Patent Publication Number: US-8534138-B2

Title: Chordal gas flowmeter with transducers installed outside the pressure boundary, housing and method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This is a continuation-in-part application of U.S. patent application Ser. No. 12/927,616 filed Nov. 19, 2010. 
    
    
     FIELD OF THE INVENTION 
     The present invention is related to a flowmeter that determines gas flow rates in a pipe by means of ultrasonic transducers that send and receive signals into and from the gas flow through a window made of a pressure containing material that is in acoustic communication with a channel in which the gas flows. (As used herein, references to the “present invention” or “invention” relates to exemplary embodiments and not necessarily to every embodiment encompassed by the appended claims.) More specifically, the present invention is related to a flowmeter that determines gas flow rates in a pipe with ultrasonic transducers that send and receive signals into and from the gas flow through a window made of a pressure containing material that is in acoustic communication with a channel in which the gas flows where the transducers are disposed in housings that acoustically isolate the transducers so as to improve the signal-to-noise ratio of the received acoustic signal. 
     BACKGROUND OF THE INVENTION 
     This section is intended to introduce the reader to various aspects of the art that may be related to various aspects of the present invention. The following discussion is intended to provide information to facilitate a better understanding of the present invention. Accordingly, it should be understood that statements in the following discussion are to be read in this light, and not as admissions of prior art. 
     Ultrasound transducers are used to transmit and receive ultrasonic signals in a flowmeter system. Several problems were solved by using the present invention, they are: The ability to remove or repair transducers from existing ultrasonic flow meters required either depressurizing the pipe gas line or the use of special tools for transducer replacement; transducers not in direct contact with the gas contained in the pipe usually have poor transducer performance resulting in poor signal detection for gas meters. Current ultrasonic gas meters use gas “wetted” transducers, that is, the transducer itself is in direct contact with the gas and cannot be removed without special tools or the elimination of the pressure in the pipe. Traditional transducer housings that put the transducer outside of the pipe pressures, such as those are used in liquid meters, have not been used since the acoustic losses through the housings combined with the noise produced by the mounting of the transducer housings make the acoustic signals unusable. The traditional transducer housings do not work in a gas environment for two reasons. First, conventional transducer housings had thick metal windows that poorly match the acoustic impedance of gas and therefore would not transmit sound into the gas. Second, the traditional transducer housings are rigidly attached to the meter body. These rigid attachments provide pathways for sound to be transmitted through the meter body and not through the gas resulting in poor signal to noise ratios. 
     The current ultrasonic gas meters have their wetted transducers exposed to the gas which can contain hydrogen sulfide or other contaminants. Hydrogen sulfide can over time deteriorate transducers made of conventional solder joints and epoxies for electrical and mechanical connections within the transducer. In current ultrasonic gas meters, a metal seal is placed behind the transducer in order to maintain the pipe pressure and to prevent gas from leaking out. So if a transducer fails, the transducer has to be replaced using special tools that prevent the transducer from bursting out of the flowmeter at high speeds due to pipe gas pressure. This may be deadly to the replacer if the tools are improperly handled because the transducer becomes a projectile under pipe gas pressure. In addition, the escaping gas is usually highly flammable, presenting an extreme hazard to the replacer and others nearby. If the gas pipeline/process is depressurized to replace transducers for safety reasons the pipeline flow ceases causing lost revenue. 
     Current gas meter transducers use either a monolithic PZT ceramic transducer or a Tonpilz transducer. These transducers suffer from poor bandwidth, poor signal to noise ratio and radial modes in the 100 to 300 kHz frequency range, the preferred ultrasonic operating frequency range for gas meters. As a result, the received signals can be very distorted. This results in poor transit time measurements and poor accuracy of a gas flowmeter Current gas meters also have metal to metal contact between parts even with wetted transducers when cases enclosing the transducers are made of metal so the flow meter can suffer from poor signal to noise ratio due to acoustic noise of the system. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention pertains to a flowmeter for measurement of gas where accuracy and reliability are essential. The flowmeter measures gas flow rates in a pipe having a channel disposed in the pipe through which gas in the pipe flows and plane waves generated by multiple upstream ultrasonic transducers and multiple downstream ultrasonic transducers propagate. The arrangement of the transducers defines two crossing planes but may have more or fewer. An important feature of this meter is that the transducer elements can be safely checked or replaced without special tools and without depressurizing the line because of housings which hold the transducer and contain the pipe pressure. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       In the accompanying drawings, the preferred embodiment of the invention and preferred methods of practicing the invention are illustrated in which: 
         FIG. 1  shows a flowmeter of the present invention. 
         FIG. 2  shows a flowmeter top section of two crossing planes (A and B). 
         FIG. 3  shows a flowmeter cross section of along either Plane A or Plane B. 
         FIG. 4  shows a gas meter arrangement. 
         FIG. 5   a  shows a gas transducer. 
         FIG. 5   b  shows an exploded view of a gas transducer. 
         FIG. 6  shows the transformer application. 
         FIGS. 7   a  and  7   b , which together are one continuous drawing, show a demonstration of transit time flow meter performance. 
         FIGS. 8   a  and  8   b , which together are one continuous drawing, show error vs. velocity in regard to the claimed invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to the drawings wherein like reference numerals refer to similar or identical parts throughout the several views, and more specifically to  FIGS. 1-3  thereof, there is shown a flowmeter  10  for detecting gas flow rates in a pipe  12 . The flowmeter  10  comprises a container  11  configured to be attached to the pipe  12  having a channel  17  through which the gas flows, and a plurality of recesses  15  that extend through the container  11  and a plurality of housings  14 . Each recess  15  has a housing  14  which contains pressure in the channel  17 . Each housing  14  has a window  24  that is in acoustic communication with the channel  17 . The flowmeter  10  comprises a plurality of transducers  32 , with one transducer  32  of the plurality of transducers  32  disposed in each recess  15 . The transducers  32  transmit ultrasonic signals into and receive ultrasonic signals from the channel  17  through the window  24  in the housing  14  in which a transducer  32  is disposed. The flowmeter  10  comprises a controller  20  in electrical communication with the plurality of transducers  32  which determines the gas flow rate through the channel  17  by measuring transit times of signals transmitted by and received by the transducers  32 . 
     The window  24  may have a thickness less than ¼ wavelength of ultrasound in the window&#39;s material. The window  24  thickness may be about 1/10 wavelength of ultrasound in the window&#39;s material. One transducer  32  of the plurality of transducers  32  may be disposed in each housing  14  disposed in each recess  15 . The housing  14  may be a pressure boundary which contains the pressure in the channel  17  and essentially prevents gas in the channel  17  from escaping into the housing  14 . The housing  14  forms a gas tight seal with the channel  17 . 
     The transducers  32  may be removed from the recesses  15  without having to depressurize the pipe  12  or having to use an extraction tool that removes the transducers  32  through a pressure containing component that would contain the pressure in the channel  17 . The ultrasonic signals transmitted and received by the transducers  32  may define a first path in a first plane and a second path in a second plane which paths cross in the channel  17 . 
     The flowmeter  10  may include acoustic isolators  22  which acoustically isolate the transducer housings  14  from the container  11 . The transducer  32  may couple to the window  24 . The window  24  is made of metal or plastic. The window  24  may be made of titanium, PEEK or PPS. 
     Each transducer  32  may be a broad band piezoelectric composite transducer  32  with a coupling coefficient greater than 0.7 out of 1 and an acoustic impedance of less than 34 Mrayls. 
     The present invention pertains to a housing  14 , as shown in  FIG. 4 , for an ultrasonic transducer  32  for a flowmeter  10  which is inserted into a recess  15  of a container  11  through which gas flows. The housing  14  comprises a shell  25  in which the transducer  32  is disposed. The shell  25  has an outer surface and a flange  34  that extends from the outer surface of the shell  25  and a plurality of acoustic ribs  26  disposed in proximity to an end of the shell  25  from which signals are emitted by the transducer  32 . The shell improves the signal-to-noise ratio to greater than 100:1, the ribs attenuate all non-gas paths of sound by at least 25%. 
     The housing  14  may include an acoustic isolator  22  disposed about the housing  14 , which isolator contacts the container  11  and the housing  14  when the transducer  32  is disposed in the recess  15  of the container  11 , with the acoustic isolator  22  disposed between the container  11  and the housing  14  so the housing  14  does not contact the container  11 . The acoustic isolator  22  may include discs disposed about the flange  34  of the housing  14 . The discs may be made of plastic, syntactic foam or rubber. Impedance matching material may not be used on the exterior surface to improve transmission of signals from the transducer  32  into the gas, but uses a window  24  thickness less than ¼ wave length, which makes the window  24  acoustically transparent. There may be no metal to metal contact between the housing  14  and the container  11 . 
     The present invention pertains to a method for detecting gas flow rates in a pipe  12 . The method comprises the steps of transmitting ultrasonic signals from a plurality of transducers  32  disposed in recesses  15  in a container  11  attached to the pipe  12  through a window  24  made of metal of each recess  15  into a channel  17  of the container  11  in which the gas flows, with one transducer  32  of the plurality of transducers  32  disposed in each recess  15  and the window  24  in acoustic communication with the channel  17 . There is the step of receiving ultrasonic signals from the channel  17  through the windows  24  by the transducers  32  in the recesses  15 . There is the step of determining the gas flow rate through the channel  17  by measuring transit times of the signals transmitted by and received by the transducers  32  with a controller  20  in electrical communication with the plurality of transducers  32 . 
     The window  24  may be a pressure boundary which contains the pressure in the channel  17  and prevents gas in the channel  17  from escaping into the housing  14 , the window  24  forming a gas tight seal with the housing  14 , and there may be the step of replacing a transducer  32  without depressurizing the channel  17  or without using an extraction tool that removes a transducer  32  through a pressure containing component that would contain the pressure in the channel  17 . 
     The transmitting step may include the step of transmitting ultrasonic signals by the transducers  32  along a first path in a first plane and a second path in a second plane which cross in the channel  17  and the receiving step may include the step of receiving ultrasonic signals by the transducers  32  from the first path and from the second path. There may be the step of acoustically isolating housings  14  in which the transducers  32  are disposed in the recesses  15  from the container  11  with acoustic isolators  22 . There may be the step of applying a force against the transducer  32  to hold the transducer  32  in contact with the window  24 . 
     The transmitting step may include the steps of generating with an upstream ultrasonic transducer  32  of the first path plane waves that propagate through the channel  17  and are received by a downstream ultrasonic transducer  32  of the first path; producing a downstream transducer  18  signal with the downstream transducer  18  from the plane waves the downstream transducer  18  receives; generating with the downstream ultrasonic transducer of the first path plane waves that propagate through the channel  17  and are received by the upstream ultrasonic transducer of the first path; producing an upstream transducer  16  signal with the upstream transducer  16  from the plane waves the upstream transducer  16  receives; and determining with the controller  20  the gas flow rate from transit times of the signals generated and received by the upstream transducer  16  and downstream transducer  18 . 
     The replacing step may include the step of replacing the transducer  32  without using an extraction tool that removes the transducer  32  through a pressure containing component that provides a gas tight, pressure-bearing enclosure, within which the transducer  32  can be unfastened from the container  11  and allowing the gas in the channel  17  to fill the enclosure without leaking into an external environment about the container  11 . The replacing step may include the step of replacing the transducer  32  without using a valve to seal the recess  15  from which the transducer  32  is removed thereby allowing the enclosure within the extraction tool to be vented. 
     Unlike the present invention, in a design in which the transducer itself is immersed in the gas, the extraction tool performs the following functions:
         1. It provides a gas tight, pressure-bearing enclosure, within which the exterior of the transducer assembly can be unfastened from the container (thereby breaking the normal pressure barrier) and allowing the enclosed gas to fill the extraction tool enclosure without leaking into the external environment.   2. It provides the means to withdraw the transducer assembly within the extraction too.   3. It provides the means—usually a valve—to close off the opening left vacant by the removal of the transducer assembly, thereby allowing the enclosed space within the extraction tool to be vented and the enclosed (presumably defective) transducer assembly to be removed.   4. It provides the means to put in place a fully functional transducer assembly within the enclosed space of the extraction tool.   5. It provides the means to insert the new transducer into the container, fasten it in place and test the transducer assembly/container joint for tightness, whereupon the extraction tool can be removed.       

     The present invention pertains to a transducer  32 , as shown in  FIG. 5 , for an ultrasonic flowmeter  10 . The transducer  32  comprises a case  58 . The transducer  32  comprises a broad band piezoelectric composite  50  disposed in the case  58  with a coupling coefficient greater than 0.7 out of 1 and an acoustic impedance of less than 34 Mrayls. 
     The transducer  32  may include a transformer  30  which matches the transducer&#39;s electrical impedance. 
     In another embodiment, the housing  14  and transducer  32  described herein, as well as the overall technique described herein, may be applied directly to a pipe  12  where the recesses  15  are formed in the pipe  12  and the housings  14  with transducers  32  are inserted into the recesses  15  in the pipe  12  itself. 
     In the operation of the invention, the flowmeter  10  is capable of measuring gas flow rates with ultrasonic transit time technology. The application is specifically applied to natural gas metering. A novel aspect of the flowmeter  10  is the transducer housing  14  which has a pressure containing window  24  less than 1/10 of a wavelength of the ultrasound of the window  24  material in thickness but nevertheless complies with the strength and tightness requirements imposed by the full pressure of the gas on its exterior. The preferred window  24  is a titanium window  24 . The titanium window  24  is thin enough such that it is nearly acoustically transparent, it serves as a hermetic seal from the natural gas which may contain hydrogen sulfide or other contaminants, and it acts as a pressure barrier to the gas in the pipe  12 . A wavelength (λ) of titanium at 200 kHz is 30.35 mm when the speed of sound in the material is 6070 m/s. The titanium window  24  is laser welded to the titanium transducer housing  14 . Laser welding is a low heat process compared to torch welding therefore there is no damage to the mechanical integrity of the λ/10 thick (3 mm) titanium window  24  to the housing  14 . The window  24  serves to maintain the mechanical integrity of the transducer housing  14  by being a pressure barrier from the pressurized gas. Typical operation pressure ratings range from below 475 psi (ANSI 150) to 3,705 psi (ANSI 1500). The operating temperatures range from −40 C to 100 C. The gas flow meter has replaceable transducers  32  without having to depressurize the line. All transducer housings  14  have acoustic ribs  26  which are spaced λ/8 to λ/4 apart to isolate and cancel the acoustic noise of the transducer housing  14  and breakup the transducer housing  14  resonance. In addition, all transducer housings  14  are acoustically isolated from the meter body by acoustic isolators  22 . 
     Special transducers  32  have been fabricated using composite piezoelectric technology. The composite piezoelectric material has a k t  of 0.75 and low Z of 17 MRayls. This enables broad band performance for an easily detectable leading edge for precise time measurements. Each transducer  32  uses a 7:1 impedance matching transformer  30  which improves signal strength by 17 dB. This transducer arrangement coupled to a titanium window  24 , λ/10 is desired for performance of an ultrasonic gas meter that uses a window  24  as a pressure barrier greater than 3,705 psi. 
     A flowmeter  10  for detecting gas flow rates in a pipe  12  preferably includes multiple paths disposed in the pipe  12  through which gas in the pipe  12  flows. The upstream transducer  16  is in contact with the titanium window  24  within the transducer housing  14  and positioned such that plane waves generated by the upstream transducer  16  propagates through the channel  17 . The downstream transducer  18  is acoustically isolated from the pipe  12  and positioned such that plane waves generated by the downstream transducer  18  propagate through the channel  17  and are received by the upstream transducer  16 , which produces an upstream transducer  16  signal that is provided to a controller  20 . The downstream transducer  18  receives the plane waves from the upstream transducer  16 , and provides a downstream transducer  18  signal that is provided to the controller  20 . The flowmeter  10  includes a signal processor, otherwise known as the controller  20 , in communication with the upstream and downstream transducers  16 ,  18  which determines the gas flow rate through the channel  17  by measuring transit times of signals transmitted by and received by the transducers. 
     Referring to  FIGS. 1-3 , the flowmeter  10  comprises a channel  17  disposed in the pipe  12  through which gas in the pipe  12  flows. The flowmeter  10  comprises multiple paths. Multiple upstream ultrasonic transducers  16  within transducer housings  14  acoustically isolated from the pipe  12  and positioned so plane waves generated by an upstream transducer  16  propagate through the channel  17 . Each path comprises a downstream ultrasonic transducer  18 , within a transducer housing  14  acoustically isolated from the pipe  12  and positioned so plane waves generated by the downstream transducer  18  propagate through the channel  17  and are received by the upstream transducer  16  which produces an upstream transducer  16  signal. The downstream transducer  18  receives the plane waves from the upstream transducer  16  and provides a downstream transducer  18  signal. The flowmeter  10  comprises a controller  20  in communication with the upstream and downstream transducers  16 ,  18  which determines the gas flow rate through the channel  17  by measuring transit times of signals transmitted by and received by the transducers. 
     The transducer housing  14  is preferably made of titanium which is corrosion resistant to natural gas contaminants such as hydrogen sulfide. The upstream transducer  16  and the downstream transducer  18  are coupled to a window  24  within the transducer housing  14 . The transducer housings  14  are acoustically isolated by acoustic isolators  22  which contact the pipe  12 . The window  24  forms a seal with the transducer housing  14  preventing gas in the pipe  12  leaking into the transducer housing  14 . The window  24  which is inclusive of the transducer housing  14  is sealed via laser welding such that hydrogen sulfide cannot leak inside. The transducer  32  couples to the acoustic window  24  using a couplant, preferably a silicone grease. A spring assembly  28  applies pressure to the transducer  32  in order to couple the ultrasonic signal more effectively to the window  24 . A spacer  38  and compression nut  40  compress the spring assembly  28  such that at least 100 psi is applied to the transducer  32 . O-rings  42  are placed around the transducer housing  14  and a bushing  44  in order to create another gas tight seal between the transducer housing  14  and the pipe  12 . The bushing  44  provides mechanical support for the transducer housing  14  and positions the transducer housing  14  within the container  11 . The load nut  46  and lock nut  48  secure the transducer housing  14  to the container  11  by applying pressure to the acoustic isolators  22  and prevents the transducer housing  14  from being forced out of the container  11  under pipe pressure. There is a gas gap radially disposed between the transducer housing  14  and load nut  46  and lock nut  48  so there is no metal to metal contact between the container  11  and the transducer housings  14 . It should be noted that basically, the container  11  with the channel  17  is an extension of the pipe  12  and for all intent and purpose in regard to this invention is considered a part of the pipe  12 . 
     Shown in  FIG. 5  is a transducer  32  consisting of a wearface  56 , piezocomposite  50  and delay line  36  that is potted in a brass case  58  with a load cylinder  52  and a cap  54 . The wearface  56  is made of impedance matching material preferably of high purity alumina (Al 2 O 3 ) greater than 96% with a density of around 3.64 gm/cm 3 , a hardness greater than 1000 Knoops and the thickness &lt;&lt;λ. The piezocomposite  50  is a 1-3 composite material preferably made from PZT-5H and epoxy (Smart Material Inc., Sarasota, Fla.). The volume fraction of PZT-5H is around 50% this produces a high coupling coefficient, k t  of 0.75 out of 1. Having a high coupling coefficient is necessary because it improves the signal to noise ratio of the ultrasonic signal. The acoustic impedance known as Z=ρv, where density ρ (kg/m 3 ) and velocity v (m/s), is around 17 MRayls. The delay line  36  serves two purposes: as a reflection delay line  36  and as an acoustic attenuator. The delay line  36  is made of metal filings filled with epoxy of at a low volume fraction, typically 15%. The delay line  36  is long enough such that the reflection is more than several wavelengths away from the piezoelectric element. A typical speed of sound for the delay line  36  is 1277 m/s. A wave length in a delay line  36  at 200 kHz is 6.3 mm. A typical length of a delay line  36  for this application is thirty two mm. Therefore, once a signal is received by the transducer  32  it takes a reflection twice the time of a delay line  36  before the reflection is received as reverberation by the transducer  32 . In this case the reflection occurs fifty microseconds later than the detectable signal. Attenuation in the delay line  36  is typically, 2.29 dB/cm, so round trip attenuation of a reflected signal would be 14.65 dB. In order to make electrical connections to piezocomposite  50 , a (+) wire  60  and a (−) wire  62  are soldered to silver foil which is bonded to the piezocomposite  50  using silver epoxy. The entire transducer  32  is potted with non conductive epoxy in order to encapsulate and insulate all components. 
     Depending on the specific operating conditions of the meter, a range of frequencies can be used, from 100 kHz to 500 kHz. A broad band composite transducer  32  is preferred for metering gas. Unique to gas applications, when flow rate &gt;60 feet/second is present the acoustic wave is distorted by the flow and the wave front is received by a transducer  32 . If a broad band composite transducer  32  is used instead of a typical narrow band monolithic PZT transducer or Tonpilz transducer there is less distortion of the received acoustic wave. The upstream and downstream transit time signals are detected in order to make a flow measurement by the controller  20 . The composite transducer  32  has a rising edge of the received ultrasonic pulse that can be more accurately detected by the controller  20  thus calculating a more accurate transit time measurement. 
     An electrical transformer  30  is put in series with each transducer  32  to match the electrical impedance of the transducer  32  to that of the electronics and cables,  FIG. 6 . The electronics are represented by an AC voltage V in series with a transformer, L 1 , the first winding of the transformer and the impedance Z of a transducer is in series with the secondary winding of the transformer, L 2 . The equivalent circuit is shown when the electronics, V, are directly in series with the impedance Z of the transducer and the impedance is reduced by the number of turns squared, N 2 . The electrical impedance of each transducer  32  (4900Ω) is reduced N 2  by 49 to 100Ω in order to match to the 100Ω transmit and receive electronics. Each transducer  32  is spring loaded by the spring assembly  28  inside the transducer housing  14  in order for the wearface  56  to make sufficient mechanical contact to the window  24 . Grease is used for acoustic coupling of the transducer  32  to the window  24 . 
     The transducer housing  14  has acoustic ribs  26 , acoustic isolators  22 , and a window  24 . The acoustic ribs  26  are spaced λ/4 to λ/8 apart in order to cancel acoustic noise. During the excitation of an ultrasonic transducer  32  which is coupled to the window  24 , a low amplitude acoustic wave either longitudinal or shear propagates along the transducer housing  14 . The wave propagates according to the wave equation: 
     
       
         
           
             
               
                 
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     When a longitudinal or shear wave is reflected from a rib interface its phase changes ω=π or 180 degrees ˜t=T/2 or x=λ/2, it then interferes with an incoming wave to destructively cancel it. Therefore,
 
 y ( x,t )= y   1 ( ct−x )− y   1 ( ct+x )=0
 
     Since the ambient noise generated in the transducer housing  14  can be at many frequencies and amplitudes, cancellation is not complete. The noise cancellation improves the signal to noise ratio of the received ultrasound signal up 10 dB. 
     The acoustic isolators  22  are preferably made of Polyether Ether Ketone (PEEK) disks (thickness &gt;λ) that fit around the transducer housing  14  between a flange  34 . Other low acoustic impedance materials may be used, for example syntactic foam. The acoustic isolators  22  are in contact with the pipe  12  but the flange  34  is not. The total noise loss from noise attenuation can be calculated using transmission equations using the following formula: 
     
       
         
           
             
                 
             
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     Where P o  is pressure output, P in  pressure input, Z peek , the acoustic impedance of PEEK is 3 Mrayls, Z steel , the acoustic impedance of Steel is 45 Mrayls, and Z Ti , the acoustic impedance of Titanium is 30 Mrayls. The loss calculation is 22 dB but more loss is possible since the PEEK, steel and titanium parts are pressed together and not mechanically bonded. 
     The window  24  is less than wavelength thick such that it becomes virtually acoustically transparent at operating frequencies. According to transmission line theory the acoustic impedance of material becomes closer to that acoustic impedance the thinner it becomes. When the thickness of the titanium window l is λ/10 of titanium, the acoustic energy transmits through the window  24  into gas without signal distortion. The equation for transmission line theory is: 
     
       
         
           
             
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     Z A : Acoustic Impedance of Air 
     Z Ti : Acoustic Impedance of Titanium 
     Z w : Acoustic Impedance of the window  24  of thickness  1   
     C Ti : Speed of Sound in Titanium 
     f: Frequency of ultrasound wave 
     λ=C Ti /f: Wavelength in Titanium 
     β=2π/λ 
     Since titanium has lower acoustic impedance than steel (typical material of gas pipes), it is the best metal to use acoustically that is resistant to hydrogen sulfide and other contaminants. 
     The ultrasonic flow meter arrangement  10  uses multiple transducers  32  each within a transducer housing  14 , there are multiple chordal paths distributed in spacing according to numerical integration rules in order to accurately sample the velocity profile in a pipe  12 . A path consists of one transducer  32  upstream from the gas flow and another is downstream from the gas flow, both transducers  32  transmit and receive signals. The difference in transit times between the upstream and downstream signal is used to calculate a velocity per path. The path velocities are integrated by the controller  20  to calculate a flow rate. These equations can be modified for Mach number. 
     For C&gt;&gt;V: 
     L: path length 
     L chord : chord path length 
     v axial : axial gas velocity 
     Q: Volume flow 
     D: diameter of opening 
     φ: path angle 
     t 1 : upstream transit time 
     t 2 : downstream transit time 
     Δt: t 2 −t 1    
     V path : gas velocity per path 
     w i : Weighting factor per path 
     
       
         
           
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               V 
               path 
             
             = 
             
               
                 V 
                 axial 
               
               ⁢ 
               sin 
               ⁢ 
               
                   
               
               ⁢ 
               φ 
             
           
         
       
       
         
           
             
               L 
               path 
             
             = 
             
               
                 L 
                 chord 
               
               
                 cos 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 φ 
               
             
           
         
       
       
         
           
             
               
                 V 
                 axial 
               
               ⁢ 
               
                 L 
                 chord 
               
             
             = 
             
               
                 1 
                 2 
               
               ⁢ 
               
                 
                   
                     L 
                     path 
                     2 
                   
                   ⁢ 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   t 
                 
                 
                   
                     t 
                     2 
                   
                   ⁢ 
                   
                     t 
                     1 
                   
                   ⁢ 
                   tan 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   φ 
                 
               
             
           
         
       
     
     In order directly to measure volumetric flow, one must integrate the axial fluid velocity over a cross section normal to the pipe  12  axis. In order to solve for the speed of sound in gas and gas velocity, the upstream and downstream transit times need to be measured via a controller  20 . The controller  20  computes the transit time differences between the upstream and downstream transit times per path length. The V axial L chord  product is exactly the line integral of V axial dy at a chord location. The V axial L chord  product is calculated for each location x 1 , x 2 , x 3 , x 4  in  FIG. 3 , effectively dividing the pipe  12  cross-section into four segments per plane. The effective width of each segment is a fraction of the internal diameter, D, measured along the x axis. Either Legendre or Jacobian/Chebychev spacing or weighting are used for chordal flowmeters, the path locations y, and weighting factors w were not chosen arbitrarily but comply with numerical integration rules. The spacing is measured from the center of the pipe  12 , the spacing y 1 , y 2 , −y 1 , −y 2  is shown in Table 1 along with the weighting factors. The length of each chord is known either by calculation or measurement. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Flowmeter Path Spacing and Weighting Factors 
               
            
           
           
               
               
               
               
               
            
               
                 Loca- 
                   
                   
                 Jacobian/ 
                 Jacobian/ 
               
               
                 tion 
                 Legendre 
                 Legendre 
                 Chebychev 
                 Chebychev 
               
               
                 y-axis 
                 Spacing 
                 weighting 
                 Spacing 
                 weighting 
               
               
                   
               
               
                 y 1   
                  .34 * Diameter/2 
                 .77 
                  .30 * Diameter/2 
                 .72 
               
               
                 y 2   
                  .86 * Diameter/2 
                 .22 
                  .80 * Diameter/2 
                 .27 
               
               
                 −y 1   
                 −.34 * Diameter/2 
                 .77 
                 −.30 * Diameter/2 
                 .72 
               
               
                 −y 2   
                 −.86 * Diameter/2 
                 .22 
                 −.80 * Diameter/2 
                 .27 
               
               
                   
               
            
           
         
       
     
     The flow Q can now be calculated by the following equation:
 
 Q=D[w   1    L chord 1    v axial 1   +w   2    L chord 2    v axial 2   +w   3    L chord 3   +v axial 3   +w   4    L chord 4    v axial 4 ].
 
     where w 1 =w 4  and w 2 =w 4 ; Lchord 1 =Lchord 4 , Lchord 2 =Lchord 3 . 
     A 24 inch diameter (21.56″ ID) ultrasonic gas flowmeter  10  with eight paths was fabricated as described in this invention and calibrated to a known standard at the CEESI gas calibration facility in Iowa. Results show ( FIG. 5 ) the percent error as function of a range of velocities from 2 ft/s to 100 ft/s. Native linearity (that is; the 24 inch meter linearity without correction) was determined to be only +/−0.175%. The pipe  12  is fabricated from carbon steel in accordance ASME B31.3 Process Piping Code. The controller  20  is designed in compliance to UL/cUL Class 1, Division 1, Groups C &amp; D. 
     The meter sizes, flowrates and velocities are described in Table 2. Flowrates shown are based on schedule  40  pipe ID. Over-range flowrates are at 120 fps. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Meter Sizes, Flowrates, and Velocities 
               
            
           
           
               
               
               
            
               
                 Meter Size 
                 Flow Rate—ft 3 /hr 
                 Flow Rate—m 3 /hr 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Inches 
                 DN 
                 Min 
                 Max 
                 Over-range 
                 Min 
                 Max 
                 Over-range 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 8 
                 200 
                 2,500 
                 125,000 
                 150,000 
                 71 
                 3,550 
                 4,250 
               
               
                 10 
                 250 
                 3,950 
                 197,000 
                 237,000 
                 110 
                 5,580 
                 6,700 
               
               
                 12 
                 300 
                 5,600 
                 280,000 
                 336,000 
                 160 
                 7,900 
                 9.500 
               
               
                 16 
                 400 
                 8,850 
                 442,000 
                 530,000 
                 250 
                 12,500 
                 15,000 
               
               
                 20 
                 500 
                 13,900 
                 695,000 
                 834,000 
                 400 
                 19,700 
                 23,600 
               
               
                 24 
                 600 
                 20,100 
                 1,010,000 
                 1,210,000 
                 570 
                 28,500 
                 34,200 
               
               
                   
               
            
           
         
       
     
       FIG. 6  shows the transformer application.  FIGS. 7   a  and  7   b , which together are one continuous drawing, show a demonstration of transit time flow meter performance.  FIGS. 8   a  and  8   b , which together are one continuous drawing, show error vs. velocity in regard to the claimed invention. 
     Although the invention has been described in detail in the foregoing embodiments for the purpose of illustration, it is to be understood that such detail is solely for that purpose and that variations can be made therein by those skilled in the art without departing from the spirit and scope of the invention except as it may be described by the following claims.