Appel à candidatures | Recherche, Emploi

Postdoc: Gravitationally-driven turbulent exchange flows in a closed tube in the presence of a linear viscosity stratification, IMFT, Toulouse (France)

Le 1 janvier 2025

15 months, full time, starting January 2025
Toulouse, IMFT
Contacts :
Thomas Bonometti, INPT – IMFT, thomas.bonometti@imft.fr 
Jacques Magnaudet, CNRS – IMFT, jacques.magnaudet@imft.fr
Benoît-Joseph Gréa, CEA DAM, benoit-joseph.grea@cea.fr

The exchange of viscous fluids induced by a Rayleigh-Taylor instability (RTI) in a confined environment is encountered in a variety of geophysical and industrial problems. For instance, this type of flow is suspected to control the distribution of magma and gas (SO2) released in some types of volcanic eruptions (Stevenson & Blake 1998). Similarly, these exchange flows modify the pressure drop in secondary or enhanced hydrocarbon recovery processes (Joseph et al. 1997).

Topic

Gravitationally-driven turbulent exchange flows in a closed tube in the presence of a linear viscosity stratification

Laboratory

IMFT – Institut de Mécanique des Fluides de Toulouse, Allée Camille Soula, 31400 Toulouse, France

Duration 

15 months, full time, starting January 2025

Gross salary

~ 3000 euros / month, depending on previous experience

Supervision

Thomas Bonometti, INPT – IMFT, thomas.bonometti@imft.fr Jacques Magnaudet, CNRS – IMFT, jacques.magnaudet@imft.fr Benoît-Joseph Gréa, CEA DAM, benoit-joseph.grea@cea.fr

General context

The exchange of viscous fluids induced by a Rayleigh-Taylor instability (RTI) in a confined environment is encountered in a variety of geophysical and industrial problems. For instance, this type of flow is suspected to control the distribution of magma and gas (SO2) released in some types of volcanic eruptions (Stevenson & Blake 1998). Similarly, these exchange flows modify the pressure drop in secondary or enhanced hydrocarbon recovery processes (Joseph et al. 1997). They are also involved in some of the initial stages of the inertial confinement fusion process. The motivation of the proposed post-doctoral project lies in the latter context.

State of the art at IMFT

The experimental set-up available at IMFT (Fig. 1a) enables us to study the exchange of fluids with slightly different densities and their possible mixing in a closed long cylindrical tube (L=1m). Thanks to an optical device (a backlight system and a 45° mirror extending along the entire length of the tube), it is possible to follow in real time the evolution of the fronts separating the two fluids in two perpendicular planes, using a high-speed camera (Fig. 1b). A front capturing volume-of-fluid type method implemented in the in-house JADIM code can also be used to simulate this type of flow (Fig. 1c), including under

turbulent conditions (Hallez & Magnaudet 2008, 2015).

The experimental studies performed so far at IMFT have focused on low-inertia flow regimes. However, by using less viscous fluids, the set-up is also able to reach turbulent regimes. As a part of a collaboration with CEA-DAM, we are interested in turbulent configurations in which the initial interface lies within a linear and continuous vertical viscosity distribution (density jump, viscosity ramp), so that one of the fronts propagates in a fluid of an increasing viscosity. This configuration should allow us to analyze the transition from an initially turbulent, self-similar Rayleigh-Taylor flow, to a viscously-dominated exchange flow.

Working program

A series of experiments will be carried out by varying the turbulent Reynolds number (via the density jump and the bulk viscosities), as well as the magnitude and relative thickness of the viscosity stratification. The temporal evolution of the edge of the mixing zone will be determined using a schlieren technique. The cross-sectional average of the concentration of one of the fluids will be obtained with a light absorption technique.

Based on these experimental results, a closure model will be developed to predict the temporal evolution and longitudinal variation of the mean concentration in the tube cross-section. To this end, concentration fluxes will be related to mean concentration gradients via a diffusivity tensor whose components will be expressed as a function of Reynolds stresses and characteristic time scales (Hallez & Magnaudet 2015). This model will enable us to test the validity of the self-similarity laws proposed in the literature to predict the evolution of the mixing layer thickness in fluids of uniform viscosity (Dalziel et al. 2008, Lawrie & Dalziel 2011a-b).

Depending on the advancement of the project, direct simulations will be carried out with the JADIM code on the same configurations, with the circular cross-section of the tube being taken into account by using an immersed boundary method on a Cartesian grid. These simulations will give access to the local distribution of concentration and velocity components, from which turbulent fluxes and the relevant length scales will be extracted.

Candidate’s profile

The successful candidate holds a PhD in fluid mechanics. He/she is autonomous in conducting experiments, implementing optical methods and using advanced image processing techniques. He/she has a very good fundamental background in turbulence and mixing physics. Previous experience in the use of direct simulation codes would be a real plus.

Bibliography

Dalziel, S. B, Linden, P. F. & Youngs, D. L. (1999) Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability. J. Fluid Mech. 399, 1-48.

Dalziel, S. B, Patterson M. D., Caulfield, C. P. & Cooramaswamy, I. A. (2008) Mixing efficiency in high-aspect-ratio Rayleigh-Taylor experiments. Phys. Fluids 20, 065106.

Hallez, Y. & Magnaudet, J. (2008) Effects of channel geometry on buoyancy-driven mixing. Phys. Fluids 20, 4053306.

Hallez, Y. & Magnaudet, J. (2015) Buoyancy-driven turbulence in a tilted pipe. J. Fluid Mech. 762, 435-477. Joseph D.D., Bai R., Chen K.P. & Renardy Y.Y. (1997) Core-annular flows. Annu. Rev. Fluid Mech. 29, 65-90.

Stevenson D. S., & Blake, S. (1998) Modelling the dynamics and thermodynamics of volcanic degassing. Bull. Volcanol. 60, 307-317.