Time-phase averaging for the approximate solution of the flow in a hydraulic turbine

• The refurbishment of old hydropower installations and the continuos development of new installations has increased the interest for better design tools to improve their efficiency. Computational fluid dynamics has been used with great success to improve the design of the runner. However, extensive model testing has been necessary to improve the design of the surrounding waterways. Even after testing, some uncertainty has remained concerning the difference between the model scale and the full scale turbine system. The current trend is therefore to include as much as possible of the water conduits with a simultaneous solution of the flow in the turbine runner in an effort to reduce the need for model testing. However, if high numerical accuracy is required the number of mesh points for a complete model of the turbine system has to be at least 10^7. The mesh size together with the need for a time dependent mesh in the runner makes it unlikely that a full simulation with a rotating runner and advanced turbulence modeling will be possible within the next several years, even if the most optimistic estimate of future computer capacity are taken into account. It is therefore of great interest to find new approximations that will make a more refined analysis of the waterways external to the runner possible.In this paper we present a model for the runner that preserves any flow non-uniformity existing at the inlet of the runner in a realistic way through the runner. This has enabled a complete analysis of the interaction of the flow through the penstock, spiral casing and guide vanes with the flow in the draft tube. The mesh requirement and the computational time is considerably reduced compared to a full simulation with a sliding mesh model for the runner. The main drawback with the new model is believed to be that the blade wakes are averaged out of the problem.The model we propose is based on a time-phase averaging technique. The essence of the model is similar to the time averaging technique used by Adamczyk (Adamczyk, 1985), but with different averaging time and different mathematical notation that makes it possible to use the model in a general case, i.e. both for axial and radial machines. A phase function is central to the technique and is introduced for weighting in the averaging procedure. The phase function makes it possible to time average the flow inside a runner. It is constructed with generalised functions and a geometrical description of the suction and pressure side of a runner blade at a reference position. Exact equations for the time-phase averaged variables are derived by a formal time-phase averaging of the governing equations. Some of the terms are accounted for in an approximate way in the present simulation but it is possible to calculate better approximations with a simulation of an isolated runner in a rotating coordinate system. However, even with the crude approximations that we have used the simulation produces realistic results for the particle paths through the runner.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Energiteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Energy Engineering (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

Nyckelord

Energiteknik

Energy Engineering

Strömningslära

Fluid Mechanics

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