Improved Discharge Measurement Using the Pressure-Time Method in a Hydropower Plant Curved Penstock

One of the basic flow rate measurement methods applied in hydropower plants and recommended by the International Standard IEC 60041–1999 and American National Standard ASME PTC 18–2002 is the pressure-time method, generally known as Gibson method. The method consists in determining the flow rate (discharge) by integration of the recorded time course of pressure difference variations between two cross sections of the hydropower plant penstock. The accuracy of measurement depends on numerous factors and, according to the International Standard, generally is confined within the range 1.5–2.3%. Following the classical approach, the pressure-time method applicability is limited to straight cylindrical pipelines with constant diameters. However, the International Standard does not exclude application of this method to more complex geometries, i.e., curved pipeline (with elbows). It is obvious that a curved pipeline causes deformation of the uniform velocity field in pipeline cross sections, which subsequently causes aggravation of the accuracy of the pressure-time method flow rate measurement results. The influence of a curved penstock application on flow rate measurements by means of the considered method is discussed in this paper. The special calculation procedure for the problem solution has been developed. The procedure is based on the FLUENT computational fluid dynamic solver. Computations have been carried out in order to find the so-called equivalent value of the geometric pipe factor $F$ required when using the pressure-time method. An example of application of this method to a complex geometry (two elbows in a penstock) is presented. The systematic uncertainty caused by neglecting the effect of the elbows on velocity field deformation has been estimated.