A virtual flow meter downstream of various elbow configurations

Abstract

When flow meters are installed in disturbed flow conditions caused by pipe configurations such as junctions or elbows, significant measurement errors can occur.
With existing knowledge of the flow conditions, those errors can be corrected using suitable calibration factors.
This paper presents a surrogate model based on computational fluid dynamics simulation results that can predict velocity profiles downstream of single and double elbows in- and out-of-plane. 
The simulated flow profiles are decomposed into a fully-developed and a disturbed part, which allows changing the Reynolds number and roughness of the pipe wall without performing additional simulations.
Furthermore, proper orthogonal decomposition and interpolation using piecewise linear splines enables the real-time evaluation of the model for a wide range of curvature radii and distances between the elbows.
By incorporating a measurement principle, calibration factors for different flow meter designs can be predicted. 
The model is validated on the example of an ultrasonic flow meter by comparison with measurement data obtained from a clamp-on flow meter.