C. Béguin

Void Fraction Effect on Added Mass in Bubbly Flow

This paper proposes a relation for the added mass coefficient of spherical bubbles depending on void fraction based on results obtained by a semi-analytical method.This information is essential to completely characterize finely dispersed bubbly flows, where small spherical gas bubbles are present in a continuous liquid phase. Most of the closure relations for Euler-Euler or Euler-Lagrange models are obtained from experiments involving single bubbles. Their applicability to systems with high void fraction is therefore questionable.This paper uses solid harmonics to solve 3D potential flow around bubbles. Several configurations were calculated for different numbers of particles and spatial arrangements. Our results are compared with previous studies. Depending on the model proposed by previous authors, added mass forces could increase or decrease with the void fraction. This paper solves these discrepancies.The main purpose of this work is to develop simple formulas fitting our semi-analytical results. These simple formulas are suitable for further use, particularly as added mass models for multiphase flow averaged equations.Copyright

Two-Phase Damping in Vertical Pipe Flows: Effect of Void Fraction, Flow Rate and External Excitation

Predicting vibration effects in steam generators requires good knowledge of two-phase damping ζ2φ. The purpose of this work is to correlate two-phase damping in axial flow with tube transversal excitation frequency and magnitude. The test section consists of a stiff square tube subjected to internal axial flow of air-water mixture. The hydraulic diameter is 3 inches. The tube is supported with linear bearings and fitted with flexible tubing on both ends to allow motion in the transverse direction. Compression springs allow setting the natural frequency of the tube oscillation. A motor provides transverse sinusoidal excitation to the tube assembly. ζ2φ is determined from the frequency response function. As a result of this study, ζ2φ is represented as a function of excitation frequency and amplitude, void fraction and flow rate. Specific information is gained through high frame rate videos of the oscillating tube, including bubble transverse velocity and size for low void fraction, and flow pattern transitions. Indeed, it is suspected that two-phase damping is partly caused by the work rate of virtual mass forces of the gas phase. Better knowledge of the physical process involved in two-phase damping will allow better modeling and prediction of tube behavior.© 2014 ASME

Influence of Viscosity, Density and Surface Tension on Two-Phase Damping

Internal two-phase flow is common in piping systems. Such flow may induce vibration that can lead to premature fatigue or wear of pipes. In the nuclear industry in particular, failure of piping components is critical and must be avoided. Two-phase damping is considered part of the solution, since it constitutes a dominant component of the total damping in piping with internal flow. However, the energy dissipation mechanisms in two-phase flow are yet to be fully understood. The purpose of this paper is to explore the relationships between two-phase damping and fluid properties. Simple experiments were carried out in a clear vertical clamped-clamped tube to verify the effects of fluid properties on two-phase damping. Various fluids, such as air, alcohol, pure water, sugared water, glycerol, and perfluorocarbon, were combined to obtain different controlled mixtures and to determine the effect of surface tension, density and viscosity on two-phase damping. Two-phase damping ratios were obtained from free transverse vibration measurements on the tube. Two sets of experiments with stagnant and moving continuous phase were conducted. Based on dimensional analysis, we obtained a semi-empirical model for two-phase damping in bubbly and slug flow. The Void fraction and Bond number are shown to be major parameters of two-phase damping, which is described as a kinetic energy transfer from the tube to the continuous phase through added mass of the dispersed phase.Copyright

Predicting Fluidelastic Instability in Tube Array With Potential Theory

This paper studies the possibility to use potential theory to predict fluidelastic instability critical velocity in tube bundles. Potential flow is calculated semi analytically using Laurent expansions with the addition of discrete vortices behind the tube. The only experimental criterion used in this approach is the location of vortices behind the tubes. Using the linearized unsteady Bernoulli theorem we are able to model fluid forces as added mass, damping and stiffness effects. Fluid forces include coupling terms; that is the force on another tube induced by tube acceleration, velocity and location. The tube array is then described by a mass, damping and stiffness. The fluidelastic instability critical velocity becomes the solution of a linear eigenvalue problem. This approach has been compared with several experimental values of mass, damping and stiffness measurements, as well as the critical velocity. Mass matrix is in a very good agreement with experimental values, however damping and stiffness models still need some improvement. In the end, the model is able to predict the critical velocity within 20% of experimental values. This approach does not need stiffness experimental values (stability derivative) nor time delay as the stiffness, damping and mass matrices are calculated independently. The main purpose of this work is to understand the effect of induced forces involved in the fluidelastic instability.Copyright

Fluid-Structure Interactions in a Tube Bundle Subject to Cross-Flow. Part B : Two-Phase Flow Modeling

The response of a tube bundle subject to a two-phase cross-flow is investigated using a porous medium approach. This is the second of a two-part paper: in Part A new equations for the fluid and the structure were developed using a volume averaging technique. The main advantage of such an approach is that, compared to DNS, coarser and fixed meshes can be used for unsteady simulations, substantially alleviating the computational cost. The objective of part B is to extend the previous fluid-structure interaction model to two-phase flows. Following the same volume averaging technique, we describe the two-phase mixture using a Euler-Euler formulation. A model for the interaction between the gas and the liquid phase, similar to the fluid structure interaction model, in lumped into the equations. The solid structure, the gas and the liquid phases are fully coupled in a well posed set of equations. The code is verified by the method of manufactured solutions and its ability to represent fluid structure interactions in two-phase flows is assessed by comparing its predictions with results from DNS simulations and previous experimental data.

Stability Derivatives in a Parallel Triangular Tube Bundle Subject to Cross-Flow at Moderated Reynolds Number

This paper deals with the numerical and experimental determination of stability derivative inside a parallel triangular tube bundle for pitch Reynolds number Rep ∈ [60 3.104]. The present work focuses on the derivative of the lift coefficient, in the direction transverse to the flow, of the central cylinder for Rep ∈ [60 1.2.103]. We consider a viscous and incompressible flow for both approaches. First, experiments were done in a loop containing an adjustable central cylinder set with strain gauges to indirectly measure the lift derivative, via the moment of lift. Reynolds number is controlled by using a few glycerin solutions with different viscosities. In parallel, same flow conditions were simulated within 2D simulations. Comparisons were performed between experimental and numerical results. A critical Reynolds was found where the stability derivative seems to cross zero. This fact raises a question about applicability of quasi-steady model for fluidelastic instability.Copyright

Two-phase flow pattern recognition in a varying section based on void fraction and pressure measurements

In a hydroelectric turbine, the air injected during operation has an impact on the yield of the machine leading to important losses of energy. To understand those losses and be able to reduce them, a first step is to understand the pattern of the two-phase flows and describe their characteristics in the turbine. Those two-phase flows can be bubbly, intermittent, or annular, with different types of intermittent flow possible. Two-phase flow patterns are well defined in classical geometries such as cylinders with reliable descriptions available [5]. But, there is a critical lack of knowledge for flow patterns in other geometries. In our present work we take interest into a geometry that is a pipe with periodical changes of the section and realize a flow pattern map. To realize this map, we measure the pressure variations and void fraction fluctuations while changing the flow rates of water and air in our test section. We then use our physical understanding of the phenomena to analyze data and identify different flow patterns, characterize them, and build a new flow pattern map.

Experiments of air bubbles impacting a rigid wall in tap water

Trajectory and impact dynamics of bubbles in tap water were studied. Results confirm that bubbles with identical radii can be classified in two categories: fast bubbles and slow bubbles. Each category of bubble can describe zig-zag or helical motion. The aspect ratio and terminal velocity of a bubble depend on its radius and category. Restitution relations are also presented for the two categories of bubble after impact with an horizontal wall. With these relations, the state of a bubble after rebound can be predicted from its state before rebound. The aspect ratio before rebound of the bubble is found to play a key role in the dynamics of the impacts.

Fluidelastic Instability in Tube Arrays Subject to Two-Phase Cross Flow: A Porous Medium Approach

In nuclear power plants, heat exchangers undergo important flow induced vibrations, fluidelastic instability (FEI) being the most damaging one. Direct numerical simulations of such a phenomenon is currently an impossible task because of the considerable number of tubes and the two-phase nature of the flow.The novelty of the present approach is to use a porous medium to model the tube bundle and the surrounding flow. The Navier-Stokes equations are averaged on a control volume and the tubes materialized by a porosity field and source terms that model the interactions between the fluid and the solid. New sets of fully coupled equations were developed and solved with a finite element solver using high order time integration schemes. The unsteady porous medium approach already developed for single-phase flow is extended to the Euler-Euler formulation to describe the two-phase mixture. Validation and calibration of the parameters are achieved by comparing the critical flow rate and the forces acting on the tubes with results from direct numerical simulations and experimental data for single-phase flows.Copyright

Simple Model for Bubble-Wall Interaction

We have developed a model for an ellipsoidal bubble colliding with a rigid horizontal wall based on potential flow theory. The model is then compared with experiments of air bubbles surrounded by water impacting a wall. 70 impacts were observed with bubble radius between 0.3 and 2 mm and different trajectory types (helicoidal, zig-zag). Deformation and height of the first impact are the main comparison points. The proposed model is in good agreement with the height of the rebound but tends to overestimate the maximal compression for both types of trajectories.We also propose a new relation for the viscous drag coefficient correction induced by the wall confinement as well as the definition of potential pressure forces acting on bubbles close to a wall.Copyright