Volumetric flow rate prediction of disturbed pipe flow based on single path velocity data using a shallow neural network

Reliable volumetric flow rate measurements are essential in many applications like power plants or district heating. One method for calibrating flowmeters during operation is to install optical access to pipelines for a laser-optical measurement of the velocity profile along a one-dimensional (1D) path.

Currently, the volumetric flow rate Q is calculated from these measurements by integrating the 1D profile under the assumption of rotational symmetry. This method delivers reliable results only for fully developed and slightly disturbed flows.

The approach presented here uses a shallow neural network (SNN) to predict the 2D profile based on a 1D path. For this purpose, numerical simulations of pipe flows with disturbances due to different elbow configurations are used to generate a dataset of 2D profiles with corresponding 1D paths.

The performance of the SNN is validated with velocity profiles at different downstream positions from cases not included in and partially outside the parameter space of the training dataset.

The SNN reduces the mean relative error of Q from 1.96 % for the rotationally symmetric approach to 0.35 % considering all investigated cases. In the range of 5 to 10 diameters downstream the disturbance, the SNN delivers an error of 1.23 % instead of 5.31 %.