Turbulence-driven Secondary Flow Research Articles

Mechanisms of particle preferential concentration induced by secondary motions in a dilute turbulent square duct flow

Particle-laden turbulent square duct flows at Reτ = 300 (based on the duct half-width and the mean friction velocity) are investigated using direct numerical simulation with one-way coupled Lagrangian particle tracking. Four particle-to-fluid density ratios are considered with the corresponding shear Stokes number St+ = 0.31, 25, 125, and 260. Particle motion is governed by drag, lift, added-mass, and pressure gradient forces. The main purpose of this work is to examine the effect of the turbulence-driven secondary flows on particle preferential accumulation and their dependence on the Stokes number. Results obtained indicate that the cross-stream secondary motions encourage inertial particles to accumulate preferentially in the duct corners, where the maximum of the cross-sectional particle concentration occurs. The extent of accumulation here is strongly dependent on the Stokes number, with the greatest accumulation found at St+ = 25. Interestingly, the maximum of the intensity of the secondary particle velocity along the corner bisector is also achieved at St+ = 25, whereas in the region adjacent to the wall, it is found to decrease with a particle Stokes number. Additionally, it is observed that the higher inertia particles are more easily trapped in the stagnation zone of secondary flows with low turbulence intensity in the corner region. In the near-wall region, the heavier particles (St+ ≥ 25) are prone to reside and form elongated clusters along the low-speed streamwise velocity streaks, with this trend less pronounced with the increasing Stokes number. Along the wall, away from the corner where the secondary motion is attenuated, particle accumulation is dominated by the near-wall coherent vortices. This phenomenon is further discussed using a region-based correlation analysis between the particle spatial distribution and local flow topology. An in-depth particle dynamic analysis determines that the average cross-sectional drag force resulting from the secondary flow is mainly responsible for the particle motion throughout the duct cross section, which tends to push particles away from the walls in the near-wall region but shows the exact opposite trend in the bulk flow region. Moreover, the pressure gradient force also plays an important role for low-inertia particles. As the Stokes number is increased, the lift force becomes progressively dominant in the viscous sublayer, acting to pull particles toward the corners and walls of the duct.

Turbulent flow characteristics for enhanced thermal mixing in square and triangular jets

In this study, turbulent flows and the associated mixing characteristics are numerically investigated for noncircular jets. The selected nozzle shapes are round, square, and equilateral triangular, and a passive scalar is adopted to quantify the flow mixing. To achieve a constant mass flow rate, the same cross-sectional area is maintained, and the Reynolds stress model (RSM) is applied to show the turbulence-driven secondary flows. For Re = 21,000, the flow fields of noncircular jets are compared to those of the round jet. After 5 < x/De < 10, the half-widths of the round, square, and triangular jets increase linearly. This self-similar structure of the jet flow is rapidly developed for the noncircular jets. Compared to that for the round jet, the spreading rate for square jet increases by 20% and 27% for the triangular jet. From the mixedness values, the mixing is estimated to be enhanced by 16.7% for the square jet and 22.9% for the triangular jet. To elucidate the flow characteristics related to this feature, the scatter plots and streamlines of the secondary flows, vorticity transport equation, and anisotropy-invariant map are discussed. From the results, a balanced relationship between the entrained flow of ambient fluid and the outward spreading flow is observed, and the related turbulence structure is confirmed.

Effect of turbulence-driven secondary flow on particle preferential concentration and clustering in turbulent square duct flows

In this study, the preferential concentration and clustering of inertial particles in fully developed turbulent square duct flows are studied using large eddy simulations combined with Lagrangian approach, where the Reynolds number is equal to Reτ=600 (based on the mean friction velocity and duct full height), and the particle Stokes number ranges from 0.0007 to 1.16. The results obtained for duct flows are compared with those for channel flows under the same working conditions. Then, the effect of the secondary flow on the particle concentration in duct flows is investigated. The equation of particle motion is governed by the drag force, lift force, added mass force, pressure gradient force, and gravity. The inter-phase interaction that was considered includes one-way and two-way coupling. The simulations of a single phase are verified and in good agreement with the available literature data. For the discrete phase, particles in the duct flow are found to be more dispersed in the vertical direction compared with the channel flow. In near-wall regions, a small fraction of particles tends to accumulate in duct corners, forming stable particle streaks under the effect of the secondary flow. Meanwhile, most particles are likely to reside preferentially in the low-speed flow regions and form elongated particle streaks steadily in the middle region of duct or channel floors. The Voronoi diagram analysis shows that the near-wall secondary flows in the square duct could cause particle clusters to transfer from regions of high to low concentration, and this trend increases with particle size. In addition, two-way coupling is found to enhance the near-wall particle accumulation and to promote particles to form more elongated streaks than one-way coupling. Finally, the mechanism responsible for the particle preferential concentration in turbulent square duct flows is determined.

Turbulent flow over spanwise-varying roughness in a minimal streamwise channel

We report direct numerical simulations in a minimal streamwise domain of turbulent channel flow over spanwise-alternating patches of rough and smooth walls. Despite the minimal streamwise domain overpredicting streamwise-velocity fluctuations and inhibiting the meandering of long turbulent structures, it captures the rotational behaviour of mean secondary flows also observed in other studies with spanwise-varying roughness. To extend the study of spanwise-varying roughness, we prescribe a lateral velocity to the wall roughness to mimic flow over oblique patches of roughness. Far from the wall, long-lived turbulent structures are convected in the direction of the moving roughness, but their speeds are only weakly perturbed from a preferential value of around 40% of the friction velocity. The turbulence-driven secondary flows laterally convect at comparable speeds, but depend on the roughness patch width.

Reynolds stress and turbulence energy spectra analysis of &amp;lt;italic&amp;gt;Re&amp;lt;/italic&amp;gt;-understanding the turbulence constitutive equation DNS data in square and rectangular annular ducts

Through systematic Direct Numerical Simulation (DNS) of the fully-developed turbulence inside a square annular and rectangular annular ducts, the current research established detailed turbulence statistics database, which included: (1) the mean flow field (mean streamwise velocity and turbulence-driven secondary flow or historically the secondary flow of Prandtl second kind); (2) the turbulent Reynolds stresses; and (3) the turbulence energy spectra. The current paper presented the characteristics of the complete Reynolds stress fields, including uu , vv , ww , uv , uw , vw , and provided a convincing validation of these results using the existing experimental measurements from Cheesright (1990) and the DNS data of Gavrilakis (1992). The DNS predicted Reynolds stress fields made it possible to conduct in-depth interrogation of the mechanisms of turbulence-driven secondary flow near the 90° convex corner. The current paper raised a fundamental issue of the isotropic assumption implicitly contained in the conventional constitutive equation of turbulence based on the analogy between the turbulence and molecular motions. Via in-depth observation of the characteristics of Reynolds stresses and turbulence energy spectra, the paper put forward the proposal to develop new constitutive equation of turbulence using the tensor form of eddy viscosity. The research is targeted to provide a capability to fully understand the anisotropic properties of turbulence in engineering practices and to further develop a high-fidelity RANS-based turbulence-closure model using more and more reliable DNS data.

Computer Simulation of Turbulent Flow Phenomena in Nuclear Fuel Pin Subassemblies

This paper focuses on the turbulence phenomena that have been identified by computational fluid dynamics (CFD), and that are peculiar to the flows in tight lattice nuclear fuel subassemblies, eccentric annuli and two-rectangular channels interconnected by a narrow gap. The CFD methods employed are the Direct Numerical Simulation of turbulence (DNS) and Large Eddy Simulation (LES) techniques. Highlighted phenomena include turbulence-driven secondary flows inside a subchannel, local turbulent-laminar transition in the narrow gap region between two adjacent fuel pins, and global pulsation of the flow across the length of a fuel subassembly. Special attention will be paid on linkage to the physics, limitation of the computational capability of the CFD methods, and the usefulness of the technology in reference to the foreseeable future.

The Significance of Simple Invariant Solutions in Turbulent Flows

Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. A significant advance in this respect has been the numerical discovery of simple invariant sets, such as nonlinear equilibria and periodic solutions, in well-resolved Navier-Stokes flows. This review describes some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows. It is shown that the near-wall regeneration cycle of coherent structures can be reproduced by such solutions. The typical similarity laws of turbulence, i.e., the Prandtl wall law and the Kolmogorov law for the viscous range, as well as the pattern and intensity of turbulence-driven secondary flow in a square duct can also be represented by these simple invariant solutions.

Traveling-waves consistent with turbulence-driven secondary flow in a square duct

We present numerically determined traveling-wave solutions for pressure-driven flow through a straight duct with a square cross section. This family of solutions represents typical coherent structures (a staggered array of counter-rotating streamwise vortices and an associated low-speed streak) on each wall. Their streamwise average flow in the cross-sectional plane corresponds to an eight-vortex pattern much alike the secondary flow found in the turbulent regime.

Inertial particle resuspension in a turbulent, square duct flow

Particle resuspension in a turbulent, square duct flow is studied using large eddy simulation combined with Lagrangian particle tracking under conditions of one-way coupling, with the particle equation of motion solved with the Stokes drag, lift, buoyancy, and gravitational force terms. Here, resuspension is taken to mean the movement of particles in close proximity to the duct walls back in to the mainstream of the flow. The flow considered has a bulk Re=250 k, with four particle sizes ranging from 5 to 500 μm examined. The results demonstrate that turbulence-driven secondary flows within the duct play an important role in the resuspension process. In the vertical direction, resuspension is promoted by the drag force arising from the secondary flows, which is balanced by the gravitational force, with this effect increasing with decreasing particle size. In the horizontal direction, particle resuspension is promoted by the particle’s inertial force, with this effect increasing with increasing particle size. For resuspension in both directions, the drag force dominates small particle resuspension, while for large particles the lift force is also a contributing factor. In the horizontal direction, the effect of the lift force varies with the direction of the secondary flow and becomes more significant when a particle is large or close to the duct wall. The influence of the lift force is also larger in the vertical than in the horizontal direction due to the effects of gravity.

S0506-3-4 水平正方形ダクトにおける乱流・浮力駆動二次流れ([0506-3]乱流における運動量,熱,物質の輸送現象(3))

Direct numerical simulations of fully developed turbulent flows in a horizontal square duct heated from below are performed at bulk Reynolds numbers Re_b = 3000, 4400 in the range of bulk Richardson numbers 0 &le; Ri &le; 1.03 to characterize turbulence- and buoyancy-driven mean secondary flow. It is observed that for 0.025 &lsim; Ri &lsim; 0.25 turbulence-driven secondary flow of a usual eight-vortex pattern is deformed by the effect of buoyancy into turbulence- and buoyancy-driven flow represented by single large-scale circulation and four corner vortices of opposite sense of rotation to the circulation. This remarkable structural difference in the corner regions can be interpreted in terms of combined effects, on instantaneous streamwise vortices, of the large-scale circulation and of the geometrical constraint by impermeable duct walls.

Direct numerical simulation of turbulence in a square annular duct

Direct numerical simulation (DNS) is performed to investigate the fully developed turbulence in a straight square annular duct. The mean flow field and the turbulent statistics are compared with existing experiments and numerical results. The comparisons and the analysis of the DNS data led to the discovery of the turbulent boundary layers of concave and convex 90° corners, a corner flow similarity and the scaling characteristics of corner turbulence. Analysis of the mean streamwise velocity near the concave and convex 90° corners resulted in establishing the ‘law-of-the-corner’ formulations. Comparing these formulations with the ‘law-of-the-wall’ relation, both damping and enhancing mechanisms analytically represented by the van Driest damping function, and the enhancement function were revealed for the concave and convex corner turbulence. The investigation captures the distinctive turbulence-driven secondary flows for both convex and concave 90° corners, and a corner flow similarity rule is discovered, which is associated with the pattern of these secondary flows. A turbulence energy spectrum analysis provides the distinctive features of the fully developed turbulence in the wall and corner regions. The validity of the turbulence eddy viscosity concept is evaluated based on these turbulence energy spectra. The turbulence-driven secondary-flow generation mechanisms are investigated by analysing the anisotropy of the Reynolds stresses.

Analysis of low Reynolds number turbulent flow phenomena in nuclear fuel pin subassemblies of tight lattice configuration

This paper focuses on the numerical simulation of low Reynolds (Re) number turbulence flow phenomena in tightly packed fuel pin subassemblies and in channels of irregular shape such as eccentric annuli. Highlighted phenomena include (i) turbulence-driven secondary flows inside a subchannel, (ii) local turbulent-laminar transition in the narrow gap region, and (iii) global flow pulsation across the gap along the channel length. These phenomena are simulated by Computational Fluid Dynamics (CFD). The CFD methods employed here are those of Direct Numerical Simulation (DNS) of turbulence, Large Eddy Simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) equations approach. Complicated turbulent flow structure is due to strong anisotropy in the non-uniform channel geometry that is characterized by wide open channels connected by a narrow gap. The secondary flows in subchannels play an important role in transporting small eddies generated in the wider region toward the narrow gap. Periodic cross-flow oscillations are calculated to appear in the vicinity of the gap region, and the coherent structure is transported in the main flow direction. This macroscopic flow process prevails in the low Re turbulent flow regime and is called as global flow pulsation. Finally a brief discussion is made on their influences onto the mixing between two subchannels that must be taken into account during natural circulation decay heat removals.

Assessment of the RANS Turbulence Models for a Turbulent Flow and Heat Transfer in a Rod Bundle

A computational fluid dynamics (CFD) analysis has been performed to assess the Reynolds Average Navier-Stokes (RANS) turbulence models to predict a turbulent flow and heat transfer in a triangular rod bundle with pitch-to-diameter ratios (P/Ds) of 1.06 and 1.12. The CFD predictions using various turbulence models were compared with experimental results. Anisotropic turbulence models such as the nonlinear k - [curly epsilon] and the second-order closure models predicted the turbulence-driven secondary flow in the triangular channel and the distributions of the time mean velocity and temperature showing significantly improved agreement with the measurements from the linear standard k - [curly epsilon] model. The anisotropic turbulence models predicted the turbulence structure for a rod bundle with a large P/D fairly well but could not predict the very high turbulence intensity of the azimuthal velocity observed in the narrow flow region (gap) for a rod bundle with a small P/D.

A turbulence model study for simulating flow inside tight lattice rod bundles

Performances of various turbulence models are evaluated for calculation of detailed coolant velocity distribution in a tight lattice fuel bundle. The individual models are briefly outlined and compared with respect to the prediction of wall shear stress and velocity field, for a fully developed flow inside a triangular lattice bundle. Comparisons clearly show the importance of proper modeling of the turbulence-driven secondary flows in subchannels. A quadratic k– ɛ model, which showed promising capability in this respect, is adjusted in its coefficients, and the adjusted model is applied to fully developed flow in an infinite triangular array, with various Reynolds numbers. The results show that the inclusion of adequate anisotropy modeling enables to accurately reproduce the wall shear stress distribution and velocity field in tight lattice fuel bundles.

Numerical Prediction of Secondary Flows in Complex Areas Using Concept of Local Turbulent Reynolds Number

A new model of turbulence is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. The main idea of a Multi-Scale Viscosity (MSV) model can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of the local turbulent Reynolds number below some critical one. Therefore, in MSV, the only empirical parameter is the critical Reynolds number. Multi-scale viscosity has been verified on the pipe flow and applied to simulation of turbulence-driven secondary flow in elementary cell of the infinitive hexagonal rod array. Since MSV can predict turbulent viscosity anisotropy in directions normal and parallel to the wall, it is capable to calculate secondary flows in the cross-section of the rod bundle. Calculations have shown that maximal intensity of secondary flow is about 1% of the mean axial velocity for the low-Re flows (Re=8, 170), while for higher Reynolds number (Re=160, 100) the intensity of secondary flow is as negligible as 0.2%.

난류에 의해 야기되는 이차유동 예측성능에 대한 비선형 κ-ε 난류모델의 평가

Nonlinear relationship between Reynolds stresses and the rate of strain of nonlinear k-models is evaluated theoretically by using the boundary layer assumptions against the turbulence-driven secondary flows in noncircular ducts and then their prediction performance is validated numerically through the application to the fully developed turbulent flow in a square duct. Typical predicted quantities such as mean axial and secondary velocities, turbulent kinetic energy and Reynolds stresses are compared with available experimental data. The nonlinear k- model adopted in a commercial code is found to be unable to predict accurately duct flows with the prediction level of secondary flows one order less than that of the experiment.

Numerical Prediction of Secondary Flows in Complex Areas Using Concept of Local Turbulent Reynolds Number

A new model of turbulence is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. The main idea of a Multi-Scale Viscosity (MSV) model can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of the local turbulent Reynolds number below some critical one. Therefore, in MSV, the only empirical parameter is the critical Reynolds number. Multi-scale viscosity has been verified on the pipe flow and applied to simulation of turbulence-driven secondary flow in elementary cell of the infinitive hexagonal rod array. Since MSV can predict turbulent viscosity anisotropy in directions normal and parallel to the wall, it is capable to calculate secondary flows in the cross-section of the rod bundle. Calculations have shown that maximal intensity of secondary flow is about 1% of the mean axial velocity for the low-Re flows (Re=8, 170), while for higher Reynolds number (Re=160, 100) the intensity of secondary flow is as negligible as 0.2%.

Large-eddy simulations of turbulent flow in a rotating square duct

The turbulent flow at low Reynolds numbers in a rotating straight square duct was simulated using the large-eddy simulation technique. The rotation axis is parallel to two opposite walls of the duct, and the pressure-driven flow is assumed to be fully developed, isothermal and incompressible. The Reynolds number based on the friction velocity (Reτ=300) was kept constant in the range of the rotational numbers studied (0⩽Roτ⩽1.5) Computations were carried out using a second-order finite volume code with a localized one-equation dynamic subgrid scale model. Simulations of rotating channel flows were initially carried out and were seen to be in agreement with experiments and direct numerical simulations reported in the literature. The study of the flow in a rotating square duct revealed the influence of the Coriolis force on the spatial distribution of the average velocity fields and Reynolds stresses. At low rotation rates, turbulence-driven secondary flows developed near the corners convect the rotation-generated cross-stream currents. At moderate and high rotation rates, the mean secondary flow structure consists essentially of two large counter-rotating cells convecting low/high momentum fluid from the stable/unstable side to the unstable/stable side. Inspection of the terms of the transport equations of the average axial velocity and vorticity components shows the mechanisms responsible for the changes in the average flow structure. Spatial distributions of the Reynolds stresses are mainly influenced by the changes that rotation induces in the main strain rates. It has been found that, globally, at the low Reynolds number studied, rotation tends to significantly reduce the overall turbulence level of the flow.

Prediction of Solid/Free-Surface Juncture Boundary Layer and Wake of a Surface-Piercing Flat Plate at Low Froude Number

Results are reported of a RANS simulation investigation on the prediction of turbulence-driven secondary flows at the free-surface juncture of a surface-piercing flat plate at low Froude numbers. The turbulence model combines a nonlinear eddy viscosity model and a modified version of a free-surface correction formula. The different elements of the model are combined and the model constants calibrated based on the premises that the anisotropy of the normal stresses is mainly responsible for the dynamics of the flow in the juncture region, and an accurate modeling of the normal-stress anisotropy as obtained from the data is a primary requirement for the successful prediction of the overall flow field. The predicted mean velocity, streamwise vorticity, turbulent kinetic energy, and other quantities at the juncture are then compared with data and analyzed with regard to findings of related studies. In agreement with the experimental observations, the simulated flow at large depths was essentially two-dimensional and displayed all the major features of zero pressure gradient boundary layer and wake, including the anisotropy of normal stresses in the near-wall region. In the boundary-layer free-surface juncture region, the major features of interest that were predicted include the generation of secondary flows and the thickening of the boundary layer near the free surface. In the wake free-surface juncture region, even though secondary flows and a thickening of the wake width near the free surface were predicted in accordance with the experimental observations, the overall comparison with the experiment was not as satisfactory as the boundary-layer juncture. This is partly due to the lack of a strong coherent flow structure in the wake juncture and the presence of possible wave effects in the wake in the experiments. An examination of the terms in the Reynolds-averaged streamwise vorticity equation reconfirmed the importance of the anisotropy of the normal Reynolds stresses in the production of streamwise vorticity. The free-surface wave elevations were negligible for the present model problem for the nonzero Froude number studied. Finally, concluding remarks are presented with regards to extensions for practical geometries such as surface ship flows.

A numerical prediction on the turbulent flow in closely spaced bare rod arrays by a nonlinear k− ϵ model

Fully developed turbulent flows in closely spaced bare rod arrays have been studied numerically by using a nonlinear κ− ϵ model. This model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in non-circular ducts. Results of the calculation are compared with experimental data. The present computations yield reasonable agreement with experiments. However, the modeling of the transport effect by large scale cross gap eddy motion is required.