Mass flow meter

Abstract

The present invention provides a mass flow meter. The mass flow meter includes a tubular housing (250) extending along a longitudinal axis. The tubular housing is configured to receive a flow of a fluid (351) therethrough. A flexible plate (352) extends along at least a portion of the tubular housing and is at least partially coupled to an inner wall of the tubular housing on either side of a longitudinal end of the flexible plate, thereby allowing the flexible plate to oscillate torsionally. At least one electromagnetic actuator system (302, 303) is configured to apply at least two rocking torques to the flexible plate sufficient to cause the flexible plate to oscillate torsionally. At least two sensor systems (301, 304) are configured to measure the rocking of the flexible plate as a function of time at a position resulting from the applied at least two rocking torques. The present invention also provides a method for measuring a mass flow rate through at least one tubular housing.

Description

[Technical field]

[0001] The present invention relates to a mass flow meter and method for measuring the mass flow rate of a fluid through a tubular housing, and more particularly to a mass flow meter having a flexible plate. Also described is a method and method for using the mass flow meter. [Background technology]

[0002] Fluids such as liquid CO2 for carbon capture and storage (CCS), fluid petroleum products, natural gas, hydrogen, and water are often transported in pipelines. Such fluids are often transported under high pressure. The pipelines may be on the ocean floor at great depths or on land. Onshore facilities such as oil refineries and other processing facilities may also transport fluids through pipelines. The fluids are transported in pipelines with large dimensions. Also, the fluids are usually low density. Liquid H2, for example, has a low density, while gaseous H2 has an extremely low density. High density fluids such as liquid CO2 and natural gas are often transported / stored on the ocean floor at great depths and with a water temperature of 4°C, or in long pipelines with cooling equipment. Liquid CO2 may not be transported at atmospheric pressure or at environmental temperatures above 4°C, as it requires too high a pressure to allow for pipeline transportation for practical reasons (such as the thickness of the pipeline). On the ocean floor at 4°C, the pressure would be around 90 bar. It is therefore possible and practical to build pipelines to transport liquid CO2 on the ocean floor. Liquid CO2 has a mass density of approximately 1.1 tonnes per cubic meter. Liquid H2 has a mass density of approximately 70 kg per cubic meter. Fluid transport can be monitored in real time by measuring the amount of fluid moving through the pipeline. Mass flow measurements may be preferred over volumetric flow measurements because mass does not change with changes in pressure or temperature. For this reason, mass flow measurements may be more accurate. Mass flow meters based on ultrasonic measurements may not be applicable to liquids such as liquid CO2, because ultrasound is attenuated by liquids.

[0003] A mass flow meter using traditional Coriolis technology works by vibrating a pipe carrying a flowing fluid between an inlet and an outlet. This pipe vibration provides a oscillation, which is the variation of the pipe's measurement (e.g., position) about a center value. The inertia of the flowing fluid resists the oscillation, causing the pipe to twist. This twisting creates a time lag (phase shift) in the pipe's oscillation on the inlet and outlet sides. This phase shift is directly affected by the mass of the fluid passing through the pipe. Traditional Coriolis flow meters split the fluid flow into two pipes to provide zero net driving force.

[0004] Traditional direct Coriolis mass flow measurement may not be suitable for measuring the mass flow rate of high pressure fluids, especially low density fluids. Indirect mass flow measurement of high pressure fluids can be performed using differential pressure and / or density of the fluid, but may be inaccurate.

[0005] For example, hydrogen and CO2 transport pipes have very large dimensions (up to 24 or 30 inches in diameter) and pressures are typically 100 bar to 200 bar. Existing Coriolis mass flowmeters have a maximum diameter of 16 inches and cannot be used to measure the mass flow rate of fluids in such large pipes. When transporting fluids at very high pressures, such as 300 bar, the maximum diameter available for conventional Coriolis flowmeters is 6 inches to 7 inches, which requires a large thickness to withstand the pressure. When measuring low density fluids, Coriolis flowmeters need to be thin tubular walls to detect mass flow rates. Thin tubular walls cannot withstand high pressures. Therefore, existing Coriolis mass flowmeters may not be usable for high pressure applications unless the line size is very small, for example, for high pressure fluids above 100 bar. Existing Coriolis mass flowmeters need to be thick to withstand such high pressures, resulting in structures that are too rigid to vibrate to detect mass flow rates. For pipelines with high operating pressures and / or large diameters, the metal pipes that transmit the pressure for the Coriolis flowmeters are thick. Therefore, applying force to the measurement pipe using an electromagnetic actuator is not possible in such thick pipelines. Also, a conventional Coriolis flowmeter may not be able to measure the mass flow rate of low density fluids, since it requires high speeds of fluid flow to provide a signal, and such high speeds are not possible here. Conventional Coriolis flowmeter designs use tubes with smaller diameters compared to pipes for fluid flow, so the pressure may drop more than mass flowmeters due to the Venturi effect. For H2, the pressure drop in a conventional Coriolis mass flowmeter can be, for example, 50 bar to 100 bar. This pressure drop can cause the fluid, for example liquid CO2, to boil, reducing the measurement accuracy of the mass flowmeter.

[0006] US Patent No. 5,392,656 describes a mass flow meter having a non-vibrating conduit providing a flow path divided into two parallel and equal sub-passages by a planar member whose leading and trailing edges are fixed to the wall of the flow path. The planar member is torsionally vibrated about its central axis substantially coinciding with the centerline of the flow path. Two actuators are disposed inside the conduit opposite each other. The actuators may extend into or through the wall of the conduit to close to the planar member. A pair of vibration sensors detect the torsional vibration of the planar member at two different cross sections of the flow path, respectively. The mass flow rate of the medium moving in the flow path is determined as a function of the phase angle difference between two alternating electrical signals provided by the pair of vibration sensors, respectively. By locating the actuators close to the planar member, a limited vibration torque can be applied to the planar member.

[0007] US Patent No. 10,393,560 B2, the entire contents of which are incorporated herein by reference, describes a mass flow meter 200 having a tubular housing 202, a flexible plate 204, an actuator 210, and at least two sensors 214 (214a, 214b, 214c, 214d) and 216 (216a, 216b, 216c, 216d), as shown in Figure 1. The tubular housing 202 may be generally circular and cylindrical with a length L, a wall thickness T, and an inner radius R that define a gap 206. The tubular housing has an inlet 202i for the fluid flow 102 and an outlet 202o for the fluid flow 102. The flexible plate 204 may be coupled to an inner wall of the tubular housing such that the flexible plate can vibrate torsionally. The actuator 210 may be configured to apply a rocking torque to the flexible plate sufficient to cause the flexible plate to torsionally oscillate. At least two sensors 214 and 216 may be configured to measure the rocking of the flexible plate as a function of time at different locations. The mass flow meter may also include a computing device 212 in electrical communication with the at least two sensors. The computing device 212 is configured to determine a mass flow rate of the fluid passing through the tubular housing from a phase shift between the rocking of the flexible plate measured by the at least two sensors.

[0008] Since high pressure fluids are often transported in pipes with thick walls that are difficult to vibrate with sufficient strength for a mass flow meter, the mass flow meter described in US Patent No. 10,393,560 B2 is provided with a tubular housing containing a flexible plate that vibrates torsionally. The vibration of the plate varies with the flow of fluid therethrough. By measuring the oscillation of the flexible plate at different positions, the phase lag of the oscillation of the plate can be measured and related to the mass flow rate of the fluid passing through the tubular housing. Summary of the Invention [Problem to be solved by the invention]

[0009] Measuring the mass flow rate of low density and / or high pressure fluids can pose sensitivity challenges with prior art solutions. [Means for solving the problem]

[0010] The present invention provides an improved mass flow meter.

[0011] The present invention provides a mass flow meter that includes a tubular housing extending along a longitudinal axis. The tubular housing is configured to receive a flow of fluid therethrough. The mass flow meter also includes a flexible plate extending along at least a portion of the tubular housing. The flexible plate is at least partially coupled to an inner wall of the tubular housing on either side of a longitudinal end of the flexible plate, thereby allowing the flexible plate to torsionally oscillate. The at least one electromagnetic actuator system is configured to apply at least two rocking torques to the flexible plate sufficient to cause the flexible plate to torsionally oscillate. The at least two sensor systems are configured to measure the oscillation of the flexible plate as a function of time at a position resulting from the applied at least two rocking torques.

[0012] Further, a net sum of the at least two rocking torques applied to the flexible plate may be zero or substantially zero. The at least two rocking torques may be in opposite directions. The sum of the at least two rocking torques may be less than a maximum value of the at least two rocking torques.

[0013] Furthermore, the at least one electromagnetic actuator system may include an electromagnetic device disposed outside the tubular housing and a magnetizable material disposed inside the tubular housing. The electromagnetic device may include at least one coil disposed outside the tubular housing. The magnetizable material may be disposed on a flexible plate. The magnetizable material may include at least one permanent magnet. The magnetizable material may include at least one permanent magnet group, where the permanent magnets may be symmetrically arranged side by side to form a dipole. The magnetizable material may include four permanent magnet groups forming a quadrupole. Alternatively, the magnetizable material may include four permanent magnet groups forming a dipole. Each of the two sensor systems of the mass flow meter may include a pickup. In an embodiment, the at least one electromagnetic actuator system may be adapted to function as a sensor system as well.

[0014] The at least one coil may be arranged to provide an alternating electromagnetic field that alternately magnetizes and demagnetizes the magnetizable material.

[0015] In one embodiment, the tubular housing of the mass flow meter may be a liner of a non-magnetic material. The pressure housing may be disposed outside the liner.

[0016] In a further aspect, the present invention provides a method for measuring a mass flow rate through at least one tubular housing, the method comprising receiving a flow of fluid through the at least one tubular housing, the tubular housing including a flexible plate extending along at least a portion of the at least one tubular housing and at least partially coupled to an inner wall of the at least one tubular housing on both sides of a longitudinal end of the flexible plate, whereby the flexible plate can torsionally vibrate. The method further comprises driving the flexible plate in the at least one tubular housing to vibrate in a torsional mode at a selected frequency by applying at least two rocking torques to the flexible plate by at least one actuator system to torsionally vibrate the flexible plate, measuring a plurality of rocking motions of the flexible plate by at least two sensor systems configured to measure the rocking motions of the flexible plate as a function of time at at least two positions resulting from the applied at least two rocking torques, and determining a mass flow rate of the fluid flowing through the at least one tubular housing based on a phase shift between the rocking motions measured at the at least two positions.

[0017] The net sum of the at least two rocking torques applied to the flexible plate may be zero or substantially zero. The at least two rocking torques may be in opposite directions. The sum of the at least two rocking torques may be less than the maximum of the at least two rocking torques. For example, when three rocking torques are applied, the sum of all rocking torques is zero or substantially zero.

[0018] In a further embodiment, the mass flow meter described above or the method described above may be used to measure the mass flow rate of CO2, NH3, H2 or natural gas fluids.

[0019] The improved mass flow meter described above provides increased sensitivity, particularly for low density and low viscosity fluids such as gases, e.g., CO2, NH3, H2, or natural gas. The mass flow meter also provides increased sensitivity for liquid CO2, liquid NH3, liquid H2, or liquid natural gas (LNG), which are often transported at high pressure. The mass flow meter can also measure the mass flow rate of two-phase and multi-phase fluids.

[0020] The use of at least two actuator systems arranged symmetrically around the longitudinal center of the flexible plate increases sensitivity. The two actuator systems can excite the flexible plate at the second harmonic vibration or higher even harmonics. This allows the mass flow meter to be adapted to the specific fluid flow being measured. The use of two torques contributes to exciting the desired correction. The torques are in opposite directions and the sum of the torques may be about zero or substantially zero. The second and fourth harmonic vibrations may be the most practical choice for reasons that will be explained later, but the third harmonic may also be implemented using asymmetric torques. Even higher odd harmonics are possible.

[0021] The use of two actuator systems increases the quality (Q) value of the mass flowmeter. A higher Q value provides a sharper resonance peak for the flexible plate. As a result of the sharper resonance peak and therefore narrower frequency range, the mass flowmeter is less susceptible to noise from the surroundings. A higher Q value also means that the ratio of the energy input from the actuators to the flexible plate and the energy obtained from the oscillation of the flexible plate is higher. Therefore, less energy is required to drive the system. Increasing the Q value of the mass flowmeter results in an increased signal, reduced noise, and improved measurement sensitivity.

[0022] In some applications, the use of a conductive tubular housing may be undesirable or impossible. In some applications, such as high operating pressures (e.g., typically above 200 bar) and / or large diameter pipes (e.g., typically above 24 inches), a pressure-transmitting metal tubular housing may be too thick to electromagnetically actuate the torsion of a flexible pipe. In such applications, it is desirable to locate the actuator and sensor inside the tubular housing. This may protect the actuator and / or sensor coils. Pressure from the fluid flowing inside the tubular housing may be transferred to the external pressure-bearing housing. This may be done, for example, by using a metal membrane filled with liquid (e.g., oil) or a molded plastic that transfers the process pressure to the pressure-bearing metal tubular housing. The tubular housing may be a liner. The pressure housing may be located outside the liner. The electromagnetic actuator may be located inside the pressure housing and outside the liner. The space between the pressure housing and the liner may be filled with a liquid or solid filler, which may transfer pressure from the fluid flow inside the liner to the pressure housing. The filling material also serves to protect the electromagnetic actuator. The tubular housing may be a liner, so it does not need to withstand high pressures in the fluid flow. The flexible plate may be soft enough to measure mass flow of gases. For example, high pressures can be measured in the form of fluid flow or multiphase flow of liquid or gaseous CO2, NH3, H2 or natural gas. The liner with the flexible plate does not need to withstand high pressures itself, and the flexible plate is designed to be flexible and soft enough for large diameters, so the mass flow meter may be used in large diameter pipes.

[0023] The actuator system and the sensor system may be placed at positions that correspond to the maximum amplitude of the fourth harmonic torsional oscillation of the flexible plate, i.e., 1 / 8, 3 / 8, 5 / 8, 7 / 8 of the length of the tubular housing, while leaving enough space for both the actuator system and the sensor system of the mass flow sensor. [Brief description of the drawings]

[0024] Exemplary embodiments of the invention will now be described with reference to the accompanying drawings. [Figure 1A] 1 is a perspective view of an exemplary embodiment of a prior art mass flow meter including a tubular housing and a flexible plate disposed within the tubular housing; [Figure 1B] FIG. 1B illustrates the prior art solution of FIG. 1A showing the forces due to torsion acting on the flexible plate, where the flexible plate is shown in the resulting actuated state. [Figure 2A] FIG. 1 is a perspective view of an exemplary embodiment of a mass flow meter including a tubular housing and a flexible plate disposed within the tubular housing, where the mass flow meter is provided with two actuator devices disposed about a longitudinal center of the flexible plate and two sensors disposed about a longitudinal center of the flexible plate, the flexible plate being shown in an actuated state. [Figure 2B] FIG. 1 is a perspective view of an exemplary embodiment of a mass flow meter including a tubular housing and a flexible plate disposed within the tubular housing, where the mass flow meter is provided with two actuator devices centered about a longitudinal center of the flexible plate and two sensors centered about the longitudinal center of the flexible plate, where the flexible plate is shown in an unactuated state, and where the flexible plate is provided with a group of magnets or magnetizable material. [Figure 2C] FIG. 1 is a perspective view of an exemplary embodiment of a mass flow meter including a tubular housing and a flexible plate with an actuator device disposed within the tubular housing and centered about a longitudinal center of the flexible plate, the flexible plate shown in an unactuated state and having magnets or magnetizable material disposed on the flexible plate. [Figure 3A] FIG. 1 is a perspective view of a flexible plate having four vanes that may be used in a mass flow meter, where the flexible plate is shown in a twisted first harmonic operating state. [Figure 3B]FIG. 3B is a perspective view of the flexible plate of FIG. 3A having four vanes that may be used in a mass flow meter, where the flexible plate is shown in a twisted second harmonic operating state; [Figure 3C] FIG. 3B is a perspective view of the flexible plate of FIG. 3A having four vanes that may be used in a mass flow meter, where the flexible plate is shown in a twisted third harmonic operating state; [Figure 3D] FIG. 3B is a perspective view of the flexible plate of FIG. 3A having four vanes that may be used in a mass flow meter, where the flexible plate is shown in a twisted fourth harmonic operating state; [Figure 4A] 1 is a further exemplary perspective view of a mass flow meter having two tubular housings arranged adjacent and parallel to one another and a flexible plate disposed within each tubular housing, the two flexible plates including four vanes, the two flexible plates shown in anti-phase first harmonic positions; [Figure 4B] FIG. 5 illustrates the mass flow meter of FIG. 4, showing fluid flows Vz1 and Vz2 entering respective tubular housings, where an actuator system actuates two flexible plates with forces −Fx1 and Fx2, respectively, that provide antiphase first harmonic excitations. [Figure 4C] 4C are cross-sectional views of each of the two tubular housings of FIG. 4B showing the four vanes, the actuator system, and the forces acting on the vanes -Fx1 and Fx2. [Figure 5A] FIG. 1 is a cross-sectional view of one embodiment of an electromagnetic actuator system for a mass flow meter, in which a group of permanent magnets forming dipoles are disposed on each of four vanes of a flexible plate forming a quadrupole cross section, and a coil system of the electromagnetic actuator system is disposed outside the tubular housing. [Figure 5B]FIG. 1 is a cross-sectional view of one embodiment of an electromagnetic actuator system for a mass flow meter, in which permanent magnet groups each forming a dipole are disposed on four vanes of a flexible plate that form cross sections of the four dipole groups, respectively, and two coil systems are disposed on either side of the center of the flexible plate that surround the flexible plate. [Figure 5C] FIG. 1 is a cross-sectional view of one embodiment of an electromagnetic actuator system for a mass flow meter, in which permanent magnet groups each forming a dipole are disposed on four vanes of a flexible plate that form cross sections of two dipole groups, respectively, and two coil systems are disposed on either side of the center of the flexible plate that surround the flexible plate. [Figure 6] FIG. 2 is a cross-sectional view of a tubular housing of a mass flow meter having an inner liner and an outer tube that function as a pressure containment. [Figure 7] FIG. 1 is a flow diagram illustrating an example embodiment of a method for measuring mass flow rate. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0025] The accompanying drawings are illustrative and are not necessarily to scale, and are intended to illustrate exemplary embodiments of the subject matter disclosed herein, and therefore should not be considered as limiting the scope of the present disclosure.

[0026] Exemplary embodiments are described below with reference to the drawings, which are intended to provide an understanding of the principles of the disclosed mass flowmeter, e.g., regarding the structure, function, manufacture and use of the mass flowmeter and its different parts. The drawings are not necessarily drawn to scale.

[0027] FIG. 1 shows a prior art mass flow meter 200 having a fluid channel 100 (e.g., a pipe or pipeline) containing a flowing fluid and a mass flow meter 200 at least partially coupled thereto at each end. The mass flow meter 200 has a tubular housing 202 and a flexible plate 204 configured to oscillate torsionally. Measurement of the movement of the flexible plate 204 can thereby be related to the mass flow rate of the flowing fluid. The mass flow rate can be directly measured by the mass flow meter 200 regardless of the shape of the tubular housing 202. The prior art mass flow meter is provided with one actuator 210 located on a surface at the longitudinal center of the tubular housing 204. The actuator is configured to apply a rocking torque to the flexible plate sufficient to cause the flexible plate to oscillate torsionally. The frequency of the actuator may be set to the resonant frequency of the flexible plate. Two sensors 214 and 216 are positioned symmetrically about the longitudinal center of the tubular housing and measure the oscillations of the flexible plate as a function of time at these two locations resulting from an applied oscillation torque.

[0028] FIG. 1B illustrates the mass flowmeter of FIG. 1A with a torsion applied to the flexible plate. As shown, the longitudinal axis A of the flexible plate is parallel to the x-axis of the mass flowmeter. The force F applied by the actuator A , -F A may be parallel to the y-axis and have opposite directions. These forces may act along some or all of the width of the flexible plate. The applied force F A , -F A changes in magnitude and direction to provide a rocking torque that stimulates the flexible plate to vibrate in a torsional mode. The resulting Coriolis force, F, acting on the flexible plate C , F C is the angular velocity Ω y , Ω y A torsional vibration is applied.

[0029] When a flexible plate is excited to vibrate in a torsional mode and interacts with the fluid flow being measured, a phase shift occurs between the vibrations at two different locations of the flexible plate. The mass of the flowing fluid affects the excitation of the flexible plate, causing a delay of the excitation or wave traveling along the flexible plate. This delay can be viewed as a sort of Doppler effect as it travels longitudinally along the flexible plate.

[0030] The phase shift is approximately proportional to the mass flow rate of the fluid. Thus, the sensors may be spaced apart to provide a sufficiently long travel length for the flow of the fluid along the flexible plate before being detected by a second sensor. A direct measurement of the mass flow rate of the fluid may be achieved by determining a proportionality constant of the mass flow meter. An estimation of the mass flow rate of the fluid may be performed by a computing device that receives the sensor signals from the sensor system.

[0031] 2A and 2B show an exemplary embodiment of a mass flow meter 310 having a tubular housing 350. The tubular housing may be generally cylindrical in shape having a length L, a wall thickness T, and an inner radius R that defines a gap 353. The length L and gap 353 of the tubular housing 300 extend along a longitudinal axis A between a housing inlet and a housing outlet located at opposite ends of the tubular housing 350. The tubular housing 300 may be substantially straight between the housing inlet and the housing outlet. Surfaces of the tubular housing that contact the fluid flow may be rounded and smooth to avoid unnecessary friction that would impede the fluid flow.

[0032] The tubular housing 353 can take on other geometric shapes depending on, for example, the fluid channel (e.g., pipeline) and fluid flow to be monitored, as well as other circumstances such as the ambient temperature and / or pressure, the temperature and / or pressure of the fluid flow, the material of the fluid channel and tubular housing, etc. The shape and / or material of the tubular housing may be approximately the same as the shape and / or material of the fluid channel. The tubular housing may be formed from any suitable material including, for example, polymers, ceramics, metals, metal alloys (e.g., steel, copper and copper alloys, aluminum and aluminum alloys, etc.).

[0033] The mass flow meter 310 may be integrally formed with the fluid channel. x 351 passes through the mass flow meter. The inlet and outlet of the mass flow meter housing may form a fluid-tight coupling with a fluid channel or a pipeline pump, dispenser, etc. of the fluid system. Examples of fluid-tight couplings include, but are not limited to, threaded couplings, clamps, welds, etc.

[0034] The mass flow meter 310 may be disposed within a pipeline. In this case, the tubular housing is not exposed to pressure from the surroundings, allowing the mass flow meter to be used in high pressure environments. This allows the tubular housing to be made of a much thinner and lighter material than the pipeline. The tubular housing may be a liner. The liner may be formed from a non-magnetizable material. The liner may be formed from a conductive material or a non-conductive material. A pressure housing 390 (FIG. 6) may be disposed outside the liner 391. The pressure housing may be formed from a conductive material.

[0035] The electromagnetic actuator system (302, 303) may include an electromagnetic device disposed outside the tubular housing and a magnetizable material disposed inside the tubular housing. The two forces from the actuator system are F A1 , -F A1 and F A2 , -F A2These forces are the same as torques. The resulting Coriolis force -F C , F C acts on the flexible plate with angular velocity Ω y and Ω y The torsional vibration of the flexible plate is generated. The net sum of the two rocking torques applied to the flexible plate may be zero or substantially zero. The at least two rocking torques may be in opposite directions to each other as shown in FIG. 2A. The sum of the at least two rocking torques may be less than the maximum of the at least two rocking torques. For example, when three rocking torques are applied, the sum of all the rocking torques is zero or substantially zero. The mass flow meter is provided with two sensor systems (301, 304).

[0036] FIG. 6 shows an embodiment of a mass flow meter with an inner liner 391 and an outer tube 390 that act as pressure containments. The electromagnetic actuators 302, 303 and the sensor system 301, 304 may be located inside the pressure housing and outside the liner. The space between the pressure housing and the liner may be filled with a liquid or solid filler to transfer the pressure from the fluid flow 351 inside the liner 391 to the pressure housing. This filler may also serve to protect the electromagnetic actuator and the sensor system. If the tubular housing is a liner, it does not need to withstand the high pressure of the fluid flow. This solution may be used, for example, for measuring high pressure fluids where the outer pressure housing is too thick to use an electromagnetic actuator.

[0037] FIG. 2A shows a flexible plate 352 disposed within a tubular housing. The flexible plate is shown at second harmonic oscillation. The tubular housing forms a cavity 353. The flexible plate 352 can extend in the direction of a longitudinal axis A of the tubular housing 350. The flexible plate 352 may extend along at least a portion of the tubular housing 350. The flexible plate can be at least partially coupled to an inner wall of the tubular housing 350 (e.g., a wall of the cavity 353) at one or more locations. The flexible plate may be partially coupled to the inner wall of the tubular housing at both of its longitudinal ends. For example, a first end of the flexible plate can be at least partially coupled to the tubular housing at or near the housing inlet i, and a second end of the flexible plate can be at least partially coupled to the tubular housing at or near the housing outlet. Alternatively, the flexible plate may be attached at one of its ends to the tubular housing 350. In further embodiments, two or more flexible plates 352 may be disposed within a housing (not shown).

[0038] 2B, the flexible plate 352 may have the form of a substantially planar plate. The flexible plate may have a width W approximately equal to the inner diameter (2R) of the tubular housing 350. The small gap between the walls of the cavity 353 and the flexible plate 352 allows the fluid V x 2B )。 Because the gap is small, the flexible plate interacts with nearly the entirety of the fluid flow passing through the tubular housing. In some embodiments, the flexible plate may have a curved shape in an equilibrium or unfixed state (not shown). In some embodiments, the flexible plate may be stretched or elongated and tensioned to change the resonant frequency of the flexible plate when mounted inside the tubular housing.

[0039] The mass flow meter may include actuator systems 302, 303. The actuator system may be configured to apply at least two rocking torques to the flexible plate sufficient to torsionally oscillate the flexible plate. The actuator system may include two actuators 302, 303, as shown in Figures 2A and 2B. As shown in Figures 2A and 2B, the two actuators are disposed outside the tubular housing 350. Disposing outside the tubular housing may include, for example, disposing on a surface of the tubular housing or adjacent to an outer surface of the tubular housing. The actuator systems 302, 303 may be disposed at different longitudinal positions of the tubular housing. The actuators may be disposed symmetrically about the longitudinal center of the flexible plate 352.

[0040] The actuators 302, 303 may be configured to apply a rocking torque to the flexible plate 352 to vibrate the flexible plate in a torsional mode at a selected frequency. The torsional mode may be a resonant frequency of the flexible plate including not only the fundamental frequency but also even and odd harmonics. The torsional mode may be a second harmonic rocking, a third harmonic rocking, or a fourth harmonic rocking as shown in Figs. 3A-3D, respectively, although higher harmonics may also be applied. In Figs. 2A and 2B, the actuators 302, 302 are positioned at 3 / 8 and 5 / 8 of the length of the flexible plate. The sensors or sensor systems 301, 304 for detecting the result of the interaction of the fluid flow with the actuated flexible plate 352 are positioned at positions corresponding to 1 / 8 and 7 / 8 of the length of the flexible plate. These positions (1 / 8, 3 / 8, 5 / 8, 7 / 8) correspond to the positions of maximum amplitude of the fourth harmonic oscillation of the flexible plate, which will be described later.

[0041] At least two actuators may be used. A net sum of the at least two rocking torques applied to the flexible plate by the at least two actuators may be zero or substantially zero. The at least two rocking torques may be in opposite directions to each other. The sum of the at least two rocking torques may be less than the maximum of the at least two rocking torques. For example, when applying three rocking torques, the sum of all rocking torques is zero or substantially zero.

[0042] The actuators 302, 303 may be electromagnetic actuators. The electromagnetic actuators may be in the form of one or more electromagnetic coils. The electromagnetic coils are coils that may have a magnetic core. The coils may be disposed around the tubular housing or may be disposed around a magnetic core provided by a magnetic material 150, 151, 152, 153, 154, 155, 156, 157 disposed in or on the flexible plate. At least a portion of the flexible plate 352 may be formed from a magnetic material (e.g., metal, metal alloy, steel, polymer, etc.). The flexible plate 352 may include one or more embedded permanent magnets 150, 151, 152, 153, 154, 155, 156, 157. The magnetic material or permanent magnets 150, 151, 152, 153, 154, 155, 156, 157 may also be disposed on an outer surface of the flexible plate 352. The magnetic material and permanent magnets 150, 151, 152, 153, 154, 155, 156, 157 may be positioned on the flexible plate at a location within the magnetic field from the coil. The permanent magnets or magnetic material of the flexible plate may be positioned in a location corresponding to the coil, as shown in FIG. 2B, to effectively actuate the flexible plate with the magnetic field from the coil. The coil may be connected to a controller 300 or, for example, a computing device, for controlling a current supplied to the coil that generates a magnetic field to apply an oscillating torque to the flexible plate at a selected frequency. At least one of the magnitude, frequency and / or phase of the current applied to the coil may be controlled to enable the generation of one or more magnetic fields that apply an oscillating torque to the flexible plate. The flexible plate may be driven at a resonant frequency, whether at a fundamental frequency, an even harmonic, or an odd harmonic. The controller may be, for example, a computer or a power supply. The coil may be configured to receive feedback, for example, from a sensor system, to drive the flexible plate at resonance.

[0043] As mentioned above, the mass flow meter 310 may also include sensor systems 301, 304 for measuring the interaction of the mass flow rate with the torsionally vibrating flexible plate 352. The sensor systems 301, 304 may be configured to measure the movement of the flexible plate 352 as a function of time. xThe movement of the flexible plate may be measured at locations upstream and downstream of the longitudinal center C with respect to the flow of 351. The movement of the flexible plate 352 may be characterized by any parameter of the flexible plate that oscillates as a function of time as the flexible plate oscillates torsionally. Exemplary parameters include, but are not limited to, linear and / or angular parameters such as position, velocity, acceleration, and displacement. In certain embodiments, angles, angular velocities, and angular accelerations may be measured. In other aspects, stress and / or strain may be measured. The sensor system 301, 304 may be in the form of pickup sensors disposed at locations along the tubular housing. The pickup sensors may measure the rotational speed and direction of the flexible plate. The pickup sensors may be based on the Hall effect, for example, or may be magnetic pickup sensors. The magnetic pickup sensors may be coils disposed, for example, on the outside of the tubular housing, embedded in the tubular housing, embedded in a portion of the tubular housing, or adjacent to the tubular housing. In other embodiments, the sensors may be in the form of electromagnetic sensors. The electromagnetic sensor may be an electromagnetic coil, the coil being arranged around the tubular housing and the magnetic core being provided by a magnetic material, provided on or in the flexible plate, as described above for the actuator system. The electromagnetic sensor may also be the actuator system itself in some embodiments. In this case, the electromagnetic actuator system may be controlled to switch between an actuation mode for applying a rocking torque to the flexible plate and a detection mode for detecting the movement of the flexible plate. The mode switching may be performed continuously or intermittently during the measurement by the mass sensor. In other embodiments, the sensor system may be in the form of a strain gauge arranged at the end of the flexible plate. No velocity or acceleration occurs at the end of the flexible plate. The sensor system may be connected to a computing device or controller or other device that receives the sensor signal from the sensor system.A computing device, controller, or other device may also control the sensor system.

[0044] The sensor system 301, 304 may include multiple sensors located at different positions within the mass flow meter. The sensor system may be located at the position where the flexible plate exhibits the largest movement when excited by an applied torque. In Fig. 2A and Fig. 2B, the sensor system is as described above, with two sensors located at the positions where the fourth harmonic oscillation of the flexible plate exhibits the largest amplitude. These positions are 1 / 8, 3 / 8, 5 / 8, and 7 / 8 of the length of the flexible plate. Measuring the maximum parameter value ensures a large signal output from the sensor system, improving the sensitivity. Actuating the flexible plate by the actuator system at the position of maximum amplitude increases the energy transfer to the flexible plate, contributing to the increased sensitivity of the mass flow sensor. By using two sensors, the first sensor can be located at the 1 / 8 position and the second sensor at the 7 / 8 position, as shown in Fig. 2A. This leaves space for the actuator system at the 3 / 8 and 5 / 8 positions of the length of the flexible plate, as shown in Fig. 2A and as described above. Driving the flexible plate at the second, third, fourth and higher harmonics may improve the Q factor and sensitivity of the mass sensor. Simply put, the Q factor refers to the relationship between the energy of the oscillating flexible plate and the energy input to the flexible plate to cause the oscillation. In general, the torsion applied to the flexible plate should be in a position such that the flexible plate oscillates significantly when torque is applied. In this maximum amplitude position, the flexible plate will experience the largest changes in velocity and acceleration when exposed to a fluid flow. These changes are measured by the sensor system of the mass flow meter. Placing the sensor and actuator system at a position corresponding to the fourth harmonic of the flexible plate may also be used for the second and third harmonics. In this case, the placement of the sensor and actuator system will be close to the maximum amplitude of the oscillation of the flexible plate. In the embodiment shown in Figures 2A and 2B, the mass flow meter can be driven in both odd and even harmonic conditions. This provides flexibility for the mass flow meter and the possibility to adapt it to the actual flow conditions and the information available from the mass flow meter.In the even harmonic regime, the net sum of the rocking torques on the moving plate is zero or substantially zero. To allow for detection of mass flow in two-phase flows, such as bubbly liquid flows, the mass flow meter may be capable of being driven in multiple modes simultaneously. This may be advantageous for measuring the mass flow of, for example, CO2, NH3, H2, or LNG.

[0045] The flexible plate may be provided with a number of vanes. The number of vanes may be two, three, four, eight or more. The vanes may extend radially outward at an angle of about 90° to each other. The angle between the vanes may vary. The vanes may have approximately equal widths. The number of vanes and the angle between the vanes may vary depending on the characteristics of the fluid flow to be measured and other factors such as the environment or surroundings of the fluid flow. The vanes increase the stiffness of the flexible plate and prevent bending of the flexible plate without increasing the torsional stiffness of the flexible plate. The mass sensor is based on applying a swinging torque to the flexible plate to cause harmonic swinging of the flexible plate, and the high sensitivity to twisting increases the sensitivity of the flexible plate to the viscosity of the fluid. For example, for low density fluids such as liquid gases such as H2 and high density liquids such as CO2, the torsional stiffness needs to be low to measure the mass flow rate of H2 or CO2 with sufficient sensitivity.

[0046] 3A-3D show an embodiment of a flexible plate 352 having four vanes. The vanes are arranged in a cross configuration, arranged at 90 degrees to each other. The figures show the flexible plate in different torsional harmonic modes actuated by an actuator system. The figures show the maximum amplitude positions in different harmonic modes. FIG. 3A shows the actuation of the flexible plate in a first harmonic oscillation. In this first harmonic state, the maximum amplitude occurs at the longitudinal center of the flexible plate. Placing the actuator system near the longitudinal center provides the maximum Q value for the flexible plate. The location and placement of the sensors will vary depending on the type of sensor used. FIG. 3B shows the actuation of the flexible plate in a second harmonic oscillation. The maximum amplitude occurs at ¼ and ¾ of the length of the flexible plate, which provide the maximum Q value for the system. FIG. 3C shows the actuation of the flexible plate in a third harmonic oscillation. The maximum amplitudes are observed at 1 / 6, 3 / 6, and 5 / 6 of the length of the flexible plate. Figure 3D shows the actuation state of the flexible plate in the fourth harmonic oscillation, where the maximum amplitudes are observed at 1 / 8, 3 / 8, 5 / 8, and 7 / 8 of the length of the flexible plate.

[0047] 2C shows an embodiment in which actuator system 305 is positioned at positions A1 and A2 near the longitudinal center of the flexible plate extending over assigned magnetic materials or permanent magnets 152, 153, 154, 155. The magnetic materials or permanent magnets are arranged asymmetrically with respect to their magnetic poles, and actuation forces F are applied to the flexible plate at positions A1 and A2 in the directions indicated by the arrows by driving a common coil system. A1 , -F A1 and F A2 , -F A2are respectively applied (FIG. 2A). The sensor systems 301, 304 may be the same sensor systems as in FIG. 2A and FIG. 2B. The actuator system covers an area of ​​the flexible plate. The actuator system of FIG. 2B may be provided by an electromagnetic actuator system having at least two coils arranged around the tubular housing and magnets 152, 153, 154, 155 (e.g. permanent magnets or magnetizable material) in, on or embedded in the flexible plate 352. Each coil may include multiple windings covering a first and a second area of ​​the tubular housing. Each coil may be arranged side by side such that the first and second areas cover the entire area of ​​the actuator system shown in FIG. 2C. Also, each coil may be arranged at a distance from the center of the tubular housing in the area shown by the actuator system in FIG. 2C. The two permanent magnet groups forming a dipole may be arranged on or in the flexible plate, and may be partially or completely embedded in the flexible plate. The coils may be positioned at a sufficient distance from each other to apply at least two rocking torques to the flexible plate which vibrates torsionally with the permanent magnets. The two dipole permanent magnet groups may be positioned asymmetrically with respect to their magnetic poles. Each permanent magnet may be a bar magnet, and the group may be formed by placing each bar magnet side by side with the poles facing the same direction to provide a stronger magnet. The group may also include multiple layers of bar magnets. By forming two dipole permanent magnet groups, a stronger magnetic dipole is formed, increasing the magnetic field and, therefore, the torque applied to the flexible plate. By driving the two coils symmetrically, i.e., driving the two coils with currents having the same frequency and phase, the magnetic fields from the two coils are in the same direction at the same time. Because the two dipole magnet groups are positioned with opposing dipoles, the flexible plate will experience two opposing rocking torques applied to the flexible plate at magnet group positions A1, A2. The net sum of the rocking torques on the flexible plates may be zero or substantially zero.By using two coils, the actuator system may be configured to apply at least two oscillation torques to the flexible plate sufficient to cause the flexible plate to torsionally oscillate. The embodiment of FIG. 2C may cause the flexible plate to oscillate with a first harmonic oscillation.

[0048] 4A and 4B show a further embodiment of the mass flow meter 310. Here, two tubular housings 350 are arranged side by side. Each tubular housing is provided with a flexible plate 352. Each flexible plate extends along at least a portion of the tubular housing and is at least partially coupled to the inner wall of the tubular housing at both longitudinal ends of the flexible plate. This allows the flexible plate to vibrate torsionally. The two flexible plates are shown in anti-phase first harmonic positions. The fluid flow to be measured is arranged to flow through both tubular housings. The flexible plates may be provided with a number of vanes. In FIG. 4A and 4B, each flexible plate is provided with four vanes arranged at an angle of 90 degrees to each other. The actuator system 340 may be arranged in the longitudinal center area of ​​the flexible plates. One actuator system may be provided to cover both tubular housings. This common actuator system may for example have a coil covering the two tubular housings. A permanent magnet or magnetizable material may be provided in each flexible plate. Alternatively, an actuator system may be provided in each tubular housing. The actuator systems are each -F x1 and F x2 The two flexible plates may be actuated with a force of 0.1 to 0.25 to provide anti-phase first harmonic oscillations as shown.

[0049] The two flexible plates are shown with first harmonic torsional excitation, but the first harmonic torsional vibrations are in anti-phase. As fluid flows through both of the mass flowmeter's tubular housings and interacts with the flexible plates oscillating in anti-phase, the sensitivity of the composite signal from the mass flowmeter's sensor may be increased. The torsional stiffness of the flexible plates may have slight variations along their length, and by oscillating two similar flexible plates out of phase, the slight variations in torsional stiffness can be averaged out.

[0050] FIG. 4C shows a cross section of each of the two tubular housings of FIG. 4B, showing the four vanes, the actuator system, and the forces F acting on the vanes. x1 and F x2 A four vane flexible plate configuration as shown in Figures 4A-4C may be used, for example, in the mass flow meter shown in Figures 2A-2C.

[0051] An example of the coil and permanent magnet configuration of the electromagnetic actuator system is shown in Fig. 5A-5C for a flexible plate with four vanes. Fig. 5A-5C are cross-sectional views of the permanent magnet configuration. Fig. 5A shows a cross-sectional view of a quadrupole, where the coil systems 360, 361, 362, 363 of the electromagnetic actuator system are arranged on the outside of the tubular housing. The magnets in the vanes are arranged with alternating poles facing outwards (north, south, north, south). Fig. 5B shows a cross-sectional view of four sets of dipoles of permanent magnets, showing two coil systems 370, 371 surrounding the flexible plate on either side of the center of the flexible plate. The magnets are arranged with pole pairs facing outwards (north, north, south, south). Fig. 5C shows a cross-sectional view of two sets of dipoles of permanent magnets, showing two coil systems 380, 381 surrounding the flexible plate on either side of the center of the flexible plate. The magnets within the vanes are arranged with different poles facing outwards (north, south), forming a dipole.

[0052] In FIG. 5A, the electromagnetic actuator system has permanent magnet groups arranged on four vanes of the flexible plate, respectively. Each magnet group is formed by dipole bar magnets arranged side by side. The dipole direction changes from vane to vane as shown in FIG. 5A. In the first vane, the N pole faces outward, in the second vane, the N pole faces inward, in the third vane, the N pole faces outward, and in the fourth vane, the N pole faces inward. The S poles of the first and third vanes face each other, and the N poles of the second and fourth vanes face each other. Also in FIG. 5A, the magnet groups facing each other have dipoles facing each other. The magnet groups may be arranged around the longitudinal center of the flexible plate. Two coils may form a common coil system surrounding the flexible plate in the region of the longitudinal axis of the flexible plate. By controlling the phase of the current applied to the coil, the dipole direction between the vanes is alternating, thereby exerting opposing rocking torques on each vane of the flexible plate, and the frequency of the current is controlled to torsionally excite the flexible plate with harmonic rocking, and the magnitude of the current is controlled to control the amplitude of the vane rocking to a desired magnitude.

[0053] In the embodiment of FIG. 5B, two electromagnetic actuator systems 370, 371, each as shown in FIG. 5A, may be arranged symmetrically with respect to the longitudinal center of the flexible plate. The first actuator system may be arranged at 3 / 8 of the longitudinal length of the flexible plate, and the second actuator system may be arranged at 5 / 8 of the longitudinal length of the flexible plate. Each actuator system may include a group of permanent bar magnets arranged side by side (symmetrically arranged) with the same poles facing in the same direction, forming a dipole in each vane at the same position (3 / 8 and 5 / 8) as the two coils surrounding the flexible plate. In this embodiment, the two dipole magnet groups in each vane face in the same direction. The two electromagnetic actuator systems may be driven with currents of opposite phase (asymmetric). This imparts a twist to the flexible plate, resulting in a fourth harmonic oscillation of the flexible plate. Increasing the number of windings also strengthens the magnetic field of the coils.

[0054] In FIG. 5B, if the two permanent magnet groups of the actuator system are arranged asymmetrically with respect to each other, i.e., the magnetic poles of the two permanent magnet groups are oriented in opposite directions, the coils of each actuator system will be driven symmetrically, i.e., with the same frequency, phase, and amplitude. In FIG. 5A, the actuator system has two coils. The two coils are driven with currents of opposite phase. The permanent magnet groups of FIG. 5A may also be arranged such that the dipoles of each magnet group are oriented in the same direction. The currents applied to the two coils shown in FIG. 5A are of opposite phase but of the same frequency and magnitude.

[0055] The magnet group shown in Figure 5A forms a quadrupole. With eight vanes and one magnet group per vane, this forms an octupole. A multipole arrangement of permanent magnets increases the twist for the same applied current. In the embodiment shown in Figures 5A and 5B, bar magnets are used, but circular magnets may also be used. Also, multiple magnet groups may be provided on each vane depending on the twisting force required.

[0056] The magnet group may have various configurations. As shown in FIG. 5B, the magnet group may be arranged symmetrically. It may also be arranged asymmetrically (not shown) in which the poles of the magnet group are arranged in opposite directions at the 3 / 8 and 5 / 8 positions of the same vane. The currents in the coils of the actuator system of the asymmetrically arranged magnet group are in phase (symmetric) and act such that the net sum of the at least two rocking torques acting on the flexible plate is zero or substantially zero. The at least two rocking torques are in opposite directions. The sum of the at least two rocking torques may be less than the maximum value of the at least two rocking torques.

[0057] The arrangement of the magnetic material and the frequency, phase, and magnitude of the current flowing through the coil can be designed according to the principle of a reluctance motor to generate a torque based on magnetic reluctance. The flexible plate with the magnetizable material corresponds to the rotor of the reluctance motor. The coils arranged outside the tubular housing correspond to the poles of the stator. The current in the coil is controlled to change phase over time to obtain the desired effect of generating a torque corresponding to the movement between the stator and rotor of the reluctance motor. In this configuration according to the principle of a reluctance motor, an actuator system may be used as a sensor system, as described above. Also, the current phase and frequency applied to the coil are driven intermittently in time to switch between a torque generation mode that generates a torque in the flexible plate and a detection mode that detects the movement of the flexible plate due to the applied torque. The configuration based on the principle of a reluctance motor may apply a torque that drives the flexible plate in a first harmonic state when the two electromagnets are driven in antiphase (asymmetric).

[0058] The actuator system having an electromagnetic actuator and a permanent magnet (embedded permanent magnet) may be arranged in various configurations to achieve torsional vibration of the flexible plate at the resonant frequency of the flexible plate. In embodiments having an electromagnetic actuator and embedded permanent magnets, the material of the housing need not be a magnetic material.

[0059] FIG. 7 is a flow diagram illustrating an exemplary embodiment of a method for measuring mass flow rate. A mass flow meter is connected to a flow of fluid to be measured. The fluid flows through at least one tubular housing. At least one actuator system vibrates a flexible plate in the at least one tubular housing in a torsional mode at a selected frequency by applying at least two oscillation torques to the flexible plate to torsionally oscillate the flexible plate. The multiple oscillations of the flexible plate are measured by at least two sensor systems configured to measure the oscillations of the flexible plate as a function of time. The sensor systems measure the oscillations at at least two positions due to the applied at least two oscillation torques. A mass flow rate of the fluid flowing through the at least one tubular housing is determined based on a phase shift between the oscillations measured at the at least two positions.

[0060] The net sum of the at least two rocking torques applied to the flexible plate may be zero or substantially zero. The at least two rocking torques may be in opposite directions, in which case the two torques cancel each other out, resulting in a significantly improved differential measurement. The sum of the at least two rocking torques may be less than the maximum of the at least two rocking torques.

[0061] Mass flow meters may be used, for example, to measure the mass flow rate of CO2, NH3, H2, LNG, or other gas streams at high pressure.

[0062] Although exemplary embodiments of the present invention have been described herein, it will be apparent to one of ordinary skill in the art that other embodiments incorporating its concepts may be used. The above and other examples are intended for illustrative purposes only, with the actual scope of the invention to be determined based on the following claims.

Claims

1. 1. A mass flow meter comprising: a tubular housing extending along a longitudinal axis, the tubular housing configured to receive a fluid flow therethrough; a flexible plate extending along at least a portion of the tubular housing, the flexible plate being at least partially coupled to an inner wall of the tubular housing on either side of a longitudinal end of the flexible plate such that the flexible plate can vibrate torsionally; at least one electromagnetic actuator system configured to apply at least two oscillation torques to the flexible plate sufficient to torsionally oscillate the flexible plate, wherein a sum of the at least two oscillation torques is less than a maximum of the at least two oscillation torques; at least two sensor systems configured to measure oscillations of the flexible plate as a function of time at positions resulting from the at least two applied oscillation torques; a mass flow meter including:

2. The mass flow meter of claim 1 , wherein a net sum of the at least two oscillating torques applied to the flexible plate is zero or substantially zero.

3. The mass flow meter according to claim 1 or 2, wherein at least two of the oscillation torques are in opposite directions to each other.

4. 10. The mass flow meter of claim 1, wherein at least one of the electromagnetic actuator systems includes an electromagnetic device disposed outside the tubular housing and a magnetizable material disposed inside the tubular housing.

5. The mass flow meter of claim 1 , wherein the electromagnetic device includes at least one coil disposed outside the tubular housing.

6. The mass flow meter of claim 4 , wherein the magnetizable material is disposed on the flexible plate.

7. The mass flow meter of claim 4 , wherein the magnetizable material includes at least one permanent magnet.

8. 5. The mass flow meter of claim 4, wherein the magnetizable material includes at least one group of permanent magnets, the permanent magnets being symmetrically arranged side by side to form a dipole.

9. The mass flow meter of claim 4 , wherein the magnetizable material includes four permanent magnets forming a quadrupole.

10. 5. The mass flow meter of claim 4, wherein the magnetizable material includes four permanent magnets forming a dipole.

11. The mass flow meter of claim 1 , wherein each of the two sensor systems includes a pickup.

12. The mass flow meter of claim 1 , wherein at least one of the electromagnetic actuator systems is adapted to also function as a sensor system.

13. 10. The mass flow meter of claim 1, wherein the tubular housing is a liner of a non-magnetizable material.

14. The mass flow meter of claim 13 further comprising a pressure housing disposed outside the liner.

15. The mass flow meter of claim 5 , wherein at least one of the coils is arranged to provide an alternating electromagnetic field that alternately magnetizes and demagnetizes the magnetizable material.

16. 1. A method for measuring mass flow through at least one tubular housing, comprising: receiving a flow of fluid through at least one of the tubular housings, wherein the tubular housing includes a flexible plate extending along at least a portion of the at least one tubular housing and at least partially coupled to an inner wall of the at least one tubular housing on either side of a longitudinal end of the flexible plate, whereby the flexible plate is capable of torsional vibration; driving the flexible plate within the at least one tubular housing to vibrate in a torsional mode at a selected frequency by applying at least two rocking torques to the flexible plate by at least one actuator system to torsionally vibrate the flexible plate, wherein a sum of the at least two rocking torques is less than a maximum value of the at least two rocking torques; measuring a plurality of oscillations of the flexible plate with at least two sensor systems configured to measure oscillations of the flexible plate as a function of time at at least two locations resulting from the at least two applied oscillation torques; determining a mass flow rate of fluid flowing through at least one of the tubular housings based on a phase shift between the oscillations measured at at least two locations; A method comprising:

17. 17. The method of claim 16, wherein the net sum of the at least two rocking torques applied to the flexible plate is zero or substantially zero.

18. 17. The method of claim 16, wherein at least two of the oscillating torques are in opposite directions.

19. CO ２ , N.H. ３ , H ２ Use of a mass flow meter according to any one of claims 1 to 15 or a method according to any one of claims 16 to 18 for measuring the mass flow rate of a fluid flow of natural gas.

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