Modelling and Simulation in Engineering

Volume 2016 (2016), Article ID 4729128, 11 pages

http://dx.doi.org/10.1155/2016/4729128

## Studies of Two-Phase Flow at a Chute Aerator with Experiments and CFD Modelling

^{1}Hydraulic Engineering, Royal Institute of Technology (KTH), 100 44 Stockholm, Sweden^{2}Fluid Mechanics, Vattenfall R&D, 814 70 Älvkarleby, Sweden^{3}Civil Engineering, Haute Ecole d’Ingénierie et d’Architecture de Fribourg (HEIA-FR), 1705 Fribourg, Switzerland^{4}Laboratory of Hydraulic Constructions, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

Received 17 May 2016; Accepted 25 July 2016

Academic Editor: ShengKai Yu

Copyright © 2016 Penghua Teng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The chute aerator of a spillway is a structure in such a sense that air is, in the intense emulsification, entrained into the high-velocity water flow. Correctly predicting the air entrainment and two-phase flow pattern at the aerator would contribute to reliable spillway operation. Based on experimental data, 2D numerical simulations are preformed to predict streamwise air concentrations in the aerated flow, in which a two-fluid model is used. Depending on the air bubble size, relatively good agreement is seen with the experiments in the air cavity zone. The simulations give rise to higher air concentration downstream of the cavity, which is presumably due to underestimation of the interfacial forces in the two-fluid model.

#### 1. Introduction

Spillways are important hydraulic structures for dam safety. If the water flow velocity exceeds, for example, 20 m/s and the cavitation index drops below a certain limit, damage may occur due to cavitation in the chute bottom, which affects the safety of the spillway [1]. Hence, protecting spillways from cavitation damage is a primary goal of engineering design. The use of aerators is probably the only economic countermeasure for the purpose. An aerator entrains air into high-speed flow, alleviates the negative pressure near the chute bottom, and thus avoids the risk of cavitation.

Driven by engineering practice, researchers have investigated aerators both in the laboratory and through prototype observations [2–8]. Kramer and Hager [9] examined, through experiments, flow velocity, air concentration, and air bubble size distributions; they concluded that the bubble rise velocity in chute flows depends on the Froude number. Pfister and Hager [7, 8] analyzed the effects of geometrical parameters on streamwise distributions of air concentration downstream of aerators.

For many years, physical models have been the major tool to study the characteristics of the aerated flow. Computational Fluid Dynamics (CFD) has emerged as an important alternative in multiphase flow modelling. Both methods are undoubtedly complementary to each other. With CFD, it is possible to obtain, in detail, air-water flow fields of the aerated flow so as to understand the effects of governing parameters necessary for a project in question.

The Volume of Fluid (VOF) method is an interface tracking scheme addressing the topological changes of the air-water interface in free-surface flows [10]. To describe its hydraulic performance, the VOF model is often used to simulate the aerated flow of a spillway [11–14].

In an air-water flow, exchange behaviors between the dispersed air phase and continuous water phase affect forces between the phases. Hence, the correct modelling of forces and turbulence is of prime importance for capturing the physics. The two-fluid model differs from the VOF model in such a way that the momentum and continuity equations are solved for each phase. Furthermore, the interaction force between phases, the drag force, the virtual mass force, and the turbulent dispersion force are modelled in the momentum equations.

The two-fluid model was used to simulate the complex hydrodynamics of air-water flow in industrial applications [15–17]. Zhang [18] carried out three-dimensional (3D) modelling with the model. He focused on evaluations of such parameters as the diameter of air bubble, wall function, and interphase exchange models. Zhang et al. [19] performed two-dimensional (2D) simulations using the model, in which the turbulence dispersion force was included in the momentum equations. They concluded that the inclusion of the turbulence dispersion force gave better results of air concentration in the flow, which agreed well with the experimental data [20].

Physical model tests of an aerator were performed at the Laboratory of Hydraulics, Hydrology, and Glaciology (VAW), ETH, Zurich [7, 8]. Based on its configurations, CFD modelling is performed using the two-fluid model. The simulations, time dependent and in 2D, examine the transport of air in the flow. Included in the study are evaluations of air cavity length, air-entrainment rate, and air concentration distributions. The effect of bubble diameter, a dominating factor in the two-fluid model, is also considered on the momentum exchange between air and water. With regard to the experimental results, the purpose of the study is to evaluate the suitability of the two-fluid model in solution of the two-phase flow at the aerator and to learn about the air-water features of the flow.

#### 2. Physical Model

The experimental set of data was obtained from a hydraulic model test of an aerator conducted in a flume 0.3 m wide and 6.0 m long at VAW, ETH, Zurich (Figure 1) [7]. One aerator configuration, without offset but with a deflector, is selected for the numerical modelling (Figure 2). The chute bottom angle is set herein to = 30° with the horizontal plane; the defector angle is = 8.13° with the chute bottom. The chute length upstream of the aerator is 2.0 m. The height of defector () is 0.0133 m. The water depth of the approach flow is = 0.084 m. The approach flow Froude number is defined as = = 7.52, where is the mean approach flow velocity and is the acceleration of gravity.