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

Demuren, A. O.

doi:10.2514/3.10616

Cited by 24 publications

(3 citation statements)

References 15 publications

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“…They reveal secondary flow structures in the plane normal to the primary flow 6,7,9,10 , among which are the stationary helicoidal flows observed in straight channels (Prandtl refers to them as "secondary flow of the second kind " 11 ). They were originally associated with duct corners 10,12,13 , where they were attributed to the turbulence anisotropy 3,12,[14][15][16][17] . Recent experiments reported their existence in wide channels (aspect ratio of about 10), where they arrange themselves as pairs of counter-rotating vortices aligned with the stream direction 6-8 .…”

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Recirculation cells in a wide channel

et al. 2014

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Secondary flow cells are commonly observed in straight laboratory channels, where they are often associated with duct corners. Here, we present velocity measurements acquired with an Acoustic Doppler Current Profiler in a straight reach of the Seine river (France). We show that a remarkably regular series of stationary flow cells spans across the entire channel. They are arranged in pairs of counter-rotating vortices aligned with the primary flow. Their existence away from the river banks contradicts the usual interpretation of these secondary flow structures, which invokes the influence of boundaries. Based on these measurements, we use a depth-averaged model to evaluate the momentum transfer by these structures, and find that it is comparable with the classical turbulent transfer.

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Recirculation cells in a wide channel

et al. 2014

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“…Direct numerical simulations have been performed for a square duct [4,5] and for a plane duct [6] that provide valuable data for evaluation of turbulence models. Further discussions on experiments and calculation methods for flow in non-circular ducts involving turbulence-driven secondary motions are found in References [1,11,12]. Gessner and Jones [9] and Gessner and Emery [10] provided experimental data for square and rectangular ducts for several Reynolds numbers.…”

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Numerical and experimental investigation of turbulent flow in a rectangular duct

Rokni¹,

Olsson

Sundén³

1998

Int. J. Numer. Meth. Fluids

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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.

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“…This secondary flow, which is driven by turbulence and will be referred to here as corner flow, is characterized by a pair of counter-rotating vortices that transfer momentum from the mean flow into the corner. Although corner flows are relatively weak, being only 1-3% of the freestream velocity, they have a significant effect on wall shear stress and heat transfer in the corner [2].…”

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Supersonic Corner Flow Predictions Using the Quadratic Constitutive Relation

2016

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A series of Reynolds-averaged Navier-Stokes simulations is performed for a supersonic wall-bounded turbulent corner flow. These simulations are compared to a high-order implicit large-eddy simulation for the same geometry and flow conditions. Inclusion of the quadratic constitutive relation in the Reynolds-averaged Navier-Stokes simulation results in significant improvement in qualitative agreement with the large-eddy simulation: specifically, the presence of secondary flow (a counter-rotating vortex pair). The range of valid values for the constant in the quadratic constitutive relation formulation is explored. Additionally, the effects on this range from different turbulence models and momentum thickness Reynolds numbers for the corner are also examined. These effects of the quadratic constitutive relation are explored using both the finite difference fluid solver OVERFLOW and the finite volume fluid solver US3D. The results indicate that the quadratic constitutive relation term directly affects the strength of the vortex pair in the secondary flow and that its influence appears directly dependent on all the aforementioned parameters. Nomenclature Cf = skin-friction coefficient C cr = quadratic constitutive relation constant k = turbulent kinetic energy L = distance of vortex core from corner l = reference length M = Mach number O ij = antisymmetric rotation tensor p = pressure Re=m = unit Reynolds number Re θ = momentum thickness Reynolds number S = strain-rate tensor T = temperature u = streamwise velocity v = normal velocity w = spanwise velocity x = streamwise distance y = wall-normal/spanwise distance z = spanwise distance α = angle of vortex core from nearest wall δ = boundary-layer thickness, 0.99u ∞ δ ij = Kronecker delta θ = boundary-layer momentum thickness μ = dynamic viscosity ρ = density τ = Reynolds-stress tensor Subscripts t = turbulent w = wall 1 = first cell off the wall ∞ = freestream Superscripts QCR = quadratic constitutive relation t = turbulent = inner coordinates − = time mean 0 = fluctuations

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

Cited by 24 publications

References 15 publications

Recirculation cells in a wide channel

Recirculation cells in a wide channel

Numerical and experimental investigation of turbulent flow in a rectangular duct

Supersonic Corner Flow Predictions Using the Quadratic Constitutive Relation

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