An aeroelastic model of Coriolis mass and density meters operating on aerated mixtures

A lumped parameter, aeroelastic model of Coriolis mass flow and density meters is presented which addresses the effects of compressibility and inhomogeneity introduced by aerated fluids. The model addresses U-tube Coriolis meters containing radially outward and inward flows of a aerated fluid. The mass flow rate and density of the fluid measured by the Coriolis meter are given by solution of an eigenvalue problem governing the dynamics of the aeroelastic system. Mass flow is determined by the phase lag between the displacement of the out-bound and in-bound tubes in the lowest frequency bending mode of the system. Fluid density is related to the natural frequency of this mode.The aerated fluid is assumed to be a well-mixed, dispersed bubbly flow in which the bubbles are small compared to the diameter of the tube. Under this assumption, the effects of compressibility can be incorporated using a lumped parameter model of the first acoustic cross mode of the tube. The effects of inhomogeneity introduced by the bubbles are incorporated using a lumped parameter model of a bubble in a oscillatory acceleration field contained in an viscous, incompressible fluid. The resulting aeroelastic equations of motion for the Coriolis meter show that the behavior of the system is influenced by non-dimensional parameters characterizing the aerated mixtures including reduced frequency, void fraction, and fluid viscosity parameters.The model is used to examine the effect of aeration for a range of parameters considered to be broadly representative of the commercially available Coriolis meters. Results show that aeration can significantly influence the aeroelastic behavior of Coriolis meters, but that, if appropriately considered, Coriolis meters can be used to provide accurate characterization of aerated fluids.