Secondary flow coefficient of overbank flow

This paper presents a 2D analytical solution for the transverse velocity distribution in compound open channels based on the Shiono and Knight method （SKM）, in which the secondary flow coefficient （K-value） is introduced to take into account the effect of the secondary flow. The modeling results agree well with the experimental results from the Science and Engineering Research Council-Flood Channel Facility （SERC-FCF）. Based on the SERC-FCF, the effects of geography on the secondary flow coefficient and the reason for such effects are analyzed. The modeling results show that the intensity of the secondary flow is related to the geometry of the section of the compound channel, and the sign of the K-value is related to the rotating direction of the secondary flow cell. This study provides a scientific reference to the selection of theK-value.     

Analytical solutions for transverse distributions of stream-wise velocity in turbulent flow in rectangular channel with partial vegetation

The theory of poroelasticity is introduced to study the hydraulic properties of the steady uniform turbulent flow in a partially vegetated rectangular channel. Plants are assumed as immovable media. The resistance caused by vegetation is expressed by the theory of poroelasticity. Considering the influence of a secondary flow, the momentum equation can be simplified. The momentum equation is nondimensionalized to obtain a smooth solution for the lateral distribution of the longitudinal velocity. To verify the model, an acoustic Doppler velocimeter (ADV) is used to measure the velocity field in a rectangular open channel partially with emergent artificial rigid vegetation. Comparisons between the measured data and the computed results show that the method can predict the transverse distributions of stream-wise velocities in turbulent flows in a rectangular channel with partial vegetation.     

Two-dimensional analytical solution for compound channel flows with vegetated floodplains

This paper presents a two-dimensional analytical solution for compound channel flows with vegetated floodplains. The depth-integrated N-S equation is used for analyzing the steady uniform flow. The effects of the vegetation are considered as the drag force item. The secondary currents are also taken into account in the governing equations, and the preliminary estimation of the secondary current intensity coefficient K is discussed. The predicted results for the straight channels and the apex cross-section of meandering channels agree well with experimental data, which shows that the analytical model presented here can be applied to predict the flow in compound channels with vegetated floodplains.     

Influence of Hall current and Joule heating on entropy generation during electrokinetically induced thermoradiative transport of nanofluids in a porous microchannel

A comprehensive theoretical study of entropy generation during electrokinetically driven transport of a nanofluid is of prime concern in the paper. The flow is considered to take place on a wavy channel under the action of an external transverse magnetic field and an external pressure gradient. Navier slips at the walls of the channel and thermal radiation have been taken into account in the study. The theoretical study has been carried out by developing a mathematical model by taking into account the effects of Joule heating, viscous dissipation, and the transverse magnetic field on heat transfer during the electrokinetic transport of the fluid. The derived analytical expressions have been computed numerically by considering the nanofluid as a mixture of blood and ferromagnetic nanoparticles. Variations in velocity, streaming potential, temperature distribution, Nusselt number, and Bejan number associated with the electrokinetic flow in capillaries have been investigated by the parametric variation method. The results have been presented graphically. The present investigation reveals that streaming potential decreases due to the Hall effect, while for the cooling capacity of the microsystem,we find an opposite behavior due to the Hall effect. The study further reveals that the fluidic temperature is reduced due to increase in the Hall current, and thereby thermal irreversibility of the system is reduced significantly. The results presented here can be considered as the approximate estimates of blood flow dynamics in capillaries during chemotherapy in cancer treatment.     

Simple analytical model for depth-averaged velocity in meandering compound channels

A simple but applicable analytical model is presented to predict the lateral distribution of the depth-averaged velocity in meandering compound channels. The governing equation with curvilinear coordinates is derived from the momentum equation and the flow continuity equation under the condition of quasi-uniform flow. A series of experiments are conducted in a large-scale meandering compound channel. Based on the experimental data, a magnitude analysis is carried out for the governing equation, and two lower-order shear stress terms are ignored. Four groups of experimental data from different sources are used to verify the predictive capability of this model, and good predictions are obtained. Finally, the determination of the velocity parameter and the limitation of this model are discussed.     

Electric field in the transverse cross section of the channel of an MHD generator

During the motion of a partially ionized gas in magnetohydrodynamic channels the distribution of the electrical conductivity is usually inhomogeneous due to the cooling of the plasma near the electrode walls. In Hall-type MHD generators with electrodes short-circuited in the transverse cross section of the channel the development of inhomogeneities results in a decrease of the efficiency of the MHD converter [1]. A two-dimensional electric field develops in the transverse section. Numerical computations of this effect for channels of rectangular cross section have been done in [2, 3], At the same time it is advisable to construct analytic solutions of model problems on the potential distribution in Hall channels, which would permit a qualitative analysis of the effect of the inhomogeneous conductivity on local and integral characteristics of the generators. In the present work an exact solution of the transverse two-dimensional problem is given for the case of a channel with elliptical cross section stretched along the magnetic field. The parametric model of the distribution of the electrical conductivity of boundary layer type has been used for obtaining the solution. The dependences of the electric field and the current and also of the integral electrical characteristics of the generator on the inhomogeneity parameters are analyzed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 3–10, January–February, 1973.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

带滩槽地形的连续弯道中纵向流速横向分布解析

本文基于沿水深积分的动量方程,假定二次流项和弯道附加应力项沿横断面呈线性分布,提出了预测弯道垂线平均纵向流速的解析计算方法,进一步提出了河槽区和河滩区垂线平均纵向流速沿断面分布的求解模式,并将其应用于带滩槽地形的反向连续弯道水槽中. 根据实测数据率定计算参数,该模式可计算不同出口水深条件下断面垂线平均纵向流速分布,计算结果与实测数据吻合良好.分析了线性分布假设中参数随水深变化的取值规律和沿横断面分布特点,并对参数进行了敏感性分析,分析表明线性假设中一次项系数分区位置对流速峰值的大小和位置影响较大,常数项根据地形横比降变化进行分区取值,流速计算值对常数项在水平段和斜坡段分区位置较为敏感,并根据参数的敏感度提出了参数沿水槽的均值作为参考值.讨论了动量方程中二次流项和弯道附加应力项沿弯道的横向分布规律,进一步认识线性假设的适用范围,结果表明线性假设在本文试验水槽中适用于弯道沿程.研究成果有助于认识带滩槽地形的连续弯道纵向流速分布特征及其形成机制.      

Analytical Investigation of the Effect of Viscous Dissipation on Couette Flow in a Channel Partially Filled with a Porous Medium

An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated.     

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers: a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.     

The influence of a magnetic field on free convection in a finite vertical channel

An approximate analytical solution is presented for developing free convection flows of electrically conducting fluids between finite vertical channels which are subjected to a uniformly applied transverse magnetic field. Specifically, the basic approximation lies in the linearization of the governing boundary layer type of equations. It is demonstrated that the application of a transverse magnetic field reduces the induced flow rate in the channel and the heat transfer to the fluid.     

MHD free-convective flow of micropolar and Newtonian fluids through porous medium in a vertical channel

We have studied the fully-developed free-convective flow of an electrically conducting fluid in a vertical channel occupied by porous medium under the influence of transverse magnetic field. The internal prefecture of the channel is divided into two regions; one region filled with micropolar fluid and the other region with a Newtonian fluid or both the regions filled by Newtonian fluids. Analytical solutions of the governing equations of fluid flow are found to be in excellent agreement with analytical prediction. Analytical results for the details of the velocity, micro-rotation velocity and temperature fields are shown through graphs for various values of physical parameters. It is noticed that Newtonian fluids prop up the linear velocity of the fluid in contrast to micropolar fluid. Also the skin friction coefficient at both the walls is derived and its numerical values are offered through tables.     

Flow of Particulate-Fluid Suspension in a Channel with Porous Walls

The problem of the dispersed particulate-fluid two-phase flow in a channel with permeable walls under the effect of the Beavers and Joseph slip boundary condition is concerned in this paper. The analytical solution has been derived for the longitude pressure difference, stream functions, and the velocity distribution with the perturbation method based on a small width to length ratio of the channel. The graphical results for pressure, velocity, and stream function are presented and the effects of geometrical coefficients, the slip parameter and the volume fraction density on the pressure variation, the streamline structure and the velocity distribution are evaluated numerically and discussed. It is shown that the sinusoidal channel, accompanied by a higher friction factor, has higher pressure drop than that of the parallel-plate channel under fully developed flow conditions due to the wall-induced curvature effect. The increment of the channel’s width to the length ratio will remarkably increase the flow rate because of the enlargement of the flow area in the channel. At low Reynolds number ranging from 0 to 65, the fluids move forward smoothly following the shape of the channel. Moreover, the slip boundary condition will notably increase the fluid velocity and the decrease of the slip parameter leads to the increment of the velocity magnitude across the channel. The fluid-phase axial velocity decreases with the increment of the volume fraction density.     

Translational nonequilibrium of a gas flow into vacuum in a constant-section channel

A single-species gas flow into vacuum in a constant-section channel is computed by means of the Direct Simulation Monte Carlo method. It is shown that the longitudinal, transverse, and total kinetic temperatures are significantly different in the head part of the flow, which is a consequence of the arising translational nonequilibrium. The flow is almost self-similar in the entire region of flow expansion (except for distributions of the transverse and total kinetic temperatures in the head part of the gas flow), which allows one to predict flow parameters at times greater than those used in simulations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 54–59, July–August, 2006.     

Behavior of near-field dilution of thermal buoyant jet discharged horizontally in compound open-channel

The RNG κ-ε model considering the buoyancy effect, which is solved by the hybrid finite analytic method, is used to simulate the mixture of the horizontal round thermal buoyant jet in compound open channel flow. The mixing features near the spout and flowing characteristic of the secondary currents are studied by numerical simulation. Meanwhile, （1） the distribution of the measured isovels for stream-wise velocity, （2） secondary currents, （3） the distribution of the measured isovels for temperature of typical cross-section near the spout, were obtained by the three-dimensional Micro ADV and the temperature measuring device. Compared with experimental data, the RNG κ-ε model based on buoyancy effect can preferably simulate the jet which performs the bifurcation phenomenon, jet reattachment （Conada effect） and beach secondary currents phenomenon with the effect of ambient flow, buoyancy, and secondary currents of compound section and so on.     

Development of a generalized multi‐layer model for 3‐D simulation of free surface flows

A mathematical model was developed for three‐dimensional (3‐D) simulation of free surface flows. In this model, the flow depth is divided into a number of layers and shallow water equations are integrated in each layer to derive the hydrodynamic equations. To give a general form to this model, each layer is assumed to be non‐horizontal with varying thickness in the flow domain. A non‐orthogonal curvilinear coordinate system is employed in the model, to allow for flexibility in dealing with the irregular geometry of natural watercourses. Due to the similarity in governing equations, two‐dimensional (2‐D) depth averaged programs can be developed into a multi‐layer model. The development for a depth averaged program and its numerical scheme is described in this paper. Experimental data and semi‐analytical solutions are used to evaluate the performance of the model. Three different cases of open channel flow are tested: 1‐flow in a straight open channel, 2‐the flow development region in a channel, and 3‐flow in a meandering channel. It is shown that the model has the capability to predict velocity distribution and secondary flows in complex 3‐D flow conditions. Copyright © 2004 John Wiley & Sons, Ltd.     

Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function

Squeezed air film between two closely spaced vibrating microstructures is the important source of energy dissipation and has profound effects on the dynamics of microelectromechanical systems (MEMS). Perforations in the design are one of the methods to model these damping effects. The literature reveals that the analytical modeling of squeeze film damping of perforated circular microplates is less explored; however, these microplates are also an imperative part of the numerous MEMS devices. Here, we derive an analytical model of transverse and rocking motions of a perforated circular microplate. A modified Reynolds equation that incorporates compressibility and rarefaction effects is utilized in the analysis. Pressure distribution under the vibrating microplate is derived by using Green’s function and also derived by finite element method (FEM) to visualize the pressure distribution under perforated and non-perforated areas of the microplate. The analytical damping results are validated with previous renowned analytical models and also with the FEM results. The outcomes confirm the potential of the present analytical model to accurately predict the squeeze film damping parameters.     

Flow stability in a channel with porous walls

We study the stability of the flow which forms in a plane channel with influx of an incompressible viscous fluid through its porous parallel walls. Under certain assumptions the study of the stability reduces to the solution of modified Orr-Sommerfeld equation accounting for the transverse component of the main-flow velocity. As a result of numerical integration of this equation we find the dependence of the local critical Reynolds number on the blowing Reynolds number R₀, which may be defined by two factors: the variation of the longitudinal velocity profile with R₀ and the presence of the transverse velocity component. A qualitative comparison is made of the computational results with experimental data on transition from laminar to turbulent flow regimes in channels with porous walls, which confirms that it is necessary to take into account the effect of the transverse component of the main-flow velocity on the main-flow stability in the problem in question.Flows in channels with porous walls are of interest for hydrodynamic stability theory in view of the fact that they can be described by the exact solutions of the Navier-Stokes equations by analogy with the known Poiseuille and Couette flows. However, in contrast with the latter, the flows in channels with porous walls (studies in [1], for example) will be nonparallel.The theory of hydrodynamic stability of parallel flows has frequently been applied to nonparallel flows (in the boundary layer, for example). In so doing the nonparallel nature of the flow has been taken into account only by varying the longitudinal velocity component profiles. A study was made in [2, 3] of the effect of the transverse component of the main flow on its stability. In the case of the boundary layer in a compressible gas, a considerable influence of the transverse velocity component on the critical Reynolds number was found in [2] and confirmed experimentally. A strong influence of the transverse velocity component on the instability region was also found in [3] in a study of the flow stability in a boundary layer with suction for an incompressible fluid.     

Three‐dimensional numerical simulation of compound meandering open channel flow by the Reynolds stress model

Turbulent flow in a compound meandering open channel with seminatural cross sections is one of the most complicated turbulent flows as the flow pattern is influenced by the combined action of various forces, such as centrifugal force, pressure, and shear stresses. In this paper, a three‐dimensional (3D) Reynolds stress model (RSM) is adopted to simulate the compound meandering channel flows. Governing equations of the flow are solved numerically with finite‐volume method. The velocity fields, wall shear stresses, and Reynolds stresses are calculated for a range of input conditions. Good agreement between the simulated results and measurements indicates that RSM can successfully predict the complicated flow phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.