Working principle and mathematical model of mass flowmeter

Working principle of mass flowmeter Mass flowmeter is based on Newton's second law: force = mass×Acceleration (F=ma). When a particle with a mass of m moves with a velocity V in a pipe rotating at an angular velocity ω to the P axis, the particle is subjected to two components of acceleration and its force: 1) normal acceleration, that is, centripetal accelerationαr, whose magnitude is equal to ω2r, towards the P axis; 2) Tangential angular velocityαt is the Coriolis acceleration, its value is equal to 2ωV, and its direction is the same asαrVertical. Due to the compound motion, in the particleαThe Coriolis force Fc=2ωVm acts on the t direction, and the pipeline acts a reverse force -Fc=-2ωVm on the particle. When the density isρWhen the fluid flows at a constant velocity V in a rotating pipe, any pipe with a length Δx will be subjected to a tangential Coriolis force ΔFc: ΔFc=2ωVρAΔx (1) where: A———The flow cross-sectional area of ​​the pipe. Since there is a relation: qm=ρVA So: ΔFc=2ωqmΔx (2) Therefore, the mass flow rate can be measured by directly or indirectly measuring the Coriolis force of the fluid flowing in the rotating tube. The mathematical model is further deduced from formula (2) (the relevant mathematical derivation is omitted), and the following mathematical model is obtained: (3) where: qm———Mass flow rate; K———A quantity that only determines the size of the measuring tube structure. When the measuring tube has a certain structure and a certain temperature, K is a certain value; G———Measure the shear elastic modulus of the tube material; at a certain temperature, K is a certain value; ω———The natural frequency of the main vibration of the measuring tube; ωθ———Natural frequency of the torsional vibration of the measuring tube; Δt———The time difference between the two detection signals of the measuring tube. The lag time between the left and right detection signals is measured by a time difference detector in the circuit. this“Time difference”Δt is digitally measured, processed, and filtered to reduce noise and improve measurement resolution. The time difference is multiplied by the flow calibration coefficient to represent the mass flow.

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