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

2012 ◽  
Vol 709 ◽  
pp. 1-36 ◽  
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.

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

1998 ◽  
Vol 120 (2) ◽  
pp. 280-284 ◽  
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.

scholarly journals On closure problem of incompressible turbulent flow

2018 ◽  
Author(s):  
BOHUA SUN
Keyword(s):  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Unsolved Problem ◽  
Incompressible Flows ◽  
Closure Problem ◽  
Fluctuation Velocity ◽  
Reynolds Stress Tensor ◽  
Three Components

This paper attempts to clarify an issue regarding the lasting unsolved problem of turbulence, namely the closure problem. This study shows that all perspectives regarding the numbers of un- known quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor. The current literatures have a consensus that the Reynolds stress tensor has six unknowns; however, this study shows that the Reynolds stress tensor actually has only three ones, namely the three components of fluctuation velocity. With this new understanding, the closed turbulence equations for incompressible flows are proposed.

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

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.

Effect of Pipe Inclination on Solids Distribution in Partially Stratified Slurry Flow

2019 ◽  
Author(s):  
Václav Matoušek ◽  
Jan Krupička ◽  
Jiří Konfršt ◽  
Pavel Vlasák
Keyword(s):  
Uniform Distribution ◽  
Cross Section ◽  
Inclination Angle ◽  
Concentration Profile ◽  
Stratified Flow ◽  
Concentration Profiles ◽  
Horizontal Pipe ◽  
Pipe Cross Section ◽  
Test Loop ◽  
Pipe Inclination

Abstract Partially stratified flows like flows of sand-water slurries exhibit non-uniform distribution of solids (expressed as a vertical profile of local volumetric concentration) in a pipe cross section. The solids distribution in such flows is sensitive to pipe inclination. The more stratified the flow is the more sensitive its concentration profile is to the pipe slope. In general, the distribution tends to become more uniform (less stratified) if the inclination angle increases from zero (horizontal pipe) to positive values (ascending pipe) up to 90 degree (vertical pipe). In a pipe inclined to negative angles (descending pipe) the development is different. The flow tends to stratify more if it changes from horizontal flow to descending flow down to the angle of about −35 degree. If the angle further decreases towards −90 degree, then the flow becomes less stratified reaching uniform distribution at the vertical position. This also means that the same flow exhibits a very different degree of stratification in ascending and descending pipes inclined to the same (mild) slope say between ±10 and ±40 degree. The rather complex development of the solids distribution with the variation of the inclination of pipe is insufficiently documented experimentally and described theoretically in predictive models for a concentration profile in partially stratified flow. In order to extend the existing limited data set with experimental data for partially stratified flow of medium sand slurry, we have carried out a laboratory experiment with the slurry of narrow graded fraction of sand with the mean grain size of 0.55 mm in our test loop with an invert U-tube inclinable to arbitrary angle between 0 and 90 degree. A pipe of the loop has an internal diameter of 100 mm. Both legs of the U-tube have a measuring section over which differential pressures are measured. Radiometric devices mounted to both measuring sections sense concentration profiles across a pipe cross section. Furthermore, the discharge of slurry is measured in the test loop. In the paper, experimental results are presented for various inclination angles with a small step between 0 and ±45 degree and a development in the shape of the concentration profiles with the changing inclination angle is analyzed. For the analysis, it is critical to distinguish between suspended load and contact load in the flow as the two loads tend to react differently to the flow inclination. The measured concentration profiles and pressure drops are compared with predictions by the layered model adapted for taking the flow inclination into account.

Sign in / Sign up

Export Citation Format

Share Document