The character of swirl in turbulent pipe flow with reference to its effect on flowmeters

A theoretical and experimental investigation of the character of in turbulent pipe flow has been carried out and some implications for the use of flowmeters considered. An extensive survey of Industrial users of flowmeters has been made, involving the participation of over 70 companies, which provides information about current industrial practice, attitudes and understanding. Axisymmetric perturbations of fully developed turbulent pipe flow been studied using the mixing-length model of turbulence. A linearised theory finds the character of small perturbations, decaying exponentially in the axial direction, in which the tangential and axial motion are independent. A non-linear similarity theory finds the flow field at a particular cross-section of the pipe assuming it to be determined by the specification of the Reynolds number, the pipe's roughness and the swirl number at that cross-section. Laser Doppler Anemometry was used to measure axial and tangential velocities on 4 equidistant cross-sections of a pipe following a double right-angle bend in two perpendicular planes. It was found the tangential velocity had the form of a solid body rotation decayed exponentially. The axial velocity profile after the bend asymmetrical, having the form of a horseshoe which rotated with swirl whilst returning to its fully developed form. Theoretical studies of the effect of the measured axial velocity profiles on the accuracy of electromagnetic and ultrasonic flowmeters presented. It is suggested that the decay of the level of swirl in turbulent flow after a double bend be modelled by the factor exp(-6fz/D) where f is the friction factor in fully developed flow and z/D the dimensionalised axial distance. The accuracy of flowmeters installed at particular locations downstream can then be predicted the appropriate error characteristics of flowmeters are known. Some indications of these characteristics are presented