FINITE ELEMENT ANALYSIS OF VIBRATION BASED MASS FLOW SENSOR

Abstract

The primary objective of present work was to develop an analytical simulation tool for curved tube vibration based mass flow sensors using finite element analysis. This was implemented by developing the analytical simulation tool using the fluid structure interaction (FSI) theory based on Euler's Bernoulli beam. The Equation of motion in out of plane vibration for U-tube was derived and consider because the Coriolis force is maximum compare to in plane vibrations. We idealize fluid as incompressible and inviscid. The governing equations were derived by using Newton's force principle. Hermite cubic shape functions were used to fmd out the natural frequency and mode shapes of the tubes considering the two degrees of freedom for each node (deflection and slope). After weak formulation the Galerkin technique was used to derive the stiffness, mass and damping matrices. MATLAB code was developed to obtain the different modal frequency and mode shapes for different boundary conditions. The beam analysis without considering the fluid was carried out and observed that the results were very well predicted with exact solution with 4 % of error. Further the numerical simulation have been carried out to get a better physical insight into the behavior of different design parameters like Flow velocity, length of the vertical and horizontal tube, tube material, sensor location etc. which affects the performance of the mass flow sensors. The phase difference linearly varies with the flow velocity this trend of observation was similar to the previous study by sultan et al.