Keywords: mass flow meter, Coriolis, mechanics. INTRODUCTION The mass flow meter is now favored by the user because it can directly measure the mass flow of the fluid in the pipe without having to measure the volume of the measured fluid separately as in the past. Flow and density are then calculated. In addition, its accuracy and stability are high, and its turndown ratio is also relatively large, but its performance-cost ratio is too high. For manufacturers, this is a very profitable product, so the development, trial production and promotion of this product have always been positive.
Principle The principle of the Coriolis mass flowmeter is essentially the use of the resonance characteristics of an elastomer: a metal pipe element in the vibration of the teammate fluid and without fluid flow (in the vicinity of the resonance zone), the dynamic response characteristics thereof are measured, and the resonance system is obtained. The relationship between the phase difference (time difference) and mass flow. The difference between the dynamic response characteristics of the resonance of the metal tube element with fluid flow and the dynamic response characteristics of the metal tube without fluid flow is due to the Coriolis effect. The so-called Coriolis effect means that when a particle moves relative to a rotating reference frame, an inertial force that is different from the normal centrifugal force acts on the particle. Its size and direction can be expressed by 2mvXw (formula). This was first discovered by French scientist Coriolis. A flow meter constructed using the above-described principle of the elastic member is also referred to as a Coriolis mass flow meter. Therefore, the theoretical analysis and development of mass flowmeters are difficult to calculate the dynamic resonance characteristics of flexible metal tubes. This is mainly determined by vibration analysis of the elastomer by solid mechanics theory. The current literature reports that one kind of dynamic response analysis of flexible tubes.
1. Dynamic response analysis of flexible tubes (i) Analysis of flexible tubing Hemp and Sultan (Cranfield Institute of Technology, England) used the Euler beam theory to analyze the dynamic response of flexible tubing resonances and made specific combinations of U-tubes. Calculations.
a. Equation (Oscillatingtubeofcruvedpart)
For different geometries, the above general formulas and boundary conditions can be further simplified. For example, for a straight tube part of an elastic metal tube, a can be made infinite.
b. Boundary conditions
At the end points, there are c. numerical solutions and calculation results at the connection points of different shapes of pipe segments. 
The authors calculated the fundamental frequency of the U-shaped element and its resonant vibration modes (displacement mode and bending mode), as well as the relationship between its phase and flow rate. The theoretical calculations agree well with the experimental values.
(ii) Analysis of flexible straight tubes Raszillier and Durst (University of Erlangen, Germany) used the Euler beam theory to consider the fluid as a moving string and analyzed the dynamic response of resonance of a one-dimensional flexible straight tube. a. Equation (Oscillatingtubeofstaightpart)
b. Boundary conditions 
c. Numerical Solution and Calculation Results The author used a rather complicated solving process to calculate the fundamental vibration frequency and the resonant vibration mode of the straight pipe with and without fluid flow, and calculated the phase difference and flow rate from this. The relationship between.
2. Dynamic Response Analysis of Rigid Straight Pipes Casce la assumes that the visualization is rigid, can avoid calculating the fundamental frequency of the above elastic tube and its resonant vibration mode of displacement, which can further simplify the calculation. Finally, a simple root result can also be obtained: vibration displacement and Relationship between traffic.
Practical design problems The above-mentioned dynamic response analysis of resonance is very detailed but academic. The engineers are most concerned with guiding the resonance frequency of the elastic tube and the stress distribution of the tracheal wall and the strength of fatigue resistance is sufficient. The simplest approach is to use the structural analysis software package SAP, or ANSYS for analytical calculations.
Selection of Elastic Components From a mechanical point of view, designing a mass flow meter requires the selection of a suitable primary sensing element in order to increase the Coriolis effect of the primary element as much as possible. This includes the choice of the best shape for the sensing element and the choice of the best material and wall thickness for the flexible metal tube. The shape of components can be roughly classified into four types, namely: elbow and straight pipe; single pipe and multiple pipe (double pipe). In the selection process, the principle is to balance the performance of the selected primary component, the best range of use and the cost of these three factors. In general, the more complex the chosen shape, the higher the Coriolis effect, but the more complex the production process and technology, the higher the cost. Usually a primary element always belongs to the combination of two of the above four types: a combination of an elbow shape and a double shape.
At present, mass flowmeters designed on the principle of Coriolis force have a variety of geometric shapes for primary components, such as:
Double U-type or triangular-type double S-type double w-type double K-type double-helical type single-tube multi-ring type single-J single straight-tube type double-straight type Some mechanical problems that urgently need to be solved 1. Theoretically speaking, the accuracy of the Coriolis mass flowmeter is not affected by the operating conditions of the fluid being measured, but the actual conditions are indeed affected by the various conditions of the fluid (although this effect is small). It was not clear at the moment. The authors estimate that this is due to the additional Coriolis effect caused by secondary eddy currents in the pipe of the primary component.
Because the fluid on the north side is always viscous, the velocity profile in the cross section of the pipe is approximately parabolic (large viscous case) and power-type (small viscous case) rather than a uniform velocity profile. The flow velocity on the wall of the pipeline is zero, and the flow velocity on the centerline is the largest. In this way, the Coriolis acceleration at different radial positions of the cross section is not the same. Thus, the non-uniform Coriolis effect produces secondary vortices whose direction is perpendicular to the direction of the rotation vector of the vibrating tube. For fluids under different working conditions, the flow state in the sensible tube of the flowmeter is not the same, resulting in additional Coriolis effect, and its size is also different. This will change the accuracy of the flowmeter beyond the range given by the manufacturer.
2. In principle, mass flowmeters can measure two-phase fluids, but in practice, measurement errors are also large, making it impossible for the industry to accept applications in this field. Currently, this issue is being further studied. The authors estimate the causes of the above problems, ibid.
3. In addition, due to the vibration of the primary component, it is greatly affected by external vibrations. This problem has attracted the attention of manufacturers and research is underway. The author thinks that this problem should start from the design of the anti-vibration components and the circuit, but first of all should analyze the phenomenon of frequency shift and frequency lock, and then find the appropriate anti-vibration measures.
Material Problems Since the metal tube is vibrated at the time of the sensor, consideration must be given to the ability of the tube to withstand fatigue in various environments and to withstand corrosion. As we all know, the ability to increase the resistance to fatigue damage is to reduce the vibration amplitude of the metal tube, increase the wall thickness of the vibration tube, and select the appropriate metal material. Most of the current use of 316L stainless steel, the more ideal metal material is Hastelloyoy, or NiCrMo alloy, its resistance to fatigue damage is stronger than 316L, especially the case of practical chloride corrosion. ? Titanium is the best, but the latter is too expensive.
Coriolis mass flowmeters are particularly suitable for flow measurement of non-Newtonian fluids with a high viscosity, ie particularly suitable for measuring viscous or even difficult-to-flow media such as:
All kinds of things slurry latex mixed slurry paint coating vitamin pulp pulp heavy oil polymer polymer slurry. . . .
Therefore, the West has applied Coriolis mass flow meters to various industrial fields: chemical and pharmaceutical industries, food and beverage, refrigeration, energy, and petrochemical industries. In the above industries, most of them are used in the control of the mixing process of ingredients. In addition, it is also used in vehicles and on the backbone of loading and unloading.
Accuracy problems At present, Western manufacturers claim that the accuracy of Coriolis mass flow meters can reach 0.5%, or even 0.2% or 0.1%. However, special care must be taken in actual use. The accuracy in the low flow range is generally lower than the above accuracy. In addition, the zero drift of the secondary instrument, especially after a period of use, does not reach the value given by the manufacturer.
According to the long-term estimation, there are about 150,000 mass flowmeters currently in operation in various soil and industrial sectors in the world. Mass flowmeters now account for about 3% to 5% of the total number of flowmeters produced and sold each year in the West. However, because the mass flowmeters contain high value-added technology, their profits can be as high as 70%, so Western companies have benefited from it.
From the current development of flowmeters around the world, there is no doubt that Coriolis mass flowmeters appear to quickly occupy a larger market in the area of ​​metrology, which was originally dominated by capacity measurement. This is a very profitable product. With the fierce competition in the market, the price/performance ratio will be appropriately reduced. However, only after the price/performance ratio is greatly reduced can it be widely used in the industry.
The authors of domestic promotion and application problems believe that the expectations for Coriolis mass flowmeters in China have been too high in recent years and that they can be used anywhere. This is a misunderstanding. As we all know, in the industrial production process, the measurement of various parameters, such as temperature, pressure, etc., is the most complex in terms of flow measurement, and it is difficult for the industry to measure accurately. However, the flow measurement methods and principles are the most numerous and varied. So far, there are no fewer than a dozen or even hundreds of flow meters. At present, no matter what kind of flow meter can not squeeze another instrument out of the market, but dominate the world, but have their own fields of application. When selecting the type of flow meter, if it can meet the purpose of use, any one can choose simple and reliable, it will not use a complex structure. In addition, under the condition of balancing the one-time investment of the selected instrument and the annual maintenance cost, the best investment is selected. With the Coriolis mass flow meter, other meters can be used instead of Coriolis mass flow meters, because the former is always cheaper than the latter.
Domestic production problems in the domestic production of Coriolis mass flow meters, as China will soon become a member of the GATT, we must first pay attention to intellectual property issues in order to avoid causing legal disputes. At present, the mass flow meter's elastic element has a variety of shapes, mainly after the appearance of the former geometric shape, and the shape of the primary element to be developed later must avoid the patented shape. In the secondary circuit design philosophy, we must also pay attention to some of the key parts, whether the manufacturer has applied for patent filing, in the secondary instrument's shape design and circuit layout must also catch up with our country before joining GATT, as soon as possible Get out of the copy or imitation stage, otherwise it will cause legal disputes over intellectual property rights. In addition, the product can only reduce costs after the formation of a certain volume, and it is competitive. Therefore, it is a long-term and arduous task to independently manufacture Coriolis mass flowmeters in China.
References 1. G. Sultanand J. Hemp, J. of Sound & Vibration (1989) 123(3), 473.
2. H. Raszillier and F. Durst, Arch. Of Applied Mechanics (1991) 61 (3), 192.
3.F.Cascetla,et.al,Measurement(1991)no.3&4.(end
Principle The principle of the Coriolis mass flowmeter is essentially the use of the resonance characteristics of an elastomer: a metal pipe element in the vibration of the teammate fluid and without fluid flow (in the vicinity of the resonance zone), the dynamic response characteristics thereof are measured, and the resonance system is obtained. The relationship between the phase difference (time difference) and mass flow. The difference between the dynamic response characteristics of the resonance of the metal tube element with fluid flow and the dynamic response characteristics of the metal tube without fluid flow is due to the Coriolis effect. The so-called Coriolis effect means that when a particle moves relative to a rotating reference frame, an inertial force that is different from the normal centrifugal force acts on the particle. Its size and direction can be expressed by 2mvXw (formula). This was first discovered by French scientist Coriolis. A flow meter constructed using the above-described principle of the elastic member is also referred to as a Coriolis mass flow meter. Therefore, the theoretical analysis and development of mass flowmeters are difficult to calculate the dynamic resonance characteristics of flexible metal tubes. This is mainly determined by vibration analysis of the elastomer by solid mechanics theory. The current literature reports that one kind of dynamic response analysis of flexible tubes.
1. Dynamic response analysis of flexible tubes (i) Analysis of flexible tubing Hemp and Sultan (Cranfield Institute of Technology, England) used the Euler beam theory to analyze the dynamic response of flexible tubing resonances and made specific combinations of U-tubes. Calculations.
a. Equation (Oscillatingtubeofcruvedpart)
b. Boundary conditions
(ii) Analysis of flexible straight tubes Raszillier and Durst (University of Erlangen, Germany) used the Euler beam theory to consider the fluid as a moving string and analyzed the dynamic response of resonance of a one-dimensional flexible straight tube. a. Equation (Oscillatingtubeofstaightpart)
2. Dynamic Response Analysis of Rigid Straight Pipes Casce la assumes that the visualization is rigid, can avoid calculating the fundamental frequency of the above elastic tube and its resonant vibration mode of displacement, which can further simplify the calculation. Finally, a simple root result can also be obtained: vibration displacement and Relationship between traffic.
Practical design problems The above-mentioned dynamic response analysis of resonance is very detailed but academic. The engineers are most concerned with guiding the resonance frequency of the elastic tube and the stress distribution of the tracheal wall and the strength of fatigue resistance is sufficient. The simplest approach is to use the structural analysis software package SAP, or ANSYS for analytical calculations.
Selection of Elastic Components From a mechanical point of view, designing a mass flow meter requires the selection of a suitable primary sensing element in order to increase the Coriolis effect of the primary element as much as possible. This includes the choice of the best shape for the sensing element and the choice of the best material and wall thickness for the flexible metal tube. The shape of components can be roughly classified into four types, namely: elbow and straight pipe; single pipe and multiple pipe (double pipe). In the selection process, the principle is to balance the performance of the selected primary component, the best range of use and the cost of these three factors. In general, the more complex the chosen shape, the higher the Coriolis effect, but the more complex the production process and technology, the higher the cost. Usually a primary element always belongs to the combination of two of the above four types: a combination of an elbow shape and a double shape.
At present, mass flowmeters designed on the principle of Coriolis force have a variety of geometric shapes for primary components, such as:
Double U-type or triangular-type double S-type double w-type double K-type double-helical type single-tube multi-ring type single-J single straight-tube type double-straight type Some mechanical problems that urgently need to be solved 1. Theoretically speaking, the accuracy of the Coriolis mass flowmeter is not affected by the operating conditions of the fluid being measured, but the actual conditions are indeed affected by the various conditions of the fluid (although this effect is small). It was not clear at the moment. The authors estimate that this is due to the additional Coriolis effect caused by secondary eddy currents in the pipe of the primary component.
Because the fluid on the north side is always viscous, the velocity profile in the cross section of the pipe is approximately parabolic (large viscous case) and power-type (small viscous case) rather than a uniform velocity profile. The flow velocity on the wall of the pipeline is zero, and the flow velocity on the centerline is the largest. In this way, the Coriolis acceleration at different radial positions of the cross section is not the same. Thus, the non-uniform Coriolis effect produces secondary vortices whose direction is perpendicular to the direction of the rotation vector of the vibrating tube. For fluids under different working conditions, the flow state in the sensible tube of the flowmeter is not the same, resulting in additional Coriolis effect, and its size is also different. This will change the accuracy of the flowmeter beyond the range given by the manufacturer.
2. In principle, mass flowmeters can measure two-phase fluids, but in practice, measurement errors are also large, making it impossible for the industry to accept applications in this field. Currently, this issue is being further studied. The authors estimate the causes of the above problems, ibid.
3. In addition, due to the vibration of the primary component, it is greatly affected by external vibrations. This problem has attracted the attention of manufacturers and research is underway. The author thinks that this problem should start from the design of the anti-vibration components and the circuit, but first of all should analyze the phenomenon of frequency shift and frequency lock, and then find the appropriate anti-vibration measures.
Material Problems Since the metal tube is vibrated at the time of the sensor, consideration must be given to the ability of the tube to withstand fatigue in various environments and to withstand corrosion. As we all know, the ability to increase the resistance to fatigue damage is to reduce the vibration amplitude of the metal tube, increase the wall thickness of the vibration tube, and select the appropriate metal material. Most of the current use of 316L stainless steel, the more ideal metal material is Hastelloyoy, or NiCrMo alloy, its resistance to fatigue damage is stronger than 316L, especially the case of practical chloride corrosion. ? Titanium is the best, but the latter is too expensive.
Coriolis mass flowmeters are particularly suitable for flow measurement of non-Newtonian fluids with a high viscosity, ie particularly suitable for measuring viscous or even difficult-to-flow media such as:
All kinds of things slurry latex mixed slurry paint coating vitamin pulp pulp heavy oil polymer polymer slurry. . . .
Therefore, the West has applied Coriolis mass flow meters to various industrial fields: chemical and pharmaceutical industries, food and beverage, refrigeration, energy, and petrochemical industries. In the above industries, most of them are used in the control of the mixing process of ingredients. In addition, it is also used in vehicles and on the backbone of loading and unloading.
Accuracy problems At present, Western manufacturers claim that the accuracy of Coriolis mass flow meters can reach 0.5%, or even 0.2% or 0.1%. However, special care must be taken in actual use. The accuracy in the low flow range is generally lower than the above accuracy. In addition, the zero drift of the secondary instrument, especially after a period of use, does not reach the value given by the manufacturer.
According to the long-term estimation, there are about 150,000 mass flowmeters currently in operation in various soil and industrial sectors in the world. Mass flowmeters now account for about 3% to 5% of the total number of flowmeters produced and sold each year in the West. However, because the mass flowmeters contain high value-added technology, their profits can be as high as 70%, so Western companies have benefited from it.
From the current development of flowmeters around the world, there is no doubt that Coriolis mass flowmeters appear to quickly occupy a larger market in the area of ​​metrology, which was originally dominated by capacity measurement. This is a very profitable product. With the fierce competition in the market, the price/performance ratio will be appropriately reduced. However, only after the price/performance ratio is greatly reduced can it be widely used in the industry.
The authors of domestic promotion and application problems believe that the expectations for Coriolis mass flowmeters in China have been too high in recent years and that they can be used anywhere. This is a misunderstanding. As we all know, in the industrial production process, the measurement of various parameters, such as temperature, pressure, etc., is the most complex in terms of flow measurement, and it is difficult for the industry to measure accurately. However, the flow measurement methods and principles are the most numerous and varied. So far, there are no fewer than a dozen or even hundreds of flow meters. At present, no matter what kind of flow meter can not squeeze another instrument out of the market, but dominate the world, but have their own fields of application. When selecting the type of flow meter, if it can meet the purpose of use, any one can choose simple and reliable, it will not use a complex structure. In addition, under the condition of balancing the one-time investment of the selected instrument and the annual maintenance cost, the best investment is selected. With the Coriolis mass flow meter, other meters can be used instead of Coriolis mass flow meters, because the former is always cheaper than the latter.
Domestic production problems in the domestic production of Coriolis mass flow meters, as China will soon become a member of the GATT, we must first pay attention to intellectual property issues in order to avoid causing legal disputes. At present, the mass flow meter's elastic element has a variety of shapes, mainly after the appearance of the former geometric shape, and the shape of the primary element to be developed later must avoid the patented shape. In the secondary circuit design philosophy, we must also pay attention to some of the key parts, whether the manufacturer has applied for patent filing, in the secondary instrument's shape design and circuit layout must also catch up with our country before joining GATT, as soon as possible Get out of the copy or imitation stage, otherwise it will cause legal disputes over intellectual property rights. In addition, the product can only reduce costs after the formation of a certain volume, and it is competitive. Therefore, it is a long-term and arduous task to independently manufacture Coriolis mass flowmeters in China.
References 1. G. Sultanand J. Hemp, J. of Sound & Vibration (1989) 123(3), 473.
2. H. Raszillier and F. Durst, Arch. Of Applied Mechanics (1991) 61 (3), 192.
3.F.Cascetla,et.al,Measurement(1991)no.3&4.(end
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