Turbulence-driven Secondary Motion Research Articles

Large-Eddy Simulations of turbulent flow through a heated square duct

The behavior of the flow through a straight square duct is examined using Large-Eddy Simulations. Both isothermal and non-isothermal conditions were considered, the latter generated with either the wall temperature or the wall heat flux held constant. Fully-developed conditions were attained by initializing the velocity field with perturbed streamwise streaks, and by employing a method for efficiently applying cyclic boundary conditions to the velocity field while minimizing aliasing errors. Results were obtained for two values of bulk Reynolds numbers, Reb=6,000 and 10,000. The numerical accuracy was checked via several alternative methods that included performing computations on grids with different resolutions, both with and without sub-grid scale models. The results were used to test some of the assumption underlying the use of RANS approaches to predict the flow and thermal fields. Of particular interest was the examination of the effects of the turbulence-driven secondary motions on the near-wall processes, especially on existence and extent of the thermal logarithmic law of the wall, and on departures from the Reynolds analogy. Their effect on the turbulent Prandtl number was quantified, and the implications on the use of Fourier's law to relate the turbulent heat fluxes to the gradients on mean temperature are discussed.

Aspect ratio effect on particle transport in turbulent duct flows

The dynamics of dilute micron-sized spherical inertial particles in turbulent duct flows is studied by means of direct numerical simulations of the carrier phase turbulence with one-way coupled Lagrangian particles. The geometries are a square and a rectangular duct with width-to-height aspect ratio AR of 3 operating at Reτ,c = 360 (based on the centerplane friction velocity and duct half-height). The present study is designed to determine the effect of turbulence-driven secondary motion on the particle dynamics. Our results show that a weak cross-flow secondary motion significantly changes the cross-sectional map of the particle concentration, mean velocity, and fluctuations. As the geometry of the duct is widened from AR = 1 to 3, the secondary vortex on the horizontal wall significantly expands in the spanwise direction, and although the kinetic energy of the secondary flow increases close to the corner, it decays towards the duct centreplane in the AR = 3 case so as the turbulent carrier phase approaches the behavior in spanwise-periodic channel flows, a fact that significantly affects the particle statistics. In the square duct the particle concentration in the viscous sublayer is maximum at the duct centreplane, whereas the maximum is found closer to the corner, at a distance of |z/h| ≈ 1.25 from the centreplane, in the AR = 3 case. Interestingly the centreplane concentration in the rectangular duct is around 3 times lower than that in the square duct. Moreover, a second peak in the accumulation distribution is found right at the corners for both ducts. At this location the concentration increases with particle inertia. The secondary motion changes also the cross-stream map of the particle velocities significantly in comparison to the fluid flow statistics. These directly affect the particle velocity fluctuations such that multiple peaks appear near the duct walls for the particle streamwise and wall-normal velocity fluctuations.

Numerical simulation of turbulent flow through a straight square duct

Turbulent duct flows are investigated using large eddy simulation at bulk Reynolds numbers, from 4410 to 250,000. Mean secondary flow is found to reveal the existence of two streamwise counter-rotating vortices in each corner of the duct. Turbulence-driven secondary motions that arise in duct flows act to transfer fluid momentum from the centre of the duct to its corners, thereby causing a bulging of the streamwise velocity contours towards the corners. As Reynolds number increases, the ratio of centreline streamwise velocity to the bulk velocity decreases and all turbulent components increase. In addition, the core of the secondary vortex in the lower corner-bisector tends to approach the wall and the corner with increasing Reynolds number. The turbulence intensity profiles for the low Reynolds number flows are quite different from those for the high Reynolds number flows. Typical turbulence structures in duct flows are found to be responsible for the interactions between ejections from wall and this interaction results in the bending of the ejection stems, which indicates that the existence of streaky wall structures is much like in a channel flow.

Nonlinear eddy viscosity modeling and experimental study of jet spreading rates

Indoor airflow pattern is strongly influenced by turbulent shear and turbulent normal stresses that are responsible for entrainment effects and turbulence-driven secondary motion. Therefore, an accurate prediction of room airflows requires reliable modeling of these turbulent quantities. The most widely used turbulence models include RANS-based models that provide quick solutions but are known to fail in turbulent free shear and wall-affected flows. In order to cope with this deficiency, this study presents a nonlinear k-ε turbulence model and evaluates it along with linear k-ε models for an indoor isothermal linear diffuser jet flow measured in two model rooms using PIV. The results show that the flow contains a free jet near the inlet region and a wall-affected region downstream where the jet is pushed toward the ceiling by entrainment through the well-known Coanda effect. The CFD results show that an accurate prediction of the entrainment process is very important and that the nonlinear eddy viscosity model is able to predict the turbulence-driven secondary motions. Furthermore, turbulence models that are calibrated for high Reynolds free shear layer flows were not able to reproduce the measured velocity distributions, and it is suggested that the model constants of turbulence models should be adjusted before they are used for room airflow simulations.

Numerical simulation for turbulence-driven secondary motion over a streamwise external corner

Numerical simulation, based on a Reynolds Stress Model (RSM), of turbulent flow over a streamwise external corner is presented. This work is an extension of an earlier experimental study (Moinuddin et al., 2004), which identified a pair of counter-rotating vortices placed around the corner of a 6 m long model. Experimental data measured at an early station is used as the inlet condition for the numerical simulation. Mean flow and turbulence statistics from numerical simulation are compared with the experimental data at a downstream station and they are found to be in excellent qualitative agreement. For the scaled mean flow data, quantitative agreement is also very good. Investigation reveals that vorticity production by secondary shear stress is dominant in generating secondary flow over an external corner, which is opposite for the case of an internal corner as found by Xu and Pollard (2001).

Experimental investigation of turbulence-driven secondary motion over a streamwise external corner

Turbulence-driven secondary motion (known as secondary flow of Prandtl's second kind) is the result of the anisotropy of Reynolds stresses. It is associated with internal or external turbulent flow in the vicinity of streamwise corners. In the last six decades the flow along the streamwise internal corner has attracted the attention of many researchers, but it is only recently at the University of Melbourne that an experimental investigation on a flow over an external corner has been undertaken. Although the turbulence-driven secondary motions are generally much smaller than those resulting from skewing of the mean spanwise vorticity (known as secondary flow of Prandtl's first kind), they have a pronounced effect on peripheral wall shear stress distributions and heat transfer rates in the corner region. In the present study the details of turbulence-driven secondary motion over the external corner are explored experimentally and a counter-rotating helical streamwise vortex pair symmetrically placed around the corner bisector is found. As expected, all mean velocity and Reynolds stress profiles on both surfaces at the same spanwise distance from the corner agree quite well, having nominal deviation. The secondary flow is observed to be directed away from the corner bisector and then flow back towards the wall. It is also revealed that far from the corner, the flow develops as a nominal two-dimensional flat-plate boundary-layer flow.

비선형 저레이놀즈수 κ-ε 난류모델에 따른 정사각형 덕트내 완전 발달된 난류유동 예측

Fully developed turbulent flow in a square duct is numerically predicted with two nonlinear low-Reynolds-number models. Typical predicted quantities such as axial and secondary velocities, turbulent kinetic energy and Reynolds stresses are compared in detail with each other. It is found that the nonlinear low-Reynolds-number model adopted in a commercial code is unable to predict accurately duct flows involving turbulence-driven secondary motion with the prediction level of secondary flows one order less than that of the experiment.

Pressure-Sensitive Paint Measurements in Planar Transonic Nozzle Flow

References 1Bradshaw, P., “Turbulent Secondary Flow,” Annual Review of Fluid Mechanics, Vol. 19, 1987, pp. 53–74. 2Demuren, A. O., and Rodi,W., “Calculations of Turbulence-Driven Secondary Motion in Non-Circular Ducts,” Journal of Fluid Mechanics, Vol. 140, 1984, pp. 189–222. 3Launder, B. E., and Rodi, W., “The Turbulent Wall Jet,” Annual Review of Fluid Mechanics, Vol. 15, 1983, pp. 429–459. 4Rodi, W., “A New Algebraic Relation for Calculating the Reynolds Stresses,” ZAMM, Vol. 56, No. 3, 1976, pp. T219–T221. 5Gatski, T. B., and Speziale, C. G., “On Explicit Algebraic Stress Models for Complex Turbulent Flows,” Journal of FluidMechanics, Vol. 254, 1993, pp. 59–75. 6Rivlin, R. S., and Ericksen, J. L., “Stress-Deformation Relations for Isotropic Materials,” Journal of Rational Mechanics and Analysis, Vol. 4, 1955, pp. 323–425. 7Speziale, C. G., Sarkar, S., and Gatski, T. B., “Modelling the PressureStrain Correlation of Turbulence: An Invariant Dynamical Systems Approach,” Journal of Fluid Mechanics, Vol. 227, 1991, pp. 245–272. 8Gibson,M.M., andLaunder,B.E., “GroundEffects on thePressureFluctuations in the Atmospheric Boundary Layer,” Journal of Fluid Mechanics, Vol. 86, 1978, pp. 491–511. 9Rung,T.,Thiele, F., and Fu,S., “On theRealizability ofNonlinearStressStrain Relationships for Reynolds Stress Closures,” Flow, Turbulence, and Combustion, Vol. 60, No. 4, 1999, pp. 333–359. 10Demuren, A. O., “On the Generation of Secondary Motion in Circularto-Rectangular Transition Ducts,” AIAA Paper 93-0681, 1993. 11Sotiropoulos, F., and Patel, V. C., “Prediction of Turbulent Flow ThroughaTransitionDuctUsing aSecond-MomentClosure,”AIAA Journal, Vol. 27, No. 11, 1994, pp. 2194–2204.

Second-Order Closure Study of Open-Channel Flows

A complete second-order closure model of turbulence is used to predict the behavior of fully developed turbulent flows in open channels of both simple and compound cross sections. This level of closure entails the solution of seven differential transport equations for turbulence quantities and is found to reproduce fairly accurately the details of the turbulence-driven secondary motions that occur in the cross-stream planes. In particular, the number, location, and strength of the secondary-flow cells are well predicted, as is their effect on the bulk properties of the mean flow. Data from simple rectangular channels are used to check the model's sensitivity to the effects of a free surface, and data from compound channels, both symmetric and asymmetric, serve to validate the model for a range of parameters typical of those encountered in practice.

Investigation of Fully Developed Turbulent Flow in a Straight Duct With Large Eddy Simulation

Large eddy simulations have been performed in straight ducts with square cross section at a global Reynolds number of 49,000 in order to predict the complicated mean and instantaneous flow involving turbulence-driven secondary motion. Isotropic grid systems were used with spatial resolutions of 256 * 642. The secondary flow not only turned out to develop extremely slowly from its initial conditions but also to require fairly high resolution. The obtained statistical results are compared with measurements. These results show that the large eddy simulation (LES) is a powerful approach to simulate the complex turbulence flow with high Reynolds number. Streaklines of fluid particles in the duct show the secondary flow clearly. The database obtained with LES is used to examine a statistical turbulence model and describe the turbulent vortex structure in the fully developed turbulent flow in a straight duct.

Prediction of Turbulent Flows in Rotating Rectangular Ducts

This paper reports on progress made in the development of a numerical predictive procedure for turbulent flows in rotating rectangular ducts. The unknown turbulent stresses were approximated with the k–ε model of turbulence while Speziale’s (1987) nonlinear stress-strain relationship was utilized to capture the turbulence-driven secondary motions. Data from stationary rectangular ducts of aspect ratios in the range 1:1 to 10:1 were used to check the model. It was found that the occurrence and consequences of these motions were well reproduced. Application of the model to rotating rectangular ducts yielded results which suggest that the interactions between the pressure and turbulence-driven motions are far more important than hitherto suspected.

Prediction of Three-Dimensional Developing Turbulent Flow in a Square Duct With an Anisotropic Low-Reynolds-Number k-ε Model

Three-dimensional developing turbulent flow in a square duct involving turbulence-driven secondary motion is numerically predicted with an anisotropic low-Reynolds-number k-ε turbulence model. Special attention has been given to both regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, the no-slip boundary condition at the wall is directly used in place of the common wall function approach. The resulting set of equations simplified only by the boundary layer assumption are first compared with previous algebraic stress models, and solved with a forward marching numerical procedure for three-dimensional shear layers. Typical predicted quantities such as mean axial and secondary velocities, friction coefficients, turbulent kinetic energy, and Reynolds shear stress are compared with available experimental data. These results indicate that the present anisotropic k-ε turbulence model performs quite well for this complex flow field.

Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section

Calculation methods for turbulent duct flows are generalised for ducts with arbitrary cross sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered in the present study.

Large Eddy Simulation of Turbulent Flow in a Square Duct

Large Eddy Simulation (LES) with a Finite Difference Method is presented for a fully developed turbulent flow in a square duct. Furthermore the present method is applied to investigation into a microbubble injected flow. The 3rd order up-wind finite difference is employed to dissipate numerical errors which arise from the convection term. Other partial differential operations in space are approximated with the 4th order central finite differences. A regular grid system is adopted and all velocity components and pressure are defined at the same grid points. Turbulence-driven secondary motion is reasonably simulated without a special anisotropic model. The microbubble and water mixture is treated as a homogeneous fluid with spatially varying properties. The local density and molecular viscosity of the mixture are represented as a function of the rate of bubble concentration in boundary layer. The turbulent structure depending upon the bubble injection in the boundary layer is studied.

Calculation of turbulence-driven secondary motion in non-circular ducts

Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate ε of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it.

Calculation of Secondary Currents in Channel Flow

A model is presented for calculating the flow in channels with turbulence-driven secondary motion, with an emphasis on open channel flow. Algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying modelled Reynolds stress equations. A simple eddy viscosity model is used for the shear stresses in the logitudinal momentum equation. The kinetic energy k, and the dissipation rate ϵ of the turbulent motion appearing in the algebraic and eddy viscosity expressions are determined from transport equations for these quantities. The restricting influence of a free surface on the length scale of turbulence is accounted for by a special free surface boundary condition for ϵ. The resulting set of equations is solved with a marching forward numerical procedure for three-dimensional boundary layers. The model is tested by application to developed two-dimensional closed and open channel flow, closed square duct flow, and flow in open channels of various width-to-depth-ratios. Most features of these flows are simulated well by the model, including the reduction of the eddy viscosity near the free surface and the depression of the velocity maximum below the surface.