Thread Content
1. Working principle: As shown in Figure 1, consider a branch pipe through which a fluid flows from point A to point B at a velocity V. This pipe is placed in a system that rotates at an angular velocity ω. Let the axis of rotation be X, and the point of intersection with the tube be O. Since the fluid particles inside the tube move axially at a velocity V and radially at an angular velocity ω, they are subjected to a tangential Coriolis force Fc. This force acts on the measuring tube, in directions opposite to each other on either side of point O, with equal magnitudes; it is given by δFc = 2ωVδm. Therefore, by directly or indirectly measuring the Coriolis force generated by the fluid flowing within the rotating tube, it is possible to determine the mass flow rate. This is the basic principle of the Coriolis mass flow meter. https://p3-tt-ipv6.byteimg.com/large/pgc-image/a8ee5e7f3217445cae95bc8e7f422b8f Figure 1: Formation of the Coriolis force Figure 2: Early designs of Coriolis mass flowmeters II. Structure The structure of the early-designed Coriolis mass flowmeters is shown in Figure 2. It will be fed into a rotating system through a pipe carrying flowing fluid, and a torque sensor mounted on the shaft is used to measure the mass flow rate. This type of flow meter has only been prototyped in the laboratory. In the design of commercial products, it is impractical to generate a Coriolis force by rotating the measurement system; therefore, vibration of the measurement tube is used as a substitute for rotational motion. In this way, the effect of the Coriolis force on the measuring tube is likewise achieved, causing the measuring tube to undergo displacement under the action of the Coriolis force. Since both ends of the measuring tube are fixed, and the forces acting on different points along the tube vary, the resulting displacements also differ, thus causing an additional distortion in the measuring tube. By measuring the phase difference at various points in this distortion process, the mass flow rate of the fluid flowing through the measuring tube can be obtained. The common types of measuring tubes include the following: S-shaped measuring tubes, U-shaped measuring tubes, double J-shaped measuring tubes, B-shaped measuring tubes, single straight-tube measuring tubes, double straight-tube measuring tubes, Ω-shaped measuring tubes, double ring-shaped measuring tubes, etc. Below, we will provide a brief introduction to their structures respectively. 1. S-shaped measuring tube mass flow meter As shown in Figure 3, the measurement system of this type of flow meter consists of two parallel S-shaped measuring tubes, a driver, and a sensor. Both ends of the tube are fixed, and a driver is installed at the center of the tube to cause it to vibrate. Sensors are installed at symmetric positions on the measuring tube, and the relative displacement between the vibrating tubes is measured at these two points. The mass flow rate is proportional to the phase difference between the oscillation frequencies measured at these two points. https://p1-tt-ipv6.byteimg.com/large/pgc-image/60e9a3ab29e647b78b3263e0fecbbcb9 Figure 3: Structure of the S-shaped mass flow meter. The working principle and operation process of this type of mass flow meter are shown in Figure 4. https://p9-tt-ipv6.byteimg.com/large/pgc-image/407d2965feae4912b2810d7ab84c8873 Figure 4: Output of the displacement sensor when there is no flow. When no fluid is flowing in the measurement tubes, the two tubes undergo symmetric motion of equal amplitude under the action of driving forces (the forces acting on each tube are of equal magnitude but in opposite directions). Since both ends of the tube are fixed, the amplitude is greatest in the middle of the tube and gradually decreases to zero at both ends. At this time, the phases measured by the two sensors are as shown in Figure 4B. It can be seen from the figure that the phase difference measured by the two sensors is zero. When the fluid inside the measuring tube flows at a velocity V, the flow velocity at any point in the fluid can be regarded as the resultant of two component velocities: Vx in the horizontal direction and Vy in the vertical direction (which is the same as the direction of vibration). Under constant flow conditions, the horizontal flow velocity Vx of the fluid remains constant. As can be seen from Figure 5, the amplitude at the inlet and outlet of the pipe is zero, and the vertical velocity Vx of the fluid particles is also zero ； https://p1-tt-ipv6.byteimg.com/large/pgc-image/26a765abcb1b4a92a2171718c838b067 Figure 5 Force analysis of the vibrating tube. When fluid particles flow into the measuring tube in the direction indicated by the vibration, their vertical flow velocity is +Vy; similarly, when they flow toward the outlet, their vertical flow velocity is -Vy. It can be inferred from this that, as the fluid particle passes through the vibrating measuring tube, its vertical velocity increases gradually from zero, reaches a maximum at some point, and then gradually decreases back to zero. According to the principles of mechanics, changes in velocity are caused by acceleration, and acceleration is the result of a force acting on an object. Based on this principle, this change in vertical velocity is called the Coriolis acceleration Ac; therefore, the Coriolis force acting on the mass M of the fluid is Fc = Mac. At two points on the measuring tube that are equidistant from the center, the magnitudes of the Coriolis forces acting on them are equal, while their directions are opposite. When this Coriolis force acts on the measuring tube, the result shown in Figure 5 is produced: a pair of forces is generated at the midpoint, causing the measuring tube to twist or deform slightly. In fact, during oscillatory motion, it is the two S-tubes that experience oscillation simultaneously; their directions of motion are opposite, and the forces acting on them are equal, as shown in Figure 6. https://p26-tt.byteimg.com/large/pgc-image/cb50afbd6f7a4d47996bd68caad47a5a Figure 6: The Coriolis force acting on the measuring tubes. As the oscillatory motion proceeds, the measuring tubes are periodically separated and brought together; accordingly, the Coriolis force acts periodically on these two tubes. By using the displacement sensors installed on the measuring tubes, labeled A and B, the changes in the relative position of the measuring tubes caused by the Coriolis force can be measured, which is usually expressed as the phase difference between the two points, as shown in Figure 7. The magnitude of this phase difference is proportional to the mass flow rate. https://p6-tt-ipv6.byteimg.com/large/pgc-image/6ddac2d5d2e0480cb424e1331586dc43 Figure 7: Output of the displacement sensor. 2. Mass flow meter with U-shaped measuring tube: As shown in Figure 8, the U-shaped tube can be of either single or double tube configuration. The working principle of the single-tube type is as follows: https://p26-tt.byteimg.com/large/pgc-image/3777396cea1346869578ed52269d129b Figure 8a: Single U-shaped tube structure; https://p26-tt.byteimg.com/large/pgc-image/528101272e5f4793a8e2c99263116a95 Figure 8b: Double U-shaped tube structure. As shown in Figure 9, the electromagnetic drive system drives the U-shaped measuring tube to vibrate at a fixed frequency. When the fluid is forced to move vertically along the tube, during the first half of the vibration cycle, the tube moves upward; the fluid inside the tube exerts a downward force in front of the driving point, which opposes the upward movement of the tube, while it exerts an upward force behind the driving point, accelerating the tube’s upward movement. The combination of these two forces causes the measuring tube to twist ； During the other half cycle of vibration, the direction of twisting is reversed. https://p26-tt.byteimg.com/large/pgc-image/ecbcac25315b43c987e404c4938379c3 Figure 9: Principle of operation of the U-tube. The degree of twisting of the measuring tube is proportional to the mass flow rate, which in turn is related to the flow of fluid through that tube. Electromagnetic sensors are installed on the measuring tubes on both sides of the driving point in order to measure the phase difference in their movement; this phase difference is directly proportional to the mass flow rate flowing through the tube. In the double U-shaped measuring tube structure, the vibration directions of the two measuring tubes are opposite to each other, resulting in a phase difference of 180 degrees in their twisting, as shown in Figure 10. Compared to single-measurement tube types, the detection signal of dual-tube types is amplified, and their flow capacity is also improved. https://p26-tt.byteimg.com/large/pgc-image/33223349658b4e13885dc4c0b2e673fb Figure 10: Schematic diagram of tube deformation. 3. Dual J-tube mass flow meter: As shown in Figure 11, two J-tubes are arranged symmetrically around the pipeline as the center ； The actuator mounted on the J-shaped section causes the tube to vibrate at a certain fixed frequency. https://p6-tt-ipv6.byteimg.com/large/pgc-image/0e620b87956a44218fec166f9a44e7c4 Figure 11: Structure of the J-tube mass flow meter. Its working principle is shown in Figure 12; when the fluid in the measuring tube flows at a certain speed, vibrations cause a Coriolis force effect on the fluid within that tube. This Coriolis force acts on the measuring tube, but the directions of the Coriolis forces generated in the upper and lower tubes are different; this results in different additional movements in the straight sections of the tubes, thereby creating a phase difference in the relative displacement. https://p6-tt-ipv6.byteimg.com/large/pgc-image/ad41f31e75fd4f8da0d8b984e6e4f2d0 Figure 12: Working principle of J-shaped tubes. In a dual J-shaped tube measurement system, the two tubes vibrate in opposite directions at the same time, thereby increasing the phase difference in their relative displacement between the upper and lower straight sections. As shown in Figure 13, when the fluid is not flowing, the phase difference of the displacement signals measured by sensors A and B is zero. https://p1-tt-ipv6.byteimg.com/large/pgc-image/fe649b19441c489da8de91c13312c062 Figure 13: Vibration state of the measuring tube when there is no fluid flow. When fluid flows through the measuring tube, the effect of the reaction force generated by the Coriolis force on the measuring tube in the direction that drives its vibration is shown in Figure 14. When Tube 1 moves apart and Tube 2 moves closer, the upper part of Tube 1 moves faster while its lower part moves slower; for Tube 2, the opposite occurs—its upper part moves slower and its lower part moves faster ； As shown in Figure 15, there is a phase difference between the signals measured by the sensors installed at the upper and lower parts. The magnitude of this signal directly reflects the mass flow rate. https://p1-tt-ipv6.byteimg.com/large/pgc-image/baf748aec2b3469e9d3e5816fb3c179e Figure 14: Vibration state of the measuring tube when there is flow. https://p1-tt-ipv6.byteimg.com/large/pgc-image/3e723cabd7de4cb7b4844a2374a4abf7 Figure 15: Sensor output signal. 4. B-type tube mass flow meter: As shown in Figure 16, the flow measurement system consists of two parallel B-type tubes. The fluid under test is evenly distributed to two B-shaped measuring tubes via a flow divider. The drive device is mounted at the center between the two tubes, driving the measuring tubes to vibrate at a certain stable harmonic frequency. When the measuring tube moves outward, as shown in Figure 17a, the straight sections are pushed apart from each other; under the action of the driver, circuits L1' and L1'' move closer to each other, and similarly, circuits L2' and L2'' also move closer to each other. Since each loop is fixed at one end to the flowmeter body, rotational motion is suppressed in the end region and thus concentrated near the node. https://p6-tt-ipv6.byteimg.com/large/pgc-image/eac58b1921654ad9a123e5002b806a63 Figure 16: Structure of the B-type tube mass flow meter. Under the action of the Coriolis force, the speed at which the fluid in the loops L1’ and L1’’ approaches each other decreases; conversely, the speed at which the fluid in the other two loops, L2’ and L2’’, approaches each other increases. https://p26-tt.byteimg.com/large/pgc-image/f0edf95fb2644c939070bc3364f28978 Figure 17: Stress conditions on the B-shaped tube during operation. When the tube moves inward, as shown in Figure 17b, the opposite situation occurs. Under the action of the driving force, the straight pipe sections move towards each other, while the two loops on the two cross-sections move in opposite directions. The Coriolis force generated by the fluid in the pipeline, acting on this basic motion, accelerates the separation speed of the L1' and L1'' circuits, while reducing the separation speed of the L2' and L2'' circuits. By properly installing sensors between the two circuits at the end face, these movements induced by the Coriolis force can be used to accurately determine the mass flow rate of the fluid. 5. Single straight-tube mass flow meter. The structure of this type of flow meter is shown in Figure 18; the measurement system consists of a straight tube fixed at both ends (with flanges) and a vibration driver mounted on it. https://p3-tt-ipv6.byteimg.com/large/pgc-image/12eb20f97b334b409a297fa56ec06cc2 Figure 18: Structure of a single straight-tube mass flow meter. When there is no flow of fluid in the tube, the driver causes the tube to vibrate; as a result, no Coriolis force is generated in the fluid. The forces acting on points A and B are equal, and their rates of change are the same, as shown in Figure 19b. https://p1-tt-ipv6.byteimg.com/large/pgc-image/6ffff99af7054f278f9fba768ecad4ce Figure 19: Working principle of the single straight-tube mass flow meter. When the fluid in the measurement tube flows at a velocity V, the effect of the vibrating force at point C (which is upward at this time) causes the fluid particles to accelerate as they move from point A to point C. This results in a reaction force F1 that slows down the upward movement of the tube ； Between point C and point B, the fluid particles are decelerated, thereby increasing the upward movement speed of the tube. As a result, the two forces in opposite directions on either side of point C cause the tube to deform, and the phase difference of this deformation is proportional to the mass flow rate of the fluid flowing through the tube. 6. Dual straight-tube mass flow meter. Figure 20 shows the structure of the dual straight-tube mass flow meter: https://p6-tt-ipv6.byteimg.com/large/pgc-image/b9023ec5fcbb416499c886d1d5f8e25d. Compared to a single straight tube, the dual straight-tube design reduces pressure losses and enhances the signals detected by the sensor. The actual structure is as shown in Figure 20; the driver is located at the center, while the two photoelectric sensors are positioned symmetrically on either side of the center. In the configuration shown in Figure 20a, the measurement tube is minimally affected by axial forces. The operating principle of the dual straight-tube mass flow meter is shown in Figure 21. When no fluid is flowing, the phases of the displacements generated by the tubes and sensed by the photoelectric sensors are identical ； When a fluid medium flows through two vibrating measuring tubes, a Coriolis force is generated. This force causes opposite displacements on both sides of the vibration node. The fluid medium in the portion of the measuring tube preceding the vibration node dampens the oscillation of the tube; in other words, the rate of displacement of the tube slows down ； The fluid medium in the measuring tube after vibration intensifies the oscillations; that is, the displacement velocity of the tube increases. The phase difference between the two ends is measured using a photoelectric sensor; this phase difference is proportional to the mass flow rate in the measuring tube when the oscillation frequency remains constant. https://p26-tt.byteimg.com/large/pgc-image/9ecccaab8bf044b4adf19e28c1a37bce Figure 21: Principle of measurement using two straight pipes. 7. Ω-shaped measuring tube mass flow meter. The structure of this flow meter is shown in Figure 22. The actuator is placed in the middle of the straight pipe section; when the fluid flows through the pipe at a certain speed, the vibrations generated by the actuator cause the pipes to move apart or come closer together. https://p6-tt-ipv6.byteimg.com/large/pgc-image/e7b33d00eeaa4db0a581f7b696990ddb Figure 22: Structure of the omega-shaped mass flow meter. As shown in Figure 23a, when the tubes are separated, the Coriolis force generated in the fluid ahead of the vibration point acts in the opposite direction to the force causing vibration, thereby reducing the speed of the tubes’ movement ； After the vibration point, the Coriolis force generated by the fluid in the tube is in the same direction as the vibration, accelerating the movement of the tube. When the actuator brings the tubes closer together, as shown in Figure 23b, the opposite result is produced. The phase difference between the movements of the pipe at two measurable points A and B can be measured by sensors; from this, the mass flow rate of the fluid flowing through the measuring pipe can be determined. https://p3-tt-ipv6.byteimg.com/large/pgc-image/8bddf38daf004cca9d9a9871fb358e9e Figure 23: Principle of measurement for the Ω-shaped tube mass flow meter. 8. Double-ring measuring tube mass flow meter: This type of flow meter consists of a pair of parallel coiled tubes with short straight sections, as shown in Figure 24. At the midpoint D of the tubes, a driver is installed to cause the two measuring tubes to undergo periodic, opposite vibrations. At both ends of the elliptical helical tubes, at positions equidistant from the midpoint D, two sensors are placed to measure the relative velocity between the tubes at these two points. The phase difference between these two relative velocities is proportional to the mass flow rate of the fluid flowing through the measuring tubes. https://p26-tt.byteimg.com/large/pgc-image/2207a01e426343cb81a6d206bd6fded7 Figure 24: Double-loop mass flow meter. Its working principle is as follows: When there is no flow of fluid in the measuring tube, the oscillating force causes deformation in the tube; this deformation is the same on both sides of the midpoint. At the two sensing points, the phase difference of the vibration displacements is zero. When fluid flows through the tube, before the point of maximum amplitude, the fluid particles experience a force opposite to the direction of vibration due to the Coriolis force, while after that point, a force in the same direction as the vibration occurs. Since at the same moment the forces acting on the two measuring tubes are equal in magnitude but opposite in direction, this results in an increase or decrease in the speed of tube movement at the two sensing points. By measuring the phase difference between these two points, it is possible to determine the mass flow rate of the fluid passing through the tube. III. Structural characteristics of mass flow meters In a measurement system, the Coriolis force exerted by fluid particles on the measuring tube is very small, which poses great difficulties for accurate measurement. To generate a strong enough signal in the measuring tube, it is necessary to increase the effect of the Coriolis force on it, or to increase the deformation of the measuring tube under the same Coriolis force. In principle, Fc = 2ωVM; when the fluid under test remains constant, increasing either ω or V is necessary to raise Fc. In practice, as ω increases, it is necessary to raise the vibration frequency and amplitude on the instrument. An increase in vibration frequency seriously affects the lifespan of the measuring tube, while an increase in amplitude requires more power to be supplied. An increase in V means an increase in flow velocity, which in turn increases the static pressure in the measuring tube as well as the pressure loss caused by the flow meter across the entire system. These are detrimental to both the flow meter itself and the entire system. On the other hand, from a structural design perspective, it is necessary to consider improving the efficiency with which the Coriolis force acts on the vibrating tube as well as enhancing the sensing capability of the sensor; the improvement of the latter’s performance will not be discussed here. To improve the efficiency of the Coriolis force acting on the measuring tube, it is necessary to enhance the overall system elasticity of the measuring tube in terms of its structural design, reduce rigidity, use materials with good elasticity and stable performance, and select the oscillation frequency of the system accurately. Thus, under the same Coriolis force, the deformation of the measurement tube increases. Generally speaking, the thinner the wall of the measuring tube and the longer its length, the better the structural elasticity of the system, and the more pronounced the Coriolis force acting on the tube. This can increase the deformation of the measuring tube, improve the signal-to-noise ratio, and reduce external interference. The stress acting on the measuring tube should not be concentrated at a single point, so as to prevent mechanical fatigue. Different forms of stress also have a certain impact on the fatigue of the tube and its measurement sensitivity. For different structures, due to their varying design approaches, each has its own characteristics; however, there are also some issues, and no single format can be perfect. In response to these issues, manufacturers are also continuously improving their products to enhance their performance and boost their competitiveness. Next, a brief analysis is provided on the impact of specific structures on performance. 1. Shape of the measuring tube: The increase in the elasticity of the measuring system enhances the effect of the Coriolis force acting on the vibrating tube system; it also increases interference from external mechanical noise and the size of the instrument. The measuring tube should have as few sharp bends as possible, and its inner diameter should be increased as much as feasible, in order to reduce pressure losses. The signal-to-noise ratio of the dual-measurement-tube type increases, as does its flow capacity; it is therefore widely used. 2. Pipe wall: An increased wall thickness makes the pipe more rigid and also increases its inertial mass during flow. This reduces the impact of density variations caused by uneven distribution of gases in the fluid on pipe vibration. It also improves the pressure and wear resistance of the measuring pipe, but it reduces the elasticity of the system, affecting the sensitivity of the measurements. 3. Manufacturing and installation: The shape of the measuring tubes must be kept symmetrical during the manufacturing process; in a dual-measuring-tube configuration, the two tubes must be identical. The sensors must be positioned accurately to minimize the impact of variations in density or viscosity on the measurement results. The instability in traffic quality distribution affects the accuracy of the measurement results. In principle, the magnitude of the Coriolis force acting on the measuring tube depends only on the mass flow rate of the fluid, and is independent of the fluid’s density and viscosity. But changes in density bring about additional inertial forces ； Changes in viscosity result from different adhesive layers on the inner wall of the measuring tube, leading to varying boundary layer effects. As a result, the mass distribution within the measuring tube becomes unstable, affecting the accuracy of the measurement results.