6) - R dimensionless radial coordinate, eq. (14a) - R _c dimensionlessr _c, eq. (14a) - R _t dimensionlessr _t, eq. (14a) - t temperature, °C - bulk temperature, °C, eq. (27) - t ₀ inlet temperature of the melt, °C - t _w tube wall temperature, °C - T dimensionless temperature, eq. (14c) - T _w dimensionless tube wall temperature - T dimensionless bulk temperature - u ₁ variable, s^–1, eq. (4) - u ₂ variable, s^–1, eq. (5) - U ₁ dimensionlessu ₁, eq. (18) - U ₂ dimensionlessu ₂, eq. (18) - v velocity in-direction, m/s - average velocity of the melt, m/s - V dimensionlessv, eq. (14b) - dimensionless , eq. (15) - z r _c — centre length of the tube, m - Z dimensionlessz, eq. (14e) - heat transfer coefficient, W/m² K - shear rate, s^–1, eq. (8) - — shear rate, s^–1 - apparent viscosity, Pa · s, eq. (7) - ₀ — apparent viscosity, Pa · s - angular coordinate, rad, fig. 1 - thermal conductivity, W/m K - melt density, kg/m³ - axial coordinate, rad, fig. 1 - rate of strain tensor, s^–1, eq. (8) - (—p) pressure drop, Pa     

A control volume finite element method for three-dimensional three-phase flows

A novel control volume finite element method with adaptive anisotropic unstructured meshes is presented for three-dimensional three-phase flows with interfacial tension. The numerical framework consists of a mixed control volume and finite element formulation with a new P₁DG-P₂ elements (linear discontinuous velocity between elements and quadratic continuous pressure between elements). A “volume of fluid” type method is used for the interface capturing, which is based on compressive control volume advection and second-order finite element methods. A force-balanced continuum surface force model is employed for the interfacial tension on unstructured meshes. The interfacial tension coefficient decomposition method is also used to deal with interfacial tension pairings between different phases. Numerical examples of benchmark tests and the dynamics of three-dimensional three-phase rising bubble, and droplet impact are presented. The results are compared with the analytical solutions and previously published experimental data, demonstrating the capability of the present method.     

Combined free and forced convection for developed flow in curved pipes with finite curvature ratio

Combined free and forced convection for developed flow in a curved pipe with arbitrary curvature ratio is studied numerically. The curved pipe is heated with axially uniform heat flux, while the wall temperature is maintained peripherally uniform. The buoyancy force is accounted by the Boussinesq approximation. The effects of the Dean, Prandtl, and Rayleigh numbers and especially of a wide range of curvature ratios on the flow resistance and the average heat transfer rate are presented. The significant distortion of the dividing streamline and the appearance of the secondary flow with one dominant cell for pipe flow with higher buoyancy force and curvature ratio are also discussed.     

Multifield computational fluid dynamics model of particulate flow in curved circular tubes

Limitations of mass transfer resulting from non-optimized fluid mechanics can severely affect the performance of synthetic membrane filtration systems. To improve membrane efficiency, modern applications of this technology have extensively used curved membrane ducts that take advantage of Dean vortices (i.e., curvature-induced secondary flows) to minimize membrane fouling. This paper is concerned with a complete three-dimensional analysis of single-phase and two-phase particle/liquid flows around a curved membrane tube. The proposed multidimensional model was implemented in an advanced (next-generation) multiphase computational fluid dynamics (CFD) solver, NPHASE. The results of simulations have been validated against experimental data and compared against other findings available in the literature. The consistency and accuracy of the present approach have been demonstrated. The novel aspects of this work include: the demonstration that azimuthal vortices may bifurcate at Dean numbers lower than previously anticipated, the use of vorticity magnitude as a measure of vortex strength, and the explanation of the role that Dean vortices play to mitigate the effect of gravity on particle settling. The overall results have direct relevance to synthetic membrane fouling during filtration of particle suspensions.     

A finite difference method for 3D flows about bodies of complex geometry in rectangular co-ordinate systems

A finite difference simulation method is developed for 3D flow about a body of complex geometry. The Navier–Stokes equation is approximated by a high-order-accurate difference scheme in the framework of rectangular co-ordinate systems. The configuration of the 3D body is represented by use of both surface porosity and volume porosity and the no-slip body boundary conditions are approximately implemented on the boundary cells. The validity of the method is demonstrated by a numerical test of flow past a sphere at a Reynolds number of 1000. The complicated structure of separated vortices is well revealed by this test computation. The versatility of the method is shown by application to an ocean-engineering problem of flow about a bay with an island.     

Instability of a slip flow in a curved channel formed by two concentric cylindrical surfaces

Instability of a slip flow in a curved channel formed by two concentric cylindrical surfaces is investigated. Two cases are considered. In the first (Taylor–Couette flow) case the flow is driven by the rotation of the inner cylindrical surface; no azimuthal pressure gradient is applied. In the second case (Dean flow) both cylindrical surfaces are motionless, and the flow is driven by a constant azimuthal pressure gradient. The collocation method is used to find numerically the critical values of the Taylor and Dean numbers, which establish the instability criteria for these two cases. The dependencies of critical values of these numbers on the ratio between the radii of concave and convex walls and on the velocity slip coefficient are investigated.     

Molecular model and flow calculation: I. The numerical solutions to multibead-rod models in homogeneous flows

The Galerkin method is used to solve the diffusion equation of the distribution function in configurational space for a multibead-rod model, and the dimensionless components of the extra stress tensor are then calculated by means of the expression of ensemble average. The material functions for steady-state shear flow and uniaxial flow and the mechanical properties of rigid-rodlike molecule suspensions in superposed flows are obtained numerically. The results indicate that it is promising to employ the multibead-rod models without the constitutive equation in numerical simulations of flows of suspensions. The project supported by the National Natural Science Fundation of China.