Questions regarding flow meters

The mass flow meter commonly referred to is one that operates on the Coriolis principle; its mechanism involves the fact that when the internal tubes of the mass flow meter vibrate, the mass flow rate through those tubes causes changes in the vibration frequency and amplitude of the tubes, and it is by measuring these changes that the mass flow rate is determined. Mass flow meters are relatively expensive ； Rotary flow meters are relatively inexpensive, have lower accuracy compared to mass flow meters, and must be installed in vertical pipes. Therefore, mass flow meters are used only in applications that require high precision.

One can study the \"Handbook of Automatic Control Design in Petrochemical Industry\" (3rd edition).

A Coriolis mass flow meter (hereinafter referred to as CMF) is a device that directly measures mass flow, based on the principle that when a fluid moves in a straight line within a rotating frame, a Coriolis force is generated that is proportional to the mass flow rate. 　　Commercially viable CMF was first introduced to the market in the late 1970s by the American company Micro Motion, and by the mid-to-late 1980s, instrument manufacturers around the world began developing it as well. By 1995, more than 40 companies around the world had introduced CMFs of various types, with the global installation volume estimated to be between 180,000 and 200,000 units. World annual sales in 1995 were estimated to be between 40,000 and 45,000 units. 　　The application of CMF in our country started relatively late; it began with the introduction of complete sets of equipment along with a small number of imported instruments in the mid-1980s, and later shifted to the import of individual units needed for technical upgrades. By 1997, the estimated number of such units in use was between 3,500 and 4,500. By 1997, China already had 4 manufacturing plants that developed their own CMF products for the market; for example, the Taihang Instrument Factory had a complete LZL series, and several joint ventures were established to introduce foreign technology for the production of various instruments. 1. Principle and Structure As shown in Figure 1, when a particle of mass m moves at velocity V within a pipe that rotates with an angular velocity ω about axis P, the particle experiences acceleration in two components as well as corresponding forces: Figure 1 Coriolis force ① Normal acceleration, namely centripetal acceleration αr, whose magnitude is equal to ω²r, directed toward axis P ； 　　② The tangential angular velocity αt, namely the Coriolis acceleration, has a value of 2ωV and its direction is perpendicular to αr. Due to the combined motion, a Coriolis force Fc=2ωVm acts on the particle in the αt direction, while the pipe exerts an opposite force on the particle, namely -Fc=-2ωVm. 　　When a fluid with density ρ flows at a constant velocity V through a rotating pipe, any segment of the pipe of length Δχ is subjected to a tangential Coriolis force ΔFc, given by ΔFc = 2ωVρAΔx (1). Here, A represents the cross-sectional area of the pipe; since the mass flow rate is qm = ρVA, it follows that ΔFc = 2ωqmΔx (2). Therefore, by directly or indirectly measuring the Coriolis force on the fluid flowing in the rotating pipe, it is possible to determine the mass flow rate. 　　However, it is difficult to generate the Coriolis force through rotational motion; currently, CMF is generated by pipe vibration. That is, a thin-walled measurement pipe fixed at both ends is excited at a frequency at which the pipe resonates or is near resonance (or at a harmonic frequency of that), and the fluid flowing within the pipe generates a Coriolis force that causes opposite-directional bending in the two halves of the pipe before and after the midpoint. The amount of bending is detected using electromagnetic (or optical) methods in order to determine the mass flow rate. Figure 2 Coriolis mass flow sensor A--drive coil ； B--Detection probe. Since the density of the fluid affects the vibration frequency of the measuring tube, and there is a fixed relationship between density and frequency, CMF can also be used to measure the fluid density. 　　The CMF consists of a flow sensor and a converter (or flow computer). Figure 2 shows an example of a flow sensor, which mainly consists of a measurement tube and its supporting bridge frame, coil A or detection probe B in the vibration excitation system for the measurement tube, and a temperature sensing element for correcting the effect of temperature on the Young’s modulus of the measurement tube material. The converter mainly consists of a vibration source unit, a signal detection unit, and a signal processing unit ； Flow rate calculation also includes functions such as configuration settings, engineering unit conversion, signal display, and communication with the host computer. 　 2. Advantages 　　(1) It measures mass flow directly, offering high measurement accuracy. 　　(2) It covers a wide range of measurable fluids, including various liquids with high viscosity, slurries containing solids, liquids with a small amount of gas uniformly distributed within them, and gases with sufficient density (gases at high pressure). 　　(3) The amplitude of the measuring tube is small, so it can be considered a non-active component ； There are no obstructions or moving parts inside the measuring tube. 　　(4) It is insensitive to the upstream and downstream flow velocity distribution, thus no requirements for straight sections upstream or downstream are necessary. 　　(5) The flow measurement value is insensitive to the viscosity of the fluid, and the density of the fluid has an extremely minor impact on the flow measurement value. 　　(6) One CMF can perform multi-parameter measurements. The fluid density and temperature can be measured simultaneously while determining the mass flow rate; this also makes it possible to derive measurements of volume flow rate, solute concentration, as well as the proportion of each phase (or component) in liquid-solid two-phase fluids (or immiscible binary liquids). 3. Disadvantages 　　(1) A considerable portion of CMF designs have high flow velocities, resulting in significant pressure losses. The pressure loss of some CMF models is 100% higher than that of positive-displacement instruments. 　　(2) The maximum diameter of the current CMF is 150 mm, so it cannot be measured using larger-diameter tubes. A considerable number of CMF models are large in weight and volume. 　　(3) It can only be used for medium and high-pressure gases, not for low-pressure gases. It is generally believed that the gas pressure of the existing CMF should not be lower than 0.1 MPa. Because the density of low-pressure gases is very low and their mass flow rate is small, it is not possible to generate a sufficiently large Coriolis force that can be detected. 　　(4) A bubble content in the liquid that exceeds a certain limit can significantly affect the measurement values. 　　(5) It is sensitive to external vibration disturbances. To prevent the impact of pipeline vibration, a considerable number of CMF model flow sensors have high installation requirements. 　　(6) The price is relatively high. 4. Classification 　　 To date, CMF has developed over 30 series, and their main difference lies in the innovations in the structure of the flow sensor’s measurement tube ； Improve performance such as instrument accuracy, stability, and sensitivity ； Increase the radius of curvature of the measuring tube, improve stress distribution, and reduce fatigue damage ； Enhance resistance to vibration interference, etc. Therefore, the measurement tubes come in various shapes and structures; hence, this section will only classify and discuss them from different perspectives. Classified by the shape of the measurement tube, there are curved types and straight types ； 　　Classified by the number of measurement tube sections, there are single-tube type and double-tube type ； 　　Classified by the connection method of the double-tube measurement section, there are parallel type and series type ； 　　Classified by the arrangement between the fluid flow direction in the measuring tube and the process pipeline flow direction, there are parallel and vertical arrangements. 4.1 Classification by the shape of the measuring tube 　　(1) Curved type: The U-shaped design was the first to be introduced to the market; shapes that have since been developed and are still in production include Ω-shaped, S-shaped, B-shaped, ring-shaped, and oval-ring-shaped ones. It is designed to be curved in order to reduce stiffness, allowing for thicker wall thicknesses compared to straight pipes ； However, it can accumulate gases and residues, causing additional errors. 　　(2) Straight type: The straight measurement tube CMF does not easily accumulate gas and is easy to clean. When measuring the slurry in a vertical installation, solid particles do not tend to settle inside the tube during periods of downtime. Flow sensors are small in size and light in weight, but have relatively thin wall thicknesses, resulting in measurement values that are significantly affected by erosion. However, in recent years, companies that originally manufactured curved CMF products have begun to develop straight-tube versions, and there is a trend toward an increase in the straight-tube series. 4.2 Classification by the number of measurement sections The measurement sections referred to here are independent measurement tubes through which the fluid flows, each vibrating and enabling the detection of the Coriolis force. 　　(1) Single-tube type: The products developed in the initial stage were of the single-tube type; however, due to their susceptibility to interference from external vibrations, dual-tube types have since become more common in order to counteract such vibrations. However, in recent years, there has been a trend toward developing new models with single tubes again. 　　(2) Dual-tube type: The dual-tube type can reduce sensitivity to external vibrations and facilitates the measurement of phase difference. 4.3 Classification by the connection method of the dual-tube measurement sections 　　(1) Parallel type: After flowing into the sensor, the fluid is divided into two streams by a mainfold in the upstream pipeline, entering the two parallel measurement sections; it then enters the downstream pipeline through a collector with the same shape as the mainfold. The splitter should distribute the flow as evenly as possible, but during use, the deposition of foreign substances or wear on the splitter can alter the original flow pattern, causing zero-point drift and resulting in additional errors. 　　(2) Series type: The fluid flows through the first measurement section and is introduced into the second measurement section via a guide block. This method does not suffer from the disadvantages caused by changes in shunt flow, and is suitable for shear-sensitive fluids. 4.4 Classification by the arrangement between the fluid flow direction in the measurement tube and the flow direction in the process pipeline （1）Parallel arrangement: The measurement tube is arranged so that the fluid flow direction is parallel to that of the process pipeline; this arrangement is used in many models. 　　(2) Vertical direction: The measuring pipeline is arranged perpendicular to the process pipeline, and the flow sensor as a whole is not within the plane affected by pipeline vibrations, thus offering strong resistance to such vibrations. 　 5 Application Overview and Selection Considerations 5.1 Application Overview The main measurement parameter of CMF is mass flow rate; the second measurement parameter is fluid density, with fluid temperature being an additional measurement parameter. Furthermore, the volumetric flow rate can be derived from the mass flow rate and fluid density, as well as the concentration of solutes in a two-component solution or the concentration of the immiscible second component, and the solid content in liquid-solid two-phase flows. The most common applications of CMF are in situations where it is necessary to measure total quantities or control/measure flow rates with a focus on quality – not the quality of the product itself, but rather the mass. Specifically, this includes measurement for trade settlement and transfer, as well as for internal accounting purposes within enterprises ； Batch measurement of materials in a batch process (replacing the previous time-consuming and labor-intensive weighing process) ； Control of pipeline blending. The literature cites several specific application examples. 　　Density is the second parameter measured in CMF; it is used for quality control during production, such as to determine the degree of solution dilution, and to prevent the seller from intentionally diluting the solution at the time of transfer ； Determining the concentration of solutes in a solution, measuring the flow rate or total amount of solutes in the solution, such as the yield of oil from an oil-water mixture flowing out of an oil well ； Determine the type of liquid in flow and route it accordingly; for example, distinguish between the finished product fluid and the cleaning fluid flowing alternately, and send them to different downstream pipelines. 　　In the early days, CMF was used only for liquids, and later its application was extended to high-pressure gases; it was not until the early 1990s that instruments suitable for medium-pressure gases became available. According to Micro Motion, by 1997 the company had 7,500 CMF units in use for gas applications, of which 6,000 were used at compressed natural gas vehicle refueling stations①. 　　The application of CMF in high-pressure natural gas vehicle refueling stations has become mature and is gradually gaining consensus. OIML (International Organization of Legal Metrology) formulated an \"International Measurement Procedure\" for this purpose, and issued the first draft committee version for comments in January 2000. The CMF developed by the China National Institute of Testing Technology in our country was also tested at automobile fueling stations in 1996, and by 1999, dozens of units had been installed. 　　An overseas market analysis firm’s estimate of the distribution of CMF applications across various industries shows that the petrochemical industry accounts for 57%, energy and utilities 18%, the food and beverage as well as pharmaceutical industries 14%, and others 11%; the food and pharmaceutical sectors make up a significant proportion of this. The industries that make extensive use of it domestically are capital-intensive sectors such as oil, chemicals, and energy, while it is rarely used in the food industry. 5.2 Considerations regarding instrument performance 5.2.1 Measurement accuracy 　　(1) Basic error, zero-point stability, repeatability error 　　CMF expresses the basic error mainly in terms of \"range error plus zero-point instability\". It is neither a citation error (usually expressed as %FS) nor another form of relative error; it can easily give users the illusion of high precision ； For instruments with poor zero-point stability, at low flow rates or near the lower limit of flow, the zero-point instability can often be many times greater than the range error, resulting in significant inaccuracies; this factor should be taken into consideration when selecting such instruments. 　　When measuring liquids, the range error among the basic errors is usually between ±(0.1～0.5)%R, while the repeatability error is generally 1/4 to 2/3 of the basic error. When the same instrument is used to measure gases, its measurement accuracy is lower than that when measuring liquids. For example, the Elite series of CMFs has a basic error of (±0.1%R + zero-point instability) when measuring liquids; the manufacturer claims that the error is ±0.5%R when measuring gases①, but test reports indicate that the measurement error is better than ±2%R. As can be seen from the figures in the reports, when measuring gases at lower pressures, the measurement error is close to or slightly exceeds 1%, with zero-point instability being the main factor contributing to this. The liquid flow rate ratio is mostly in the range of (10:1) to (50:1), with some reaching as high as (100:1) to (150:1). When using it to measure low-pressure gases, it should be noted that the upper measurable flow rate will be significantly reduced; for example, the CMF100 model (with diameters of 25/40 mm) has a maximum flow rate of only about 4% of its rated flow rate when measuring compressed air at 0.175 MPa②. 　　CMFs typically used for gases do not require gas calibration; instead, they use the instrument constants calibrated with water. It is generally believed that there is little difference between the two. There are still some differences in practice; according to literature, the CMF100 model achieves an accuracy of better than 2% within the fluid density range from 1000 kg/m3 (water) to 2 kg/m3 (air at 0.175 MPa), using the instrument constants calibrated by the manufacturer, with most errors being less than ±0.5%③. 　　Zero-point instability is usually expressed as %FS or in terms of flow rate in kg/min, and it generally lies within the range of ±(0.01–0.04)%. For instruments with zero-point instability of ±0.04% FS and a range of 20:1, the error due to zero-point instability at the lower flow rate can reach ±0.8% of the flow rate at that measurement point. 　　(2) Effect of hydrostatic pressure variation In the early days of CMF use, it was believed that flow measurement values were not affected by liquid hydrostatic pressure; however, as its application areas expanded and more practical experience was gained, it was proven that such values are indeed influenced by fluid hydrostatic pressure. In fact, an increase in fluid pressure enhances the stiffening effect of the vibrating tube (for measurement purposes) as well as the Bourdon effect of the bent vibrating tube, thereby affecting the instrument constants. Although the impact is not significant, it cannot be ignored for high-precision CMF. 　　For example, the static pressure effect of Micro Motion’s D300/D600 models is approximately - (0.135～0.075)%/105Pa ； The CMF100/200/300 models are smaller, at approximately -(0.003～0.09)%105Pa④. The influence is one-way and can be compensated for. 　　(3) Effect of fluid temperature The fluid temperature affects the elastic modulus of the material used in the measuring tube, as well as the damping properties of the adhesive and bandage that hold the sensing elements to the measuring tube; the former influences the instrument constant (range), while the latter affects the zero point. Although CMFs are all equipped with temperature sensors to compensate for changes in elastic modulus based on its temperature coefficient, this coefficient is an average statistical value; due to differences in manufacturing and heat treatment, there can be undercompensation or overcompensation compared to the actual temperature coefficient, resulting in a temperature-induced effect. The impact is two-way. 　　For example, the temperature effect of Micro Motion’s D series is ±(0.01–0.1)%/10°C of the rated flow rate, while that of the CMF series is smaller, at ±(0.0025–0.01)%/10°C④. 　　(4) Actual measurement accuracy The measurement accuracy under actual operating conditions can be evaluated by using the root mean square of the basic error, pressure effect, and temperature effect. 5.2.2 Flow Range and Pressure Loss As mentioned earlier, the wide flow range of CMF is actually due to a high set upper limit for flow rate; when calculated based on the density of water, the velocity at the nominal diameter can reach 8–12 m/s, or even 15–16 m/s. Other flow meters such as positive-displacement or turbine types, on the other hand, have a value of only 3–5 m/s, which is about 1/3 of that of CMF. The flow velocity inside the CMF measuring tube is even higher; as a result, most models exhibit significant pressure losses. When used with low-viscosity liquids such as water, these losses range from 0.1 to 0.2 MPa, and this factor should be taken into consideration when making a selection. 　　One of the main factors considered when selecting the CMF size based on operating conditions is to estimate that the gauge pressure loss (or pressure drop) remains within the allowable limits of the piping system. Allowing for a pressure drop, to achieve the best measurement accuracy, the maximum flow rate used should be as high as possible within the flow range. Typically, the nominal diameter of CMF is smaller than (or equal to) the pipe diameter; those that are larger than the pipe diameter are rare. 　　The pressure drop of CMF increases as the fluid viscosity increases. Figure 3 shows the series of flow-rate vs. pressure drop curves for fluids with different viscosities for the D150 model (bore diameter 40/50 mm) ①. μ=1mPa·s corresponds to the viscosity of room-temperature water, while μ=0.01mPa·s corresponds to the viscosity of most gases. As can be seen from the graph, the pressure drop for a liquid with a viscosity of 500 mPa·s is 10 times that of water. In instruments, high-viscosity liquids flow in a laminar flow state, and there is a linear relationship between the pressure drop Δp and the flow rate qm (i.e., Δp = kqmn, where n = 1 and k is a coefficient) ； At low viscosity, it is turbulent flow, following a quadratic relationship (i.e., n=2) ； The relationship line for medium viscosity is broken-line; at low flow rates, flow is laminar, while at medium to high flow rates it is in a transitional zone where flow shifts from laminar to turbulent, with n ranging between 1 and 2.