Coupled Lagrangian and Eulerian simulation of bubbly flows in vertical pipes: validation with experimental data using multi-sensor conductivity probes and laser doppler anemometry

Understanding the dynamics of multiphase systems is an issue of particular interest in the field of Computer Fluid Dynamics (CFD) applied to Nuclear Reactor Safety. A better knowledge of the forces that act on the bubbles moving in a continuous turbulent random fluid field is of importance for a complete description of the bubble's motion and to obtain for instance the radial and axial void fraction distribution inside the reactor channels. Experiments specifically designed to understand the forces that act on the bubbles are a tool necessary to validate the models implemented inside the CFD codes. With this goal in mind, an upward isothermal co-current air-water flow in a vertical pipe (52 mm inner diameter) has been experimental investigated. Local measurements of void fraction, interfacial area concentration (IAC), interfacial velocity and Sauter mean diameter were measured using a four sensor conductivity probe. Liquid velocity and turbulence intensity were also measured using Laser Doppler Anemometry (LDA). Different air-water flow configurations were investigated for a liquid flow rate ranged from 0.491 m/s to 3 m/s and a void fraction up to 25 pc. For each two-phase flow configuration twenty five radial position and three axial locations were measured by the conductivity probe methodology, and several radial profiles were also measured with LDA at different axial positions. Numerical simulations of these experiments for bubbly flow conditions were performed by coupling a Lagrangian code that tracks the 3D motion of the individual bubbles in cylindrical coordinates (r, φ, Z) inside the fluid field under the action of the following forces: buoyancy, drag, lift, and wall lubrication. Also we incorporate a 3D stochastic differential equation model to account for the random motion of the individual bubbles in the turbulent velocity field of the carrier liquid. This type of models denoted as continuous random walk models are used to predict the turbulent diffusion of the bubbles in the fluctuating velocity field of the carrier fluid. Also we have considered the deformation that suffers the bubbles when they touch the walls of the pipe and are compressed until they rebound. The velocity and turbulence fields of the liquid phase were computed by solving the time dependent mass, energy, and momentum conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate ε transport equations were simultaneously solved by using the k, epsilon model or the renormalized group model (RNG) model in a (r,z) grid by the finite volume method using the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel because when integrating the 3D stochastic differential equations that take into account the motion of the bubbles in the fluid field we must consider the effect of the turbulence on the bubble's motion. To do this we must know the turbulence field that feels the bubble at each position along the path trajectory. Good predictions were obtained for the bubbles trajectories and the void fraction distribution in the channels when we consider that the lift radial force depends on the bubble's size and the bubbles are distorted, expressing this deformation in terms of the Eoetvos number. (authors)