Mass flow meter

Our website provides a very detailed explanation of the principles behind Coriolis mass flow measurement. http://www.shakic.com/cp/yetizhiliangllj.htm

2L is very dedicated; I often see them online. I used to visit Baidu Knows quite frequently as well

1. Basic theory: The Coriolis effect is a natural phenomenon that was quantified in 1835 by Gaspard Gustave de Coriolis, a mathematics professor at the Polytechnic School in Paris. The Coriolis effect can explain why matter moving freely on the Earth’s surface appears to move in a curved path within a rotating reference frame. When an object moves in translation relative to such a frame, in addition to the centripetal force, another force acts on it; this force is called the Coriolis force. For example, suppose the reference frame is a disk rotating at a constant angular velocity around axis O (Figure 3.3.1), with the direction of rotation indicated by the vector in the diagram. When an object moves along a radius at a speed V’, an \"inertial force\" FK = 2V’·ωm acts on that object. The direction of this force is perpendicular to V’, and this force, FK, is the Coriolis force. It depends both on the object’s speed V’ relative to the rotating reference frame and on the angular velocity ω of the reference frame. Figure 3.3.1 The Coriolis mass flow meter converts continuous rotational motion into vibration. There is an electromagnetically driven system in the detector, which causes the measurement tube to vibrate at its inherent frequency; this creates a rotating reference frame, and its vibration is similar to that of a tuned tuning fork. When a particle located within a rotating body moves toward or away from the center of rotation, an inertial force is generated; Figure 3.2.2 illustrates this principle. When a particle of mass m moves at a constant velocity V within a pipe that rotates around a fixed point O with an angular velocity ω, there will be a centripetal force Fr=ω2r·△m acting along the normal direction to the rotation ； In the direction of the tangent, the particle also exerts a reaction force on the tube wall; this force is given by Fc=2ωV·△m. This force is the Coriolis force. Here, ω represents the angular velocity of the rotating body, V is the radial velocity of the particle within the rotating body, and △m is the mass of the particle. The formula shows that, at a constant rotational angular velocity, the magnitude of the Coriolis force acting on a particle is proportional to the product of its mass and its velocity. Therefore, the mass flow rate can be determined by directly or indirectly measuring the Coriolis force exerted by the fluid in the rotating pipe. This is the basic principle of CMF. Principles of CMF measurement – 2. Principles of CMF measurement: Taking Micromotion’s U-shaped vibrating tube as an example, a quantitative analysis of the measurement process in Coriolis mass flow meters is conducted. The amplitude of vibration in Micromotion’s U-shaped tubes is usually less than 1 mm, with a frequency of around 80 Hz. Figure 3.3.3 shows the measuring tube in a state of vibration; the fluid is forced to undergo vertical motion along the tube. During the upward-moving half-cycle of vibration, the fluid flowing into the instrument exerts a downward force, counteracting the upward force on the tube. Conversely, the fluid flowing out of the instrument exerts an upward force, resisting the reduction in the tube’s vertical position and thus pushing the tube upward. The combination of the two reaction forces causes the flow measurement tube to twist ； This is the Coriolis effect. During the other half-cycle of vibration, the tube moves downward and the direction of twisting is reversed. The library shows a fluid flowing through a measuring tube, with a mass of m and a velocity of V; it rotates at an angular velocity ω relative to the O–O axis. Thus, the Coriolis effect arises: The principle of CMF measurement – According to this principle, F = 2mωV (1), where F and ω are vectors, and Mj represents the mass contained within the measuring tube of length L (i.e., the mass of the fluid in half of the tube). Figure 3.3.4 shows a schematic illustration of the rotation of the measuring tube. The velocity vectors at the inlet and outlet of the fluid are in opposite directions. When viewing this measuring tube from the rear end, it appears as two leads (as seen along the R–R axis in Figure 3.3.4). The forces F1 and F2 generated by the fluid in the inlet and outlet pipes are also in opposite directions, but they have equal magnitudes. Due to the vibration of the tube relative to the O–O axis, this force generates a vibrating torque M relative to the R–R axis (with radius r). CMF measurement principle — The CMF measurement principle is given by: M = F1·r1 + F2·r2. (2) Since F1 = F2 and r1 = r2, equations (1) and (2) yield: M = 2Fr = 4ω·V·m·r. (3) Mass m is defined by density ρ, tube cross-sectional area A, and length L; velocity V is defined as the distance covered per unit time. The mass flow rate Q is determined by the mass of material that passes through a given point per unit of time; that is, m=ρ·A·L and V=L/t, so Q=m/t. By substituting these values into the equation Q=mv/L, where L is the length of the pipe, equation (3) becomes: M=4ω·r·Q·L (4). The torque M causes an angular deflection, namely a twisting angle θ, relative to the R–R axis. This torsional angle is greatest at the midpoint of the vibration tube’s movement (as shown in Figure 3.3.5). Figure 3.3.5 illustrates the principle of CMF measurement based on the pressure forces acting at the end of the measuring tube. However, the deflection caused by M is counteracted by the elastic force K exerted by the stretching of the measuring tube. In general, for any torsional force, the torque T is defined as T = Kθ (5). Since T = M, by combining equations (4) and (5), the mass flow rate Q can be related to the deflection angle θ through an appropriate equation. Kθ Q= (6) 4ω·r·L; the product of the velocity Vt (linear velocity) at the center of the tube’s axis and the time interval is related to θ as represented by geometric shapes. Vt ·△t Sinθ= (7) Principle of CMF measurement – The principle of CMF measurement: Since θ is very small, it is almost equal to Sinθ. For small rotation angles, Vt is the product of ω and the tube length L; that is, θ = Sinθ and Vt = ωL. Thus, equation (7) becomes: ω·L·△t / θ = (8) r. Combining equations (6) and (8) gives: K·ω·L·△t / Δt = Q / (4r2ω·L) (9). Principle of CMF measurement – The principle of CMF measurement: Therefore, the mass flow rate Q is proportional only to the time interval t and certain geometric constants; it is independent of ω, and hence independent of the vibration frequency of the measuring tube. The mass flow rate is obtained by measuring the deflection angle θ using an electromagnetic inductor. As shown in Figure 6, the inductor, which is positioned across the central axis of the measurement tube, measures θ as a function of time. When there is no flow, the time difference between the upward and downward impacts on either side of the measurement axis is 0; as the flow rate increases and θ increases, the time difference t between the upward and downward impact signals also increases. The amount of distortion measured is directly proportional to the flow rate; the sensor transmits the time difference caused by the twisting of the pipe to the transmitter in the instrument, which then processes and converts it. Transmission system

Reply to 4# xuq1973: Why can’t I see the picture? :o

Here’s a demonstration animation made by Micromotion; however, the Chinese version has issues and can’t be used, so only the English version is available. http://www.emersonprocess.com/micromotion/tutor/index.html

Along the way, as I passed by, I didn’t quite understand it

It is recommended to find a sample directly; it has everything included