Patent Publication Number: US-2022214200-A1

Title: Coriolis mass flow sensors having different resonant frequencies

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation of U.S. patent application Ser. No. 16/846,061, “Coriolis Mass Flow Sensors Having Different Resonant Frequencies,” filed Apr. 10, 2020. The subject matter of all of the foregoing is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     Field of the Disclosure 
     The present disclosure generally relates to Coriolis mass flow sensors (also referred to as “flow sensors” or “flow cells”), and specifically to flow sensors that have different resonant frequencies. 
     Description of the Related Arts 
     A flow process system, e.g., a process skid, usually includes a number of similar or even identical flow sensors. Cross-talk is a phenomenon where two or more flow sensors having identical operating resonant frequencies which will cause harmonic interference with each other. The cross-talk can include electrical cross-talk, mechanical cross-talk, and/or fluid pulsation based cross-talk. The cross-talk can cause inaccurate measurement by the flow sensors. A flow process system can also include pumps. Operation of the pumps can interfere with vibration within the flow sensors, which also causes inaccurate measurement by the flow sensors. 
     Conventionally, heavy enclosures are used in flow sensors to mitigate cross-talk and pump interference. These enclosures are usually made from metal, e.g., stainless steel. However, metal enclosures can be expensive and are not suitable for single use/disposable applications. Also, sterilization of flow sensors having metal enclosures is typically done by using chemicals, which is not effective and can cause malfunction of the flow sensors. Thus, improved technologies for mitigating cross-talk and pump interference are needed. 
     SUMMARY 
     Embodiments relate to a flow measurement system including a plurality of flow sensors and a plurality of connected flow paths for flow of fluids. The flow sensors can operate simultaneously to measure flow rates and/or densities of different fluids. Each flow sensor is positioned along at least one of the connected flow paths. Each flow sensor includes one or more flow tubes and a support clamping the flow tubes. The support can be cast around the flow tubes or formed around the flow tubes through over-molding. The flow tubes of different flow sensors have different resonant frequencies as a result of a difference in their tube lengths, materials, wall thicknesses, weights, other parameters relating to resonant frequency, or some combination thereof. Thus, cross-talk between the flow sensors can be reduced or eliminated, even without the use of metal enclosures. In some embodiments, each flow sensor includes a plastic enclosure and can be sterilized by using Gamma irradiation. 
     The flow measurement system can also include at least one pump that pumps a fluid into one or more of the flow sensors. The pump may operate at a frequency that is similar to or same as the resonant frequency of the flow sensor and, therefore, interfere with the operation of the flow sensor. To mitigate this interference, a dampener is positioned between the pump and the flow sensor. The fluid flows through the dampener before it enters the flow sensor. The dampener mitigates vibration of the fluid caused by the pump. 
     In some embodiments, each flow sensor includes a plastic enclosure and can be sterilized by using Gamma irradiation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The teachings of the embodiments can be readily understood by considering the following detailed description in conjunction with the accompanying drawings. 
         FIG. 1  is a diagram illustrating a flow measurement system containing a plurality of flow sensors, in accordance with an embodiment. 
         FIG. 2  is a perspective view of a flow sensor including U-shaped flow tubes, in accordance with an embodiment. 
         FIG. 3  illustrates a tube length of U-shape flow tubes, in accordance with an embodiment. 
         FIG. 4  illustrates a wall thickness of U-shaped flow tubes, in accordance with an embodiment. 
         FIG. 5  illustrates attachments mounted on U-shaped flow tubes, in accordance with an embodiment. 
         FIG. 6A  illustrates a flow sensor including a V-shaped flow tube, in accordance with an embodiment. 
         FIG. 6B  illustrates a flow sensor system including the flow sensor, in accordance with an embodiment. 
         FIG. 7  illustrates a tube length of a flow sensor including a V-shape flow tube, in accordance with an embodiment. 
         FIG. 8  illustrates an attachment mounted on a V-shaped flow tube, in accordance with an embodiment. 
     
    
    
     The figures depict embodiments of the present disclosure for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles, or benefits touted, of the disclosure described herein. 
     DETAILED DESCRIPTION 
     Embodiments relate to a flow measurement system including a plurality of flow sensors, at least one pump, and at least one dampener that are positioned along connected flow paths. Each flow sensor includes at least one flow tube, a support clamping the flow tube, and a plastic enclosure. The flow tube of each flow sensor has a different resonant frequency, so that cross-talk among the flow sensors can be reduced or even eliminated. The flow sensor can be calibrated during manufacturing and calibration factors generated during the calibration can be stored in a memory chip of the flow sensor for adjusting flow measurements by the flow sensor during operation. The flow sensor can be sterilized, e.g., by using Gamma irradiation, after the calibration. Further calibration or sterilization by a user of the flow meter may not be required. Each dampener can be installed between a pump and one of the flow sensors to mitigate interference from the operation of the pump on the operation of the flow sensor. 
       FIG. 1  is a diagram illustrating a flow measurement system  100  containing a plurality of flow sensors  110 ,  120 , and  130 , in accordance with an embodiment. The flow measurement system  100  also includes two pumps  113  and  123 , three controllers  115 ,  125 , and  135 , three dampeners  117 ,  127 , and  137 , and a mixing manifold  140 . In other embodiments, the flow measurement system  100  may include additional, fewer, or different components. For instance, the flow measurement system  100  can include more flow sensors, pumps, or dampeners. The flow measurement system  100  can be a part of a process skid, e.g., a biopharmaceutical or pharmaceutical skid. 
     A first fluid  150  and a second fluid  160  enter the flow measurement system  100 . The flow measurement system includes connected flow paths for flow of the first fluid  150  and the second fluid  160 . The first fluid enters the pump  113 , which pumps the first fluid  150  into the dampener  117 , and then flows from the dampener  117  to the flow sensor  110 . The second fluid  160  enters the pump  123 , which pumps the second fluid  160  into the dampener  127 , and then flows from the dampener  127  to the flow sensor  120 . The flow sensor  110  measures flow characteristics (e.g., mass flow rate, volumetric flow rate, flow density, etc.) of the first fluid  150 , the flow sensor  120  measures flow characteristics of the second fluid  160 . 
     The flow path of the first fluid  150  (also referred to as “first flow path”) and the flow path of the second fluid  160  (also referred to as “second flow path”) are connected at the mixing manifold  140 , where a third fluid  170  is generated and a third flow path starts. The third fluid  170  can be a mixture or blend of the first fluid  150  and the second fluid  160 . In some embodiments, the mixing manifold  140  includes another fluid or matter that can be mixed or react with the first fluid  150  and the second fluid  160  to generate the third fluid  170 . The mixing manifold  140  may include a pump that pumps the third fluid  170  to the dampener  137 . The third fluid flows from the dampener  137  to the flow sensor  130 . The flow sensor  130  measures flow characteristics of a third fluid  170 . 
     The flow sensors  110 ,  120 , and  130  can operate simultaneously. Each flow sensor includes a pair of flow tubes having different characteristics (e.g., different tube length, different wall thickness, different material, different weight, or some combination thereof) from the flow tubes of the other flow sensors and, thereby, has a different resonant frequency. Due to the different resonant frequencies, cross-talk between the flow sensors  110 ,  120 , and  130  can be reduced or even eliminated. As one example, the flow tubes of each flow sensor may be made of a different material. Examples of the material includes stainless steel, Polyetheretherketone (PEEK), Perfluoroalkoxy alkanes (PFAs), Polyvinylidene difluoride (PVDF), Polytetrafluoroethylene (PTFE), and Fluorinated ethylene propylene (FEP). Other than the differential resonant frequencies, the flow sensors  110 ,  120 , and  130  may be similar to or same as each other. 
     In some embodiments, at least two of the flow sensors  110 ,  120 , and  130  can have an identical flow rate range. A flow rate range of a flow sensor is a range of flow rates that the flow sensor measures. The flow rate range can depend on the inner diameter of one or more flow tubes of the flow sensor. For instance, when the inner diameter of the flow tube is in the range from 0.1 mm to 0.3 mm, the flow rate range of the flow sensor is 0.05 g/min to 5 g/min. When the inner diameter of the flow tube is in the range from 0.3 mm to 0.9 mm, the flow rate range of the flow sensor is 0.25 g/min to 50 g/min. When the inner diameter of the flow tube is in the range from 5.5 mm to 6.5 mm, the flow rate range of the flow sensor is 15 g/min to 3 kg/min. When the inner diameter of the flow tube is in the range from 7.8 mm to 12.5 mm, the flow rate range of the flow sensor is 90 g/min to 20 kg/ min. When the inner diameter of the flow tube is in the range from 15 mm to 60 mm, the flow rate range of the flow sensor is 1 kg/min to 250 kg/min. 
     Taking the flow sensor  110  for example, the flow sensor  110  includes two flow tubes  119  that provide a flow path of the first fluid  150  in the flow sensor  110 . The flow tubes  119  can vibrate, e.g., as driven by magnets and coils. As the first fluid  150  flow through the flow tubes  119 , Coriolis forces produce a twisting vibration of the flow tubes  119 , resulting in a phase shift of the flow tubes  119 . Also, the first fluid  150  changes the resonant frequency of the flow tubes  119 . The flow sensor  110  generates signals, e.g., electrical signals, that represent the phase shift and/or change in its resonant frequency. The signals are sent to the controller  115  through an interface connector on the flow sensor  110 . 
     In some embodiments, the flow sensor  110  also includes a memory chip (not shown in  FIG. 1 ) that stores calibration information that can be used to adjust flow measurements made by the flow sensor  100 . For instance, the calibration information can include one or more flow rate calibration factors. Each flow rate calibration factor indicates a difference between a flow rate measured by the flow sensor  110  and a reference flow rate and can be used to adjust flow rates measured by the flow sensor  110 . The calibration information can also include one or more flow density calibration factors. Each flow density calibration factor indicates a difference between a flow density measured by the flow sensor  110  and a reference flow density and can be used to adjust flow densities measured by the flow sensor  110 . The calibration information can be determined during manufacturing. 
     The flow sensor  110  can include a temperature probe (not shown in  FIG. 1 ) that measures temperatures of the first fluid  150 . The measured temperatures can be used to adjust flow rates and/or densities measured by the flow sensor  100 . 
     In the embodiment of  FIG. 1 , the flow sensors  110 ,  120 , and  130  include U-shaped flow tubes. Flow sensors in other embodiments can include flow tubes of other forms, such as V-shaped. More details about flow sensors are described below in conjunction with  FIGS. 2-8 . 
     The controller  115  receives signals from the flow sensor  110  and conducts flow analysis based on the signals. The flow analysis includes, for example, determination of flow rate based on signals representing phase shift of the flow tubes  119 , determination of flow density based on signals representing change in resonant frequency of the flow tubes  119 , detection of bubbles in the first fluid  150  based on change in flow density, determination of other flow characteristics of the first fluid  150 , or some combination thereof. 
     The controller  115  can read out the calibration information from the memory chip of the flow sensor  110  and use the calibration information in its flow analysis. For example, the controller uses a flow rate calibration factor to determine a flow rate of the fluid or uses a flow density calibration factor to determine a density of the fluid. The controller  115  can also receive temperature information from the temperature probe and use the temperature information to dynamically adjust the flow analysis. For instance, the controller can input the temperature information into a model and the model can output adjusted flow rate and/or flow density. 
     In some embodiments, the controller is a flow transmitter. In  FIG. 1 , each flow sensor is connected to a respective controller for flow analysis. The flow sensor  110 , cradle (usually made of stainless steel) of the flow sensor, and the controller  115  together can be referred to as a flow meter or a flow meter system. 
     In some embodiments, the pumps  113  and  123  are identical and the dampener  117  and  127  are identical. Taking the pump  113  as an example, it can be a diaphragm based pulsating pump (such as Quattroflow Model SU-1200 Pump, SU-4400 Pump, SU-150 Pump, SU-30 Pump and SU-5050 Pump, etc), a peristaltic pump, or other types of pumps. The flow sensor  110  measures flow characteristics based on vibration caused by the fluid flowing through the flow sensor. However, the pump  113  can operate at a frequency that is similar to or same as the resonant frequency of the flow sensor  110  and cause the first fluid  150  to vibrate or pulsate. This can degrade operation of the flow sensor  110 , such as inaccurate measurement, erratic report, etc. The pulsating operation of the pump  113  may also degrade operation of the flow sensors  120  and  130 , which is referred to destructive harmonic interference 
     The dampener  117  mitigates the destructive harmonic interference from the pump  113  on the flow sensor  110 . As the first fluid  150  flows though the dampener  117 , the vibration of the first fluid  150  at the frequency of the pump  113  can be reduced or even eliminated. 
       FIG. 2  is a perspective view of a flow sensor  200  including U-shaped flow tubes  210 , in accordance with an embodiment. The flow sensor  200  can be an embodiment of one of the flow sensors  110 ,  120 , and  130  in  FIG. 1 . In addition to the flow tubes  210  (individually referred as “flow tube  210 ”), the flow sensor  200  also includes a support  220  for the flow tubes, an electromagnetic assembly  230 , two flow path assemblies, an electronic assembly, and an enclosure assembly. The flow sensor  200  may include additional, fewer, or different components. For example, the flow sensor  200  may include a temperature assembly for measuring temperatures of the fluid or other sensor for measuring other properties of the fluid.  FIG. 1  shows two flow tubes  210 , but the flow sensor  200  may have one flow tube  210  or more than two flow tubes  210 . 
     The flow tubes  210  allow the fluid to flow through them. The flow tubes  210  vibrate as driven by the electromagnetic assembly  230 , and their vibration can be changed by the flow of the fluid. For instance, the flow tubes  210  can twist, which results in a phase shift. Also, the vibration resonant frequency can change. The mass flow rate of the fluid can be directly determined based on the phase shift. The density of the fluid can be directly determined based on the change in vibration resonant frequency. More details regarding the vibration of the flow tubes  210  and the determination of the flow rate and density are described below in conjunction with the electromagnetic assembly  230 . 
     As shown in  FIG. 2 , each flow tube  210  is a U-shaped tube having two parallel tubular legs. The fluid flows into one of the tubular legs (referred as “inlet tubular leg”) and flows out from the other tubular leg (referred as “outlet tubular leg”). The flow tube  210  can have a curvilinear shape. One advantage of such a curvilinear shape is that there are no corners so there are no abrupt changes in direction along the flow path of the fluid. Accordingly, possible accumulation of solids or any other contaminants inside the flow tubes  210  that may cause increased pressure drop or cause the flow tubes  210  to dislodge from the support  220 , which can result in particle contamination, is eliminated. In some other embodiments, the flow tube  210  can be in other shapes, such as V-shape, square, rectangular, triangular, elliptic, or straight. 
     Each flow tube  210  has a thin wall that is less than 1 mm thick, e.g., 0.05 mm to 0.60 mm thick. In some embodiments, the thickness of the wall is 5% to 16% of the outer diameter of the flow tube  210 . The outer diameter of the flow tube  210  can be in a range from 0.2 mm to 60 mm. With such a thin wall, the flow tube  210  has good accuracy even at low fluid flow rates, such as 0.05-0.5 gm/min of mass flow rate or 0.05-0.5 ml/min of volumetric flow rate. 
     In the embodiment of  FIG. 2 , the two flow tubes  210  are identical, i.e., they have identical shape and dimensions. In some other embodiments, the two flow tubes  210  can be different. The flow tubes  210  may be made of metal (such as stainless steel) or a polymer material (such as Polyetheretherketone (PEEK), Perfluoroalkoxy polymers (PFAs), polyvinylidene difluoride (PVDF), Polytetrafluoroethylene (PTFE), and Fluorinated ethylene propylene (FEP)). 
     The support  220  provides structural support for the flow tubes  210 . The support  220  may be fabricated by casting around the tubular legs of the flow tubes  210  or formed around the tubular legs of the flow tubes  210  through over-molding. The support  220  includes tubular channels through which the flow tubes  210  extend. The support  220  clamps the outer surface of the two tubular legs of each of the flow tubes  210  to hold the flow tubes  210 . Compared with other fabrication methods (e.g., injection molding), pressure exerted on the flow tubes  210  and temperature of the flow tubes  210  during the casting process is low so that deformation of the flow tubes  210  can be avoided. More details regarding the casting are described below in conjunction with  FIGS. 2-5 . 
     The support  220  is a single integral piece. It may include integrated features such as one or more port extensions  223  (individually referred as “port extension  223 ”) and isolation plates  225  (individually referred as “isolation plate  225 ”) to secure stability of the flow tubes  210 . The port extensions  223  clamp the tubular legs of the flow tubes  210 . An inner surface of each port extension  223  contacts the outer surface of the corresponding tubular leg. The isolation plates  225  connect adjacent port extensions  223 . The isolation plates  225  can establish the boundary conditions of vibration of the flow tubes  210  and maintain stability of the flow tubes  210 . The flow tubes  210  can vibrate in opposite phases (referred as “anti-phase vibration”) similar to a tuning fork and vibrate together in unison (referred as “in-phase vibration”). The natural frequencies of the anti-phase vibration and in-phase vibration can be close or even identical, resulting in vibrational excitation energy shared uncontrollably between the two vibrational modes, which causes instability of the flow tubes  210 . The vibrational boundary conditions created by the isolation plates  225  can separate the natural frequencies of the anti-phase vibration and in-phase vibration to prevent instability of the flow sensor  200 . The dimensions and thickness of the isolation plates  225  can be determined based on the frequency response characteristics of the flow tubes  210 . In some embodiments, the isolation plates  225  are integrated with the port extensions  223 , both of which are integrated with the support  220 . 
     The electromagnetic assembly  230  drives vibration of the flow tubes  210 . The electromagnetic assembly  230  includes three magnets, three coils, and two racks. The magnets are mounted on one of the two racks, which is attached on one of the flow tubes  210 . The coils are mounted to the other rack, which is attached on the other flow tube  210 . One of the three coils, e.g., the coil in the middle, can receive an alternating current, e.g., from a controller (e.g., a flow transmitter) connected to the flow sensor  200 . The alternating current causes the magnet corresponding to the coil to be attracted and repelled, thereby driving the flow tubes  210  to move towards and away from each another. 
     The electromagnetic assembly  230  also detects changes in the vibration of the flow tubes  210  due to the flow of the fluid and outputs electrical signals that can be used to measure flow rate and density of the fluid. When the fluid flows through the flow tubes  210 , Coriolis forces produce a twisting vibration of the flow tubes  210 , which results in a phase shift. As the magnets and coils are mounted on the flow tubes, the phase shift can be captured by the magnets and coils, e.g., represented by electrical signals of the coils and be used to determine a mass flow rate of the fluid. 
     The density of the fluid relates to the resonant frequency of the flow tubes  210 . The density of the fluids can thereby be determined by monitoring the change in the resonant frequency of the flow tubes  210 . The resonant frequency of the flow tubes  210  depends at least on the density of the fluid present in the flow tubes  210  and the density of a material of the flow tubes  210 . 
     The inlet flow path assembly provides a flow path for the fluid to flow into the flow tubes  210 . The inlet flow path assembly includes a Y block  242 A, a Y block adapter  244 A, a tubing elbow  246 A, a barb adapter  248 A, and a hose barb  249 A. The Y block  242 A includes a top/inlet port on one side and two bottom/outlet ports on the other side. It is formed with an internal channel that connects the top port to the two bottom ports. The outlet ports of the Y block  242 A are assembled and bonded onto the inlet tubular legs of the flow tubes  210 . The inlet port the Y block  242 A is bonded to the Y block adapter  244 A, which is bonded to one end of the tubing elbow  246 A. The tubing elbow  246 A forms an angle that is greater than 90° and provides a sweep turn to the fluid. Compared with a 90° turn, the fluid encounters a lower shear force when it flows through the tubing elbow  246 A, which protects matters in the fluid from being damaged or destructively impacted. The matters in the fluid can be organic matters, such as live cells, protein, virus, bacteria, etc. The other end of the tubing elbow  246 A is connected to the barb adapter  248 A, which is also connected to the hose barb  249 A. The hose barb  249 A can be connected to a hose as required by the user when the user installs the flow sensor  200 . More details about Y block and hose barb are described below in conjunction with  FIGS. 8-10 . 
     The outlet flow path assembly provides a flow path for the fluid to flow out from the flow tubes  210 . Similar to the inlet flow path assembly, the outlet flow path assembly includes a Y block  242 B, a Y block adapter  244 B, a tubing elbow  246 B, a barb adapter  248 B, and a hose barb  249 B, which are connected similarly as the components of the inlet flow path assembly described above. The hose barb  249 B can be connected to another hose as required by the user when the user installs the flow sensor  200 . 
     The hose barbs  249 A and  249 B are aligned in a straight line, as illustrated by the dashed line in  FIG. 2 . Such an alignment is desirable for installing the flow sensor  200  into a system (e.g., a process skid) having a flow path arranged in a straight line. It is easier to install and plumb the flow sensor  200  in such a flow path. In other embodiments, the inlet and outlet flow path assemblies can have different components and different alignments for fitting in different flow paths. 
     The components of the inlet and outlet flow path assemblies can be made from a polymer (such as PEEK) by various processes, such as machining, extruding, injection molding, bending, etc. The components can be bonded together by using a glue, such as epoxy resin. These components and the glue can be sterilized by using Gamma irradiation, e.g., they are compliant for Class VI Gamma sterilization up to 50 kGy. 
     In some embodiment, the flow sensor  200  may have inlet and outlet flow path assemblies different from these in  FIG. 2 . For instance, each flow path assembly has an end block, a barb adapter, and a hose barb. The end block connects the flow tubes  210  to another flow device (such as a hose, tubing, or other types of plumbing). A channel is formed inside the end block to allow the fluid to flow through it. The channel defines a flow path of the fluid inside the end block. The flow path of the fluid inside the end block has no right angle (90°) turns to avoid high shear force exerted on the fluid. The barb adapter may be similar to the barb adapter  248 A or  248 B and can be glued on an inner surface of the end block. The hose barb can be similar to the hose barb  249 A or  249 B. The end block, barb adapter, and hose barb may form a straight line. 
     The electronic assembly facilitates storage and transmission of data associated with the flow sensor  200 . The electronic assembly includes a printed circuit board (PCB)  253 , at least one memory chip (not shown in  FIG. 2 ) mounted on the PCB  253 , an interface cable  255  connected to the PCB  253 , and an interface connector  257  connected to or assembled on the PCB  253 . 
     The PCB  253  provides structural support for components mounted on it, such as the memory chip. The memory chip stores calibration information of the flow sensor  200 . The calibration information can be used to adjust a flow rate or density measured by the flow sensor  200 . In some embodiments, the calibration information includes a plurality of calibration factors. Each calibration factor is for adjusting a flow rate, such as a low flow rate (e.g., about 1 liter/minute), medium flow rate (e.g., about 10 liter/minute), or high flow rate (e.g., from 20 liter/minute to 200 liter/minute). The calibration information can be read out from the memory chip, e.g., by a flow transmitter, through the interface connector  257 . 
     The interface cable  255  connects the coils to the PCB  253 . In  FIG. 2 , the interface cable  255  is also assembled onto the PCB  253  that provides structural support to the interface cable  255 . More details about the electronic assembly are described below in conjunction with  FIG. 7 . 
     The enclosure assembly encloses the flow tube  210 , the support  220 , the electromagnetic assembly  230 , and the electronic assembly and provides structural support to them. The enclosure assembly, shown in cut away in  FIG. 2 , includes an enclosure cup  260  and an enclosure lid  265 . The enclosure lid  265  can be mounted on the enclosure cup  260 , e.g., through bolts. In some embodiments, the enclosure assembly is made of a polymer material, e.g., polycarbonate or PEEK. 
     The flow tubes  210  and the support  220  can be integrated and disposed as one piece. For instance, the flow tubes  210  are removably mounted on the electromagnetic assembly  230  and the support  220  are removably mounted on the enclosure lid  265 , e.g., through mounting tabs and bolts. This way, the flow tubes  210  and the support  220  can be removed from the electromagnetic assembly  230  and enclosure assembly, and new flow tubes and a new support can be mounted on the electromagnetic assembly  230  and enclosure assembly. In some embodiments, the flow tubes  210 , the support  220 , and the electromagnetic assembly  230  are integrated to be one piece and they can be disposed as one piece when needed. This design is suitable for disposable applications, such as applications where flow sensors need to be disposed to avoid contamination from fluids used in a previous process batch. With such a design, the flow tubes  210  and the support  220  can be disposed as one piece, e.g., after single use, and the other components of the flow sensor  200  can be reused. Compared with disposing the whole flow sensor  200 , this is more environmentally friendly and cost efficient. 
       FIG. 3  illustrates a tube length  315  of U-shape flow tubes  310 , in accordance with an embodiment. The flow tubes  310  (individually referred to as “flow tube  310 ”) are identical, and they can be an embodiment of the flow tubes  119  in  FIG. 1 . Each flow tube  310  includes two parallel tubular legs that are clamped by a support  320 . The support  320  includes port extensions  330  (individually referred to as “port extension  330 ”) and isolation plates  340  (individually referred to as “isolation plate  340 ”). Each tubular leg contacts an isolation plate  340  of the support  320  at a contact point  350 . The tube length  315  of the flow tubes  310  is a vertical distance from the tip  360  of the U to the contact point  350 . 
     The tube length  315  affects the resonant frequency of the flow tubes  310 . Flow sensors within a single flow measurement system can have flow tubes of different tube lengths to mitigate cross-talk between the flow sensors. The tube length difference between two flow sensors can be 0.5 mm or more. In some embodiments, the maximum tube length difference between any two flow sensors relates to the number of flow sensors in the flow measurement system and a tube length design tolerance of individual flow sensors. For instance, in an embodiment where the tube length design tolerance requires the tube length of an individual flow sensor to be in a range from 100 mm to 150 mm and the flow measurement system includes 11 flow sensors, the maximum tube length difference is 5 mm. 
       FIG. 4  illustrates a wall thickness  415  of U-shaped flow tubes  410 , in accordance with an embodiment. The flow tubes  410  can be identical and can be an embodiment of the flow tubes  119  in  FIG. 1 . Each flow tube  410  is in a form of a tube. The wall thickness  415  is the thickness of the tube wall, e.g., the difference between the inner radius of the tube and the outer radius of the tube. 
     The wall thickness  415  affects the resonant frequency of the flow tubes  410 . Flow sensors within a single flow measurement system can have flow tubes of different wall thicknesses to mitigate cross-talk between the flow sensors. The wall thickness difference between two flow sensors can be 0.1 mm or more. In some embodiments, the maximum wall thickness difference between any two flow sensors relates to the number of flow sensors in the flow measurement system, a design tolerance for the flow tube outer diameter (e.g., the maximum threshold for the flow tube outer diameter), and a design tolerance for the flow tube inner diameter (e.g., the minimum threshold for the flow tube inner diameter). 
       FIG. 5  illustrates attachments  510  mounted on U-shaped flow tubes  520 , in accordance with an embodiment. The two flow tubes  520  are identical, and the two attachments  510  are identical. Each of the attachments  510  (individually referred to as attachment  510 ) is mounted on one of the flow tubes  520  (individually referred to as flow tube  520 ) to add weight on the flow tube  520 . With the add-on weight, the flow tubes  510  can have a different resonant frequency due to the change in weight. In the embodiment of  FIG. 5 , the attachment  510  is in a form of a short tube that encloses a portion of the flow tube  520  including the bottom of the U. The inner diameter of the attachment  510  is the same as or slightly larger than the outer diameter of the flow tube  520 . In other embodiments, the attachment  510  can be in other forms, such as a piece attached on the bottom of the U, etc. The attachment  510  may be mounted at different positions on the flow tube  520 . 
     In some embodiments, the weight of the attachment  510  is at least 0.1 gram, e.g., in a range from 0.1 gram to 1 gram. In a flow measurement system containing multiple flow sensors, one of the flow sensors may have no attachment mounted on it and the other flow sensors may have attachments of different weights so that all the flow sensors have different weights and different resonant frequencies from each other. Taking the flow measurement system  100  in  FIG. 1  for example, in one embodiment, the flow sensor  110  includes no attachment mounted on its flow tubes  119 , but the flow sensor  120  includes the attachments  510 , and the flow sensor  130  includes attachments heavier than the attachments  510 . The weight difference between any two of the flow sensors  110 ,  120 , and  130  can be at least 0.1 gram so that the flow sensors  110 ,  120 , and  130  have different resonant frequencies from each other. 
       FIG. 6A  illustrates a flow sensor  600  including a V-shaped flow tube  610 , in accordance with an embodiment. The flow sensor  600  also includes two supports  620  (individually referred as “support  620 ”), a magnet assembly, and an enclosure.  FIG. 6B  illustrates a flow sensor system  650  including the flow sensor  600 , in accordance with an embodiment. The flow sensor system  650  also includes a cradle  660  where the flow sensor  600  can be mounted. 
     The cradle can be made of stainless steel. The cradle  660  maintains a position of the flow sensor  600  and prevents impact of external vibration on the flow sensor  600 . The cradle can be made of metal, e.g., stainless steel. The cradle  660  includes a coil assembly, which includes sense coils  673  and  675  and a drive coil  677 , and a locking assembly, which includes two latches  682  and two grooves  688 . 
     The flow tube  610  has a V shape. It includes two ports  613  and  615  at opposite ends. A fluid can enter the flow tube from one of the two ports  613  and  615  and exit from the other port. The fluid encounters a smaller pressure drop in the V-shaped flow tube  610 , compared with a U-shaped flow tube. The flow tube  610  has a thin wall and small inner diameter. The thickness of the wall can be less than 1 mm, e.g., in a range from 0.05 mm to 0.60 mm. The inner diameter of the flow tube  610  can be 0.10 mm to 0.81 mm. Such dimensions make the flow tube  610  suitable for measuring low flow rates, e.g., flow rates from 0.05 gm/min to 0.5 gm/min. Also, the flow rate turndown of the flow sensor  600  (i.e., the operation range of the flow sensor) can exceed  120  :1, which is better than typical flow rate turndowns. 
     As shown in  FIG. 6B , each of the two ports  613  and  615  can be locked in a groove  688  of the locking assembly of the cradle by using a latch  682 . The locking assembly can prevent the flow tube  610  from rotating. In some embodiments, the flow tube  610  is fabricated by extruding a polymer (e.g., PEEK) to form a straight tube and then bending the tube into the desired V-shape. 
     The two supports  620  in  FIG. 6A  provides structural support to the flow tube  610 . Each support  620  has a form of a ring. Each support  620  clamps the flow tube  610 , and the flow tube  610  extends through the two supports  620 . The supports  620  can be fabricated by casting around the flow tube  610 . Other fabrication techniques, e.g., injection molding, cannot form the supports  620  without deforming the flow tube  610 . In some embodiments, the supports  620  are identical. 
     The magnet assembly includes a drive magnet  642 , a drive magnet mount  644 , two sense magnets  646 , and two sense magnet mounts  648 . The drive magnet  642  is glued onto the drive magnet mount  644 , and the sense magnets  646  are glued to the sense magnet mounts  648 , e.g., by using Loctite M-31CL epoxy. The drive magnet mount  644  and sense magnet mounts  648  are attached on the flow tube  610 . The drive magnet  642  couples with a drive coil  677  of the coil assembly in the cradle  660  for driving the flow tube  610  to vibrate, e.g., at a fixed resonant frequency. The sense magnets  646  couple with sense coils  673  and  675  shown in  FIG. 6B  to generate two electrical signals indicating change in the vibration of the flow tube  610  due to Coriolis forces and the phase shift between the two electrical signals which corresponds to the mass fluid flow rate through the flow tube(s)  610 . 
     The enclosure includes two halves  640  and  645 . It encloses a portion of the flow tube  610 , e.g., the portion between the supports  620 , and the magnet assembly. In some embodiments, the flow tube  610 , the supports  620 , and the magnet assembly (or the flow tube  610  and the supports  620 ) are integrated. For instance, they can be inserted into or removed from the enclosure as one piece. They can also be disposed as one piece after single use. In some embodiments, the flow sensor  600  itself, including the enclosure, can be installed on or removed from the cradle  660  as one piece and be disposed after single use. 
       FIG. 7  illustrates a tube length  715  of a flow sensor  700  including a V-shape flow tube  710 , in accordance with an embodiment. An embodiment of the flow sensor  700  is the flow sensor  600  in  FIG. 6 . Part of the flow tube  710  is enclosed in a V-shaped enclosure  720 . The flow sensor  700  is mounted on a cradle  730 . The tube length  715  is a distance from the bottom of the enclosure  720  to the top of the cradle  730  in the Y direction. 
     The tube length  715  affects the resonant frequency of the flow sensor  700 . Flow sensors that operate within a single flow measurement system can have flow tubes of different tube lengths to mitigate cross-talk between the flow sensors. The tube length difference between two flow sensors can be 0.5 mm or more. In some embodiments, the maximum tube length difference between any two flow sensors is determined by the number of flow sensors in the flow measurement system and a tube length design tolerance of individual flow sensors. For instance, in an embodiment where the tube length design tolerance design tolerance requires the tube length of an individual flow sensor to be in a range from 100 mm to 150 mm and the flow measurement system includes 11 flow sensors, the maximum tube length difference is 5 mm. 
     The tube length  715  can be determined based on an angle  740  of the V. V-shape flow sensors having different tube lengths may have different angles. For instance, a V-shape flow sensor having a larger tube length has a smaller angle compared with a V-shape flow sensor having a smaller tube length. 
       FIG. 8  illustrates an attachment  810  mounted on a V-shaped flow tube  820 , in accordance with an embodiment. The attachment  810  adds weight on the flow tube  820 . With the add-on weight, the flow tube  820  can have a different resonant frequency due to the change in weight. In the embodiment of  FIG. 8 , the attachment  810  is in a form of a rectangular piece that clamps the tip of the V. In other embodiments, the attachment  810  can be in other forms, such as a short V-shape tube that encloses a portion of the flow tube  820 . The attachment  810  may be mounted at different position on the flow tube  820 . 
     In some embodiments, the weight of the attachment  810  is at least 0.1 gram, e.g., in a range from 0.1 gram to 1 gram. In a flow measurement system containing multiple flow sensors, one of the flow sensors may have no attachment mounted on it, another flow sensor may have the attachment  810  mounted on it, and yet another flow sensor may have an attachment heavier than the attachment  810 . 
     The language used in the specification has been principally selected for readability and instructional purposes, and it may not have been selected to delineate or circumscribe the inventive subject matter. It is therefore intended that the scope of the disclosure be limited not by this detailed description, but rather by any claims that issue on an application based hereon. Accordingly, the disclosure of the embodiments is intended to be illustrative, but not limiting, of the scope of the disclosure, which is set forth in the following claims.