Scalewise invariant analysis of the anisotropic Reynolds stress tensor for atmospheric surface layer and canopy sublayer turbulent flows

The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensorSand rotation rate tensorΩand calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensorsSandΩare studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensorsSandΩ, in which the scalar coefficients depend on simultaneous invariants of these tensors.

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Reynolds stress tensor and pressure-related turbulence transport terms of a turbulent shear layer flow impinging on a cavity trailing corner

10.2514/6.2022-0891 ◽

2022 ◽

Author(s):

Jose R. Moreto ◽

Xiaofeng Liu

Keyword(s):

Shear Layer ◽

Stress Tensor ◽

Reynolds Stress ◽

Turbulent Shear ◽

Reynolds Stress Tensor ◽

Turbulent Shear Layer ◽

Layer Flow ◽

Turbulence Transport

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LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

Volume 2C: Turbomachinery ◽

10.1115/gt2018-75792 ◽

2018 ◽

Author(s):

Jean-François Monier ◽

Nicolas Poujol ◽

Mathieu Laurent ◽

Feng Gao ◽

Jérôme Boudet ◽

...

Keyword(s):

Strain Rate ◽

Stress Tensor ◽

Reynolds Stress ◽

Constitutive Relation ◽

Strain Rate Tensor ◽

Separation Flow ◽

Compressor Cascade ◽

Corner Separation ◽

Reynolds Stress Tensor ◽

Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

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Experimental study of particle-driven secondary flow in turbulent pipe flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.104 ◽

2012 ◽

Vol 709 ◽

pp. 1-36 ◽

Cited By ~ 12

Author(s):

R. J. Belt ◽

A. C. L. M. Daalmans ◽

L. M. Portela

Keyword(s):

Turbulent Flow ◽

Secondary Flow ◽

Stress Tensor ◽

Reynolds Stress ◽

Cross Section ◽

Circular Pipe ◽

Horizontal Pipe ◽

Pipe Cross Section ◽

Reynolds Stress Tensor ◽

Pipe Flows

AbstractIn fully developed single-phase turbulent flow in straight pipes, it is known that mean motions can occur in the plane of the pipe cross-section, when the cross-section is non-circular, or when the wall roughness is non-uniform around the circumference of a circular pipe. This phenomenon is known as secondary flow of the second kind and is associated with the anisotropy in the Reynolds stress tensor in the pipe cross-section. In this work, we show, using careful laser Doppler anemometry experiments, that secondary flow of the second kind can also be promoted by a non-uniform non-axisymmetric particle-forcing, in a fully developed turbulent flow in a smooth circular pipe. In order to isolate the particle-forcing from other phenomena, and to prevent the occurrence of mean particle-forcing in the pipe cross-section, which could promote a different type of secondary flow (secondary flow of the first kind), we consider a simplified well-defined situation: a non-uniform distribution of particles, kept at fixed positions in the ‘bottom’ part of the pipe, mimicking, in a way, the particle or droplet distribution in horizontal pipe flows. Our results show that the particles modify the turbulence through ‘direct’ effects (associated with the wake of the particles) and ‘indirect’ effects (associated with the global balance of momentum and the turbulence dynamics). The resulting anisotropy in the Reynolds stress tensor is shown to promote four secondary flow cells in the pipe cross-section. We show that the secondary flow is determined by the projection of the Reynolds stress tensor onto the pipe cross-section. In particular, we show that the direction of the secondary flow is dictated by the gradients of the normal Reynolds stresses in the pipe cross-section, $\partial {\tau }_{rr} / \partial r$ and $\partial {\tau }_{\theta \theta } / \partial \theta $. Finally, a scaling law is proposed, showing that the particle-driven secondary flow scales with the root of the mean particle-forcing in the axial direction, allowing us to estimate the magnitude of the secondary flow.

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Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer

Journal of Fluids Engineering ◽

10.1115/1.2820645 ◽

1998 ◽

Vol 120 (2) ◽

pp. 280-284 ◽

Cited By ~ 17

Author(s):

A. Mazouz ◽

L. Labraga ◽

C. Tournier

Keyword(s):

Surface Roughness ◽

Turbulent Flow ◽

Stress Tensor ◽

Reynolds Stress ◽

Pipe Flow ◽

Duct Flow ◽

Reynolds Stress Tensor ◽

Entire Thickness ◽

Anisotropy Tensor ◽

Flow Turbulence

The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.

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