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.     

Numerical simulation of turbulent flows in trapezoidal meandering compound open channels

Three‐dimensional (3D) numerical study is presented to investigate the turbulent flow in meandering compound open channels with trapezoidal cross‐sections. The flow simulation is carried out by solving the 3D Reynolds‐averaged continuity and Navier–Stokes equations with Reynolds stress equation model (RSM) for steady‐state flow. Finite volume method (FVM) is applied to numerically solve the governing equations of fluid flow. The velocity magnitude, tangential velocity, transverse velocity and Reynolds stresses are calculated for various flow conditions. Good agreement between the simulated and available laboratory measurements was obtained, indicating that the RSM can accurately predict the complicated flow phenomenon. Comparison of the calculated secondary currents of four cases (one being inbank flow and other three being overbank flow) with different water depths reveals that (i) the inbank flow exhibits different flow behaviors from that of the overbank flow does and (ii) the water depth has significant effects on the magnitude and direction of secondary currents. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical investigation of a water flow in a rib-roughened channel by using Reynolds stress model

In this paper, water flow in a rib-roughened channel is investigated numerically by using Reynolds stress turbulence models (RSM) on a three-dimensional (3-D) domain. Computational results for mean streamwise velocity component and turbulent kinetic energy show good agreements with available experimental data. Five rib pitch-to-height ratios (p/h) of 1, 5, 10, 15 and 20 are analysed for six different Reynolds numbers (Re) of 3000, 7000, 12,000, 20,000, 40,000 and 65,000. Velocity vectors, streamlines and Reynolds stresses are showed for these ratios and Re numbers. Streamlines revealed that Reynolds numbers do not affect flowfield but play an important role in the Reynolds stresses.     

Calculation of turbulent fluid flow and heat transfer in ducts by a full Reynolds stress model

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts by different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with a full Reynolds stress model (RSM). The turbulent heat fluxes are modelled by a SED concept, the GGDH and the WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models are implemented for an arbitrary three‐dimensional channel. Fully developed condition is achieved by imposing cyclic boundary conditions in the main flow direction. The numerical approach is based on the finite volume technique with a non‐staggered grid arrangement. The pressure–velocity coupling is handled by using the SIMPLEC‐algorithm. The convective terms are treated by the van Leer scheme while the diffusive terms are handled by the central‐difference scheme. The hybrid scheme is used for solving the ε equation. The secondary flow generation using the RSM model is compared with a non‐linear k–ε model (non‐linear eddy viscosity model). The overall comparison between the models is presented in terms of the friction factor and Nusselt number. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical modeling of turbulent compound channel flow using the lattice Boltzmann method

The flow of water in a straight compound channel with prismatic cross section is investigated with a relatively new tool, the lattice Boltzmann method. The large eddy simulation model is added in the lattice Boltzmann model for nonlinear shallow water equations (LABSWE^TM) so that the turbulence, caused by lateral exchange of momentum in the shear layer between the main channel and floodplain, can be taken into account and modeled efficiently. To validate the numerical model, a symmetrical compound channel with trapezoidal main channel and flat floodplain is tested. Similar to most natural watercourses, the floodplain has higher roughness values than the main channel. Different relative depths, D_r (the ratio of the depth of flow on the floodplain to that in the main channel), are considered. The Reynolds number is set at 30 000 in the main channel. The lateral distributions of the longitudinal velocity, the boundary shear stress, the Reynolds stress and the apparent shear stress across the channel are obtained after the large eddy simulation is performed. The results of numerical simulations are compared with the available experiment data, which show that the LABSWE^TM is capable of modeling the features of flow turbulence in compound channels and is sufficiently accurate for practical applications in engineering. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

A direct numerical simulation of low Reynolds number turbulent flows in an open‐channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter‐rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open‐channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Reynolds stress modelling of rectangular open‐channel flow

A Reynolds stress model for the numerical simulation of uniform 3D turbulent open‐channel flows is described. The finite volume method is used for the numerical solution of the flow equations and transport equations of the Reynolds stress components. The overall solution strategy is the SIMPLER algorithm, and the power‐law scheme is used to discretize the convection and diffusion terms in the governing equations. The developed model is applied to a flow at a Reynolds number of 77000 in a rectangular channel with a width to depth ratio of 2. The simulated mean flow and turbulence structures are compared with measured and computed data from the literature. The computed flow vectors in the plane normal to the streamwise direction show a small vortex, called inner secondary currents, located at the juncture of the sidewall and the free surface as well as the free surface and bottom vortices. This small vortex causes a significant increase in the wall shear stress in the vicinity of the free surface. A budget analysis of the streamwise vorticity is carried out. It is found that both production terms by anisotropy of Reynolds normal stress and by Reynolds shear stress contribute to the generation of secondary currents. Copyright © 2006 John Wiley & Sons, Ltd.     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

Experiments on the linear instability of flow in a wavy channel

The effects of wall corrugation on the stability of wall-bounded shear flows have been examined experimentally in plane channel flows. One of the channel walls has been modified by introduction of the wavy wall model with the amplitude of 4% of the channel half height and the wave number of 1.02. The experiment is focused on the two-dimensional travelling wave instability and the results are compared with the theory [J.M. Floryan, Two-dimensional instability of flow in a rough channel, Phys. Fluids 17 (2005) 044101 (also: Rept. ESFD-1/2003, Dept. of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada, 2003)]. It is shown that the flow is destabilized by the wall corrugation at subcritical Reynolds numbers below 5772, as predicted by the theory. For the present corrugation geometry, the critical Reynolds number is decreased down to about 4000. The spatial growth rates, the disturbance wave numbers and the distribution of disturbance amplitude measured over such wavy wall also agree well with the theoretical results.     

压力梯度对湍流逆梯度输运的影响

研究Birkhoff系统的一般Lie对称性导致的非Noether守恒量. 得到非Noether守恒 量的存在定理，举例说明结果的应用.     

A numerical study of flow through wavy-walled channels

A numerical procedure is developed for the analysis of flow in a channel whose walls describe a travelling wave motion. Following a perturbation method, the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are calculated using the pseudospectral collocation method. Although limited by the linear analysis, the present approach is not restricted by the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel. Using the computed wall shear stresses, the positions of flow separation and reattachment are determined. The variations in velocity and pressure with frequency of excitation are also presented. © 1998 John Wiley & Sons, Ltd.     

A numerical study of turbulent flow over a two‐dimensional hill

Calculations of mean velocities and Reynolds stresses are reported for the recirculating flow established in the wake of two‐dimensional polynomial‐shaped obstacles that are symmetrical about a vertical axis and mounted in the water channel downstream of a fully developed channel flow for Re=6×10⁴. The study involves calculations of mean and fluctuating flow properties in the streamwise and spanwise directions and include comparisons with experimental data [Almeida GP, Durão DFG, Heitor MV. Wake flows behind two‐dimensional model hills. Experimental Thermal and Fluid Science 1993; 7: 87–101] for flow around a single obstacle with data resulting from the interaction of consecutive obstacles, using two versions of the low‐Reynolds number differential second‐moment (DSM) closure model. The results include analysis of the turbulent stresses in local flow co‐ordinates and reveal flow structure qualitatively similar to that found in other turbulent flows with a reattachment zone. It is found that the standard isotropization of production model (IPM), based on that proposed by Gibson and Launder [Ground effects on pressure fluctuations in the atmospheric boundary layer. Journal of Fluid Mechanics 1978; 86(3): 191–511], with the incorporation of the wall reflection model of Craft and Launder [New wall‐reflection model applied to the turbulent impinging jet. AIAA Journal 1992; 32(12): 2970–2972] predicts the mean velocities quite well, but underestimates the size of the recirculation region and turbulent quantities in the shear layer. These inadequacies are circumvented by adopting a new cubic Reynolds stress closure scheme based on that more recently developed by Craft and Launder [A Reynolds stress closure designed for complex geometries. International Journal of Heat and Fluid Flow 1996; 17: 245–254] which satisfies the two component limit (TCL) of turbulence. In this model the geometry‐specific quantities, such as the wall‐normal vector or wall distance, are replaced by invariant dimensionless gradient indicators. Also, the model captures the diverse behaviour of the different components of the stress dissipation, ε_ij, near the wall and uses a novel decomposition for the fluctuating pressure terms. Copyright © 2001 John Wiley & Sons, Ltd.     

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

We perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

摆动河槽水动力稳定性特征分析

河流形态与水动力结构息息相关,形态约束水动力结构,水动力结构则通过泥沙运动进一步塑造形态,在自然界河流中形成一对辩证互馈关系.天然河流形态形式多样,大致可以分为顺直、微弯、分叉和散乱游荡几种类型,其中微弯及多个弯曲构成的河型为河流动力演化中最重要的一环.多个弯曲构成的河型可用正弦派生曲线来描述,它也是天然河流主槽与水动力结构复杂相互作用的结果.作为探讨这一过程的力学作用机理,构建摆动槽道并研究槽道摆动与其内部流动结构的互馈关系,既是流体力学研究的热点内容,也是目前河流动力过程研究的基础内容.在此重点讨论这一互馈关系前一部分,即水流对摆动边界的响应.文中建立了随体坐标系下摆动河槽与内部水流动力响应理论模型,通过给定摆动弯曲槽道的不同特征参数,研究讨论了正弦派生型摆动边界下的槽道水流动力稳定性特征,明确了弯曲槽道摆动对其内部主流及扰动水流结构的影响,确定弯曲槽道摆动波数、摆动频率对扰动流发展影响的相应参数定量关系,得到了槽道弯曲度和摆动特征对其内部水流不同尺度扰动影响的阈值选择性范围.     

An eddy viscosity model with near‐wall modifications

An extended version of the isotropic k–ε model is proposed that accounts for the distinct effects of low‐Reynolds number (LRN) and wall proximity. It incorporates a near‐wall correction term to amplify the level of dissipation in nonequilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz' inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate that the present model is a significant improvement over the standard eddy viscosity formulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐scale turbulence effects were simulated through a shear‐improved Smagorinsky model (SISM), which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical analysis of developing turbulent flow in a 180° bend tube by an algebraic Reynolds stress model

A numerical analysis has been performed for three‐dimensional developing turbulent flow in a 180° bend tube with straight inlet and outlet section used by an algebraic Reynolds stress model. To our knowledge, numerical investigations, which show the detailed comparison between calculated results and experimental data including distributions of Reynolds stresses, are few and far between. From this point of view, an algebraic Reynolds stress model in conjunction with boundary‐fitted co‐ordinate system is applied to a 180° bend tube in order to predict the anisotropic turbulent structure precisely. Calculated results are compared with the experimental data including distributions of Reynolds stresses. As a result of this analysis, it has been found that the calculated results show a comparatively good agreement with the experimental data of the time‐averaged velocity and the secondary vectors in both the bent tube and straight outlet sections. For example, the location of the maximum streamwise velocity, which appears near the top or bottom wall in the bent tube, is predicted correctly by the present method. As for the comparison of Reynolds stresses, the present method has been found to simulate many characteristic features of streamwise normal stress and shear stresses in the bent tube qualitatively and has a tendency to under‐predict its value quantitatively. Judging from the comparison between the calculated and the experimental results, the algebraic Reynolds stress model is applicable to the developing turbulent flow in a bent tube that is known as a flow with a strong convective effect. Copyright © 2005 John Wiley & Sons, Ltd.     

Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.