# Performance prediction model for positive displacement helical screw flowmeters

• Volker Bernd Klügl

Student thesis: Doctoral Thesis

### Abstract

A general model is developed describing the performance of positive displacement flowmeters. This model allows to predict the performance of any positive displacement meter if 8 coefficients describing the meter design are known. The logic is that a flowmeter performs at a defined pressure loss for a given speed. This pressure loss times flowrate is then energy balanced against all internal loses. Pressure loss and speed are the reasons for leakage. Rotational speed times the theoretical swept volume is the theoretical flowrate and this flowrate, when combined with leakage flow can be used to calculate the effective or true flowrate. The 8 coefficients describe the influence of the design of a meter on laminar leakage flow, turbulent leakage flow, speed related leakage flow, viscous friction, mechanical friction, constant friction, impulse energy losses and ball bearing friction, respectively.

This model was applied to a twin-screw type displacement flowmeter which uses two helical rotors which form separate pockets and allow the flow-rate of the fluid to be measured. Based on the general prediction model it was found that for this type of flowmeter mainly two coefficients are the reasons for deviation from linearity. These are the constant friction power losses KC produced by mechanical sliding and the turbulent leakage flow losses Kt ur . When the values of KC and Ktur are zero then the error against flowrate is constant.

A complete model of an actual twin-screw type displacement flowmeter was realised, determining all 8 loss coefficients. In order to do so, tests with a twin-screw type displacement flowmeter have been carried out on the overall meter performance, leakage flow losses and bearing friction. The theoretical work includes the determination of all 8 coefficients based on a study of the rotor geometry of the meter and a calculation of the fluid forces and torques acting on the rotors.

The theoretical results of the final performance prediction model were compared with experimental results and show a good accordance. It was found that one optimal circumference clearance value can be determined for every different fluid property and flowrate. The flowmeter performance may be increased by minimising mechanical sliding and turbulent leakage flow losses.
Date of Award May 1998 English

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