Hosein Foroutan1

Department of Mechanical and Nuclear Engineering,

The Pennsylvania State University, 338C Reber Building,

University Park, PA 16802 e-mail: hosein@psu.edu

Savas Yavuzkurt

Department of Mechanical and Nuclear Engineering,

The Pennsylvania State University, 327 Reber Building,

University Park, PA 16802 e-mail: sqy@psu.edu

Flow in the Simplified Draft Tube of a Francis Turbine Operating at Partial Load—Part I:

Simulation of the Vortex Rope

Numerical simulations and analysis of the vortex rope formation in a simplified draft tube of a model Francis turbine are carried out in this paper, which is the first part of a two-paper series. The emphasis of this part is on the simulation and investigation of flow using different turbulence closure models. Two part-load operating conditions with same head and different flow rates (91% and 70% of the best efficiency point (BEP) flow rate) are considered. Steady and unsteady simulations are carried out for axisymmetric and three-dimensional grid in a simplified axisymmetric geometry, and results are compared with experimental data. It is seen that steady simulations with Reynolds-averaged

Navier–Stokes (RANS) models cannot resolve the vortex rope and give identical symmetric results for both the axisymmetric and three-dimensional flow geometries. These RANS simulations underpredict the axial velocity (by at least 14%) and turbulent kinetic energy (by at least 40%) near the center of the draft tube, even quite close to the design condition. Moving farther from the design point, models fail in predicting the correct levels of the axial velocity in the draft tube. Unsteady simulations are performed using unsteady

RANS (URANS) and detached eddy simulation (DES) turbulence closure approaches.

URANS models cannot capture the self-induced unsteadiness of the vortex rope and give steady solutions while DES model gives sufficient unsteady results. Using the proper unsteady model, i.e., DES, the overall shape of the vortex rope is correctly predicted and the calculated vortex rope frequency differs only 6% from experimental data. It is confirmed that the vortex rope is formed due to the roll-up of the shear layer at the interface between the low-velocity inner region created by the wake of the crown cone and highly swirling outer flow. [DOI: 10.1115/1.4026817]

Keywords: vortex rope, draft tube, hydraulic turbine, turbulence modeling, jet injection control technique 1 Introduction

Hydropower is a renewable and sustainable energy source with many technical, economical, and environmental benefits. Storage capability and fast response make hydropower an ideal form of power generation. However, the variable energy demand requires hydraulic turbines to be operated over an extended range of conditions quite far from their design point (the best efficiency point).

Hydraulic turbines operating at partial load have a high level of swirl at the draft tube inlet as the difference between the swirl generated by the wicket gates and the angular momentum extracted by the runner. The decelerated swirling flow in the draft tube may lead to flow instabilities, resulting in the formation of a helical precessing vortex called the vortex rope. The flow instability with formation of the vortex rope is the main cause of efficiency reduction and pressure fluctuations experienced by a

Francis turbine operating at part-load conditions. These pressure fluctuations become more serious if their corresponding frequency approaches the natural frequency of the power plant structures.

This can result in vibration of the whole installation [1].

Given the strong influence that vortex rope has on the power plant performance, investigating the mechanism of its formation and controlling its effects are necessary for improving hydropower plant efficiency and preventing structural vibrations.

In recent years, there has been increased interest in computational studies of flow in draft tube of hydroturbines. Common numerical techniques and turbulence models give a good accuracy in predicting the draft-tube characteristics at the BEP. However, one challenge for the numerical simulation is to predict the partialload operating regimes, where a vortex rope appears in the draft tube. Sick et al. [2] performed simulations of a draft-tube vortex in a pump-turbine using the Reynolds stress model (RSM). The results of the numerical simulations showed an overestimation of the vortex rope frequency by 12% but a good agreement for the pressure fluctuation amplitude, comparing with the experimental data. URANS simulations of the runner and draft tube were carried out and compared to the experimental data by Ciocan et al. [3]. They utilized two-equation standard k-e turbulence model and a relatively coarse mesh for computations. Vortex rope frequency and pressure fluctuation amplitude were predicted with 13% and 3% error, respectively, while mean axial velocity is underestimated near the centerline. Zhang et al. [4] investigated the characteristics and control of the draft tube flow under part-load conditions using the URANS simulation of the “sole draft tube flow”. The computations were carried out using the Re-Normalization Group (RNG) k-e turbulence model with logarithmic wall functions. Steady and unsteady simulations of flow in a draft tube were performed by Vu et al. [5] to predict draft tube losses over a wide range of turbine operation. The two-equation k-e turbulence model was used. They stated that, as the operating conditions depart from the best efficiency point, the performance of the k-e turbulence model tends to deteriorate, particularly at partial load.

The majority of hydraulic machinery flow simulations are based on the RANS equations, due to the ease of use and lower 1Corresponding author.

Manuscript received October 6, 2013; final manuscript received February 7, 2014; accepted manuscript posted February 12, 2014; published online March 6, 2014. Assoc. Editor: Kenji Takizawa.