Finite element modelling of Coriolis mass flowmeters with arbitrary pipe geometry and unsteady flow conditions

• An overview of present pipe models described in the literature and their shortcomings is given.
• A model, extending state of the art pipe models, is described for unsteady flow.
• Boundary conditions and valid simplifications are discussed.
• Different model reductions techniques to minimize computational effort are compared.
• Calculation and model agree well with measurements and results from the literature.

The behaviour of Coriolis mass flowmeters (CMFs) with arbitrary pipe geometry is investigated in this paper regarding the effects of unsteady flow, geometry and damping. Timoshenko׳s beam theory, the finite element method (FEM), Mathworks Matlab and Simulink are used for creating a suitable model. Various physical quantities such as Coriolis, centrifugal and gravitational forces, mass inertia, mass flow, unsteady flow forces, damping and material parameters are considered to increase model precision. Stiffening effects due to fluid deflection are partly neglected in the model. The use of exact finite elements and model reduction via modal transformation results in fast and accurate numerical computation which corresponds well with experimental data. As a consequence, this approach allows further optimization of pipe geometries, actuation positions and concepts, actuation und flow control systems and signal processing concepts without co-simulation.