ONE of the most distinguishing characteristics of today’s deregulated power market is its variable demand, which means that profitability often depends on the ability to efficiently operate at partial loads. This creates special challenges in hydro power turbines because at partial loads these turbines often exhibit strong swirl at the runner outlet. As the incoming swirling flow decelerates in the diffuser cone, a hydrodynamic instability arises that looks like a rope twirling around in the draft tube, hence the name vortex rope. The vortex rope creates high-pressure unsteady fluctuations on the walls of the draft tube, which could lead to fatigue damage over time. This phenomenon is especially severe when the frequency of the oscillations of the vortex rope matches the resonant frequency of the turbine or of the circuit. It is not possible to measure the vortex rope in an actual operating turbine; so engineers designing these systems need a way to simulate the frequency, pressure pulsation amplitude, and other parameters under various operating conditions and turbine geometries. This information makes it possible to design the turbine in order to reduce the magnitude of the vortex rope and to withstand the remaining pressure fluctuations without any fatigue damage.
Computational fluid dynamics (CFD) is the obvious tool of choice for simulating flow within a turbine. CFD is a powerful technique that provides an approximate solution to the coupled governing fluid flow equations for mass, momentum and energy transport. The flexibility of the technique makes it possible to solve these equations in very complex spaces, unlike simpler modelling methods that are sometimes used for turbine design.
GE Energy engineers selected Ansys CFX software from Ansys in Pennsylvania, US, as their modelling tool. The main reason is the huge computational resources required to accurately simulate the vortex rope. ‘The computational requirements are caused by several factors,’ says Bernd Nennemann, Research Assistant for GE Energy. ‘First of all the swirling movement of the rope often covers most of the draft tube. This means that a relatively fine mesh is required to capture the pressure fluctuations generated by its movement. Secondly, the vortex rope is an unsteady phenomenon, so accurate predictions require that the flow problem be solved many times at very small time steps.’
For these reasons the ability to efficiently utilise parallel processors was a critical requirement in selecting CFD software. Ansys CFX provides parallel operation out of the box on any combination of single or multiple CPU or networked UNIX workstations or Windows NT machines, including mixed UNIX/Windows NT clusters. The software decomposes the grid with virtually no memory overhead on the master processor. Recompiling is not required when the processor configuration changes. CFX also improves the traditional CFD solver performance by solving the full hydrodynamic systems of equations simultaneously across all grid nodes. This technique can provide solutions up to 100x faster than traditional CFD codes while also increasing robustness and reliability, says Ansys. The coupled solver is designed to deliver on all types of problems but is particularly powerful in flows where inter-equation coupling is significant. The GE engineers used a Linux cluster with 16 AMD Athlon processors. The simulations described here were solved in approximately 25 days using four of the processors.
Physical testing
Physical testing played an important role in this project by providing measurements that correlated to the computer simulation.
A team of researchers at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland, worked with a scale model of a hydraulic turbine. The model simulates a turbine built in 1926, with 4.1m diameter runner, which is owned by Alcan. The original draft tube geometry is of the Moody type. For the purpose of the research project, a specially designed elbow draft tube with one pier replaces the original Moody draft tube.
In order to measure the phenomena of interest in low flow rate turbine operating conditions, G.D. Ciocan and M. Iliescu delivered, for the first time, experimental data of the velocity field in the vortex rope development zone. The measurements were performed using a Dantec 3D PIV system, consisting of two double-frame Hi-Sense cameras synchronised with a double-pulsed laser, and a processor unit for the real-time velocity field data processing.
For optical access necessities, a transparent cone was especially designed, with two large symmetric windows for the cameras’ access and a narrow one for the laser access, all of them having flat external surfaces to minimise the optical distortions. The velocity field is obtained simultaneously with the rope vapors volume for several pressure conditions.
J. Arpe provided experimental pressure fluctuations data, using a HP-VXI system for acquiring simultaneously the signals of 96 pressure transducers mounted on the draft tube’s wall. In order to achieve a good dynamic range for the frequency analysis, the signals were sampled at 200Hz.
The flow investigation was carried out under the FLINDT (Flow Investigations in Draft Tube) project framework, coordinated by Prof. F. Avellan, and sponsored by major hydro turbine manufacturers such as Alstom, GE Energy, VA Tech Hydro and Voith Siemens Hydro Power Generation and by Electricité de France.
cfd modelling
GE Energy engineers selected the runner and draft tube as the computational domain in order to provide a compromise between solution accuracy and computational resources. The mass flow and flow directions were specified at the inlet boundary based on a previous stage flow analysis of the stay vane, guide vane and runner assembly. An outlet boundary condition was specified for the outflow.
A steady state solution was first achieved for the flow domain and used to start the unsteady simulation. A time step of 1º of revolution was selected. It took about 1000 time steps to start the fluctuations from a steady state solution and another 3000 time steps to reach the periodic unsteady state. The numerical solution was well converged after 11,500 time steps or 24 runner revolutions. Pressure and velocity were monitored at 1200 different positions and unsteady solutions written every 10 time steps.
Simulation results
Comparison of the simulation predictions and physical measurements showed very good agreement. The numerically calculated static pressure fluctuations matched up well against the experimental data. The pressure fluctuation amplitude was well predicted at the runner outlet and its evolution in the cone was in good agreement with experimental data for all sensors’ angular positions. The difference between the experimental results and numerical predictions was less than 2.5% for mean pressure level, approximately the same as the measurement accuracy. The numerical mean velocity field also showed good agreement with the physical measurements. The phase average vector field shows only a small difference, being closer to the cone wall in the numerical simulation. The vorticity field, which shows the vortex position, was well predicted by the numerical calculations with a difference of 5% of the radius between the predicted position and the measured one. The vortex intensity is about 18% smaller in the numerical calculations. This difference can be explained by the relatively coarse mesh used for the draft tube geometry, especially in the draft tube cone region.
‘While vortex ropes have been simulated in the past, this is the first time that a simulation of a rotating rope has been compared to detailed experimental measurements, currently in cavitation-free conditions’ says Thi Vu, Senior Hydraulic Engineer for GE Energy. ‘The accuracy of the predictions for vortex global quantities, pressure pulsation amplitude and vortex frequency is very good. The quantitative analyses of mean velocity field, phase average velocity field, vorticity and vortex centre position also show good agreement.
‘These results confirm the use of CFX to simulate the vortex rope,’ continues Vu. ‘We are moving ahead to use this new method for the purpose of designing new hydroelectric turbines and troubleshooting problems with existing turbines. In particular, we are planning to take advantage of the parallel capabilities of CFX by utilising a larger number of faster processors to reduce solution times, preferably to less than 24 hours. Ansys CFX enables us to design turbines faster and for a wide range of operation, helping to make GE Energy more competitive in the market place.’
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