Localised turbulence and a short contraction: better mixing in a channel

In 2011, while at the University of Newcastle (Australia), I presented this work at the 13th European Turbulence Conference (ETC13) in Warsaw, with Lyazid Djenidi (University of Newcastle) and Sedat Tardu (LEGI, Grenoble). The topic: how to create and sustain local turbulence in a channel to mix better, and what a short contraction adds.

My contribution: as first author, I developed the LBM code coupled with its thermal solver, ran the simulations, then handled the data post-processing and analysis.

Why it is hard

• In small systems, as in microfluidics, the flow is at a low Reynolds number: it stays laminar and fluids mix poorly.
• Creating a locally turbulent region is one of the most effective ways to improve mixing.
• The idea I studied: a pair of pulsed jets placed in the channel, followed by a series of short contractions.
• The pulsed jets generate two pairs of counter-rotating longitudinal vortices with a hairpin shape. Their interaction produces localised turbulence.
• The contraction accelerates the flow and stretches the vortices: it intensifies vorticity, and therefore turbulence.

The method

• Velocity: I solved the flow with the lattice Boltzmann method (LBM, 19-velocity lattice). It describes the propagation and collision of the particle distribution functions between neighbouring nodes.
• Temperature: energy (advection-diffusion) equation, solved by a coupled thermal solver; I wrote the whole code in Fortran 90.
• Parameters: Reynolds number Re_D = 1000, Prandtl number Pr = 0.75.
• Domain: channel 150 H long, 2 H high (60 mesh points) and 4 H wide. Poiseuille profile at the inlet, convective outlet, no-slip walls at fixed temperatures (+1 at the bottom, −1 at the top), periodic in the spanwise direction.

The interaction of the jets homogenises the temperature

• At t* = 25, the interaction of the two jets creates new vortical structures, mainly near the walls. They carry heat in the wall-normal direction and tend to homogenise the temperature field.
• At t* = 30, viscosity takes over and prevents new structures from forming. To sustain the turbulent region, the flow must be stretched: that is the role of the contraction.

The contraction intensifies turbulence

• Energy increases further: the streamwise component E_x rises while E_y and E_z decrease. Energy is transferred more intensely from the lateral components to the streamwise one.
• All three vorticity components become significantly larger than without contraction.

• The streamwise heat flux (uθ) changes little.
• The wall-normal flux (vθ) is markedly altered: the contraction mainly affects heat transport towards the walls.

Key takeaways

• A short contraction placed downstream of pulsed jets reinforces the "natural" mechanism of localised turbulence: more energy, more vorticity, and modified heat transport towards the walls.
• I see it as a simple option, with no moving parts, to improve mixing in slow flows.

Further reading

N. Lefeuvre, L. Djenidi, S. Tardu, Momentum and scalar transport in a localised synthetic turbulence in a channel flow with a short contraction, Journal of Physics: Conference Series 318, 052047 (2011), PDF · DOI