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

Abstract

In 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 nonaxisymmetric 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 crosssection. 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, ∂τ rr /∂r and ∂τ θθ /∂θ . 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.

Developments in the Flow of Complex Fluids in Tubes

“…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 a similar way in particle-laden fully developed turbulent flow of Newtonian fluids even in smooth circular tubes, secondary flow of the second kind can be promoted by a non-uniform non-axisymmetric particle forcing, which makes the Reynolds stress tensor anisotropic, Belt et al [379]. Small enough droplets in suspension would behave in the same way as solid particles, and much that can be said about a suspension of solid particles also applies to a suspension of small droplets.…”

“…Belt et al [379] further split Φ into two components, a component independent of the secondary flow, Φ o , and another dependent on the secondary flow,…”

Dynamics of liquid–liquid flows in horizontal pipes using simultaneous two–line planar laser–induced fluorescence and particle velocimetry

“…They deduced two symmetrical pairs of counter-rotating vortices in the bottom continuous aqueous (water-glycerol solution) layer and concluded that the non-uniform turbulent kinetic energy along the fluid-pipe perimeter of the continuous phase could be responsible for the generation of secondary flows in stratified-dispersed flows. Further, Belt et al, (2012) used laser droplet anemometry to study secondary flows in single-phase water in horizontal pipes with fixed particles at the bottom section, which, however, modifies the small-scales of the flow, especially around the particles, leading to non-uniformity in the Reynolds stress tensor and generating secondary flows.…”

Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

“…Types of flows Re p Kim and Balachandar (2012) An isolated finite-sized particle subjected to isotropic turbulent cross-flow 100, 250, 350 Zeng et al (2010) A finite-sized stationary particle in a channel flow of modest turbulence 40 ∼ 450 Lucci et al (2010) Finite-sized solid spherical particles in decaying isotropic turbulence O (10) (65/75/280) Belt et al (2012) Particle-laden secondary flow in turbulent pipe flows 110, 217 Xu and Bodenschatz (2008) Particles in intense turbulent water flows 22, 35, 55 Kidanemariam et al (2013) Horizontal open channel flow with finite-size, heavy particles 15 ∼ 20 Laín and Sommerfeld (2012) Pneumatic conveying of spherical particles in horizontal ducts 40 Dorgan and Loth (2004) Particles released near the wall in a turbulent boundary layer 10 −5 ∼ 30 Zeng et al (2008) Turbulent channel flow over an isolated particle of finite-size 42 ∼ 295, 325/455 Tenneti and Subramaniam (2014) Gas-solid flows 20, 50 Wang et al (2008) Sedimentation of 1, 2 or 105 particles in a channel flow about 17.3, 503 García-Villalba et al (2012) Vertical plane channel flow with finite-size particles 132 Uhlmann (2008) Vertical particulate channel flow 136 Uhlmann and Doychev (2014) The gravity-induced motion of randomly distributed, finite-size, heavy particles in quiescent fluid in triply periodic domains ing on a sphere near the wall and experimentally study translational and rotational motion of a particle slightly heavier than the fluid in a rotating drum filled with water. Lin and Lin (2013) numerically studied the effects of finite particle Reynolds numbers up to Re p = 50 on the model for normal lubrication force on a particle moving towards a solid wall using the immersed boundary method.…”

“…Zeng et al ( 2008; considered the turbulent channel flow over an isolated particle with variable sizes and locations. There are also pipe flows laden with particles, such as the experimental study of turbulent flow driven by particles in pipe flows ( Belt et al, 2012 ) and the gassolid flows in wall-bounded vertical risers ( Laín and Sommerfeld, 2012;Lu et al, 2013;Wang et al, 2013 ). In addition, Lucci et al (2010) numerically simulated the turbulent flow around moving spherical particles dispersed in a decaying isotropic turbulent flow.…”