WO2020128512A1

WO2020128512A1 - Speed of sound sensor using an acoustic cavity

Info

Publication number: WO2020128512A1
Application number: PCT/GB2019/053660
Authority: WO
Inventors: David Lawrence; Vincenzo PIAZZA; Hilary MEANWELL; Andrew Dames
Original assignee: Sentec Ltd
Priority date: 2018-12-20
Filing date: 2019-12-20
Publication date: 2020-06-25
Also published as: GB201820883D0

Abstract

A sensor for use in determining speed of sound in a gas (2) is disclosed. The sensor comprises a resonator (7) comprising a housing (8) defining an acoustic cavity (9) which is ellipsoid, a transmitter (10) arranged to generate a sound wave (12) in the cavity, a receiver (11) arranged to detect a sound wave in the cavity and a set of one or more passages (13) through the housing for allowing gas to freely pass in and out of the cavity from outside the cavity. The set of one or more passages is configured such that the one or more passages run in a line (36) (for example, a circle or ellipse) around a perimeter of the housing and the line has a length (for example, a circumference, C of circle or ellipsoid). The line coincides with a pressure node of a resonant cavity mode and a sum of the length(s) of the one or more passages in a direction along the line is at least 25% of the length.

Description

Speed of sound sensor

Field

The present invention relates to a sensor for measuring speed of sound.

Background

The speed of sound, c, of a gas can be measured using an acoustic cavity which contains the gas and which is provided with an acoustic transmitter and an acoustic receiver.

The transmitter and the receiver are used to excite acoustic waves in the cavity and to detect amplitude of the waves at the receiver. When the frequency of excitation coincides with the resonant frequency of one of the acoustic modes of the gas- containing cavity, the amplitude of the detected signal reaches a local maximum. A calibration constant (which may be experimentally determined using a known gas or calculated from the known shape of the cavity) is used to convert the resonant frequency into the speed of sound value.

The measured speed of sound can be used to determine other useful gas properties. For example, the speed of sound of a binary mixture of two known gases or two known mixtures of gases permits the composition of the binary mixture to found when the temperature is known. This is of interest in a wide range of industries where there is a need to mix two known gases or two known mixtures of gases with a desired ratio. Speed-of-sound or gas-composition sensors also are of use in applications where it is desirable to verify that the composition of a binary mixture of two known gases or two known mixtures of gases is consistent with what is expected, for example, before using compressed mixtures for diving.

Mixtures of air and helium (He) or air and hydrogen (H₂) are of interest, for example for leak detection applications. Figure 1 is a plot of calculated values of speed of sound of air and helium and air and hydrogen as a function of molar fraction of helium and hydrogen respectively at a temperature of 300 K and a pressure of 101,325 Pa.

A speed of sound sensor or a gas composition sensor can be used in other applications including monitoring the consistency of a gas mixture, for example, for air quality monitoring purposes. Such a sensor can be used to raise a warning when the speed of sound changes more than a given amount and so indicate that the composition of the mixture is not what is expected. Figure 2 is a plot of calculated speed of sound of a mixture of air and carbon dioxide as a function of molar fraction of carbon dioxide at a temperature of 300 K and a pressure of 101,325 Pa.

For a given cavity, more than one acoustic mode typically exists. For example, in a cylindrical cavity having a length, L, which is filled with gas having a speed of sound, c, the resonant frequencies /„ of axial acoustic modes can be calculated in the ideal case as fn = n c/ (2 L) where n is the mode index which is a positive, non-zero integer. The presence of multiple modes can create difficulties when trying to determine the composition of a mixture of gases as knowledge of the mode index, n, is needed to determine the speed of sound, c. For example, a first mixture having a speed of sound of 400 ms^-1 and a second mixture having a speed of sound of 800 ms^-1 would both generate a resonance at 8 kHz in a 50 mm long cavity. This corresponds to the second longitudinal mode for the first mixture and to the first longitudinal mode for the second mixture. Thus, a way of determining which mode is being excited is needed, for example by acquiring the signal in a broad range of frequencies and determining the mode index by counting local maxima of the signal. Such an approach, however, can negatively affect the measurement speed and the power consumption of the sensor.

The quality factor of the acoustic mode that is being used can affect the accuracy of the measurement. A high quality factor is desirable because it corresponds to a sharp resonance that can be easily detected and whose frequency can be measured with a high degree of precision. Thus, the accuracy of determining the resonant frequency of the cavity directly affects the accuracy in the measured speed of sound. In the case of a mixture of air and helium or a mixture of air and H2, an uncertainty of ±0.1% in the speed of sound corresponds to an error of approximately ±0.002 in the molar fraction of helium or hydrogen.

Gas can be introduced into the cavity using passages which allow the gas to diffuse in and out of the cavity. For example, US 3 468 157 A describes an acoustical chamber having a cylindrical passageway provided with a gas inlet conduit and a gas outlet conduit for passing a gas through the chamber. In another example, US 5 768 937 A describes an acoustic cell which includes multiple acoustic cavities fluidly coupled together. US 5 369 979 A describes an ultrasonic gas measuring device which includes a cylindrical housing means which incorporates an inner chamber, a gas inlet and a gas outlet at the ends of the housing. US 6481 288 Bi describes a resonator in the form of a rigid sphere having gas diffusion passages to enable gas to diffuse in and out of the resonator.

The passages in these devices, however, tend to affect operation of the cavity by lowering the quality factor or by shifting the acoustic modes from their ideal location. The passages can also affect the speed of response of the sensor.

Summary

According to a first aspect of the present invention there is provided a sensor for use in determining speed of sound in a gas. The sensor comprises a resonator comprising a housing defining an acoustic cavity which is an ellipsoid or which comprises an ellipsoid, a transmitter arranged to generate a sound wave in the cavity, a receiver arranged to detect a sound wave in the cavity and a set of one or more passages through the housing for allowing gas to freely pass in and out of the cavity from outside the cavity. The set of one or more passages is configured such that the one or more passages run in a line around a perimeter of the housing and the line has a length. The line coincides with a pressure node of a resonant cavity mode and a sum of the length(s) of the one or more passages in a direction along the line is at least 25% of the length.

Since the one or more passages run in a line which coincides with the pressure node of the cavity, a high value of quality factor, Q, can be maintained for a particular acoustic mode. Furthermore, the positioning of the passage can be used not only to select a particular acoustic mode, such as a p-type mode, but also damp other unwanted modes, e.g., a d-type mode, or s-type mode. Preferably, the length is a circumference. Preferably, the line is a circle or ellipse or an arc of a circle or ellipse.

The term“coincides” is intended to mean that the line passes in a region where the pressure value is within a range between the minimum and 10% of the maximum pressure value. In other words, the line may be slightly to one side or the other of the pressure node, but still close to the pressure node.

The one or more passages may be arranged such that the line passes through the passages.

There may be more than one sets of one or passages. For example, there may be two loops of passages, for example, offset with respect to each other along an axis or long axis of the ellipsoid. The acoustic cavity preferably mainly comprises an ellipsoid (in other words, at least 50 % of the inner surface area of the housing defining the cavity has a given ellipsoid shape). The gas may be a mixture of two or more gases. The mixture may include air. The mixture may include hydrogen or helium.

Preferably, the sum of the length(s) is at least 50% of the circumference. More preferably, the sum of the length(s) is at least 75% of the circumference. The sum of the length(s) may be 100% of the circumference.

The resonant cavity mode is preferably a p-type mode. However, the resonant cavity mode maybe a d-type mode. The cavity may have a diameter or a longest length, d, and the diameter or longest length is between 1 and 10 cm. The housing may have a wall thickness, t, between 0.05 and 2 cm. The passage(s) in the set of one or more passages may have a diameter or a longest length, l, of at least 0.2 times a shortest length of the cavity. The passage(s) in the set of one or more passages may comprise holes which are circular or elliptical. The passage(s) in the set of passages may comprise slots which are polygonal, preferably rectangular.

The cavity may have a quality factor for a given acoustic mode, preferably a lowest acoustic mode which has a p-type shape, of at least 10. The quality factor may be at least 50, between 50 and 500 or more than 500.

The transmitter may comprise a speaker. The transmitter may comprise a piezoelectric transducer. The receiver may comprise a microphone. The receiver may comprise a piezoelectric transducer.

The ellipsoid maybe a sphere. The transmitter and receiver maybe disposed on diametrically opposite sides of cavity. The set of passages may be disposed in a midplane between the transmitter and receiver. The set of passages are disposed in a plane corresponding to a p-type pressure mode node. The set of passages are disposed in two planes corresponding to d-type pressure mode nodes. The ellipsoid is a spheroid. The transmitter and receiver maybe disposed on diametrically opposite sides of cavity on the longest axis of the cavity. The set of passages may be disposed in a midplane between the transmitter and receiver. The set of passages are disposed in a plane corresponding to a p-type pressure mode node.

The set of passages maybe disposed in two planes corresponding to d-type pressure mode nodes.

The transmitter and receiver may be provided by a single transducer. The acoustic cavity has a centre and a line passes through the centre of the cavity. The set of passages may be disposed in a plane perpendicular to the line and passing through the centre. The single transducer may comprise a piezoelectric transducer comprising a first common electrode, a second electrode and a third, reference electrode. The sensor may further comprise a temperature sensor, a humidity sensor and/ or a pressure sensor.

According to second aspect of the present invention there is provided the sensor of the first aspect of the present invention and a control unit for generating an excitation signal for driving the sensor and processing a received signal generated by the sensor, the control unit including at least one processor for processing the received signal.

The at least one processor may be configured to calculate a resonant frequency of an acoustic mode in dependence upon the received signal. The at least one processor may be configured to calculate a value of speed of sound in the gas in dependence upon the received signal. The at least one processor may be configured, in the calculation, to compensate for temperature, pressure and/or humidity of the gas. The at least one processor may be configured to calculate a value of gas composition in dependence upon the received signal. The at least one processor may be configured to calculate an acoustic impedance in dependence upon amplitude and phase of at least two received signals and to determine a value of a ratio, y, of gas heat capacities in dependence on the acoustic impedance. The at least one processor maybe configured to determine first and second heat capacities, for example, the heat capacity at constant volume and the heat capacity at constant pressure, in dependence on the ratio, y. The at least one processor may be configured to calculate a value of gas mean molecular mass in dependence upon an amplitude and phase of the received signal. The excitation signal may be a continuous wave. The excitation signal may have a frequency between l kHz and 20 kHz. According to a third aspect of the present invention there is provided an instrument comprising the system of the second aspect of the present invention.

According to a fourth aspect of the present invention there is provided apparatus comprising a pipe or a vessel having wall(s) defining a passage or cavity, respectively, the sensor of the first aspect of the present invention disposed in the passage or cavity and a support arranged to mount the sensor in the passage or cavity, wherein the support comprises a material for absorbing vibration.

According to a fifth aspect of the present invention there is provided a method or operating the system of second aspect of the present invention. The method comprises causing generation of sound waves in the cavity of the sensor and processing the signals received from the sensor.

According to a sixth aspect of the present invention there is provided a method comprising determining an amplitude and phase of a received signal from a transducer, calculating an acoustic impedance in dependence upon the amplitude and phase of the received signal, determining a value of a ratio, y, of gas heat capacities in dependence on the acoustic impedance, determining first and second heat capacities in dependence on the ratio, y and storing and/or displaying the ratio, y, the first heat capacity and/or the second heat capacity.

According to a seventh aspect of the present invention there is provided a computer program comprising instructions which, when executed by at least one processor, causes the at least one processor to perform the method of the fifth or sixth aspect of the present invention.

According to an eighth aspect of the present invention there is provided a computer program product comprising a computer readable medium storing the computer program of the seventh aspect of the present invention. According to a ninth aspect of the present invention there is provided a system for measuring the speed of sound of a gas using ellipsoidal or mainly ellipsoidal acoustic cavity with passages optimally located and shaped to provide a high quality factor for the lowest-frequency mode, while also suppressing the quality factor of neighbouring modes.

According to a tenth aspect of the present invention there is provided a method and apparatus for measuring the speed of sound and other thermodynamic properties of a gas or of a mixture of gases. Knowing the speed of sound of a gas can allow determining additional useful gas properties. For example, measuring the speed of sound of a binary mixture of two known gases permits the determination of the composition of the mixture when the temperature is known.

According to a eleventh aspect of the present invention there is provided an ellipsoidal or spherical acoustic resonator with equatorial holes. A first, second and/or third principal axes of the resonator may (each) have a (respective) length between 1 cm and 10 cm and/or a wall thickness of 0.1 mm to 2 mm. The holes maybe >0.2 times the length of a shortest of the first, second and/or third principal axes. According a twelfth aspect of the present invention there is provided an ellipsoidal or spherical acoustic resonator with equatorial slots. A first, second and/or third principal axes of the resonator may (each) have a (respective) length between 1 cm and 10 cm and/or a wall thickness of 0.1 mm to 20 mm. The slots maybe >0.3 times and/or or a width > 0.2 times the length of a shortest of the first, second and/or third principal axes.

The resonator may have a quality factor for a first acoustic mode larger than or equal to 50 when filled with a gas. The gas may be a pure gas or a mixture of at least two different gases. The gas (i.e., the pure gas or the gas mixture) may have a mean molecular mass value. The gas may have a heat capacity at constant pressure value.

The gas may have a heat capacity at constant volume value. The gas may have a heat capacity ratio value. The gas may be a first mixture of two know gases or a second mixture of two known mixtures of gases. The first and second mixtures may have a respective composition value. The resonator may be provided with a microphone or a piezoelectric element as a receiving transducer. The resonator may be provided with an electromagnetic speaker or a piezoelectric element as the transmitting transducer. The resonator may be provided with a single transducer, for example, an electromagnetic speaker or a single piezoelectric element, for acting as both a transmitting transducer and a receiving transducer. The single piezoelectric element may have a feedback electrode acting as transmitting and receiving transducer. The resonator maybe provided with a temperature sensor, a pressure sensor and/or a humidity sensor. The resonator or system may be provided with electronic means to excite the transmitting transducer with a signal and to detect the signal from the receiving transducer. The resonator or system may comprise a processing unit with firmware able to calculate the resonant frequency of at least one acoustic mode of said acoustic resonator. The processing unit with firmware may measure the temperature of the gas using a temperature sensor. The processing unit with firmware may measure the temperature of the gas with an accuracy better than or equal to ±1 °C, better than or equal to ±0.5 °C, better than or equal to ±0.1 °C, better than or equal to ±0.05 °C, or better than or equal to ±0.01 °C. The processing unit with firmware may measure the pressure of the gas using a pressure sensor. The processing unit with firmware may measure the pressure of the gas with an accuracy better than or equal to ±10000 Pa, better than or equal to ±1000 Pa, better than or equal to ±100 Pa, or better than or equal to ±10 Pa. The processing unit with firmware measures the humidity of the gas using a humidity sensor. The processing unit with firmware may measure the relative humidity of the gas with an accuracy better than or equal to ±20%RH, better than or equal to ±4%RH, or better than or equal to ±1%RH. The processing unit with firmware may convert a resonant frequency of at least one acoustic mode into a speed of sound value. The processing unit with firmware may convert a resonant frequency of at least one acoustic mode into a speed of sound value compensating for the gas temperature. The processing unit with firmware may convert a resonant frequency of at least one acoustic mode into a speed of sound value compensating for the gas pressure.

The processing unit with firmware may convert a resonant frequency of at least one acoustic mode into a speed of sound value compensating for the gas humidity.

The processing unit with firmware may convert a resonant frequency of at least one acoustic mode into a speed of sound value having an accuracy better than or equal to ±2%, better than or equal to ±1%, better than or equal to ±0.5%, or better than or equal to ±0.1%. The processing unit with firmware may convert the speed of sound value to a gas composition value. A processing unit may measure the amplitude and phase of the transmitter vibrations and convert them to an acoustic impedance value. A processing unit may measure the amplitude and phase of the transmitter vibrations and convert them to a gas heat capacity ratio. A processing unit may measure the amplitude and phase of the transmitter vibrations and convert them to a gas mean molecular mass value.

According to a thirteenth aspect of the present invention there is provided an instrument with a speed of sound and or gas composition capability and or heat capacity capability and or heat capacity ratio capability and or mean molecular mass capability, comprising the resonator or system

According to a fourteenth aspect of the present invention there is provided a speed-of- sound sensor based on an acoustic cavity with gas passages having a geometry that enhances the quality factor of the fundamental acoustic mode while suppressing neighbouring modes to improve speed-of-sound measurements.

Brief Description of the Drawings

Certain embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

Figure 1 shows plots of calculated speed of sound of air-and-helium and air-and- hydrogen mixtures as a function of molar fraction of helium and hydrogen respectively at 300 K and 101,325 Pa;

Figure 2 shows a plot calculated speed of sound of a mixture of air and carbon dioxide at 300 K and 101,325 Pa;

Figure 3 is a schematic diagram of a system for measuring speed of sound in a gas including a sensor;

Figure 4 is schematic cross-sectional view of a sensor;

Figure 5 is a schematic block diagram of a control circuit shown in Figure 3 connected to two transducers;

Figure 6 is a schematic block diagram of a control circuit connected to one transducer which may have two or three terminals;

Figure 7 is a schematic side of view of a first sensor;

Figure 8 is a schematic side view of a second sensor;

Figure 9 is a schematic side view of a third sensor;

Figure 10 is a schematic side view of a fourth sensor;

Figure 11 is a schematic side view of a fifth sensor;

Figure 12 schematic diagram of pressure distribution for a p-type acoustic mode in a cavity;

Figure 13 illustrates a circle of formed by intersection of a zero-pressure node and housing of a resonator for a p-type acoustic mode;

Figure 14 illustrates passages locate on the circle shown in Figure 13;

Figure 15 schematic diagram of pressure distribution for a d-type acoustic mode; Figure 16 illustrates two circles of formed by intersection of two zero-pressure nodes and housing of a resonator for a d-type acoustic mode;

Figure 17 illustrates passages locate on the circles shown in Figure 16;

Figure 18 is a partial perspective view of a sensor which includes a piezoelectric transducer which has a feedback electrode, and which serves as a transmitter and receiver;

Figure 19 is a schematic cross-sectional view of a sixth sensor;

Figure 20 is a schematic cross-sectional view of a seventh sensor;

Figure 21 is a schematic cross-sectional view of an eighth sensor;

Figure 22 is a schematic cross-sectional view of a ninth sensor; Figure 23 shows plots of measured acoustic spectrum in the proximity of a first resonant mode of a spherical cavity with slots, in which amplitude of the signal is represented by a solid line (left axis) and its phase with respect to an excitation signal is represented by a dashed line (right axis), and the measured quality factor is 320;

Figure 24 shows plots of measured acoustic spectrum for a first acoustic mode illustrating suppression of a neighbouring mode for a sphere with two opposite 20 mm diameter holes on the equatorial line as a function of size of two additional holes placed orthogonally with respect to the first two holes;

Figures 25a and 25b shows plots of experimental amplitude and phase respectively of a transmitter transducer for acoustic cavity filled with air and corresponding best fits; Figure 25c and 25d are expanded views of the plots shown in Figures 25a and 25b respectively;

Figure 25 shows plots of calculated heat capacity ratio, y, and mean molecular mass of different natural gas mixtures with the addition of hydrogen gas;

Figure 26 shows plots, for a spherical cavity, of measured and expected argon/helium ratio against argon mixing ratio obtained from mixing argon and helium with known partial pressures and deviation of the measured ratio from the expected value;

Figure 27 is a schematic side view of a sensor in a pipe; and

Figure 28 is a schematic top view of a sensor in a pipe.

Detailed Description of Certain Embodiments

System 1 for measuring speed of sound

Referring to Figure 3, a system 1 for measuring speed of sound in a gas 2 is shown. The system 1 includes a sensor assembly 3 (herein referred to simply as a“sensor”) and a sensor control unit 4 (herein referred to simply as a“control unit”) for generating an electrical signal 5 for driving the sensor 3 and processing a signal 6 generated by the sensor 3. The electrical signal 5 may be a continuous wave (CW) at one or more different frequencies, a chirp, white noise, pink noise or another suitable waveform. The signal 5 maybe have a duration (i.e., occur in a window) of, for example, too ms or more. The electrical signal may have a frequency between 1 kHz and 20 kHz. The sensor 3 comprises a resonator 7 comprising a housing 8 (or“wall”), which defines an acoustic cavity 9 (herein also simply referred to as a“cavity”) containing some of the gas 2, and first and second transducers 10, 11. The housing 8 may be formed from a suitable plastic, such as ABS, PEEK, PVC, or PTFE, a glass-filled plastic, a ceramic, a glass, or from a metal or metal alloy, such as steel, brass, or copper. The first transducer 10 receives an excitation signal 5 from the electronic circuitry 4 and generates a sound wave 12 (or“acoustic wave”) in the cavity 9 which propagates through the gas 2. The second transducer 11 receives the sound wave 12 and generates a corresponding electrical signal 5 (or“received signal”). Herein, the first and second transducers 11, 12 are also referred to as the“transmitter” and“receiver”, respectively. As will be explained in more detail hereinafter, two separate transducers 10, 11 can be used. Alternatively, a single transducer may serve as both the transmitter and receiver. This can lower the manufacturing costs of the sensor 3 and simplify its manufacture.

Referring also to Figure 4, the resonator 7 includes a set of passages 13 through the wall 8 of the resonator between inner and outer walls 14, 15. Gas 2 can freely pass in and out of the cavity 9 from outside the resonator 7 (schematically illustrated by dashed arrows).

As will be explained in more detail hereinafter, the passages 13 are configured ( e.g ., have geometry and dimensions) and positioned so as to help ensure a high value of quality factor, Q {e.g., > 50), while also providing a fast response (e.g., < 5 s). The passages 13 can take the form of holes, e.g. circular holes, or slots, e.g. a rectangular slot.

Referring also to Figure 5, the control unit 4 includes a driver 16 for driving the excitation signal 5 and a front end 17 for the received signal 6. The front end 17 may include an ADC and/ or amplifier. The control unit 4 includes a processing unit 18, which may take the form of microcontroller, for calculating a resonant frequency, a speed of sound, a gas composition and/or other relevant data based on a measurement made using the sensor 3. The processing unit 18 includes at least one processor 19, memory 20 and non-volatile storage 21 (which may be read-only) which stores control software 22 (which may take the form of read-only software, i.e., firmware) and a mixture models 23, and input/output interface(s) 24.

The control unit 4 may receive signals from sensors 25 measuring ambient conditions, such as, for example, temperature and/or pressure. The sensors 25 may include a temperature sensor 26, a humidity sensor 27 and/or a pressure sensor 28. The control unit 4 also includes one or more input devices 29, which may, for example, enable a user to instruct the system 1 to take a measurement, and one or more output devices 30 for outputting, for example, a measurement or calculation. An output device 30 may take the form of a display. An output device 30 or an integrated input/output device 29, 28 may take the form of an interface to a wired or wireless communications network (not shown).

The control unit 4 may take the form of a computer system, for example, in the form of lap-top computer.

Referring to Figure 6, the control unit 4 may be connected to a single transducer 10, 11 which serves as both transmitter and receiver. Suitable switches (not shown) may be provided or included in the driver 16 and front end 17 or a multiplexer (not shown) may be interposed between the driver 16 and front end 18 and the transducer 10, 11. As will be explained in more detail hereinafter, the transducer 10, 11 may take the form of three-electrode transducer 51 (Figure 18) wherein one of the electrodes 54 (Figure 18) is a feedback electrode which can be used to determine measure phase and so allow acoustic impedance to be measured.

Resonators

The acoustic cavity 9 generally takes the form of an ellipsoid, such as a sphere or spheroid, preferably a prolate spheroid. The cavity maybe defined by the equation (x²/a²) + (y²/b²) + (z²/ c²) = 1 where a, b, c are non-zero, positive, real numbers. In the case of a sphere, a = b = c. In the case of spheroid, c < a or c > a.

As will be explained in more detail later, the acoustic cavity 9 may include steps, a central cylindrical portion and/or a truncated, central ellipsoid part ( e.g ., where a = b = ad and outer, end ellipsoidal segment parts (e.g., where a = b = a₂ ¹ aj. The inner and outer surfaces 14, 15 of the housing 8 of the resonator 7 have the same shape (e.g., a homoeoid). However, the inner and outer surfaces 14, 15 need not have the same shape. For example, the inner surface 14 maybe ellipsoidal or mainly ellipsoidal and outer surface may have a different shape. Referring to Figure 7, a first resonator 7₁ is shown. The first resonator 7₁ comprises an acoustic cavity 9 which is ellipsoid having first, second and third axes. The cavity 9 has a first length, d, along the first axis 31 (herein shown parallel to the x-axis) and second length, e, along the second axis (not shown) and third axis 33, parallel to the y and z axes, respectively, where d > e.

First and second transducers 10, 11, for example, in the form of piezoelectric elements, are disposed at opposite ends 34, 35 of the resonator 7₁ along the long axis 31 (i.e., the first axis). The resonator 7₁ includes a set of passages 13, in this case taking the form of elongated, rectangular slots having a width, w, and a length, l along the surface of the resonator (i.e., measured along the arc). The slots 13 are arranged midway (“equidistant”) between the ends 34, 35 of the resonator 7₁ running around a circle 36 (herein referred to as an“centre circle”) and orientated lengthwise along the circle. The slots 13 are separated (along an arc of the circle) by a distance, s.

The circle 35 has a circumference, C. The sum, L, of the lengths, l, of the passage(s) 13 is such that L ³ 0.25 C. Preferably, L ³ 0.50 C and more preferably, L ³ 0.75 C. If there are n passages of equal length, then L = n.l. It is possible for there to be a single, continuous passage 13, i.e., n= 1, l = L = C and s = o, for example, in an arrangement in which the housing 8 consists of two hemi-ellipsoids held closely together, separated by a gap, i.e., width, w.

As will be explained in more detail later, this arrangement can be particularly advantageous since the effect on the quality factor of acoustic modes having a zero- pressure plane substantially coincident with the equatorial plane is minimal (resulting from the lowest-frequency mode of the ellipsoid) while providing significant damping to the neighbouring acoustic modes. Referring to Figures 8 and 9, second and third resonators 7₂, 7₃ are shown.

The second and third resonators 7₂, 7₃ are similar to the first resonator 7₁ (Figure 6) except that the first and second transducers 10, 11 are not located at the ends 34, 35 of the resonator. Referring in particular to Figure 8, the first and second transducers io, 11 are disposed in the same elliptical hemisphere, in this case, in the lower elliptical hemisphere.

Referring in particular to Figure 9, the first and second transducers 10, 11 are disposed in the same half of the ellipsoid, in this case, in the left half of the ellipsoid.

In the examples hereinbefore described, the resonators are spheroid. A resonator may, however, be spherical. Referring to Figure 10, a fourth resonator h_L is shown.

The fourth resonator 7₄ comprises an acoustic cavity 9 which is spherical having first, second and third axes. First and second transducers 10, 11, for example, in the form of piezoelectric elements, are disposed on opposite points 37, 38 of the resonator 7₄ thereby defining an axis 39 and a midplane 40. Where the midplane 39 intersects the housing 8’, a great circle 41 is defined. The resonator 7₄ includes a set of passages 13’, in this case taking the form of circular hole having a diameter, 2 r, (where r is the radius) along the surface of the resonator. The holes 13’ are arranged midway between the points 36, 37 running around the great circle 41. The slots 13 are separated (along an arc of the circle) by a distance, s. Thus, the sum, L, of the diameters of the passage(s) 13 is such that L ³ 0.25 C. Preferably, L ³ 0.50 C and more preferably, L ³ 0.75 C. If there are n passages of equal length, then L 2.P.G.

Similar to previous examples, there is a minimum amplitude midway between the opposite points 37, 38. Therefore, by positioning the passages 13 at a point of minimum amplitude, energy loss is reduced and degradation of quality factor due to opening up the cavity is minimised.

Referring to Figure 11, a fifth resonator y₅ is shown. The fifth resonators 7₅ is similar to the fourth resonator 7₄ (Figure 10) except that the slots 13 are used instead of holes 13’. The number of passages 13, 13’ can vary. There may be at least two passages 13, 13’, for example, between two and twelve passages 13, 13’. A single passage, however, can be used. The passage can run continuously around the resonator and so separate the resonator into two halves of a sphere or spheroid. The transducers 10, 11 are preferably located at opposite extremities of the diameter perpendicular to the plane containing said equatorial plane.

Referring again to Figure 7, in some embodiments, only two of the ellipsoid axes are equal, for example, the second and third axes. Therefore, the cavity is an ellipsoid of revolution. Preferably, a first axis is longer that the other two axis and the passages are preferably placed along the equatorial circle intersecting the second and third axes. The transducers 10, 11 are preferably located at the opposite extremities of the first axis.

This geometry lowers the resonant frequency of the first mode with respect to a sphere having the same volume.

Location of passages

In embodiments herein described, the passages 13 are positioned such that the effect on the quality factor of acoustic modes having a zero-pressure plane substantially coincident with the median plane is minimal (resulting from the lowest-frequency mode of the ellipsoid) while providing significant damping to the neighbouring acoustic modes. The passages 13 take up a significant proportion (at least 25%) of the band they occupy. Preferably, they take up at least of the circumference (i.e., at least 50%) and, more preferably, they occupy a most of the circumference (i.e., at least 75%). The proportion can be between 75% and 99% and can even be 100%.

Referring to Figure 12, a pressure distribution in the form of lines (or“contours”) of equal pressure in an ellipsoid cavity 9, in particular a spherical cavity 9, for a p-type resonant mode is shown.

The cavity 9 has a resonance (herein also referred to as a“resonant mode” or simply a “mode”) with an amplitude or pressure distribution which resembles a p-type orbital. The mode has a horizontal rotation axis of symmetry. A central line 42 (shown as a dotted line) indicates the zero-pressure node. Taking into account the rotational symmetry, the node 42 is an midplane perpendicular to the rotation axis. Referring to Figure 13, the intersection of this plane 42 with the housing 8 of the acoustic cavity 9 is a circle 43 (also shown as a dotted line).

Referring also to Figure 14, placing the passages 13 on the circle 43 has the least effect on the p-mode while suppressing all the other modes that do not have zero-pressure nodes. Therefore, by positioning the passages 13 around the edge of the minimum pressure plane, energy loss is reduced and degradation of quality factor due to opening up the cavity is minimised. Referring to Figure 15, a pressure distribution in the form of lines of equal pressure in an ellipsoid cavity 9, in particular a spherical cavity 9, for a d-type resonant mode is shown.

Rotation of two crossing lines define two cones 44, with vertices at the centre, which define locus of a zero-pressure node.

Referring to Figure 16, the intersection of the cones 44 with the housing 8 of the cavity result in two vertical circles 45 Referring also to Figure 17, placing two sets of passages 13 there would suppress the p- type mode with minimal effect on the d-type mode.

Referring to Figure 18, a part of (p/o) of a resonator 7 is shown. The resonator 7 may be any of the resonators hereinbefore or hereinafter described.

In this example, a three-terminal (as opposed to two-terminal) piezoelectric transducer 51 maybe used. The piezoelectric transducer 51 includes not only a main electrode 53 which can be used for transmitter and/or receiving an acoustic signal, it includes a reference (or“feedback”) electrode 54 that can be used to measure acoustic impedance. An example of a suitable piezoelectric transducer 51 is Murata (RTM) piezoelectric diaphragm model 7BB-27-4CL0.

Referring to Figure 19 to 22, sixth, seventh, eighth and ninth resonators 7₀, 7₇, 7s, 7g are shown. Referring to Figures 19 and 20, the sixth and seventh resonators 7₀, 7₇ are generally similar to the resonators hereinbefore described but differ in that the transducer(s) 10, 11, which may be a three-terminal piezoelectric transducer 51, are mounted over a large through hole 45 to the cavity 9 and an outwardly extending cylindrical passage 56 on which the transducer 10, 11 is mounted.

Referring to Figures 21 and 22, the eighth and ninth resonators 7s, 7g are generally similar to the sixth and seventh resonators 7₀, 7₇ except that the through hole 57 is small and similar in size to the passages 13.

Adjustment for temperature and other environmental factors

The speed of sound of a gas or gas mixture depends on the temperature of the gas.

Accordingly, accuracy of conversion of a measured speed of sound into a composition value of a binary mixture can be improved by measuring the temperature of the gas or gas mixture.

Referring again to Figure 5, the system 1 may include a temperature sensor 26, for example in the form of a thermistor, provided in, on or near to the cavity 9.

In the case of time-varying temperature, the temperature sensor 26 should quickly adapt to the temperature of the gas or gas mixture. Preferably, therefore, the temperature sensor 26 is placed in good thermal contact with the gas, for example, by being placed inside the acoustic cavity 9 or in the proximity of one of the passages 13, by being integrated in one of the transducers 10, 11 or by being placed in good thermal contact with the cavity wall 8.

The presence of humidity can also affect the measured speed of sound. This is relevant in particular for those applications where one of the known mixtures is air.

Referring still to Figure 5 the system 1 may include a humidity sensor 27 provided in, on or near to the cavity 9. A value of humidity can be used by the processing unit 18 to compensate the speed of sound and provide accurate composition data. The pressure of the gas can also have an effect on the speed of sound of a gas t, although it tends to be minor compared to that caused by temperature variations, Referring still to Figure 5, the system 1 may include a pressure sensor 28 provided in, on or near to the cavity 9. Again, a value of pressure can be used by the processing unit 18 to compensate the speed of sound and provide accurate composition data.

Determining heat capacity ratio g

If the pressure of the gas is independently measured, the knowledge of the acoustic impedance of the gas allows determining the heat capacity ratio g of the mixture. Referring to Figure 3, the amplitude and phase of vibrations generated by the transmitter 10 can be expressed in terms of the acoustic impedance of the gas.

In a simplified model, where the transmitter transducer 10 is modelled as a simple harmonic oscillator coupled to the gas 2 in the cavity 9 through a gas acoustic impedance, Z, then the complex amplitude, x, of the vibrations as a function of the angular frequency, w, can be written as:

where

Here, X(w,3_¾) represents the response of the gas 2 in the cavity, /represents an arbitrary amplitude, a_p is a damping factor of the transducer, Q_p its resonant frequency, Q_g is a gas resonance in the cavity, a_g is the acoustic resonance damping factor, and a an amplitude constant that can be determined from a known gas. Measuring the complex vibration amplitude of the transmitter 10 allows the acoustic impedance, Z, of the gas 2 to be determined, for example, by using a curve fitting procedure using equations (1) and (2), to the experimental data. Further refinements of the model can be performed and the accuracy of the measurement of, Z, can be undertaken, taking into account the detailed mechanical model of the transmitter. Measuring the acoustic impedance, Z, in addition to the speed of sound, c, and the pressure, P, allows relevant thermodynamic properties of the gas to be determined including (but not limited to) the capacity ratio y = cZ/P, heat capacities at constant pressure and at constant volume C_p = Ry/ (y - 1), C_v = C_p/y, and mean molecular mass

M = yRT/c².

Referring to Figures 24a to 24d, plots of experimental amplitude and phase respectively of a transmitter transducer for acoustic cavity filled with air and corresponding best fits are shown.

Referring in particular to Figures 24a, a plot of residuals taken between the measured and fitted value is shown. Referring to Figure 26, plots are shown of calculated heat capacity ratio, y, and mean molecular mass of different natural gas mixtures with the addition of hydrogen gas.

Referring to Figure 27, plots are shown, for a spherical cavity, of measured and expected argon/helium ratio against argon mixing ratio obtained from mixing argon and helium with known partial pressures and deviation of the measured ratio from the expected value.

Referring to Figure 28 and 29, a sensor 3 is shown when deployed in a pipe 61 are shown.

The sensor 3 is orientated such the passages 13 face the flow 62 of the gas 2 and so the gas 2 flows into and out of the cavity 9.

The sensor 3 is mounted in the pipe 61 via arm-like supports 63. Spacers 64 (or “dampers”) are interposed between the sensor 3 and the supports 63. The spacers 64 comprise a disc, pad or block comprising a vibration-absorption material, such as an elastomer, rubber, Sorbothane (RTM) or other suitable material.

The sensor 3 has an outer diameter, Di, and corresponding area, At, and the pipe 61 has an inner diameter, D2, and a corresponding, A2. The size of sensor is chosen according to the flow rate of gas. The faster the gas flows, then a smaller ratio of diameters (D1/D2) can be used.

Modifications

It will be appreciated that various modifications may be made to the embodiments hereinbefore described. Such modifications may involve equivalent and other features which are already known in the design, manufacture and use of gas speed of sound sensors, gas composition sensors and other similar types of sensors and component parts thereof and which may be used instead of or in addition to features already described herein. Features of one embodiment may be replaced or supplemented by features of another embodiment.

Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure of the present invention also includes any novel features or any novel combination of features disclosed herein either explicitly or implicitly or any generalization thereof, whether or not it relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as does the present invention. The applicants hereby give notice that new claims may be formulated to such features and/ or combinations of such features during the prosecution of the present application or of any further application derived therefrom.

Claims

1. A sensor for use in determining speed of sound in a gas (2), the sensor

comprising:

a resonator (7) comprising a housing (8) defining an acoustic cavity (9) which is ellipsoid or comprises an ellipsoid;

a transmitter (10) arranged to generate a sound wave in the cavity;

a receiver (11) arranged to detect a sound wave in the cavity; and

a set of one or more passages (13) through the housing for allowing gas to freely pass in and out of the cavity from outside the cavity;

wherein the set of one or more passages is configured such that the one or more passages run in a line around a perimeter of the housing and the line has a length, wherein the line coincides with a pressure node of a resonant cavity mode and a sum of the length(s) of the one or more passages in a direction along the line is at least 25% of the length.

2. The sensor of claim 1, wherein the sum of the length(s) is at least 50% of the circumference.

3. The sensor of claim 2, wherein the sum of the length(s) is at least 75% of the circumference.

4. The sensor of any one of claims 1 to 3, wherein the resonant cavity mode is a p- type mode.

5. The sensor of any one of claims 1 to 3, wherein the resonant cavity mode is a d- type mode.

6. The sensor of any one of claims 1 to 5, wherein the cavity has a diameter or a longest length, d, and the diameter or longest length is between 1 and 10 cm.

7. The sensor of any one of claims 1 to 6, wherein the housing has a wall thickness, t, between 0.01 and 2 cm or between 1% to 10% of the diameter or a longest length, d, of the cavity.

8. The sensor of any one of claims 1 to 7, wherein the passage(s) in the set of one or more passages have a diameter or a longest length, l, of at least 0.2 times a shortest length of the cavity.

9. The sensor of any one of claims 1 to 8, wherein the passage(s) in the set of one or more passages comprise holes which are circular or elliptical.

10. The sensor of any one of claims 1 to 8, wherein the passage(s) in the set of passages comprise slots which are polygonal, preferably rectangular, and preferably rounded.

11. The sensor of any one of claims 1 to 10, wherein the cavity has a quality factor for a given acoustic mode, preferably a lowest acoustic mode which has a p-type shape, of at least 10.

12. The sensor of claim 11, wherein the quality factor is at least 50, between 50 and 500 or more than 500.

13. The sensor of any one or claims 1 to 12, wherein the transmitter comprises a speaker.

14. The sensor of any one or claims 1 to 13, wherein the transmitter comprises a piezoelectric transducer.

15. The sensor of any one or claims 1 to 14, wherein the receiver comprises a microphone.

16. The sensor of any one or claims 1 to 15, wherein the receiver comprises a piezoelectric transducer.

17. The sensor of any one of claims 1 to 16, wherein the ellipsoid is a sphere.

18. The sensor of claim 17, wherein the transmitter and receiver are disposed on diametrically opposite sides of cavity.

19. The sensor of any one of claims 1 to 18, wherein the set of passages is disposed in a midplane between the transmitter and receiver.

20. The sensor of any one of claims 1 to 18, wherein the set of passages are disposed in two planes corresponding to d-type pressure mode nodes.

21. The sensor of any one of claims 1 to 16, wherein the ellipsoid is a spheroid.

22. The sensor of claim 21, wherein the transmitter and receiver are disposed on diametrically opposite sides of cavity on the longest axis of the cavity.

23. The sensor of claim 21 or 22, wherein the set of passages is disposed in a midplane between the transmitter and receiver.

24. The sensor of claim 21 or 22, wherein the set of passages are disposed in two planes corresponding to d-type pressure mode nodes.

25. The sensor of any one or claims 1 to 24, wherein the transmitter and receiver are provided by a single transducer.

26. The sensor of claim 25, wherein the acoustic cavity has a centre, wherein a line passes through the centre of the cavity wherein the set of passages are disposed in a plane perpendicular to the line and passing through the centre.

27. The sensor of claim 25 or 26, wherein the single transducer comprises a piezoelectric transducer comprising a first common electrode, a second electrode and a third, reference electrode.

28. The sensor of any one of claims 1 to 27, further comprising a temperature sensor.

29. The sensor of any one of claims 1 to 28, further comprising a humidity sensor.

30. The sensor of any one of claims 1 to 29, further comprising a pressure sensor.

31. A system comprising:

the sensor of any one of claims 1 to 30; and a control unit for generating an excitation signal for driving the sensor and processing a received signal generated by the sensor, the electronic circuitry including a at least one processor for processing the received signal.

32. The system of claim 31, wherein the at least one processor is configured to calculate a resonant frequency of an acoustic mode in dependence upon the received signal.

33. The system of claim 31 or 32 wherein the at least one processor is configured to calculate a value of speed of sound in the gas in dependence upon the received signal.

34. The system of claim 31, 32 or 33, wherein the at least one processor is configured to calculate a resonant frequency or speed of sound in dependence upon temperature, pressure and/or humidity of the gas.

35. The system of any one of claims 31 to 34, wherein the at least one processor is configured to calculate a value of gas composition in dependence upon the received signal.

36. The system of any one of claims 31 to 35, wherein the at least one processor is configured to calculate an acoustic impedance in dependence upon amplitude and phase of at least two received signal and to determine a value of a ratio, g, of gas heat capacities in dependence on speed of sound, the acoustic impedance and pressure.

37· The system of claim 36, wherein the at least one processor is configured to calculate first and second heat capacities in dependence on the ratio, g.

38. The system of any one of claims 31 to 37, wherein the at least one processor is configured to calculate a value of gas mean molecular mass in dependence upon an amplitude and phase of the received signal.

39. An instrument comprising the system of any one of claims 31 to 38.

40. Apparatus comprising:

a pipe or a vessel having wall(s) defining a passage or chamber, respectively; the sensor of any one of claims 1 to 30 disposed in the passage or chamber; and a support arranged to mount the sensor in the passage or chamber,

wherein the support comprises a material for absorbing vibration.

41. A method, comprising:

determining an amplitude and phase of a received signal from a transducer; calculating an acoustic impedance in dependence upon the amplitude and phase of the received signal;

determining a value of a ratio, y, of gas heat capacities in dependence on the speed of sound, acoustic impedance and pressure;

optionally, determining first and/or second heat capacities in dependence on the ratio, y; and

storing and/or displaying the ratio, y, and, optionally, the first heat capacity and/or the second heat capacity.

42. A computer program comprising instructions which, when executed by at least one processor, causes the at least one processor to perform the method of claim 41.

43. A computer program product comprising a computer readable medium storing the computer program of claim 42.