A multiphase model for the hydrodynamics and total dissolved gas in tailraces

Abstract

Elevated supersaturation of total dissolved gas (TDG) has deleterious effects in aquatic organisms. To minimize the supersaturation of TDG at hydropower dams, spillway flow deflectors redirect spilled water horizontally forming a surface jet that prevents bubbles from plunging to depth in the stilling basin.

A major issue regarding the prediction of the hydrodynamics and TDG in tailraces is the effect of the spillway bubbly surface jets on the flow field. Surface jets cause significant changes on the flow pattern since they attract water toward the jet region, a phenomenon called water entrainment. Bubbles create interfacial forces on the liquid, reduce the effective density and viscosity, and affect the liquid turbulence increasing the water entrainment. Most numerical studies on dams use standard single-phase models, which have demonstrated to fail to predict the hydrodynamics and TDG distribution. In this paper, an anisotropic two-phase flow model based on mechanistic principles capable of predicting water entrainment, gas volume fraction, bubble size and TDG concentration is presented.

Good agreement between model results and field data is found in the tailrace of Wanapum Dam. The simulations capture the measured water entrainment and TDG distribution. The effect of the bubbles on the hydrodynamics and TDG distribution is analyzed.

Introduction

The Columbia and Snake River basins, the most productive sources of hydropower in the United States, are of great environmental interest, as they host the largest salmon population in the contiguous United States. After construction of the dams, 12 salmon and steelhead species were placed on the endangered species list act. Particularly, fish may be exposed to stresses associated with elevated total dissolved gas (TDG) created during voluntary or involuntary spills. Elevated TDG supersaturation may cause gas bubble disease (GBD) in fish. The effect of TDG supersaturation is complex and depends principally on TDG levels, exposure time, and swimming depth of the fish (Stroud et al., 1975, Weitkamp and Katz, 1980, Bouck, 1980). Bubbles may form under the skin, mouth, gills, fins, and eyeballs of affected fish (Canadian Council of Ministers of the Environment, 1999). Death has been observed after significant exposure to high levels of TDG by blockages of blood flow due to bubbles in the vascular system. State and Federal regulations establish water quality standards relative to TDG to protect aquatic organism (Picket and Harding, 2002, Picket and Herold, 2003, Picket et al., 2004, Maynard, 2008).

The flow in the tailrace of a large hydropower dam is usually very complex. The large energy introduced by spillway flows, mostly dissipated in the stilling basin and adjoining tailwater channel, introduces massive amounts of bubbles and creates energetic waves and sprays. If bubbles reach deep regions into the stilling basin by direct plunging or turbulent transport, they may dissolve air into the water increasing the TDG concentration in the tailrace. In deep regions, the bubbles size distribution change due both to dissolution and to compression.

In an effort to minimize the supersaturation of dissolved gases, spillway flow deflectors have been installed in several dams. As shown in Fig. 1, deflectors redirect spilled water horizontally forming a surface jet that prevents the bubbles from plunging to depth in the stilling basin, thus reducing the air dissolution. It is observed that surface jets attract water toward the jet region, a phenomenon called water entrainment. Turan et al. (2007) described the main mechanisms causing water entrainment as acceleration of the surrounding fluid as the jets decelerates, surface currents, Coanda effect and the presence of bubbles.

Wanapum Dam is located at river mile 415.8 on the Mid-Columbia River in the state of Washington, USA. It includes 12 spillway bays and 10 generating units (Fig. 2). Field-scale observations and measurements previous to the installation of the flow deflectors in Wanapum Dam showed little water entrainment from the powerhouse to the spillway. After deflector installation, entrainment increased very significantly, completely modifying the flow pattern in the tailrace. This flow pattern change in the tailrace affects fish passages performance, sedimentation processes, and TDG distribution, among others effects. Water entrainment due to single-phase surface jets has been subject of basic studies, though not in the context of spillway flows (Liepmann, 1990, Walker and Chen, 1994, Walker, 1997).

Numerical studies and field and model observations indicate that the presence of bubbles has a strong effect on the water entrainment. Bubbles reduce the effective density (and pressure), viscosity, and affect the liquid turbulence.

Model-scale experiments, which are scaled with the Froude number, fail to reproduce the entrainment observed in the prototype, thus preventing flow studies under some spillway operational conditions (Haug and Weber, 2006). Notice that since the scaling is performed based on the Froude number, the Reynolds and Weber numbers are not honored, resulting in smaller levels of turbulence and less and bigger bubbles (in dimensionless terms) than in the prototype. As a consequence, the bubble residence time is much shorter and the gas volume fractions much smaller, resulting in a rather ineffectual two-phase flow. This, along with inadequate representation of the turbulence, leads to much weaker surface jets and less entrainment for the model.

The prediction of the water entrainment in tailraces has received a vast amount of attention in the past. Earlier studies aimed at the prediction of the hydrodynamics in hydropower tailraces grossly underpredicted the water entrainment (Li and Weber, 2006). Turan et al. (2007) used an anisotropic mixture model that accounts for the gas volume fraction and attenuation of normal fluctuations at the free surface. Although this model predicted considerably more water entrainment than the standard isotropic single-phase models, the degree of the entrainment obtained on prototype scale was still underpredicted.

Numerical modeling can be very useful to understand the underlying phenomena leading to TDG supersaturation. The TDG concentration depends on extremely complex processes such as air entrainment in the spillway (pre-entrainment), entrainment when the jet impacts the tailwater pool, breakup and coalescence of entrained bubbles, mass transfer between bubbles and water, degasification at the free surface, and bubble and TDG transport. In addition, tailrace flows in the region near the spillway cannot be assumed to have a flat air/water interface, requiring the computation of the free surface shape. Water entrainment, discussed in the previous section, leads to mixing modifying the TDG field.

Earlier studies to predict TDG downstream of spillways were based on experimental programs (Hibbs and Gulliver, 1997, Orlins and Gulliver, 2000). This approach has been reasonably effective, though it can be very expensive and time-consuming. The most important source for TDG is the gas transferred from the bubbles, therefore a proper model for TDG prediction must account for the two-phase flow in the stilling basin and the mass transfer between bubbles and water. In addition, the model has to capture the water entrainment to correctly predict the TDG dilution due to powerhouse flows.

Free surface numerical models can predict the shape and evolution of the free surface and, though expensive, is today feasible to apply them to complex 3D flows. In the field of hydraulic engineering, free surface models are not yet widely applied but steadily developed (Turan et al., 2008, Ferrari et al., 2009). However, direct simulation of individual bubbles in a spillway/tailrace environment is well beyond current computer capabilities. Therefore, a two-phase flow model with space–time averaged quantities that does not resolve the interface is needed to model the effect of the bubbles on the flow field and bubble dissolution. Jakobsen et al. (2005) provide a complete review of the state of the art of two-phase flow modeling. Two-phase flow models using averaged quantities have been extensively used, mainly in the chemical and nuclear engineering communities, to simulate homogeneous tanks, bubble columns or vertical pipes. The first effort to incorporate a two-phase flow model to predict TDG at hydropower tailraces was carried out by Politano et al. (2007). The authors used a two-fluid model to predict the gas and TDG distribution in a 2D cross-section passing through a spillway bay. The model was compared against TDG field data measured before deflector installation and also used to study the effect of the bubble size on TDG concentration. In a later study, Urban et al. (2008) used a 1D two-phase flow equation to predict TDG in the tailrace of Ice Harbor Dam. The authors solved a TDG equation for three distinct regions of flow using a series of control volumes. Though this model takes into account the mass transfer between bubbles and the liquid phase, the model does not solve the hydrodynamics and uses several empirical correlations to calculate the eddy length scales and interfacial areas. Note that the water entrainment caused by deflectors cannot be captured with 1D or 2D simulations and consequently the TDG dilution due to powerhouse flows is not taken into account with these models. The difficulties associated with computation of large-scale flow fields have delayed the use of two-phase models to solve highly complex 3D flows. One example of a comprehensive (and expensive) two-phase polydisperse flow model was developed by Carrica et al. (1999) to predict the flow around a surface ship.

The primary goal of this study is to develop an unsteady 3D two-phase flow model capable of predicting the hydrodynamics, including the water entrainment from the powerhouse into the spillway region, and TDG distribution within hydropower tailraces. The model uses a Reynolds Stress Model (RSM) to provide anisotropic closure for the two-phase RANS equations, and introduces a simple but effective boundary condition to enforce zero normal fluctuations at the free surface. A modified bubble-induced turbulence term is added to the Reynolds stress components to account for suppression and production of turbulence by the bubbles. The TDG is calculated with a two-phase transport equation in which the source is the bubble/liquid mass transfer, function of the gas volume fraction and bubble size. Attention is focused on the effect of the bubbles on the turbulence field and water entrainment. The model is implemented into the commercial CFD code FLUENT using User Defined Functions (UDFs) and User Defined Scalars (UDSs). The numerical results are compared against field data for Wanapum Dam under two operational conditions.