Results of direct numerical simulation of turbulent flow in a pipe of elliptical cross-section

Within the framework of the complete Navier-Stokes equations the turbulent flow in a pipe of elliptical cross-section with semiaxis ratio b/a = 0.5 is directly calculated for the Reynolds number Re = 6000 determined from the mean-flow velocity and the hydraulic diameter. The distribution of the average and pulsatory flow characteristics over the pipe cross-section are obtained. In particular, the secondary flow in the cross-section plane, typical of turbulent flows in noncircular pipes, is calculated. The equation for the longitudinal vorticity which determines the shape and intensity of the secondary flow is analyzed. In the balance equation for the pulsation kinetic energy the behavior of all the terms that characterize energy production, dissipation and redistribution over the pipe cross-section is described.     

Direct numerical simulation of turbulent flow in a spanwise rotating square duct at high rotation numbers

In this paper, direct numerical simulations have been performed to study the effects of Coriolis force on the turbulent flow field confined within a square duct subjected to spanwise system rotations at high rotation numbers. In response to the system rotation, secondary flows appear as large streamwise counter-rotating vortices, which interact intensely with the four boundary layers and have a significant impact on flow statistics, velocity spectra and coherent structures. It is observed that at sufficiently high rotation numbers, a Taylor–Proudman region appears and complete laminarization is almost reached near the top and side walls. The influence of large organized secondary flows on the production rate and re-distribution of turbulent kinetic energy has been investigated through a spectral analysis. It is observed that the Coriolis force dominates the transport of Reynolds stresses and turbulent kinetic energy, and forces the spectra of streamwise and vertical velocities to synchronize within a wide range of scales.     

Prediction of Turbulence-Generated Secondary Mean Flow in a Square Duct

Near-wall second-moment closures have revealed a tendency to severely underpredict the strength of the turbulence-generated secondary flow in noncircular ducts. The aim of this study has been to elucidate the reasons for this failure that seems to be present at both high and low Reynolds numbers. Fully developed three-componential turbulent flow inside a straight square duct has been computed with the quasi-linear SSG second-moment closure and near-wall effects were modeled by elliptic relaxation. The results compared favourably with the reference DNS data, except that the strength of the turbulence-induced secondary flows is significantly underpredicted. A close examination of the generation mechanisms of the mean streamwise vorticity revealed that this discrepancy can be attributed to the secondary shear-stress component, the importance of which is generally overlooked. The normal-stress anisotropy was, however, adequately returned by the model and so was the variation of the friction velocity with Reynolds number over a wide Reynolds-number range. The present study supports the view that the wall-function approach should be abandoned in order to retain a physical appealing representation of the generation mechanisms of mean streamwise vorticity along internal corners. This revised version was published online in July 2006 with corrections to the Cover Date.     

Geometrical aspects of secondary motion in turbulent duct flow

Fully developed turbulent flow through straight ducts is considered. An analysis in a Reynolds stress principal-axis coordinate frame is performed with the aim of clarifying the main mechanisms responsible for turbulence-driven secondary (transverse) mean flow in noncircular ducts. Together with this, some basic properties of that flow are deduced.This work was supported by the Advanced Engineering Research Center at the University of Utah during the spring of 1990, and subsequently by the National Science Foundation under Grant DMS 8901771.     

Performance of RNG Turbulence Modelling for Forced Convective Heat Transfer in Ducts

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in straight ducts using the RNG (Re-Normalized Group) turbulence method.

A computational method has been developed to predict the turbulent Reynolds stresses and turbulent heat fluxes in ducts with different turbulence models. The turbulent Reynolds stresses and other turbulent flow quantities are predicted with the RNG κ?ε model and the RNG non-linear κ-ε model of Speziale. The turbulent heat fluxes are modeled by the simple eddy diffusivity (SED) concept, GGDH and WET methods. Two wall functions are used, one for the velocity field and one for the temperature field. All the models arc implemented for an arbitrary three dimensional duct.

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 QUICK, scheme while the diffusive terms are handled by the central-difference scheme. The hybrid scheme is used for solving the κ and ε equations.

The overall comparison between the models is presented in terms of friction factor and Nusselt number. The secondary flow generation is also of major concern.     

Turbulent flow in a duct with cusped corners

An orthogonal-cuvilinear-mesh-based finite volume calculation method has been applied to the problem of fully developed turbulent flow in the tri-cusped cornered duct formed when parallel circular rods touch in triangular array. Algebraic stress relations combined with the k-? turbulence model are used for calculation of the required stresses. A single circulation of turbulence-driven cross-plane secondary flow from the core into the duct corner has been predicted in a one-sixth symmetry region of the duct and the convective transport effects of this flow are seen to have much influence on local mean flow distributions. The turbulence field predicted by the k-? model showed significant damping in the cusped corner region where turbulent viscosities approached the laminar value. Satisfactory agreement was obtained with the limited local and overall mean flow measurements available.     

Numerical and experimental investigation of turbulent flow in a rectangular duct

Details of the turbulent flow in a 1:8 aspect ratio rectangular duct at a Reynolds number of approximately 5800 were investigated both numerically and experimentally. The three-dimensional mean velocity field and the normal stresses were measured at a position 50 hydraulic diameters downstream from the inlet using laser doppler velocimetry (LDV). Numerical simulations were carried out for the same flow case assuming fully developed conditions by imposing cyclic boundary conditions in the main flow direction. The numerical approach was based on the finite volume technique with a non-staggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with a linear and a non-linear (Speziale) k–ε model, combined with the Lam–Bremhorst damping functions for low Reynolds numbers. The secondary flow patterns, as well as the magnitude of the main flow and overall parameters predicted by the non-linear k–ε model, show good agreement with the experimental results. However, the simulations provide less anisotropy in the normal stresses than the measurements. Also, the magnitudes of the secondary velocities close to the duct corners are underestimated. © 1998 John Wiley & Sons, Ltd.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

Development of wake of a rectangular cylinder in a curved stream

In the wake of a rectangular cylinder measurements of mean velocity and some turbulent stresses are carried out in a straight duct and in a curved duct. The difference in turbulent quantities in the wake of the body, in the straight duct an in the curved duct is significant especially in the downstream side of the wake. The shear stresses are more sensitive to curvature than the normal stresses.     

Break-Up of Aerosol Agglomerates in Highly Turbulent Gas Flow

Agglomerate aerosols in a turbulent flow may be subjected to very high turbulent shear rates which through the generation of lift and drag can overcome the adhesive forces binding the constituents of an agglomerate together and cause it to break-up. This paper presents an analysis of the experimental measurements of the breakup of agglomerates between 0.1?C10???m in size, in a turbulent pipe flow followed by an expansion zone with a Reynolds numbers in the range 10⁵ to 10⁷. The analysis shows that even in wall bounded turbulence, the high turbulent shear stresses associated with the small scales of turbulence in the core can be the main source of breakup preceding any break-up that may occur by impaction at the wall. More importantly from these results, a computationally fast and efficient solution is obtained for the General Dynamic Equation (GDE) for agglomerate transport and breakup in highly turbulent flow. Furthermore the solution for the evolution of the aerosol size distribution is consistent with the experimental results. In the turbulent pipe flow section, the agglomerates are exposed continuously to turbulent shear stresses and experience more longer term breakup than in the expansion zone (following the pipe flow) where the exposure time is much less and break-up occurs instantaneously under the action of very high local turbulent shear stresses. The validity of certain approximations made in the model is considered. In particular, the inertia of the agglomerates characterised by a Stokes Number from 0.001 for the smallest particles up to 10 for 10???m particles and the fluctuations of the turbulent shear stresses are important physical phenomena which are not accounted for in the model.     

Numerical calculation of Reynolds stresses in a square duct with secondary flow

A new model for the Reynolds stress equations is presented. This model is used to obtain a theoretical solution for the problem of fully developed turbulent flow in a square duct. Nine governing equations for the axial velocity, lateral vorticity, lateral stream function and six components of the Reynolds stresses are simultaneously solved, by a finite-difference technique. To ensure numerical stability of the solution a special linearised implicit representation of the source terms is proposed, and simultaneous solution of the equations at each.mesh point is obtained. Near the wall a special procedure is used, by which the Reynolds stress equations are assumed to be in local equilibrium, and the velocity profile is assumed to be logarithmic. However, due to the secondary motion the logarithmic velocity profile is inclined to the axial direction. The results bear reasonable agreement with experimental data. Computer time requirements are moderate.     

Rotation correction of wall function and velocity structure under the couple effects of buoyancy force and rotating effects at the entry section of the smooth straight channel

This paper studies the effect of rotation on the turbulent boundary-layer flow in a rotating duct with a square cross section by using hot-wire. The experiments were conducted with the Reynolds numbers, based on the duct's hydraulic diameter (D = 80 mm) equaling 19,000. The rotation numbers (Ro) studied ranged from 0 to 0.362. Hot-wire measurements of the flow field were made at four cross sections of the rotating duct. The effects of rotation on velocity profile, semi-logarithmic mean velocity profile, and wall shear stress are discussed in this paper. Results obtained show the velocity deficit about the leading surface of the rotating duct, created by the secondary flows induced by the Coriolis force, to not increase monotonically with the increase in the Rotation number. Results obtained also show the effects of rotation to penetrate into the logarithm region, and the flow near the leading surface tends to laminarize. In this study, a correction factor is developed for logarithmic law to account for the effects of rotation, which can be used in CFD studies of rotating ducts that use wall functions.     

单一倾斜热线探头在三维湍流场中的应用

研究的目的是确立用单一倾斜热线探头进行三维湍流测试的基础技术．在阐明基本原理，基础方程式的基础上，对比实验结果，证明应用所阐明的方法、用单一倾斜热线探头进行三维湍流测试是切实可行的．对边界层壁面附近的测试结果表明考虑平均速度和变动速度的高次相关项后可以得到更加精确的实验结果．     

Verification of three-dimensional laser Doppler velocimeter measurements

An experimental comparison method is proposed for the verification of mean flow and turbulence measurements obtained with a three-dimensional laser Doppler velocimeter system. Such measurements can include large errors caused by problems unique to three-dimensional systems. Direct comparisons of laser and hot cross-wire measurements obtained in two-dimensional flows, as is the common practice, will not bear out all the errors associated with three-dimensional laser systems. It is proposed here that the errors may be adequately quantified by making the direct comparisons in a weakly three-dimensional turbulent shear flow. The weak three-dimensional flow ensures high accuracy of the cross-wire data while still generating sufficiently strong secondary mean flow and Reynolds shear stresses so that all the laser measurements may be fully verified. This type of shear flow is easily generated by introducing a weak streamwise vortex into a nominally two-dimensional turbulent shear layer.     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

A crossed hot-wire technique for complex turbulent flows

This paper describes a crossed hot-wire technique for the measurement of all components of mean velocity, Reynolds stresses, and triple products in a complex turbulent flow. The accuracy of various assumptions usually implicit in the use of crossed hot-wire anemometers is examined. It is shown that significant errors can result in flow with gradients in mean velocity or Reynolds stress, but that a first order correction for these errors can be made using available data. It is also shown how corrections can be made for high turbulence levels using available data.     

Experimental and numerical investigation of turbulent cross-flow in a staggered tube bundle

This paper presents the results of measurements and numerical predictions of turbulent cross-flow in a staggered tube bundle. The bundle consists of transverse and longitudinal pitch-to-diameter ratios of 3.8 and 2.1, respectively. The experiments were conducted using a particle image velocimetry technique, in a flow of water in a channel at a Reynolds number of 9300 based on the inlet velocity and the tube diameter. A commercial CFD code, ANSYS CFX V10.0, is used to predict the turbulent flow in the bundle. The steady and isothermal Reynolds–Averaged Navier–Stokes (RANS) equations were used to predict the turbulent flow using each of the following four turbulence models: a k-epsilon, a standard k-omega, a k-omega-based shear stress transport, and an epsilon-based second moment closure. The epsilon-based models used a scalable wall function and the omega-based models used a wall treatment that switches automatically between low-Reynolds and standard wall function formulations.

The experimental results revealed extremely high levels of turbulence production by the normal stresses, as well as regions of negative turbulence production. The convective transport by mean flow and turbulent diffusion were observed to be significantly higher than in classical turbulent boundary layers. As a result, turbulence production is generally not in equilibrium with its dissipation rate. In spite of these characteristics, it was observed that the Reynolds normal stresses approximated from the k-based two-equation models were in a closer agreement with experiments than values obtained from the second moment closure. The results show that none of the turbulence models was able to consistently reproduce the mean and turbulent quantities reasonably well. The omega-based models predicted the mean velocities better in the developing region while the epsilon-based models gave better results in the region where the flow is becoming spatially periodic.     

Numerical investigation of fully developed turbulent fluid flow and heat transfer in a square duct

Three-dimensional fully developed turbulent fluid flow and heat transfer in a square duct are numerically investigated with the author's anisotropic low-Reynolds-number k-ε turbulence model. Special attenton has been given to the regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, instead of the common wall function approach, the no-slip boundary condition at the wall is directly used. Velocity and temperature profiles are predicted for fully developed turbulent flows with constant wall temperature. The predicted variations of both local wall shear stress and local wall heat flux are shown to be in close agreement with available experimental data. The present paper also presents the budget of turbulent kinetic energy equation and the systematic evaluation for existing wall function forms. The commonly adopted wall function forms that are valid for two-dimensional flows are found to be inadequate for three-dimensional turbulent flows in a square duct.     

A unified theory of turbulent flow

Summary A critical analysis is made of the assumptions underlying Reynolds' equations for turbulent flow. It is shown that there are regions in a flow field where these assumptions break down, and it is therefore necessary to separate the flow into a turbulent core and a laminar sublayer. The importance of the boundary conditions to be imposed on the mean velocities and Reynolds stresses at the junction is emphasized as this is the way in which the effect of surface roughness enters the theory. A set of equations for calculating turbulent flows is proposed. The distinctive feature is that the turbulent stresses are represented as the difference between viscous terms with a large eddy viscosity and terms satisfying auxiliary differential equations proposed by Broszko. These terms may be associated with the free and wall turbulence respectively. The theory enables the idea of a large eddy viscosity to be applied even where the velocity gradient is large. The results obtained for specific configurations, which will be reported in detail in future papers, are previewed.     

含污染物的弱弯曲明渠弯道湍流数值模拟

建立了可模拟弯道中含污染物湍流的三维部分抛物型代数应力模型。针对左右两岸分别泄放污染物的环流非充分发展弯道流进行了计算。分析了水流结构及污染物浓度分布的特点。