Gas-liquid dispersed flows through a straight pipe have been largely studied for many decades, especially for application in the nuclear and chemical industries. The interaction between the two phases was found to involve inertial forces as well as contact forces, such as drag and lift forces, virtual mass force or turbulence-induced forces, especially when the gas-liquid mixture is dense (Delhaye 2014).

For a complex geometry rotating around a fixed axis, the usual force balance is deeply modified, with a strong impact on the particle motion. The four additional forces appearing in such a case are:

- the force due to the channel radial curvature;
- the force due to the channel axial curvature;
- the centrifugal force;
- the Coriolis force.

As part of the IFPEN project “FoReCaSt” (Multi-physics modelling of coupled phenomena), we propose to study this new force equilibrium. The post-doctoral researcher will work toward modelling and predicting the motion of a single particle, flowing with liquid through a rotating helico-semi-radial channel. This work will ultimately be used to quantify potential gas accumulation areas in the channel.

Based on work previously done at IFPEN and publications from literature (e.g. Auton et al., 1988), the post-doctoral researcher will first describe the forces acting on a single particle in a liquid flow through a rotating double-curvature channel. He will then apply the Euler-Lagrange method (Delhaye, 2014 or Prosperetti & Tryggvason, 2009) to the so-called Crocco’s equation, which give the global momentum equation in a turbomachine. In a first step, the problem can be split along two surfaces: the meridional surface (including the rotation axis), and the cylindrical surface defined around the rotation axis.

In the second step, the post-doctoral researcher will suggest a processing method to solve the projected equation along a mean curvilinear line, from the channel inlet toward its outlet. Using a code written in C++ , he will assess each force magnitude as well as the forces balance along the mean curvilinear curves on the two surfaces defined above. He will compare his results with the literature (e. g. Minemura & Murakami, 1980, Rastello et al., 2011, Zhu and Zhang, 2016).

This preliminary approach (2x 1D) will give the main trends for the forces acting on a particle following the mean curve on both the meridional surface and the cylindrical surface. By analyzing these trends, the researcher will determine the best modelling strategy to describe each force. Because of the many length scales appearing in the problem, this task will requires a deep and rigorous understanding of the underlying physics, in particular of liquid-particle interactions.

After these preliminary studies, the post-doctoral researcher will extend the above method to a 2x 2D approach, taking the two surfaces into account. This part is the most challenging as the equations become more tightly coupled. This work will enable the researcher to predict the particle motion on each surface. For example on the meridional surface, the combination of the centrifugal and inertial forces should confirm the particle deviation towards the location with a larger curvature radius and toward the rotational axis.

Once the numerical code is completed and validated for simple cases, the researcher will propose and perform a series of simulations aiming at studying the impact of the main operating and geometrical parameters which can affect the particle motion:

- Particle specific gravity;
- Particle diameter;
- Channel rotational speed;
- Channel curvatures radius;
- Phase velocities.

Depending on the progress, it might be possible to extend this work to a set of particles (Brennen, 2005), and/or to build meta-models to facilitate the visualisation and further use of the parametric study results.

As part of an innovative scientific challenge, the post-doctoral researcher will participate to congress and articles publications in journals dedicated to multiphase flows.

- Models, two-phase flow, curvature channel, rotational channel, turbomachinery.

- two-phase flow, modelling, C++, fluid mechanics.

The post-doctoral candidate must meet the following requirements: PhD degree in fluid mechanics or applied mathematics, computer science, physics, or equivalent. Knowledge of computational fluid dynamics is an advantage. IFP Energies nouvelles offers a stimulating interdisciplinary environment combining applied mathematics, fluid mechanics, chemical engineering, etc.

Send you application directly to * Marine Dupoiron*, Research Engineer at IFPEN Lyon, Applied Physical Chemistry and Mechanics Division, Fluid Mechanics Department, Tel: +33 4 37 70 34 74:

Auton, T. R., Hunt, J. C. R., and Prud’Homme, M. (1988). The force exerted on a body in inviscid unsteady non-uniform rotational ﬂow. Journal of Fluid Mechanics.

Brennen, C. E., (2005). *Fundamentals of multiphase flow*. Cambridge university press.

Delhaye, J. M. (2014). Thermohydraulique des réacteurs. EDP sciences.

Minemura, K., & Murakami, M. (1980). A Theoretical Study on Air Bubble Motion in a Centrifugal Pump Impeller. Journal of Fluids Engineering, 102(4), 446-453.

Prosperetti, A., & Tryggvason, G. (Eds.). (2009). Computational methods for multiphase flow. Cambridge university

Rastello, M., Marié, J.-L., and Lance, M. (2011). Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating ﬂow. Journal of Fluid Mechanics.

Zhu, J. and Zhang, H.-Q. (2016). Mechanistic modeling and numerical simulation of in-situ gas void fraction inside ESP impeller. Journal of Natural Gas Science and Engineering, 36, Part A:144–154.

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