On the 15th of June 2018, Deepak Kunhappan will defend his PhD entitled "Numerical modelling of long flexible fibres in inertial flows"

This PhD project was supervised by Guillaume Balarac (LEGI) and Pierre Dumont (LGP2) in collaboration with Barthélémy Harthong (3SR), and co-financed by Tec21 and the CNRS.

The defense will take place at 9 am in room K118 at the LEGI.



A numerical model describing the behavior of flexible fibers under inertial flows was developed by coupling a discrete element solver with a finite volume solver.Each fiber is discretized into several beam segments, such that the fiber can bend, twist and rotate. The equations of the fiber motion were solved usinga second order accurate explicit scheme (space and time). The three dimensional Navier-Stokes equations describing the motion of the fluid phase was discretizedusing a fourth th order accurate (space and time) unstructured finite volume scheme. The coupling between the discrete fiber phase and the continuous fluid phasewas obtained by a pseudo immersed boundary method as the hydrodynamic force on the fiber segments were calculated based on analytical expressions.Several hydrodynamic force models were analyzed and their validity and short-comings were identified. For Reynolds numbers (Re) at the inertial regime(0.01 < Re < 100, Re defined at the fiber scale), non linear drag force formulations based on the flow past an infinite cylinder was used. For rigid fibers in creeping flow, the drag force formulation from the slender body theory was used. A per unit length hydrodynamic torque model for the fibers was derived from explicit numerical simulations of shear flow past a high aspect ratio cylinder. The developed model was validated against several experimental studies and analytical theories ranging from the creeping flow regime (for rigid fibers) to inertial regimes. In the creeping flow regime, numerical simulations of semi dilute rigid fiber suspensions in shear were performed.The developed model wasable to capture the fiber-fiber hydrodynamic and non-hydrodynamic interactions. The elasto-hydrodynamic interactions at finite Reynolds was validated with against two test cases. In the first test case, the deflection of the free end of a fiber in an uniform flow field was obtained numerically and the results were validated. In the second test case the conformation of long flexible fibers in homogeneous isotropic turbulence was obtained numerically and the results were compared with previous experiments. Two numerical studies were performed to verify the effects of the suspended fibers on carrier phase turbulence and the numerical model was able to reproduce the damping/enhancement phenomena of turbulence in channel and pipe flows as a consequence of the micro-structural evolution of the fibers.


Guillaume Balarac (LEGI)



Numerical modelling of the behaviour of cellulose fibres in a fluid flow
Tec21 PhD project

Laboratoire des Ecoulements Géophysiques et Industriels