Dynamic response of small turbine flowmeters in pulsating liquid flows
The dynamic response of turbine flowmeters in low pressure gas flows (i. e. where the rotational inertia of the fluid is negligible) is well understood and methods for correcting meter signals for a lack of response are available. For liquid flows there has been a limited amount of experimental work on the response of meters to step changes but no reports have been found of the response of meters to sinusoidally pulsating flows. "Small" turbine meters are expected to behave differently from "large" meters for a number of reasons: a smaller meter would generally have: (1) a larger percentage of tip clearance leakage flow; (2) less fluid momentum between the meter blading; and, (3) less fluid friction forces on the effective surface area. In this research, arbitrarily, meters up to size 25 mm were defined as small; and within this study, meters of size 6 mm to 25 mm were investigated. The aim of the research was to investigate and to understand the response of small turbine meters to pulsating liquid flows and to provide methods for correction. Three approaches were used: (1) application of an existing theoretical model of turbine meter behaviour; (2) an experimental investigation of meter performance in pulsating flows; and (3) simulation of flow behaviour through one selected meter using CFD and extending the simulation to predict the rotor dynamics and, hence, the response of this meter to specified cases of pulsating flow. A theoretical model developed by Dijstelbergen (1966) assumes frictionless behaviour and that flow is perfectly guided by meter blading through the rotor and that fluid within the rotor envelope rotates as a "solid body". Results from this theoretical model applied for pulsating flows showed that there was likely to be positive error in predicted mean flow rate (over-registration) and negative error for predicted values of the amplitude of the pulsations (amplitude attenuation). This behaviour is due to the fundamental asymmetry between flows with increasing and decreasing angle of attack relative to the meter blades, throughout a pulsation cycle. This qualitative behaviour was confirmed by experimental work with meters up to size 25mm working with pulsation frequencies up to 300 Hz. For low frequency pulsations (below 10 Hz), the over-registration errors were within the limits of specified meter accuracy. At higher frequencies and larger pulsation amplitudes, the largest over-registration observed was 5.5 % and amplitude attenuation could be as large as 90 %. The dependence of these errors on both the flow pulsation amplitude and frequency were investigated. The theoretical model was also used as a basis for generating correction procedures, to be applied to both the mean flow and the pulsation amplitude measurements. The results from the CFD simulation showed qualitative good agreement with the experimental data. The same kind of meter error trends were observed and it was shown to provide a better correlation with the experimental trends than the theoretical model derived from Dijstelbergen. From the CFD simulation, the causes of over-registration and amplitude attenuation in turbine flowmetering were understood through the investigation of rotor dynamics coupled with fluid behaviour around meter blading within the pulsation cycle. The CFD results were used to evaluate fluid angular momentum flux and to review the validity of the assumption that fluid within the rotor "envelope" rotated as a solid body. For the case investigated, whilst the assumption that flow is perfectly guided is not inappropriate, the volume of fluid assumed to rotate as a "solid body" was found to be significantly less than the rotor envelope volume.