Abstract: This paper mainly introduces the working principle of the Rosemount Coriolis mass flow meter (CMF) sensor and transmitter, and details the mass flow measurement principle and density measurement principle of the flow meter, the signal characteristics of the transmitter, the characteristics of the DSP digital signal processor, and its applications. Keywords: Coriolis force; HART protocol; DSP digital signal processor; Chinese Library Classification Number: TP212.1 Document Identifier Code: A Article Number: 1006-883X (2003) 04-0032-05 Introduction Rosemount mass flow meters are widely used in petrochemical and other fields and are one of the most advanced flow measurement instruments in the world today. They are reliable in the measurement of our main products such as ethylene, propylene, and light hydrocarbons, with an accuracy of up to 1.7‰. They have improved the accuracy of energy and material flow measurement in our plant, avoided unnecessary losses, and created considerable economic benefits. Mass Flow Measurement Principle A mass flow meter metering system includes a sensor and a transmitter for signal processing. Rosemount mass flow meter is based on Newton's second law: force = mass × acceleration (F = ma). When a particle of mass m moves with velocity V in a pipe rotating with angular velocity ω about axis P, the particle is subjected to two components of acceleration and force: (1) normal acceleration, i.e. centripetal acceleration αr, the magnitude of which is equal to 2ωr, and is directed towards axis P; (2) tangential angular velocity αt, i.e. Coriolis acceleration, the value of which is equal to 2ωV, and is perpendicular to αr. Due to the combined motion, a Coriolis force Fc = 2ωVm acts on the particle in the direction of αt, and the pipe acts on the particle with a reverse force -Fc = -2ωVm. When a fluid of density ρ flows in a rotating pipe at a constant velocity V, any section of pipe of length Δx will be subjected to a tangential Coriolis force ΔFc: ΔFc = 2ωVρAΔx (1) where A is the cross-sectional area of ​​the pipe. Since the relationship exists: mq=ρVA, therefore: 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 sensor contains a U-shaped flow tube. When no fluid flows through the flow tube, the flow tube is driven by an electromagnetic drive coil installed at the end of the flow tube. Its amplitude is less than 1mm and the frequency is about 80Hz. When the fluid flows into the flow tube, it is forced to accept the vertical movement of the flow tube. During the half-cycle of the upward vibration of the flow tube, the fluid resists the upward movement of the tube and exerts a downward force on the flow tube; conversely, the fluid flowing out of the flow tube exerts an upward force on the flow tube to resist the downward movement of the tube and reduce its vertical momentum. This causes the flow tube to twist. In the other half-cycle of the vibration, the flow tube vibrates downward, and the twisting direction is opposite. This twisting phenomenon is called the Coriolis phenomenon, that is, the Coriolis force. According to Newton's second law, the magnitude of the flow tube torsion is directly proportional to the mass flow rate passing through it. Electromagnetic signal detectors installed on both sides of the flow tube detect its vibration. When no fluid flows through the flow tube, it does not twist, and the detection signals from the two electromagnetic signal detectors are in phase. When fluid flows through the flow tube, it twists, causing a phase difference between the two detection signals. This phase difference is directly proportional to the mass flow rate passing through the flow tube. Since this mass flow meter primarily relies on the vibration of the flow tube for flow measurement, the vibration and the force of the fluid flowing through the tube generate Coriolis force, causing each flow tube to twist. The amount of twist is proportional to the mass flow velocity passing through the flow tube during the vibration cycle. Because the twist of one flow tube lags behind the twist of the other, the sensor output signals on the mass tube can be compared by the circuit to determine the amount of twist. A time difference detector in the circuit measures the lag time between the left and right detection signals. This "time difference" ΔT is digitally measured, processed, and filtered to reduce noise and improve measurement resolution. The time difference is multiplied by a flow calibration coefficient to represent the mass flow rate. Because temperature affects the rigidity of the flow tube, the amount of torsion caused by the Coriolis force is also affected by temperature. The measured flow rate is continuously adjusted by the transmitter, which constantly monitors the output of the platinum resistance thermometer attached to the surface of the flow tube. The transmitter uses a three-phase resistance thermometer bridge amplifier circuit to measure the sensor temperature. The amplifier's output voltage is converted into frequency, which is then digitized by a counter and read into the microprocessor. The density measurement principle involves one end of the flow tube being fixed while the other end is free. This structure can be viewed as a weight/spring system suspended from a spring. Once a motion is applied, this weight/spring system will vibrate at its resonant frequency, which is related to the mass of the weight. The flow tube of a mass flow meter vibrates at its resonant frequency through a drive coil and feedback circuit. The resonant frequency of the vibrating tube is related to its structure, material, and mass. The mass of the vibrating tube consists of two parts: the mass of the vibrating tube itself and the mass of the medium inside the vibrating tube. Once each sensor is manufactured, the mass of the vibrating tube is fixed. The mass of the medium within the vibrating tube is the product of the medium's density and the tube's volume. Since the tube's volume is fixed for each sensor's diameter, the vibration frequency is directly related to the density. Therefore, for sensors with a defined structure and materials, the medium's density can be obtained by measuring the resonant frequency of the flow tube. A pair of signal detectors used for flow measurement obtains a signal representing the resonant frequency. A temperature sensor signal compensates for changes in the flow tube's rigidity caused by temperature variations. The vibration period is measured by measuring the flow tube's vibration period and temperature. The medium density is measured using the linear relationship between density and the flow tube's vibration period, along with standard calibration constants. When measuring density with a Coriolis mass flow sensor vibrating tube, the pipe's rigidity, geometry, and the mass of the flowing fluid collectively determine the natural frequency of the pipe system. Therefore, the fluid density can be deduced from the measured pipe frequency. The transmitter uses a high-frequency clock to measure the vibration period. The measured value is digitally filtered to compensate for changes in the natural frequency caused by changes in pipe rigidity due to operating temperature. The process fluid density is then calculated using the sensor's density calibration coefficient. IV. Signal Characteristics Rosemount transmitters are modular and microprocessor-enabled, utilizing ASICS digital technology and selectable digital communication protocols. When connected to sensors, they provide high-precision mass flow rate, density, temperature, and volumetric flow rate signals, converting them into analog, frequency, and other output signals. They can also be configured, monitored, and communicated with using a HART 275 communication handheld device or AMS/Prolink software. V. SP Digital Signal Processor Characteristics A DSP digital signal processor is a microprocessor that processes signals in real time. In Coriolis flow meters, the measuring tube vibrates at a known frequency; therefore, any frequencies outside this vibration range are considered "noise" and need to be removed to accurately determine the mass flow rate. For example, a 50Hz or 60Hz signal may originate from coupling with nearby power lines. Effectively "filtering" these unwanted signals requires more background information available at that moment. Figure 8 illustrates how noise appears in the original converter signal and the final filtered signal. One of the main advantages of using digital signal processing (DSP) technology compared to using time constants to suppress and stabilize signals is the ability to filter real-time signals at a higher sampling rate, reducing the flow meter's response time to abrupt changes in flow rate. The response time of multi-parameter digital (MVD) transmitters is 2–4 times faster than that of conventional transmitters using analog signal processing; this faster response time improves the efficiency and accuracy of short-batch control. Another valuable and more challenging application of DSP technology is gas measurement, where high-speed gas passing through the flow meter causes significant noise. With the High Precision Elite series sensors, noise mixed with the flow signal is minimized. DSP technology now filters this noise better, further reducing the mass flow meter's sensitivity to noise. Gas measurements using MVD transmitters show significant improvements in repeatability and accuracy. DSP technology provides a "window to processing," focusing first on the signal near the measurement tube's vibration frequency. In fact, intentionally discarding the rest of the information—which may very well be hidden within this "useless" data—paves the way for new diagnostic techniques. For example, spectral analysis may lead to advancements in measuring air-entrapped or clump-like fluid flows. Fluid adhesion to the inner wall of the measuring tube is another promising fault that can be detected by DSP technology, and spectral variations may also be used to predict sensor malfunctions. VI. Influence of the Measurement Environment 1. Influence of Fluid Pressure First, consider that the fluid pressure should not exceed the specified operating pressure. Second, consider the degree of influence of static pressure changes. Pressure changes affect the tightness of the measuring tube and the degree of the Budden effect, as well as disrupting the original zero-point offset of the measuring tube's asymmetry. Although the instrument constant variation and zero drift are small, the impact on high-precision instruments cannot be ignored when the operating pressure differs significantly from the calibration pressure. For small-diameter instruments, a large wall thickness-to-diameter ratio results in a smaller impact; for large-diameter instruments, a large wall thickness-to-diameter ratio... 2. Influence of Fluid Density Changes in fluid density alter the mass of the flow measurement system, thus changing the balance of the flow sensor and causing zero-point shift. If measuring a specific liquid, as long as zeroing is performed under the actual liquid density conditions, the density change during use is generally small and there is usually no problem. However, when measuring several liquids with significantly different densities in a single pipe, it will introduce additional errors due to zero-point variation. 3. The Effect of Fluid Viscosity: Rosemount's Coriolis mass flow meters (CMF) can measure a wide range of liquid viscosities and exhibit good measurement performance. Although there are reports discussing the impact of viscosity on measurement accuracy, experimental data is scarce. Liquid viscosity alters the damping characteristics of the system, thus affecting zero bias; it also has some impact on flow measurement values ​​at low flow rates. 4. The Effect of Heterogeneous Phase Content in Two-Phase Fluids: Manufacturers often claim that a percentage of free gas by volume has little impact on measurements. When measuring liquids with small, uniformly distributed bubbles, such as ice cream and similar emulsions, the impact may be relative. At 1% bubble content, some models have no significant impact, while others have an error of 1%–2%, with one dual-tube straight-tube model reaching 10%–15%; at 10% bubble content, the error generally increases to 15%–20%, with some models reaching as high as 80%. Furthermore, differences in fluid pressure, flow rate, viscosity, and gas-liquid mixing methods also have varying effects. All types of CMFs offer high reliability when measuring liquids containing small amounts of solids. When the solid content is high, or the solids are highly abrasive or soft (such as vegetable chunks in food broth), a single-tube straight-pipe type or a series double-pipe type should be selected. This is because if a parallel double-pipe type is used, foreign objects may adhere to the distributor or wear may cause changes in the flow rates of the two paths, resulting in errors; more seriously, a blockage in one path may not be immediately detected. 5. Environmental Vibration Effects: CMFs can operate in vibrating environments, but they must be isolated from vibration, for example, by using flexible pipe connections between them and the vibrating tubes and using vibration-isolated support frames. However, it is even more important to prevent the vibration frequency from being the same as the operating frequency or harmonic frequency of the CMF. When multiple instruments of the same model are installed in series or in parallel close to each other, especially on the same support frame, the operating frequencies of the CMFs will affect each other, causing abnormal vibrations, which in severe cases may render the instrument inoperable. When ordering, you can specifically request that the operating frequencies of the two CMFs in series be staggered. 6. Influence of Pipeline Stress: If the center of the pipeline connecting the flow sensor is not aligned (or not parallel) or the pipeline temperature changes, pipeline stress will create pressure, tension, or shear forces that act on the alignment between the CMF measuring tubes, causing asymmetry in the detection probe and resulting in zero-point fluctuations. The CMF must be zeroed after installation to eliminate or reduce this effect. If the pipeline is severely misaligned, it may be impossible to zero it. If the pipeline temperature deviates from the installation temperature, the thermal expansion (or contraction) force generated by the pipeline will also act on the flow sensor. Some CMF designs have a heavy flow divider at both the inlet and outlet of the measuring tube, which can reduce the impact of pipeline stress on the measuring tube. Straight measuring tube CMFs are particularly susceptible to thermal expansion forces; if necessary, thermal expansion isolation fittings can be installed in the pipeline. VII. Practical Applications: 1. Applications in Heterogeneous Flow: CMF is reliable in the measurement of our main products such as ethylene, propylene, and light hydrocarbons, but improper use can lead to measurement errors or even interruptions. In the measurement of light hydrocarbon raw materials, due to the complex composition of the light hydrocarbon medium, which contains both solid particles and bubbles, and is a typical heterogeneous fluid, malfunctions frequently occur during use. The fault information displayed by the transmitter is Sensor Error, Dens Overrun, Slug Flow, indicating sensor error, density exceeding the limit, and slug flow, causing the flow meter to interrupt measurement. To solve this problem, we installed a filter at the flow meter inlet to filter solid particles and limited the opening of the flow meter outlet valve to increase the inlet pressure, thereby reducing the bubble content in the light hydrocarbon medium. After taking these measures, the flow meter was put into normal operation. 2. Fault Information and Handling: When the transmitter displays Drive Overrun or Input Overrange, it indicates that the transmitter is generating an erroneous output, and the flow rate exceeds the sensor range. Check whether there is an open circuit or short circuit between the red cable and the brown cable in the transmitter and sensor, i.e., whether the sensor drive coil is open or short-circuited; check whether there is an open circuit or short circuit between the green cable and the white cable in the transmitter and sensor, i.e., whether the sensor left detection coil is open or short-circuited. A "Sensor Error" message indicates a cable problem. Check for open or short circuits between the blue and gray cables in the transmitter and sensor, specifically an open or short circuit in the sensor's detection coil. A "Power Reset" message indicates a power failure, dim lighting, or an interrupted power cycle. Check the power supply system. A "Zero Too High" or "Zero Too Low" message indicates that fluid flow was not completely stopped during sensor zeroing, causing a large offset in the zero-point flow rate calculated by the transmitter, resulting in inaccurate flow measurement. Fluid flow must be completely stopped during zeroing. In conclusion, the mass flow meter is a relatively accurate, fast, reliable, efficient, stable, and flexible flow measurement instrument. It will be more widely used in petroleum processing, chemical industry, and other fields, and is believed to have great potential in promoting flow measurement.