Keywords: Coriolis flowmeter, fluid-structure interaction, numerical modelling, coupled simulation.

A fluid conveying measuring tube that is maintained vibrating at its first natural frequency under imposed forced vibration conditions is a primary sensing element in a Coriolis flowmeter. As a result of the fluid forces acting on a straight clamped tube, the tube's first mode shape, which is otherwise symmetric with respect to the tube length, is distorted in an anti-symmetric way. This effect, which is actually caused by the appearance of the Coriolis forces, is exploited as the basic measuring principle. To enable a periodic operation of the flowmeter a point in the central cross-section of the measuring tube is harmonically excited by the first natural frequency of the measuring tube.

For reliable prediction of the measuring characteristics of the considered Coriolis mass flowmeter, a proper numerical model for the interaction between the fluid flow and the measuring tube is required. In our case this is realized by a three-dimensional coupled numerical model, which uses the finite volume method (FVM) for solving the dynamics of a viscous fluid flow, while the structural dynamics problem is considered within the finite element method (FEM) framework.

For the solution of the specified tasks commercially available codes Comet 2.1 (FVM) and Abaqus 6.4 (FEM) are used respectively, and an appropriate coupling technique exploiting the computed results of each individual problem is used to perform computer simulations of the vibrating fluid-structure system considered. Coupling is numerically based on a staggered partitioned algorithm with additional pressure predictor and interfield iterations to minimize the time lag in the fluid-structure coupling procedure.

In the numerical model of the Coriolis flowmeter the fluid and the structural domain are discretized in a way that the two meshes, based respectively on the FEM and the FVM discretization, coincide at the fluid-structure interface. As a consequence, the finite volume mesh follows in time with the motion of the tube, which is actually modelled as a shell. In order to keep in time with the same FVM mesh topology the displacements of internal nodes are correspondingly adjusted in each time step.

To achieve a fast numerical steady-state response of the considered coupled system a special two-step solution procedure has been developed. The main idea behind the proposed solution procedure is to ensure monotonic and smooth convergence by finding the steady-state response of the free oscillating coupled system first, and only then to consider the imposed excitation force to keep the system in oscillation.

The simulation results are presented for four different fluid average axial velocities: 0.2m/s, 0.4m/s, 1.5m/s and 5.0m/s. Observation of the motion exhibited by a point in the central cross-section of the tube shows, that after the excitation force is entered in the computation only a few oscillation cycles are required for the amplitudes of the kinematic values to become constant, while the phase difference established between the motion of that point and the excitation force converges close to a quarter of oscillation period. Finally, being of major significance for experimental application, the relationship is established between the phase difference of the respective responses at the two measuring points, located symmetrically to the central cross-section of the tube. Hence the fluid mass flow through the tube was analysed and discussed.

1

N. Mole, G. Bobovnik, J. Kutin, B. Štok and I. Bajsic, "Coupled Fluid-Structure Simulation of a Coriolis Flowmeter", in Proceedings of the Fourth International Conference on Engineering Computational Technology, B.H.V. Topping and C.A. Mota Soares, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 33, 2004. doi:10.4203/ccp.81.114

2

G. Bobovnik, J. Kutin, I. Bajsic, "The effect of flow conditions on the sensitivity of the Coriolis flowmeter", Flow Measurement and Instrumentation, 15, 69-76, 2004. doi:10.1016/j.flowmeasinst.2003.12.001

3

J. Kutin, I. Bajsic, "An analytical estimation of the Coriolis meter's characteristics based on modal superposition", Flow Measurement and Instrumentation, 12, 345-351, 2002. doi:10.1016/S0955-5986(02)00006-7

4

C.A. Felippa, K.C. Park, C. Farhat, "Partitioned analysis of coupled mechanical systems", Computer Methods in Applied Mechanics and Engineering, 190, 3247-3270, 2001. doi:10.1016/S0045-7825(00)00391-1

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C. Farhat, M. Lesoinne, "Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems", Computer Methods in Applied Mechanics and Engineering, 182, 499-515, 2000. doi:10.1016/S0045-7825(99)00206-6

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