CN109580765A - A kind of anti-interference biphase gas and liquid flow measuring of phase ratio method of high-responsivity - Google Patents

A kind of anti-interference biphase gas and liquid flow measuring of phase ratio method of high-responsivity Download PDF

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CN109580765A
CN109580765A CN201811421890.8A CN201811421890A CN109580765A CN 109580765 A CN109580765 A CN 109580765A CN 201811421890 A CN201811421890 A CN 201811421890A CN 109580765 A CN109580765 A CN 109580765A
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路飞
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/02Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/02Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
    • G01N27/023Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance where the material is placed in the field of a coil
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/02Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
    • G01N27/023Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance where the material is placed in the field of a coil
    • G01N27/025Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance where the material is placed in the field of a coil a current being generated within the material by induction
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/02Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
    • G01N27/04Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance
    • G01N27/06Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance of a liquid
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/72Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating magnetic variables
    • G01N27/74Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating magnetic variables of fluids

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Abstract

The invention discloses a kind of anti-interference biphase gas and liquid flow measuring of phase ratio methods of high-responsivity, belong to multiphase flow detection field.Technical solution of the present invention main points are as follows: since general detection coil magnetic field is distributed in space uniform, measured body is not in sensitive field, and conductivity, magnetic conductivity are lower, sensitivity is high when leading to traditional electromagnetic detection, poor anti jamming capability, the present invention is based on EMR electromagnetic resonance principles, work as emission system, when reception system is all in resonant state, the measurement of two-phase flow containing rate will be sensitiveer than traditional electromagnetic detection, and it is small by external electromagnetic wave interference since transmitting reception loop resonance is in same frequency.In addition the magnetic flux density of the excitation field generated using saddle-type coil measures Two-phase Flow Pipeline Transport more accurate along measurement tube axial direction distribution uniform.And the foundation of mathematical model is carried out to two phase flow on this basis, complicated two-phase flow problem is converted into relatively simple mathematical computations.

Description

A kind of anti-interference biphase gas and liquid flow measuring of phase ratio method of high-responsivity
Technical field
The invention belongs to multiphase flow detection fields.More particularly to measuring and calculating for gas-liquid two-phase flow containing rate, especially relate to And the anti-interference in two-phase flow and sensitive field detecting.
Background technique
Two-phase flow measurement is widely present in the fields such as chemical industry, petroleum, electric power, the measurement of two-phase flow containing rate and physical parameter It is of great significance to industrial production, transport.Wherein, the measurement of phase content is difficult point in two-phase flow field, because it is Characterize the basis of quality in the key of flow process, and prediction biphase gas and liquid flow, momentum and energy transmission.
The method of common diphasic stream parameter detection has: insertion type detection method: such as probe method.The detection of non-intervention mode Method: such as microwave method, optical method, electric method.Wherein electrical detection has structure simple, at low cost, fast response time and peace The advantages that Quan Xinggao, becomes everybody research hotspot.Since the conductivity between biphase gas and liquid flow is lower, result in measurement process Error, and to detection system and method design propose requirements at the higher level.
Circular coil is normally applied to two-phase flow measurement, generate the magnetic flux density of excitation field entire spatial distribution compared with Uniformly.At this point, being produced in two phase flow when the two-phase flow containing rate in the Alternating Current Excitation magnetic field in distribution uniform changes Raw eddy-current loss can generate variation therewith, and the variation of eddy-current loss can cause the size of load voltage in measuring system corresponding Variation is generated, can reflect the parameter information of gas-liquid two-phase flow containing rate indirectly by load voltage size in measuring system.But It is to be distributed due to magnetic field in entire space uniform, causes to be not in two phase flow in sensitive field, computational accuracy is not high, and vulnerable to Interference.This, which allows for general detection method, can only probably calculate two-phase flow containing rate.The design of magnetic field sources is directly related to manufacture The development of production and science and technology, it should be also distributed in addition to certain magnetic field strength by certain requirement in some space, As the magnetic flux density of excitation field is uniformly distributed along measurement pipeline.In addition when to two-phase flow, the electricity of biphase gas and liquid flow Characteristic is relative complex, can be to two-phase flow measurement process from reason if mathematical description can be carried out using its complete electrical impedance information By interpretation.For above situation, it is badly in need of being directed to two phase flow feature itself, designs a kind of responsiveness height, strong antijamming capability Measurement method, and two-phase flow measurement process can be described with mathematical model.
Summary of the invention
It is an object of the invention to solve problems of the prior art, a kind of two-phase flow measurement method is provided, makes two Mutually stream is in uniform highly sensitive magnetic field.This method has high-responsivity, high anti-jamming capacity, and can be to two phase flow Impedance information carries out mathematical description, and the variation of phase content is indicated by mathematical model.
The following are specific steps:
(1), characteristics of detection system be device include emission system and receive system, emission system by signal generator, Power amplifier, capacitor C1It is constituted with transmitting coil, wherein signal generator output end and PA signal input terminal phase Even, power amplifier forward direction output end, transmitting coil, capacitor C1Series loop is formed with power amplifier negative sense output end.It connects Receipts system is by receiving coil, capacitor C2It is formed with load in series.
(2), setting transmitting and receiving coil parameter, including transmitting coil is set as monosymmetric saddle-type coil, it incites somebody to action The vortex-like coil of plane that screw pitch is 1mm is diametrically divided from centre, and centre is connected by the rectilinear wire of identical line footpath, straight line portion Length is 50mm, and the radius of outermost layer circular arc is 50mm, and both ends circular arc turns up to the same side, and the subtended angle to center is 180 °, hair Penetrating coil turn is N1, self-induction L1, capacitor C1.Receiving coil is the spiral circular coil of uniform pitch, and receiving coil radius is r1, the number of turns N2, self-induction L2, capacitor C2.Wherein dispatch coil the number of turns is identical, N1=N2, the tested pipeline center of circle and the shape of a saddle The center of circle of coil circular arc is in same position, and parallel with transmitting coil straight line portion, receives and dispatches ray circle center coaxial placement, right The dispatch coil space D answered is set as workplace away from the mutual inductance of dispatch coil is M12, measured body and transmitting coil mutual inductance be M13, measured body and receiving coil mutual inductance M23
(3), the work of setting detection system is under same resonance frequency, and inductance, capacitor are humorous in launching circuit and reception circuit Vibration meets formulaω is the angular frequency of excitation power supply.
(4), R in launching circuit is setSFor the internal resistance of source, VSFor supply voltage, R1For launching circuit equivalent resistance, receive R in circuit2To receive circuit equivalent resistance, RLFor load;
(5), closed biphase gas and liquid flow pipeline is set as the series connection of inductance and resistance, and measurement system is established in Maxwell The average vortex loss of two phase flow is calculated in the model of systemWith eddy current value I, using formulaTwo-phase can be obtained The equivalent resistance R of stream3
(6), detection system mathematical function model is establishedIn formula, I1、I2、 I3Respectively launching circuit electric current, reception loop current, measured body loop current;
(7), for the detection of laminar flow, measuring system is established in Maxwell, when different liquid levels are calculated, The mutual inductance of tested laminar flow and transmitting coil, mutual inductance, self-induction and the equivalent resistance for being tested laminar flow and receiving coil;
(8), according to functionIt obtains from liquid level To the mapping relations one by one of stratiform flow containing rate.α in formula1For the phase content of laminar flow, r2For biphase gas and liquid flow pipe radius, liquid Face height is H;
(9), the laminar flow parameter that step (7) is calculated, i.e., mutual inductance, the measured layer of tested laminar flow and transmitting coil Mutual inductance, self-induction and the equivalent resistance of shape stream and receiving coil substitute into step (6).It is calculated under laminar flow difference phase content Receive loop current I2, according to U 'L=I2RLLoad voltage values U ' corresponding to laminar flow difference phase content is calculatedL
(10), for the detection of annular flow, measuring system is established in Maxwell, when different air column radiuses are calculated, The mutual inductance of tested annular flow and transmitting coil, mutual inductance, self-induction and the equivalent resistance for being tested annular flow and receiving coil;
(11), according to functionObtain the mapping relations one by one from air column radius to cyclic annular flow containing rate.Formula Middle α2For the phase content of annular flow, the air column radius positioned at annular flow center is R;
(12), the annular flow parameter that step (10) is calculated, i.e., the mutual inductance of tested laminar flow and transmitting coil are tested Mutual inductance, self-induction and the equivalent resistance of laminar flow and receiving coil substitute into step (6).It is calculated under annular flow difference phase content Reception loop current I2, according to U "L=I12RLLoad voltage values U " corresponding to annular flow difference phase content is calculatedL
(13), the mapping relations of phase content and load voltage under obtain two kinds of flow patterns are passed through into formula fitting.Laminar flow The corresponding relationship of phase content to load voltage can be by U 'L=-0.0004* α2-0.1836*α2+ 1.3915 characterizations, annular flow mutually contain The corresponding relationship of rate to load voltage can be by U "L=-0.00008* α2- 0.0081* α+1.4 is characterized.
The present invention is since general detection coil magnetic field is in space uniform distribution, and measured body is not in sensitive field, and electricity Conductance, magnetic conductivity are lower, and sensitivity is high when leading to traditional electromagnetic detection, poor anti jamming capability, and the present invention is based on EMR electromagnetic resonances Principle works as emission system, and when receiving system all in resonant state, the measurement of two-phase flow containing rate will be than traditional electromagnetic detection more Add it is sensitive, and due to transmitting receive loop resonance in same frequency, it is small by external electromagnetic wave interference.In addition the shape of a saddle is used The magnetic flux density for the excitation field that coil generates measures Two-phase Flow Pipeline Transport more smart along measurement tube axial direction distribution uniform Really.And the foundation of mathematical model is carried out to two phase flow on this basis, complicated two-phase flow problem has been converted into more simple Single mathematical computations.
Detailed description of the invention
Fig. 1 is measuring system three-dimensional model diagram of the present invention;
Fig. 2 is saddle-type coil structural map;
Fig. 3 is circuit topological structure figure of the present invention;
Fig. 4 is traditional induction type electromagnetic measuring system circuit topological structure figure;
The result figure that Fig. 5 laminar flow, annular flow load voltage change with phase content.
Specific implementation method
Detailed description of the present invention particular content with reference to the accompanying drawing.Two-phase flow measurement system three-dimensional tectonic model is shown in Fig. 1, Biphase gas and liquid flow pipeline center and dispatch coil coaxial placement, determine Two-phase flow's separation, to avoid because of two phase flow in measuring system Modal position variation, and keep measurement result inaccurate.And establish the Flow model of two kinds of typical biphase gas and liquid flows, i.e., laminar flow, Annular flow.
Detection system circuit model is established, and sets closed gas-liquid two-phase flow tube as the series connection of inductance and resistance, circuit Topological structure is shown in Fig. 3.V in figureSFor voltage source, M12, M13, M23Mutual inductance, transmitting coil respectively between transmitting and receiving coil The mutual inductance of mutual inductance, receiving coil and measured body with measured body, RSFor the internal resistance of source in transmit circuit, RLTo receive the negative of circuit It carries, R1, R2For circuit equivalent resistance, L3And R3Respectively measured body inductance and equivalent resistance, I1, I2, I3Respectively launching circuit Electric current receives loop current, measured body loop current.Calculate the load voltage values U under current gas-liquid two-phase flow containing rateL, According to formula UL=I2RLIt is calculated, I in formula2According toIt is calculated.Setting Traditional electromagnetic detection load voltage VL, it is assumed that circuit element parameter and circuit element parameter of the present invention are complete in traditional electromagnetic detection It is identical.Load voltage values V under current gas-liquid two-phase flow containing rateLAccording to formula VL=I12RLIt is calculated, I in formula12According toIt is calculated, circuit diagram is shown in Fig. 4, is computed and obtainsMeasuring system reactive power of the invention, system in-fighting are lower, and sensitivity is higher.
The technical scheme adopted by the invention is that: a kind of anti-interference biphase gas and liquid flow measuring of phase ratio side of high-responsivity Method, specific steps are as follows:
(1), characteristics of detection system be device include emission system and receive system, emission system by signal generator, Power amplifier, capacitor C1It is constituted with transmitting coil, wherein signal generator output end and PA signal input terminal phase Even, power amplifier forward direction output end, transmitting coil, capacitor C1Series loop is formed with power amplifier negative sense output end.It connects Receipts system is by receiving coil, capacitor C2It is formed with load in series.Frequency caused by signal generator is fixed in emission system Signal, exported via power amplifier, driving transmitting coil transmitting certain frequency electromagnetic wave, electromagnetic wave is by measured body It after the influence of eddy-current loss, is received Coil Detector and arrives, be then passed to load;
(2), setting transmitting and receiving coil parameter, including transmitting coil is set as monosymmetric saddle-type coil, it incites somebody to action The vortex-like coil of plane that screw pitch is 1mm is diametrically divided from centre, and centre is connected by the rectilinear wire of identical line footpath, straight line portion Length is 50mm, and the radius of outermost layer circular arc is 50mm, and both ends circular arc turns up to the same side, and the subtended angle to center is 180 °, hair Penetrating coil turn is N1, self-induction L1, capacitor C1.Receiving coil is the spiral circular coil of uniform pitch, and receiving coil radius is r1, the number of turns N2, self-induction L2, capacitor C2.Wherein dispatch coil the number of turns is identical, N1=N2, the tested pipeline center of circle and the shape of a saddle The center of circle of coil circular arc is in same position, and parallel with transmitting coil straight line portion, receives and dispatches ray circle center coaxial placement, right The dispatch coil space D answered is set as workplace away from the mutual inductance of dispatch coil is M12, measured body and transmitting coil mutual inductance be M13, measured body and receiving coil mutual inductance M23.Saddle-type coil generate excitation field magnetic flux density along central axes be distributed compared with Uniformly, i.e., it is uniformly distributed, therefore Two-phase Flow Pipeline Transport is measured more accurate along measurement tube axial direction;
(3), the work of setting detection system is under same resonance frequency, and inductance, capacitor are humorous in launching circuit and reception circuit Vibration meets formulaω is the angular frequency of excitation power supply.Since dispatch coil resonance is in same frequency, therefore different frequencies The electromagnetic wave of rate is weaker to the interference of detection coil;
(4), R in launching circuit is setSFor the internal resistance of source, VSFor supply voltage, R1For launching circuit equivalent resistance, receive R in circuit2To receive circuit equivalent resistance, RLFor load;
(5), closed biphase gas and liquid flow pipeline is set as the series connection of inductance and resistance, and measurement system is established in Maxwell The average vortex loss of two phase flow is calculated in the model of systemWith eddy current value I, using formulaTwo-phase can be obtained The equivalent resistance R of stream3
(6), detection system mathematical function model is establishedIn formula, I1、I2、 I3Respectively launching circuit electric current, reception loop current, measured body loop current;
(7), for the detection of laminar flow, measuring system is established in Maxwell, when different liquid levels are calculated, The mutual inductance of tested laminar flow and transmitting coil, mutual inductance, self-induction and the equivalent resistance for being tested laminar flow and receiving coil;
(8), according to functionIt obtains from liquid level To the mapping relations one by one of stratiform flow containing rate.α in formula1For the phase content of laminar flow, r2For biphase gas and liquid flow pipe radius, liquid Face height is H;
(9), the laminar flow parameter that step (7) is calculated, i.e., mutual inductance, the measured layer of tested laminar flow and transmitting coil Mutual inductance, self-induction and the equivalent resistance of shape stream and receiving coil substitute into step (6).It is calculated under laminar flow difference phase content Receive loop current I2, according to U 'L=I2RLLoad voltage values U ' corresponding to laminar flow difference phase content is calculatedL.As a result See Fig. 5 (a), load voltage can be obtained with the increase monotone decreasing of stratiform flow containing rate;
(10), for the detection of annular flow, measuring system is established in Maxwell, when different air column radiuses are calculated, The mutual inductance of tested annular flow and transmitting coil, mutual inductance, self-induction and the equivalent resistance for being tested annular flow and receiving coil;
(11), according to functionObtain the mapping relations one by one from air column radius to cyclic annular flow containing rate.Formula Middle α2For the phase content of annular flow, the air column radius positioned at annular flow center is R;
(12), the annular flow parameter that step (10) is calculated, i.e., the mutual inductance of tested laminar flow and transmitting coil are tested Mutual inductance, self-induction and the equivalent resistance of laminar flow and receiving coil substitute into step (6).It is calculated under annular flow difference phase content Reception loop current I2, according to U "L=I12RLLoad voltage values U " corresponding to annular flow difference phase content is calculatedL, knot Fruit sees Fig. 5 (b), and load voltage can be obtained with the increase monotone decreasing of cyclic annular flow containing rate;
(12), the mapping relations of phase content and load voltage under obtain two kinds of flow patterns are passed through into formula fitting.Laminar flow The corresponding relationship of phase content to load voltage can be by UL'=- 0.0004* α2-0.1836*α2+ 1.3915 characterizations, annular flow mutually contain The corresponding relationship of rate to load voltage can be by U "L=-0.00008* α2- 0.0081* α+1.4 is characterized.It is direct by mathematic(al) representation Calculate the load voltage values corresponding to phase content under current flow pattern.
The present invention makes to be tested primarily directed to the measurement of gas-liquid two-phase flow containing rate with improved electric magnetic detection system Body is in the sensitive field of electromagnetism, and detection system is in resonant state, and detection sensitivity, anti-interference ability are improved, and Two phase flow and measuring system are equivalent to circuit model, complicated two-phase flow containing rate measurement process is made to be converted into mathematical formulae It calculates.
Embodiment above describes basic principles and main features of the invention and advantage, the technical staff of the industry should Understand, the present invention is not limited to the above embodiments, and the above embodiments and description only describe originals of the invention Reason, under the range for not departing from the principle of the invention, various changes and improvements may be made to the invention, these changes and improvements are each fallen within In the scope of protection of the invention.

Claims (1)

1. a kind of anti-interference biphase gas and liquid flow measuring of phase ratio method of high-responsivity, it is characterised in that specific steps are as follows:
(1), characteristics of detection system is that device includes emission system and receives system, and emission system is by signal generator, power Amplifier, capacitor C1It is constituted with transmitting coil, wherein signal generator output end is connected with PA signal input terminal, function Rate amplifier forward direction output end, transmitting coil, capacitor C1Series loop is formed with power amplifier negative sense output end, receives system By receiving coil, capacitor C2It is formed with load in series,
(2), setting transmitting and receiving coil parameter, including transmitting coil is set as monosymmetric saddle-type coil, by screw pitch Diametrically divide for the vortex-like coil of plane of 1mm from centre, centre is connected by the rectilinear wire of identical line footpath, straight line portion length Radius for 50mm, outermost layer circular arc is 50mm, and both ends circular arc turns up to the same side, and the subtended angle to center is 180 °, emission lines Circle the number of turns is N1, self-induction L1, capacitor C1, receiving coil is the spiral circular coil of uniform pitch, and receiving coil radius is r1、 The number of turns is N2, self-induction L2, capacitor C2, wherein dispatch coil the number of turns is identical, N1=N2, the tested pipeline center of circle and saddle-type coil The center of circle of circular arc is in same position, and parallel with transmitting coil straight line portion, receives and dispatches ray circle center coaxial placement, corresponding Dispatch coil space D is set as workplace away from the mutual inductance of dispatch coil is M12, measured body and transmitting coil mutual inductance be M13, quilt Survey the mutual inductance M of body and receiving coil23
(3), the work of setting detection system is under same resonance frequency, and inductance, capacitor resonance are full in launching circuit and reception circuit Sufficient formulaω is the angular frequency of excitation power supply,
(4), R in launching circuit is setSFor the internal resistance of source, VSFor supply voltage, R1For launching circuit equivalent resistance, circuit is received Middle R2To receive circuit equivalent resistance, RLFor load;
(5), closed biphase gas and liquid flow pipeline is set as the series connection of inductance and resistance, and measuring system is established in Maxwell The average vortex loss of two phase flow is calculated in modelWith eddy current value I, using formulaTwo phase flow can be obtained Equivalent resistance R3
(6), detection system mathematical function model is establishedIn formula, I1、I2、I3Point It Wei not launching circuit electric current, reception loop current, measured body loop current;
(7), for the detection of laminar flow, measuring system is established in Maxwell, when different liquid levels are calculated, is tested The mutual inductance of laminar flow and transmitting coil, mutual inductance, self-induction and the equivalent resistance for being tested laminar flow and receiving coil;
(8), according to functionIt obtains from liquid level to layer The mapping relations one by one of shape flow containing rate, α in formula1For the phase content of laminar flow, r2For biphase gas and liquid flow pipe radius, liquid level height Degree is H;
(9), the laminar flow parameter that step (7) is calculated, i.e., the mutual inductance of tested laminar flow and transmitting coil, tested laminar flow Mutual inductance, self-induction and equivalent resistance with receiving coil substitute into step (6), the reception under laminar flow difference phase content are calculated Loop current I2, according to U 'L=I2RLLoad voltage values U ' corresponding to laminar flow difference phase content is calculatedL
(10), for the detection of annular flow, measuring system is established in Maxwell, when different air column radiuses are calculated, is tested The mutual inductance of annular flow and transmitting coil, mutual inductance, self-induction and the equivalent resistance for being tested annular flow and receiving coil;
(11), according to functionObtain the mapping relations one by one from air column radius to cyclic annular flow containing rate, α in formula2 For the phase content of annular flow, the air column radius positioned at annular flow center is R;
(12), the annular flow parameter that step (10) is calculated, i.e., the mutual inductance of tested laminar flow and transmitting coil, tested stratiform Mutual inductance, self-induction and the equivalent resistance of stream and receiving coil substitute into step (6), connecing under annular flow difference phase content are calculated Receive loop current I2, according to U "L=I12RLLoad voltage values U " corresponding to annular flow difference phase content is calculatedL
(13), by the mapping relations of phase content and load voltage under obtain two kinds of flow patterns by formula fitting, laminar flow mutually contains The corresponding relationship of rate to load voltage can be by U 'L=-0.0004* α2-0.1836*α2+ 1.3915 characterizations, cyclic annular flow containing rate arrive The corresponding relationship of load voltage can be by U "L=-0.00008* α2- 0.0081* α+1.4 is characterized.
CN201811421890.8A 2018-11-27 2018-11-27 A kind of anti-interference biphase gas and liquid flow measuring of phase ratio method of high-responsivity Withdrawn CN109580765A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111123179A (en) * 2020-01-15 2020-05-08 合肥工业大学 Method for calculating relation between radius and radial angle of final closed magnetic surface

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111123179A (en) * 2020-01-15 2020-05-08 合肥工业大学 Method for calculating relation between radius and radial angle of final closed magnetic surface

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