CN110147567B - Simulation method for obtaining internal sound field of ultrasonic flowmeter in non-ideal flow field - Google Patents
Simulation method for obtaining internal sound field of ultrasonic flowmeter in non-ideal flow field Download PDFInfo
- Publication number
- CN110147567B CN110147567B CN201910260871.XA CN201910260871A CN110147567B CN 110147567 B CN110147567 B CN 110147567B CN 201910260871 A CN201910260871 A CN 201910260871A CN 110147567 B CN110147567 B CN 110147567B
- Authority
- CN
- China
- Prior art keywords
- flow field
- field
- simulation
- flow
- sound
- Prior art date
- Legal status (The legal status 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 status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01F—MEASURING VOLUME, VOLUME FLOW, MASS FLOW OR LIQUID LEVEL; METERING BY VOLUME
- G01F1/00—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow
- G01F1/66—Measuring the volume flow or mass flow of fluid or fluent solid material wherein the fluid passes through a meter in a continuous flow by measuring frequency, phase shift or propagation time of electromagnetic or other waves, e.g. using ultrasonic flowmeters
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
- G01H9/002—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means for representing acoustic field distribution
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Abstract
The invention relates to a simulation method for obtaining an internal sound field of an ultrasonic flowmeter in a non-ideal flow field, which comprises the following steps: the method comprises the following steps: the flow field was simulated using a CFD module turbulent SST interface in COMSOL software. Step two: directly coupling the non-ideal flow field obtained in the step one into the simulation of the sound field: based on the COMSOL multi-physical field coupling function, flow field simulation results are extracted according to space coordinates through a consistent mapping function in component definition. Step three: ultrasonic propagation tracks and propagation times under non-ideal flow fields are obtained by using COMSOL ray acoustic module simulation. Step four: and a COMSOL pneumatic acoustic module and a linear potential flow frequency domain interface are used for obtaining the steady-state sound pressure distribution of the ultrasonic flowmeter in a non-ideal flow field.
Description
Technical Field
The invention belongs to the technical field of flow measurement, and relates to a simulation method for obtaining an internal sound field of an ultrasonic flowmeter in a non-ideal flow field.
Background
Ultrasonic flow meters have been developed rapidly in recent decades, and are widely applied to the fields of water conservancy and hydropower projects and natural gas trade settlement by virtue of the advantages of non-contact measurement, high precision, wide range ratio, convenience in installation and measurement and the like as a novel flow meter. As an important instrument, the ultrasonic flowmeter has many advantages, but has the defects of poor adaptability to flow field changes, unstable precision and the like, so that the ultrasonic flowmeter analyzes the propagation law of ultrasonic waves in different flow fields, improves the measurement precision, and expands the measurement range to become a focus of attention. Therefore, a simulation method for accurately and effectively obtaining a sound field is necessary.
In the classical time difference method ultrasonic flowmeter principle, the flow field is generally assumed to be ideally and uniformly distributed, the acoustic path between two transducers is a straight line, and the straight line distance between the two transducers is directly used as the sound channel length; in addition, the sound channel angle also takes a fixed value and is the included angle between the installation probe and the pipeline axis. However, in actual measurement, the flow field affects the sound field, so that the ultrasonic track is deviated, and the sound pressure is attenuated. The upper limit flow velocity of the gas ultrasonic flowmeter can reach 30-40 m/s, which is very similar to the sound velocity of 340m/s in air, so the influence of the ultrasonic flowmeter cannot be ignored. Especially, the flow fields in actual measurement are all non-ideal flow fields, so that the ultrasonic track is irregularly shifted, and the sound pressure is nonlinearly attenuated. These variations can have a severe impact on the received signal and thus on the measurement accuracy. Especially in high-speed gas measurements, the acceptance signal can fluctuate greatly, resulting in false time triggers when measuring time using the dual-threshold method, resulting in inaccurate measurement of the propagation time and poor repeatability of the measurement system. In summary, the accurate acquisition of the sound field distribution inside the ultrasonic flowmeter can improve the measurement accuracy of the gas ultrasonic flowmeter, and therefore, a simulation method capable of acquiring the sound field inside the ultrasonic flowmeter under the influence of a non-ideal flow field is necessary.
Disclosure of Invention
The invention provides a simulation method capable of directly applying non-ideal flow field distribution to obtaining an internal sound field of an ultrasonic flowmeter. By using the method, the non-ideal flow field caused by the transducer and complex non-ideal flow fields such as single elbow downstream and double elbow downstream can be considered when the sound field in the ultrasonic flowmeter is obtained through simulation. The obtained sound field is more consistent with the actual measurement condition, guidance can be provided for the design and installation of the ultrasonic transducer, and the precision of the ultrasonic flowmeter is improved. The technical scheme is as follows:
a simulation method for obtaining an internal sound field of an ultrasonic flowmeter in a non-ideal flow field comprises the following steps:
the method comprises the following steps: flow fields were simulated using a CFD module turbulent SST interface in COMSOL software: initializing the distance from the fluid to the pipe wall, so that the solution near the pipe wall is more accurate, the calculation of a flow field near a probe is facilitated, the flow field is described by setting parameters of inlet flow velocity, outlet boundary, turbulence intensity and turbulence length under different conditions, the grid size is set to be one time of ultrasonic wavelength, and non-ideal flow fields under different conditions are obtained by setting different geometric models of the pipeline.
Step two: directly coupling the non-ideal flow field obtained in the step one into the simulation of the sound field: based on the COMSOL multi-physical field coupling function, the flow field simulation result is extracted according to the space coordinate through a consistent mapping function in the component definition. The dependent variable in the sound field simulation solver is set to be a solution based on CFD flow field simulation, so that the acoustic module and the flow field module are in butt joint, and the flow field simulation result can be directly used through the subsequent arrangement of the acoustic module, so that the coupling of the sound field of the flow field is realized, and the sound field under the non-ideal flow field is obtained.
Step three: ultrasonic propagation trajectories and propagation times under non-ideal flow fields are obtained by using COMSOL ray acoustic module simulation: the boundary condition is set to frozen; the grid size is set to one wavelength; setting a background flow field according to the first step and the second step; the solver is set to specify the calculation time in a list form, the iteration step length is 0.05us, and the dependent variable is set to be a solution based on CFD flow field simulation; a point sound source simulation transducer is used for emitting a plurality of rays with 45 degrees as a direction reference, and 41 rays are emitted within +/-5 degrees.
Step four: using a COMSOL pneumatic acoustic module and a linear potential flow frequency domain interface to obtain the steady-state sound pressure distribution of the ultrasonic flowmeter in a non-ideal flow field: setting a sound source based on basic parameters of a real transducer, and setting the surface vibration speed of the probe by using a normal speed boundary condition; setting a background flow field according to the first step and the second step; the grid size is set to be 1/6-1/5 of the wavelength lambda; the source frequency was set to 125KHZ in the solver and the dependent variable was set to a solution based on CFD flow field simulation.
The invention provides a method for acquiring an internal sound field of an ultrasonic flowmeter based on COMSOL multi-physical field simulation software, and can consider the working conditions of non-ideal flow fields during actual measurement when the sound field is acquired, wherein the working conditions comprise the non-ideal flow fields caused by inserting transducers, and complex non-ideal flow fields such as single elbow downstream, double elbow downstream and the like. The sound field in the ultrasonic flowmeter under different conditions can be obtained more accurately.
Drawings
FIG. 1 cloud of ideal turbulent flow field
FIG. 2 is a cloud of non-ideal flow fields
FIG. 3 trace offset schematic
FIG. 4 trace offset comparison for two conditions
FIG. 5 sound pressure simulation results
Detailed Description
In the following, a sound field simulation method in an ultrasonic flowmeter under a non-ideal flow field considering the influence of a probe will be introduced by taking the DN100 radial type mono-channel gas ultrasonic flowmeter as an example. The ultrasonic flowmeter is basically set to be 100mm in diameter and 200mm in length of a pipeline according to an actual common ultrasonic flowmeter, a probe is set in a semi-insertion mode, the radius of the probe is set to be 15mm according to the size of a common probe, and the two transducers are oppositely arranged on two sides of the pipeline at an angle of 45 degrees. The frequency of the transducer is 125kHz, the ultrasonic wavelength lambda is 2.7mm, the medium is air, the acoustic parameter uses the self-contained default parameter of the material in COMSOL, and the density rho 0 ＝1.204kg/m 3 The speed of sound c =343m/s.
The parameter setting and implementation method of each step is given by combining the step method in the technical scheme:
the method comprises the following steps: the flow field was simulated using the CFD module turbulence in COMSOL software. Among a plurality of model interfaces of the CFD module, the SST interface which is very sensitive to fluid flow near the wall surface is selected, so that the flow field near the transducer can be better obtained. In the simulation process, the setting of the boundary conditions of the inlet and the outlet is very important. In general, a long straight pipe section of 100D-200D is added before the model to ensure that the fluid turbulence is fully developed. The turbulence fully developed by the long straight pipe section can be equivalent to the flow field distribution calculated by a turbulence formula. Therefore, in order to reduce the model geometry and shorten the computation time, an interpolation function of the flow velocity v and the radial distance y from the pipe axis is constructed by MATLAB based on the turbulence formula, is imported into the interpolation tool defined by the COMSOL component, is defined as int1 (y), and is directly called in the inlet flow velocity definition. The turbulence formula is as follows:
where v (y) represents the axial flow velocity at a radial distance y from the axis of the pipe, v max For maximum flow rate at the center of the pipe, n is determined by Reynolds number Re and pipe wall roughnessFlow rate distribution index. For smooth tubes, it can be expressed by the prandtl equation:
the outlet boundary condition is set to a pressure condition, the outlet pressure is set to 0, and the inhibit backflow option is selected to indicate that fluid continues to flow after the spool piece.
In addition, the turbulence intensity I and the turbulence length L for describing the motion characteristics of the flow field need to be set T ：
L T ＝0.07D
In the formula, re is Reynolds number, and D is the diameter of the pipeline.
To facilitate coupling to the acoustic field, the model sets the mesh size to one ultrasonic wavelength. By arranging different pipeline models, non-ideal flow fields under different conditions can be obtained.
Step two: directly coupling the non-ideal flow field obtained in the first step into the simulation of the sound field by means of a COMSOL multi-physical field coupling function. Different forms of coupling connections of multiple physical field components can be implemented using the coupling tools in the COMSOL component definition. The invention defines the simulation result of the CFD module as a new function idmap1 (x) by utilizing the consistent mapping function in component coupling, wherein x is an optional variable. The consistent mapping function is set as follows: selecting a geometric frame based coordinate system for both the frame source and the target frame; selecting a geometric model in CFD simulation in a selection domain; the target geometry selects the geometric model of the sound field simulation after label selection. It should be noted that the geometric model coordinates in the sound field simulation correspond to the geometric model coordinates in the flow field simulation. In addition, the dependent variable in the sound field simulation solver is changed into a solution based on CFD simulation, so that the two modules are in butt joint. Therefore, when a sound field simulation background flow field is set, the selectable variable x is taken as the flow velocity U, the idmap1 (U) function can be used for completely projecting the flow field information into the sound field based on the space coordinate, the coupling of the flow field and the sound field is realized, and the sound field under the non-ideal flow field is obtained.
Step three: ultrasonic propagation tracks and propagation times in non-ideal flow fields are obtained by simulation of a COMSOL ray acoustic module. The geometric model coordinates need to correspond to the flow field simulation model.
(1) Boundary conditions: because the ray acoustic module is mainly used for researching ultrasonic propagation track information and obtaining propagation time without considering problems such as reflection and the like, the boundary is set as a freezing condition, and the representative ray does not change after reaching the boundary, so that the required information can be obtained in post-processing conveniently.
(2) Background flow field: and acquiring a required non-ideal flow field based on the step one, and coupling the non-ideal flow field into the sound field simulation based on the step two. The non-ideal flow field is projected directly to the ray-acoustic module based on the spatial coordinate frame using idmap1 (U).
(3) Grid division: because a ray acoustic module is not used for solving sound pressure, and experiments show that the influence of the grid size on ray tracks and time is not large, the size of the grid is set to be 2.7mm which is one time of the wavelength of the ultrasonic wave by considering the memory of a computer and the calculation time.
(4) Setting a solver: the step size and the computation time of the iteration are specified in the form of a time list. And (4) comprehensively considering the memory of the computer, calculating the time calculation error, wherein the time step is 0.05us. And setting the dependent variable as a solution based on CFD flow field simulation, and connecting the flow field simulation with the sound field simulation.
(5) Setting a sound source: the point sound source replaces a piston-type sound source, and the pointing angle of the piston-type sound source is considered
Therefore, a plurality of rays are emitted by taking 45 degrees as a direction reference, and 41 rays are emitted within the range of +/-5 degrees so as to simulate a piston type sound source. The dependent variable setting needs to be changed into a steady-state solution based on CFD simulation, and the flow field-sound field coupling is convenient to realize. />
Step four:
(1) Setting a sound source: the ultrasonic transducer for gas actually measured by the laser Doppler vibration meter can know that the meter is excited by applying 400V peak valueThe surface vibration velocity is 0.327m/s, so the sound source vibration velocity u is set a ＝0.327m/s。
(2) Background flow field: and acquiring a required non-ideal flow field based on the step one, and coupling the non-ideal flow field into the sound field simulation based on the step two. The non-ideal flow field is projected directly to the aero-acoustic module using idmap1 (U) based on a spatial coordinate frame.
(3) Grid division: the sound field distribution research has higher requirements on the grid size. To ensure that the calculation is accurate, it is necessary to ensure that the wavelength of the acoustic wave can be divided by a plurality of grids, i.e. the grid size is smaller than the wavelength of the acoustic wave. The smaller the grid size, the more accurate the simulation results. The method adopts a free subdivision triangle mode, considers factors such as computer memory and the like, and sets the mesh size to be 1/6-1/5 of the wavelength lambda on the premise of meeting the precision requirement, namely the maximum mesh size is 0.54mm, the minimum mesh size is 0.45mm, and the mesh growth rate is 1.5.
(4) Boundary conditions: and eliminating the influence of the reflected wave on the result by adopting plane wave radiation, and acquiring the sound pressure in the transmission process and the receiving position.
(5) Solver configuration: the frequency domain module mainly sets the model solution frequency, which is set to a value of 125KHZ based on the sound source frequency. And setting the dependent variable as a solution based on CFD flow field simulation, and connecting the flow field simulation with the sound field simulation.
In order to verify the influence of the simulation provided by the invention, which considers the non-ideal flow field, turbulence is taken as an example, and the case of considering the transducer and the case of not considering the transducer are compared. The flow rate results obtained by the time difference method are compared with each other in an important point. The DN100 radial type single-channel gas ultrasonic flowmeter is taken as a research object, wherein the theoretical value of the sound path angle phi =45 degrees, the theoretical sound path L =141.4214mm, and the theoretical sound path angle phi is based on the forward and backward flow propagation time t d ,t u The traditional flow calculation formula is as follows:
TABLE 1 transducer with transducer flow rate comparison
In the context of table 1, the following,
inlet average flow rate. VL is the average flow velocity on the axes of the two transducers, namely the flow velocity obtained by simulation after being influenced by the transducers, and the result of the transducers is considered to be closer to VL, namely the simulation method provided by the invention is closer to the real condition, so that the accuracy of sound field analysis in the ultrasonic flowmeter is improved.
TABLE 2 transducer with transducer trajectory offset comparison
In Table 2, r is the distance from the source and Δ L is the amount of track offset from the line connecting the midpoints of the upstream and downstream transducers. In actual measurement, the transducer goes deep into the pipeline to generate negative flow velocity vortex in the flow field nearby the transducer. Comparing the two rows of trajectory offsets, it can be seen that when the transducer is considered, there is a negative offset, i.e. the trajectory offset caused by the actual negative flow rate vortex can be reflected. Therefore, the proposed simulation method considering the non-ideal flow field can obtain the sound field more accurately.
Claims (1)
1. A simulation method for obtaining an internal sound field of an ultrasonic flowmeter in a non-ideal flow field comprises the following steps:
the method comprises the following steps: flow fields were simulated using a CFD module turbulent SST interface in COMSOL software: initializing the distance from the fluid to the pipe wall, so that the solution near the pipe wall is more accurate, the calculation of a flow field near a probe is facilitated, the flow field is described by setting parameters of inlet flow velocity, outlet boundary, turbulence intensity and turbulence length under different conditions, the size of a grid is set to be one time of ultrasonic wave, and non-ideal flow fields under different conditions are obtained by setting different geometric models of the pipeline;
step two: directly coupling the non-ideal flow field obtained in the step one into the simulation of the sound field: based on the COMSOL multi-physical field coupling function, extracting a flow field simulation result according to a space coordinate through a consistent mapping function in component definition; setting a dependent variable in a sound field simulation solver as a solution based on CFD flow field simulation, so that an acoustic module is in butt joint with a flow field module, and the flow field simulation result can be directly used through the subsequent arrangement of the acoustic module to realize flow field sound field coupling and obtain a sound field under an nonideal flow field;
step three: ultrasonic propagation trajectories and propagation times under non-ideal flow fields are obtained by using COMSOL ray acoustic module simulation: the boundary condition is set to frozen; the grid size is set to one wavelength; setting a background flow field according to the first step and the second step; the solver is set to specify the calculation time in a list form, the iteration step length is 0.05us, and the dependent variable is set to be a solution based on CFD flow field simulation; a point sound source is used for simulating a transducer, a plurality of rays are emitted by taking 45 degrees as a direction reference, and 41 rays are emitted within a +/-5-degree range;
step four: using a COMSOL pneumatic acoustic module and a linear potential flow frequency domain interface to obtain the steady-state sound pressure distribution of the ultrasonic flowmeter in a non-ideal flow field: setting a sound source based on basic parameters of a real transducer, and setting the surface vibration speed of the probe by using a normal speed boundary condition; setting a background flow field according to the first step and the second step; the grid size is set to be 1/6-1/5 of the wavelength lambda; the acoustic source frequency was set to 125KHZ in the solver and the dependent variable was set to a solution based on CFD flow field simulation.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910260871.XA CN110147567B (en) | 2019-04-02 | 2019-04-02 | Simulation method for obtaining internal sound field of ultrasonic flowmeter in non-ideal flow field |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910260871.XA CN110147567B (en) | 2019-04-02 | 2019-04-02 | Simulation method for obtaining internal sound field of ultrasonic flowmeter in non-ideal flow field |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110147567A CN110147567A (en) | 2019-08-20 |
| CN110147567B true CN110147567B (en) | 2023-04-18 |
Family
ID=67588445
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910260871.XA Active CN110147567B (en) | 2019-04-02 | 2019-04-02 | Simulation method for obtaining internal sound field of ultrasonic flowmeter in non-ideal flow field |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110147567B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112182836A (en) * | 2020-08-26 | 2021-01-05 | 河海大学 | Modeling simulation method of condenser ultrasonic cleaner |
| CN113962169B (en) * | 2021-10-29 | 2022-10-11 | 国网上海市电力公司 | GIS breakdown discharge ultrasonic numerical simulation method considering influence of background fluid |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004078038A (en) * | 2002-08-21 | 2004-03-11 | Ishikawajima Harima Heavy Ind Co Ltd | Method for predicting silencing characteristic of nonuniform cross section pipe and nonuniform cross section sound-absorption pipe |
| CN104252559A (en) * | 2014-08-29 | 2014-12-31 | 浙江中科电声研发中心 | Numerical simulation analysis method for multi-field coupling of loudspeaker |
| CN105758474A (en) * | 2016-05-30 | 2016-07-13 | 天津大学 | Method for improving measurement accuracy of gas ultrasonic flowmeter |
| CN108416127A (en) * | 2018-02-14 | 2018-08-17 | 武汉大学 | Submarine high pressure blows down pipe-line system multiple physical field coupling simulation method and system |
-
2019
- 2019-04-02 CN CN201910260871.XA patent/CN110147567B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2004078038A (en) * | 2002-08-21 | 2004-03-11 | Ishikawajima Harima Heavy Ind Co Ltd | Method for predicting silencing characteristic of nonuniform cross section pipe and nonuniform cross section sound-absorption pipe |
| CN104252559A (en) * | 2014-08-29 | 2014-12-31 | 浙江中科电声研发中心 | Numerical simulation analysis method for multi-field coupling of loudspeaker |
| CN105758474A (en) * | 2016-05-30 | 2016-07-13 | 天津大学 | Method for improving measurement accuracy of gas ultrasonic flowmeter |
| CN108416127A (en) * | 2018-02-14 | 2018-08-17 | 武汉大学 | Submarine high pressure blows down pipe-line system multiple physical field coupling simulation method and system |
Non-Patent Citations (2)
| Title |
|---|
| Dandan Zheng.etc.."A method based on a novel flow pattern model for the flow adaptability study of ultrasonic flowmeter".《ELSEVIER》.2012,全文. * |
| 孙彦招 ; 张涛 ; 郑丹丹 ; 杨智斌 ; .气体超声流量计换能器附近回流影响声束研究.仪器仪表学报.2018,(第04期),全文. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110147567A (en) | 2019-08-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| DK202000051U1 (en) | Improved Signal Travel Time Flow Meter | |
| Zhou et al. | Multipath ultrasonic gas flow-meter based on multiple reference waves | |
| CN105698884A (en) | Improved measurement method of time difference type ultrasonic flow meter | |
| RU2478919C2 (en) | Calibration method under operating conditions of ultrasonic flow metres - counters of flow rate and volume of liquid single-phase media | |
| CN110147567B (en) | Simulation method for obtaining internal sound field of ultrasonic flowmeter in non-ideal flow field | |
| CN105758474A (en) | Method for improving measurement accuracy of gas ultrasonic flowmeter | |
| Tian et al. | Energy peak fitting of echo based signal processing method for ultrasonic gas flow meter | |
| Zheng et al. | Improvement of gas ultrasonic flowmeter measurement non‐linearity based on ray tracing method | |
| CN104390680A (en) | Flow error correction method for time difference type ultrasonic heat meter | |
| CN113671443A (en) | Deep sea target positioning method of underwater acoustic sensor network based on grazing angle sound ray correction | |
| Mu et al. | Echo signal envelope fitting based signal processing methods for ultrasonic gas flow-meter | |
| CN114001804A (en) | Calibration method and system of ultrasonic metering device based on time difference method | |
| CN114088151B (en) | External clamping type multichannel ultrasonic flow detection device and detection method | |
| Haugwitz et al. | Multipath flow metering of high-velocity gas using ultrasonic phased-arrays | |
| CN104215356A (en) | Ultrasonic-based pipeline fluid temperature measurement method | |
| CN206291930U (en) | A kind of ultrasonic wave mass flowmenter | |
| CN102680585A (en) | Ultrasonic detector based design method for water-logging probe water-spray coupling device | |
| CN109931995B (en) | Method for acquiring internal sound field of gas ultrasonic flowmeter | |
| CN102095889B (en) | Three-channel ultrasonic time difference method for measuring flow velocity | |
| CN105181050B (en) | Ultrasonic flow rate measuring instrument and the star-shaped path detection method for the instrument | |
| Zheng et al. | Study on the measurement method of wet gas flow velocity by ultrasonic flow meter | |
| Treenuson et al. | Accurate flowrate measurement on the double bent pipe using ultrasonic velocity profile method | |
| WO2015063079A1 (en) | A flow meter for ultrasonically measuring the flow velocity of fluids | |
| CN114563065A (en) | Gas ultrasonic flowmeter calibration method | |
| CN105300654B (en) | A kind of ultrasonic precision ranging system in low-speed wind tunnel |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |