WO2006134358A1 - Sonde a onde acoustique pour capter un niveau de fluide - Google Patents

Sonde a onde acoustique pour capter un niveau de fluide Download PDF

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Publication number
WO2006134358A1
WO2006134358A1 PCT/GB2006/002180 GB2006002180W WO2006134358A1 WO 2006134358 A1 WO2006134358 A1 WO 2006134358A1 GB 2006002180 W GB2006002180 W GB 2006002180W WO 2006134358 A1 WO2006134358 A1 WO 2006134358A1
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WO
WIPO (PCT)
Prior art keywords
sensor
sensing member
container
receiver
transmitter
Prior art date
Application number
PCT/GB2006/002180
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English (en)
Inventor
Alan Douglas Thomas
Brian Johnson
Original Assignee
First Inertia Switch Limited
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by First Inertia Switch Limited filed Critical First Inertia Switch Limited
Publication of WO2006134358A1 publication Critical patent/WO2006134358A1/fr

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F23/00—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm
    • G01F23/22—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water
    • G01F23/28—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water by measuring the variations of parameters of electromagnetic or acoustic waves applied directly to the liquid or fluent solid material
    • G01F23/296—Acoustic waves
    • G01F23/2965—Measuring attenuation of transmitted waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
    • G01F25/00—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume
    • G01F25/20—Testing or calibration of apparatus for measuring volume, volume flow or liquid level or for metering by volume of apparatus for measuring liquid level

Definitions

  • the present invention relates to a sensor for sensing fluid level.
  • An illustrative application of the invention is sensing fuel level in automotive fuel tanks. However the invention is not limited thereto.
  • Another type of sensor used much less frequently in automotive fuel tanks is an ultrasonic sensor which measures the time for an echo to return from the surface of the fuel to the sensor to calculate its depth. This device can only measure the fuel depth in one location.
  • the amount of fluid in a container might be detected by reverberating the container and its contents with ultrasonic vibrations and monitoring the decay of the reverberations as energy is lost from the system.
  • a relatively high-powered acoustic generator is acoustically coupled to the container walls to create the reverberations.
  • results and accuracy are subject to the container walls remaining free from dirt, ice or other acoustic energy absorptive materials.
  • This method requires a relatively high powered acoustic generator to cause sufficient reverberations in the whole tank and contents so that adequate sensitivity is attained.
  • the article "Liquid Level Sensor using Ultrasonic Lamb Waves” by Sakharov, Kuznetsov, Zaitsef, Kusnetsova and Joshi, Ultrasonics 41 (2003) 319-322” describes a non-invasive method of detecting liquid level in closed metal tanks. The method is based on the use of ultrasonic Lamb waves propagating along the tank wall.
  • a level sensor proposed in the paper uses two pairs of transducers to generate and detect Lamb waves propagating along the circumference of a gas tank. Pulsed waves are used.
  • This method has the disadvantage that the optimal wave frequency depends on the tank wall thickness and wall material, so different tanks require different frequencies.
  • An embodiment of the invention provides a sensor for sensing fluid level, comprising an elongate sensing member capable of propagating Rayleigh-Lamb waves, a transmitter acoustically coupled to the sensing member for generating Rayleigh-Lamb waves for propagation along the member, and a receiver acoustically coupled to the sensing member for detecting the Rayleigh-Lamb waves.
  • An example sensor can be installed in a container or vessel, for example a tank, to detect fluid therein.
  • the sensor can operate independently of the container or vessel and can be wholly independent of the structure and materials of the container or vessel.
  • An example sensor can further comprise an acoustic coupler coupling the transmitter to the receiver for propagating waves generated by the transmitter to the receiver in addition to propagation of waves via the sensing member.
  • An example sensor can comprise a sensing member made of an elastic solid such as metal, plastic or ceramic.
  • this member may be steel.
  • this member could comprise copper or aluminium or an alloy thereof.
  • Plastic moulded or composite sensing members may be suitable provided they retain suitable elastic properties under required operating conditions and do not substantially attenuate the waves.
  • a container for containing fluid can include an embodiment of a sensor according to the present invention.
  • the container may be a tank, for example, a fuel tank of a vehicle.
  • the container may be an open tank or reservoir.
  • the sensor can be acoustically decoupled from the container.
  • the sensor can be used to detect the level of fluid in the container.
  • the fluid may be liquid, emulsion or slurry.
  • the container may be a tank, for example, a vehicle fuel tank, a reservoir, an open tank, a pipe, or other vessel.
  • an example of a sensor according to the invention can allow the designer of the fuel tank greater freedom in locating the low point of the fuel tank away from the pump assembly point. This can allow the design of a fuel tank to include more than one low-spot as will be described hereinafter.
  • An example of the sensor of the present invention does not need parts that move either with the fluid or with applied accelerations or shock that can create wear to the detriment of the sensor.
  • An example of the sensor of the present invention can operate independently of the container.
  • An example of the sensor of the present invention can operate to detect fluid level in a container independently of changes in the acoustic characteristics of the container caused by external damping agents.
  • An example of the invention can also provide a vehicle having a tank containing a sensor according to the invention.
  • Figure 1 is a schematic cross-sectional diagram of a vehicle fuel tank in which there is an example of a sensor according to the present invention
  • FIGS. 2 and 3 illustrate alternative versions of the sensor
  • Figure 4 is a schematic cross-sectional view of another vehicle fuel tank showing another example of a sensor according to the present invention.
  • Figure 5 is a cross-sectional view of a reservoir in which there is an example of a sensor according to the present invention.
  • Figure 6 illustrates an example graph of mode velocity against frequency
  • Figure 7 is a flow chart illustrating an example of the steps of calibrating a sensor according to the present invention.
  • Figure 8 is a flow chart illustrating an example of the steps of detecting a fluid level according to the present invention.
  • Figure 9 illustrates an example graph of a transceiver voltage response against time
  • Figure 10 illustrates an example graph of the attenuation of various wave modes at various frequencies.
  • a fuel tank 2 on a vehicle comprises a closed container having a fuel inlet pipe 4 having a cap 5.
  • a pump 6 is at the bottom of the fuel tank for delivering fuel to a fuel outlet pipe 8.
  • the tank contains a fluid 15, for example a liquid, and, above the fluid, air or another gas 13.
  • a sensor 1 is able to detect the level 17 of the fluid 15.
  • a sensor 1 Inside the tank is an example of a sensor 1 according to the present invention.
  • the sensor 1 is supported in the tank by a support 18 which acoustically decouples the sensor 1 from the tank 2.
  • the mounting may be a bracket made of a plastic material that has poor acoustic transmission properties.
  • the sensor In an automotive fuel tank where the designers limit the number of openings into the tank (to reduce opportunities for fuel and vapour emissions) the sensor may be mounted on a plastic (typically acetal) fuel pump/filter assembly bracket or to the sealing plug assembly above the fuel pump/filter assembly.
  • the sensor 1 comprises an elongate sensing member 10, which is of an elastic solid material suitable to propagate acoustic waves. It can, for example, be a metal, a ceramic, or a plastic material. Some specific examples can include steel, copper, aluminium, copper alloy, aluminium alloy, and an injection moulded or extruded material that has the rigidity and elastic properties for the required operating conditions.
  • the sensing member 10 is elongate and has a rectangular cross-section.
  • the sensing member 10 can be a rectangular plate.
  • the thickness used is related to the acoustic frequency used. For cost reasons, it is desirable to use as thin a material as possible. However, the thinner the material, the higher the frequencies that are needed, and generating and sensing higher frequencies is more difficult and more expensive.
  • the thickness can be in the range of 0.2mm-10mm. In one example, a thickness of 6.3mm and a frequency of around 0.4MHz may be used.
  • the plate width can be in the range 10mm to 100mm. The plate dimensions could be scaled up for large industrial tanks. It may be possible to create the waves in a thin walled cylinder.
  • the sensor 1 extends vertically in the tank from above the maximum fuel level to a low point L which in this case is, for example, a sump spaced away from the fuel pump assembly 6.
  • the sensor 1 of Figure 1 has a transmitter 12, T and a receiver 14, R both connected at the top end of the sensing member 10.
  • the transmitter 12, T is arranged to excite the sensing member 10 so that Rayleigh-Lamb waves are generated and propagated along the sensing member 10.
  • the sensing member 10 is arranged to reflect the transmitted waves from its bottom end back to a receiver 14, R at the top end of the sensing member 10.
  • the transmitter 12, T may be an electromagnetic-acoustic transducer, a magneto-strictive transducer or a piezoelectric transducer amongst other examples.
  • the receiver 14, R may also be an electromagnetic-acoustic transducer, a magneto- strictive transducer or a piezoelectric transducer amongst other examples. In one example the same transducer is used in one mode as a transmitter and in another mode as a receiver.
  • the senor 1 is partially immersed in the fluid.
  • the transmitter 12, T is arranged to generate high-frequency (ultrasonic) waves which are propagated along the sensing member 10 as Rayleigh-Lamb waves.
  • the dimensions of the sensing member 10 may be optimised for a desired wave transmission to reduce the power requirement of the transmitter and optimise efficiency.
  • Fluid in contact with the sensing member will absorb some of the transmitted acoustic energy. Acoustic energy is absorbed by and dispersed into the fluid in contact with the sensing member 10. The amount of energy which is absorbed and dispersed depends on the depth of immersion of the sensing member into the fluid. Thus, the attenuation of the transmitted wave detected by the receiver indicates the length of the sensing member submerged in the fluid and thus the depth of the fluid.
  • the sensing member is designed to propagate Rayleigh-Lamb waves. Some modes of the wave may couple with the fluid. Other wave modes may create little displacement perpendicular to the surface of the sensing member at its surface and couple little energy into the fluid.
  • a processor 16 controls the transmitter and receiver and determines from the transmitted and received waves the depth of the fluid.
  • the processor 16 can be implemented as a microcontroller, a microprocessor, or a special purpose logic (for example an application specific integrated circuit (ASIC)) and includes memory (for example RAM and Flash RAM) and a CPU or other processing structure.
  • ASIC application specific integrated circuit
  • Figure 1 illustrates an example of a sensing member 10 where the sensing member is straight and arranged vertically in the fuel tank 2, the invention is not limited thereby, and other shapes and arrangements can be used.
  • the sensing member 101 may be curved having a transmitter 12, T at one end and a receiver R, 14 at the other end.
  • the transmitter 12 and the receiver R, 14 are shown side by side at the same location. They may be housed in a common housing indicated by the dashed box. However, the transmitter 12 and the receiver 14 may be spaced apart.
  • the sensing member 101 may extend from the transmitter at a level above the normal maximum fluid level to the bottom of the tank and then curve back to the receiver, also placed above the normal maximum fuel level at a location away from the transmitter.
  • the transmitter T, 12 may be at one end of the sensing member 10 and the receiver R, 14 at the other. As shown in Figure 3 the transmitter T, 12 may be at the top of the sensing member and the receiver at the bottom or vice versa.
  • a fuel tank 21 may have a complex shape; in this example it has two sumps each at different levels.
  • the sensing member 103 is curved having one end in one sump and the other end in another sump.
  • receivers 14, Rl and 14, R2 are at the respective ends of the sensing member 103 and the transmitter 12, T is placed on the sensing member 103 intermediate the two receivers.
  • the transmitter 12, T may be placed at the highest point of the sensing member above the maximum fuel level. Alternatively it may be at a lower location subject to immersion.
  • a fuel pump 6 is connected to the sumps by fuel lines 81, 82, and the processor 16 is coupled in any convenient manner to the receivers 14 and the transmitter 12.
  • Figure 5 shows an open tank or reservoir having a sensing member 104 which is inclined and reaching to the lowest point of the reservoir.
  • the transmitter 12 and receiver 14 are both placed at the top of the sensing member 104 above the normal maximum fluid level.
  • the Rayleigh-Lamb waves are arranged to be transmitted along the sensing member 104 and reflected from its bottom end.
  • another acoustic coupling 200 can be arranged between the transmitter and the receiver.
  • This short coupling 200 is arranged to be always above, or always below, the liquid level.
  • the transmitting wave arriving at the receiver through this link can be read by the receiver before the wave which has travelled through the sensing member 10 arrives at the receiver. Variations in the form and strength of the transmitted signal can be accounted for in the processing performed by processor 16 of both received signals to improve accuracy throughout the life of the acoustic transducers. Such inaccuracy may occur if the acoustic coupling of one or both transducer to the sensing member 10 degrades during the lifetime of the sensor.
  • two or more sensors are provided in a tank or other vessel. This is useful if the tank has a complex shape with several separate low points and/or compartments.
  • the senor relies upon the order of receiving certain wave modes. If the sensing member is configured so that it is free of discontinuities, this can avoid potential ambiguity caused by a returned wave being a reflection from a discontinuity rather than from the end of the sensing member. It is therefore advantageous for the sensing member to be free of discontinuities.
  • the fluid level can be determined as described below.
  • the senor 1 is calibrated before use. Calibration can be done in a factory before the user receives the apparatus. Alternatively, the user can perform the calibration. In order to calibrate the apparatus, a range of frequencies may have to be used, with the sensing member immersed in fluid at any range of depths varying between the tank being full and it being empty.
  • the sensing member 10, 101, 102, 103, 104 is placed in the container as described in relation to Figures 1-5.
  • a pulse of several cycles at a given frequency is sent down the sensing member 10, 101, 102, 103, 104.
  • the pulse is converted into multiple modes of vibration. Each of these modes may travel at different velocities, and each mode may be attenuated due to energy loss to the fluid.
  • the modes are attenuated more as they pass through the fluid covered length of the sensing member than they are when they pass through the length of the sensing member above the fluid level.
  • Each mode may be attenuated to a different extent, and this depends upon the degree of disturbance a wave mode causes at the sensing member/fluid interface.
  • An example of this is shown in the graph of Figure 10.
  • the number of modes created is related to the frequency of the pulse, the thickness of the sensing member 10, 101, 102, 103, 104 material and the elastic properties of the sensing member.
  • the velocity at which the modes travel along the sensing member is also related to these properties.
  • the modes are received at the receiver R.
  • Calibration data is stored in the memory of the processor 16, which allows the processor 16 to calculate the depth / level / volume of the fluid when the sensor is in operation.
  • the chosen mode should be one which is significantly affected by attenuation. This can be tested by placing the sensing member in a fluid and measuring the received amplitude of the chosen mode and comparing it with the unattenuated amplitude. If the chosen mode is one which will arrive at the receiver with some separation from other modes, this will simplify the process of selecting the chosen mode at the receiver.
  • Figure 6 illustrates the results of a simulation for a particular sensor member and particular fluid parameters. Note that different parameters will give different results, for example, if a thinner sensing member is used, a higher frequency will generally be required to produce a certain mode.
  • Frequencies of up to 1 MHz are shown in Figure 6.
  • the velocity of the modes created in the sensing member 10, 101, 102, 103, 104 were plotted.
  • three modes labelled 'a', 'b', and 'c'
  • mode V travels at the greatest velocity
  • mode 'b' travels at the lowest velocity
  • mode 'a' travels at a velocity between that of modes V and 'b'.
  • a frequency of around 0.4MHz may be chosen for the particular sensor member, and mode b may be chosen for that particular frequency. This is because mode b will arrive at the receiver last, and spaced apart from the other modes, making it easier to identify at the receiver R, 14. It should also be checked that mode b is significantly affected by attenuation. If it is not, another mode should be chosen.
  • a frequency can be chosen, a number of cycles can be chosen, and a mode can be chosen.
  • the processor 16 then generates and stores calibration data related to the selected mode, as described below.
  • Amplitude x Amplitude re y.e -ax
  • Formula and A and B are rearrangements of the same formula, 'x' is distance the wave travelled in contact with the fluid, and is measured in metres.
  • Formula B is resolved for x.
  • Alpha is a constant, called the attenuation constant, with units np/m. Alpha may be fixed for a particular sensor / fluid combination or determined by calibration with two fluid levels.
  • Amplitude ref is a reference value also measured in metres (m).
  • Calibration values can be determined by taking measurements of the received amplitude of a particular chosen mode at one or two specific fill levels, and then using these reference values to generate intermediate values by applying Formula B.
  • a look-up table for a chosen mode of a chosen frequency can then be completed with fill levels in one column and the corresponding amplitudes of the received mode in the other column. Such a look-up table may be saved by the processor 16.
  • measurements of the received amplitude of a particular mode for a set of fill levels (depths) can be taken, and a look-up table completed by the measured values themselves, and stored by the processor 16 without the use of Formula B.
  • Formula A can be used by the processor 16 to calculate x each time a measurement of a current wave mode amplitude is taken.
  • the amplitude of at least one chosen mode arriving at the receiver R is measured, and the corresponding data is stored by the processor 16 as described above.
  • Figure 7 illustrates a flow diagram of an example calibration of the sensor according to the present invention.
  • the frequency and mode are chosen.
  • the fluid depth is adjusted to generate calibration data.
  • the calibration data and information about the chosen frequency and mode are stored in processor memory. Steps A, B and C can be carried out in, for example, a factory.
  • the calibrated sensor can then be operated at step D.
  • the operating step D is illustrated in more detail in Figure 8. The step of operating can take place when the sensor is fitted to, for example, a vehicle fuel tank. When the sensor has been calibrated in this way, it is operable to sense fluid level.
  • sensing member 10, 101, 102, 103, 104 is placed into a container of fluid.
  • the processor 16 causes the transmitter T, 12 to emit a pulsed wave of a chosen frequency to the sensing member 10, 101, 102, 103, 104.
  • the frequency and number of cycles to be used could have been chosen during calibration.
  • the mode of interest could also have been chosen during calibration. Each of these modes may travel at different velocities, and each mode may be attenuated due to energy loss to the fluid. The modes may therefore arrive at the receiver 14 at different times, and in a specific and known order.
  • the processor 16 can sample the detected wave modes to generate digital data representative of the amplitude of the wave at each sample.
  • the calibration data which is stored in the memory of the processor may also comprise sample data measured and stored during calibration.
  • the memory of the processor includes at least some persistent memory (for example an electrically erasable programmable read only memory (EEPROM)) for the storage of the calibration data so that this can be maintained even if the power is turned off.
  • EEPROM electrically erasable programmable read only memory
  • the amplitude of the chosen mode at the receiver R, 14 is measured, and this value is compared with the calibration data stored by the processor 16 during calibration.
  • the processor can then calculate or discover the fluid level / fluid depth / fluid volume, either by use of a look up table derived during calibration, or by the use of Formula A or B and reference values.
  • Figure 8 shows a flow diagram of the steps completed during the operation of the calibrated sensor 1.
  • a pulse is transmitted down the sensing member.
  • the modes of the pulse are received at the receiver R.
  • the chosen mode is identified.
  • the amplitude of the chosen mode is measured.
  • the measured amplitude of the chosen mode is compared to the respective calibration data.
  • the fuel level is calculated by the processor 16.
  • Figure 9 illustrates an example of a transceiver voltage response for a particular sensor member, particular fluid parameters, a particular chosen frequency of pulse, and a particular chosen number of cycles.
  • the frequency of pulse and number of cycles may have been chosen during calibration. It is possible to measure
  • I l only the voltage response at the receiver R, but in this example a transceiver has been used in order to measure the voltage response at both the transmitter T, 12 and the receiver R, 14.
  • the example shown in Figure 9 corresponds to the example discussed above in relation to Figure 6.
  • a frequency was chosen at which three modes would be present in the sensing member, and mode b was chosen because it had good attenuation caused by the sensing member being in contact with the liquid and it was separated from the two other modes that returned before it.
  • a pulse of the chosen frequency and number of cycles was emitted down the sensing member 10, 101, 102, 103, 104.
  • This pulse produces the waveform present between 0 and about 70 ⁇ s of the graph of Figure 9. While the pulse travels down the sensing member 10 and back to the receiver R, there is little detected by the transceiver.
  • the first of the returning modes is detected at the transceiver.
  • the second of the modes is detected, and at around 155-175 ⁇ .s the third mode is detected.
  • the chosen mode was mode b, which is known to arrive third, and so the processor 16 measures the amplitude of this mode.
  • the reference value of this mode is known, and so the depth of the fluid can be found using formula B (or A). Alternatively, if there is a look-up table stored in the processor, this table may be utilised to find the fluid level.
  • Figure 10 illustrates an example of the attenuation of several wave mode amplitudes in a sensor member. It can be seen that different mode waves are affected by different amounts at different frequencies. For example, wave mode w is not attenuated at a frequency of approximately 0.6MHz, but is attenuated more at frequencies around 0.44MHz. The knowledge of a mode which is not attenuated, or only attenuated a little, at a particular frequency, can provide a useful control.
  • Energy losses from the transducer couplings to the sensing member may vary or degrade over the life of the sensor, and this can affect the amplitude of the wave modes in the sensing member. This, in turn, can affect the measurement of the fluid level as the wave transmission path becomes degraded.
  • a proportionate correction can be made to the amplitude of any wave mode which is affected by coupling to the fluid during the electronic processing of the received signal, or a warning of an error can be provided to the user.
  • the processor 16 may detect some attenuation of a wave mode which is not usually attenuated at that particular frequency (for example wave mode w at 0.6MHz in Figure 10). It may then be assumed that the detector efficiency is reduced, or that some other error has appeared in the apparatus. In order to overcome this problem, the processor 16 can compute a proportionate correction from the attenuation of the wave mode which is not usually attenuated. Subsequently, any measured value of a received wave mode can be multiplied by this factor. Alternatively, an error warning can be provided to the user.
  • This type of control can be used in parallel with the control discussed in relation to short coupling 200 shown in Figure 2.
  • a sensor for sensing fluid level comprising an elongate sensing member capable of propagating Rayleigh-Lamb waves, a transmitter acoustically coupled to the sensing member for generating Rayleigh-Lamb waves for propagation along the member, and a receiver acoustically coupled to the sensing member for detecting the Rayleigh-Lamb waves.
  • the fluid level sensed may be a liquid level, or could be the level of an emulsion or slurry.
  • a method of operating a sensor comprising: calibrating the sensor by generating calibration data of at least one wave mode determined to be significantly unaffected in amplitude when passing through a sensing member immersed in liquid; and to detect degradation in the sonic transmission path for the purpose of providing correction to the sensor level signal.
  • a method of operating a sensor comprising: calibrating the sensor by generating calibration data of at least one wave mode determined to be significantly unaffected in amplitude when passing through a sensing member immersed in liquid; and to detect degradation in the sonic transmission path for the purpose of providing a warning of an error condition.

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  • Physics & Mathematics (AREA)
  • Fluid Mechanics (AREA)
  • General Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Electromagnetism (AREA)
  • Thermal Sciences (AREA)
  • Measurement Of Levels Of Liquids Or Fluent Solid Materials (AREA)

Abstract

La présente invention concerne une sonde pour capter un niveau de fluide. Il comprend un élément sensible oblong capable de faire propager des ondes de Rayleigh-Lamb, un émetteur acoustiquement couplé à l'élément sensible de façon à générer des ondes de Rayleigh-Lamb à faire propager le long de l'élément, et un récepteur acoustiquement couplé à l'élément sensible de façon à détecter les ondes de Rayleigh-Lamb.
PCT/GB2006/002180 2005-06-14 2006-06-14 Sonde a onde acoustique pour capter un niveau de fluide WO2006134358A1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
GB0512107.4 2005-06-14
GB0512107A GB2427273A (en) 2005-06-14 2005-06-14 Fluid level sensor using Rayleigh-Lamb waves

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WO2006134358A1 true WO2006134358A1 (fr) 2006-12-21

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