State detection device

An exciting unit, applies, to a fluid, a time-changing magnetic field asymmetrical to a plane (PLN). An electrode is placed on the plane in a measuring tube, and detects a resultant electromotive force of an electromotive force based on ∂A/∂t component (A: vector potential, t: time) irrelevant to a flow velocity of the fluid and an electromotive force based on a v×B component originating from the flow velocity of the fluid. A state quantifying unit extracts the ∂A/∂t component and a variation factor dependent on a parameter to be detected, and quantifies the parameter on the basis of the variation factor. The characteristic and state of the fluid and the state in the measuring tube can be detected regardless of the flow rate of the fluid by using the same hardware arrangement as that of an electromagnetic induction type flowmeter.

This is a non-provisional application claiming the benefit of International application No. PCT/JP2005/017409 filed Sep. 21, 2005.

TECHNICAL FIELD

The present invention relates to a state detection device which detects a characteristic or state of a fluid or a state in a measuring tube through which the fluid flows.

BACKGROUND ART

Generally, in order to measure a flow rate by using a flowmeter, there is a demand for detecting a characteristic or state of the fluid and a state in a tube through which the fluid flows, together with the flow rate of a fluid to be measured. For example, in a manufacturing line for mixing a chemical solution or the like, the characteristic such as the conductivity or permittivity of the fluid is measured together with the flow rate of the fluid. Also, when a large amount of substance adheres to the inside of a measuring tube, the deposition state of the substance in the measuring tube is measured in order to know the maintenance cycle of the measuring tube. As for a sewer, a demand has arisen for measuring the state such as a level of the fluid and the deposition state of the substance adhering to the inside of the measuring tube together with the flow rate. Actually, the state of the fluid and the state in the measuring tube are measured by using a measuring device other than the flowmeter.

As described above, a demand has arisen for measuring the characteristic or state of the fluid or the state in the measuring tube though which the fluid flows, together with the flow rate of the fluid, and executing measurement processing by using basically the same hardware arrangement as that of a flowmeter. That is, there is a demand for selectively implementing various functions such as measurement of the flow rate of the fluid, measurement of the conductivity of the fluid, and simultaneous measurement of the flow rate and conductivity by using one measurement device. Since the flow rate and state are preferably measured at the same time, it is obviously important to measure the characteristic or state of the fluid regardless of the flow rate of the fluid.

When an electromagnetic flowmeter serves as the flowmeter, in addition to the above demands, a demand has arisen for measuring the characteristic or state of the fluid or the state in the measuring tube from the viewpoint of the self-diagnosis of the electromagnetic flowmeter. For example, when an insulator or the like adheres to the electrode, an electrode type flowmeter for extracting a potential from an electrode which is in contact with the fluid can neither accurately extract the potential, nor measure the flow rate with precision. To cope with this problem, when the resistance of the fluid containing the substance can be measured by using the same electrode, the deposition state of the substance adhering to the electrode can be measured, thus preventing any trouble that an abnormal flow rate measurement value is obtained. In a general electromagnetic flowmeter, an abnormal flow rate measurement value is obtained when the conductivity of the fluid falls outside a specific range. In this case, as long as the resistance of the fluid can be measured, it is determined that an output error which has occurred when the fluid having conductivity falling within the specific range flows originates from a change in the flow rate, or the fluid conductivity falling outside the specific range. As a result, the electromagnetic flowmeter can have a self-diagnosis function as the flowmeter.

As described above, a demand has arisen for meeting the request for executing various measurement processes in addition to the measurement process of the flow rate by using basically the same hardware arrangement as that of a flowmeter.

The solution to the request is not presented now. However, an electromagnetic flowmeter which detects a parameter other than the flow velocity is disclosed, as a relatively closer technique, in reference 1 (Japanese Patent Laid-Open No. 6-241855) and reference 2 (JNMIHF edition, “Flow Rate Measurement A to Z for Instrumentation Engineers”, Kogyo Gijutusha, 1995, pp. 147-148). In references 1 and 2, a device which measures the level, conductivity, and the like of the fluid is disclosed as an application of the electromagnetic flowmeter. Such electromagnetic flowmeter obtains the level of the fluid on the basis of the ratio between a signal electromotive force obtained from an electrode when driving exciting coils placed above and under a tube and a signal electromotive force obtained when driving the exciting coil placed above the tube by itself, and obtains the conductivity of the fluid on the basis of the ratio between the signal electromotive forces obtained when changing an input impedance of a pre-amplifier connected to the electrode.

DISCLOSURE OF INVENTION

Problem to be Solved by the Invention

However, an electromagnetic flowmeter disclosed in references 1 and 2 detects a characteristic or state of a fluid on the basis of the fluid between flow rate signals. Hence, a large error occurs as the flow rate of the fluid decreases to 0, and the electromagnetic flowmeter cannot detect the characteristic or state of the fluid when the flow rate is 0.

The present invention has been made to solve the above problem, and has as its object to provide a state detection device which can accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

Means of Solution to the Problem

According to the present invention, there is provided a state detection device characterized by comprising a measuring tube through which a fluid flows, an exciting unit which applies, to the fluid, a time-changing magnetic field asymmetrical to a first plane perpendicular to an axial direction of the measuring tube, an electrode which is placed on the first plane in the measuring tube to detect a resultant electromotive force of an electromotive force based on a ∂A/∂t component (A: vector potential, t: time) irrelevant to a flow velocity of the fluid and an electromotive force based on a v×B component (v: flow velocity, B: magnetic flux density) originating from the flow velocity of the fluid, the resultant electromotive force being generated by the magnetic field applied to the fluid and a flow of the fluid, and a state quantifying unit which extracts the ∂A/∂t component from the resultant electromotive force detected by the electrode, extracts, from the ∂A/∂t component, a variation factor dependent on a parameter to be detected, and quantifies the parameter on the basis of the variation factor, wherein the parameter is at least one of a characteristic and state of the fluid and a state in the measuring tube.

According to the present invention, a ∂A/∂t component is extracted from a resultant vector of a v×B component dependent on the flow velocity of the fluid and a ∂A/∂t component independent of the flow velocity of the fluid. On the basis of the detected ∂A/∂t component, a characteristic or state of the fluid or a state in a measuring tube can be measured. This is a solution to the demand for detecting the characteristic or state of the fluid and the state in the measuring tube through which the fluid flows in addition to the flow rate of the fluid. That is, the present invention can provide a device which can detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid by using basically the same hardware arrangement as that of a flowmeter. Furthermore, the technique of the present invention can cope with the demand for measuring the characteristic or state of the fluid in addition to the level, conductivity, and permittivity of the fluid.

BEST MODE FOR CARRYING OUT THE INVENTION

A logical propositional portion necessary to understand the present invention will be described. Generally known mathematical basic knowledge will be described first.

A cosine wave P·cos(ω·t) and a sine wave Q·sin(ω·t) which have the same frequency but different amplitudes are combined into the following cosine wave. Let P and Q be amplitudes, and ω be an angular frequency.
P·cos(ω·t)+Q·sin(ω·t)=(P2+Q2)1/2·cos(ω·t−ε) for ε=tan−1(Q/P)  (1)

In order to analyze the combining operation in equation (1), it is convenient to perform mapping on a complex coordinate plane so as to plot an amplitude P of cosine wave P·cos(ω·t) along a real axis and an amplitude Q of the sine wave Q·sin(ω·t) along an imaginary axis. That is, on the complex coordinate plane, a distance (P2+Q2)1/2from the origin gives the amplitude of the combined wave, and an angle ε=tan−1(Q/P) with respect to the real axis gives the phase difference between the combined wave and fit.

In addition, on the complex coordinate plane, the following relational expression holds.
L·exp(j·ε)=L·cos(ε)+j·L·sin(ε)  (2)

Equation (2) is an expression associated with a complex vector, in which j is an imaginary unit, L gives the length of the complex vector, and ε gives the direction of the complex vector. In order to analyze the geometrical relationship on the complex coordinate plane, it is convenient to use conversion to a complex vector.

The following description uses mapping onto a complex coordinate plane like that described above and geometrical analysis using complex vectors to show how an inter-electrode electromotive force behaves and explain how the present invention uses this behavior.

A physical phenomenon necessary for explanation of a state detection device of the present invention will be described next. When an object moves in a changing magnetic field, electromagnetic induction generates two types of electric fields, namely (a) electric field E(i)=∂A/∂t which is generated by a temporal change in magnetic field, and (b) electric field E(v)=v×B which is generated as the object moves in the magnetic field. In this case, v×B represents the outer product of v and B, ∂A/∂t represents the partial differential of A with respect to time. In this case, v, B, and A respectively correspond to the following and are vectors having directions in three dimensions (x, y, and z) (v: flow velocity, B: magnetic flux density, and A: vector potential (whose relationship with the magnetic flux density is represented by B=rotA). Note, however, that the three-dimensional vectors in this case differ in meaning from vectors on a complex plane. These two types of electric fields generate a potential distribution in the fluid, and electrodes can detect this potential. Consider an eddy current which is generated in a fluid by a ∂A/∂t component irrelevant to the flow velocity. The flow path or current density of the eddy current changes depending on a characteristic or state of the measuring tube including the fluid and the input impedance generated when a potential is extracted. Extracting this change as a potential makes it possible to measure a characteristic or state other than the fluid.

FIG. 1is a block diagram for explaining the first principle of the state detection device of the present invention. This state detection device includes a measuring tube1through which a fluid to be measured flows, a pair of electrodes2aand2bwhich are placed to face each other in the measuring tube1so as to be perpendicular to both a magnetic field to be applied to the fluid and an axis PAX of the measuring tube1and come into contact with the fluid, and detect the electromotive force generated by the magnetic flow and the flow of the fluid, and an exciting coil3which applies, to the fluid, a time-changing magnetic field asymmetric on the front and rear sides of the measuring tube1which are bordered on a plane PLN which includes the electrodes2aand2bperpendicular to the axis PAX of the measuring tube, with the plane PLN serving as a boundary of the measuring tube1.

As shown inFIG. 1, the present invention is configured to apply, to the fluid, a magnetic field asymmetric on the front and rear sides of the measuring tube1which are bordered on a plane PLN which includes the electrodes2aand2bperpendicular to the axis PAX of the measuring tube, with the plane PLN serving as a boundary of the measuring tube1, so as to detect the resultant vector of a v×B component dependent on the flow velocity of the fluid and a ∂A/∂t component independent of the flow velocity and extract the ∂A/∂t component independent of the flow velocity of the fluid from the resultant vector. The extracted ∂A/∂t component contains a component which changes depending on the state or characteristic of the fluid and that in the measuring tube1. The conductivity, permittivity, and level of the fluid, or a state in the measuring tube1can be measured from the values of the components regardless of the flow rate of the fluid. The flow velocity can also be calculated from the v×B component contained in the resultant vector as in a general electromagnetic flowmeter.

Assume that, of a magnetic field Ba generated by the exciting coil3, a magnetic field component (magnetic flux density) B1orthogonal to both an electrode axis EAX connecting the electrodes2aand2band the measuring tube axis PAX on the electrode axis EAX is given by
B1=b1·cos(ω0·t−θ1)  (3)

In equation (3), b1is the amplitude of the magnetic field B1, ω0is an angular frequency, and θ1is a phase difference (phase delay) between the magnetic flux density B1and ω0·t. The magnetic flux density B1will be referred to as the magnetic field B1hereinafter.

An inter-electrode electromotive force which originates from a change in magnetic field and is irrelevant to the flow velocity of a fluid will be described first. Since the electromotive force originating from the change in magnetic field depends on a time derivative dB/dt of the magnetic field, and hence the magnetic field B1generated by the exciting coil3is differentiated according to
dB1/dt=−ω0·b1·sin(ω0·t−θ1)  (4)

If the flow velocity of the fluid to be measured is 0, a generated eddy current is only a component originating from a change in magnetic field. An eddy current I due to a change in the magnetic field Ba is directed as shown inFIG. 2. Therefore, an inter-electrode electromotive force E which is generated by a change in the magnetic field Ba and is irrelevant to the flow velocity is directed as shown inFIG. 2within a plane including the electrode axis EAX and the measuring tube axis PAX. This direction is defined as the negative direction.

At this time, the inter-electrode electromotive force E is the value obtained by multiplying a time derivative −dB1/dt of a magnetic field whose direction is taken into consideration by a proportion coefficient rk, and substituting θ1+θ00into the phase θ1(rk and θ00are associated with the conductivity and permittivity of the fluid to be measured and the structure of the measuring tube1including the arrangement of the electrodes2aand2b), as indicated by the following equation:
E=rk·ω0·b1·sin(ω0·t−θ1−θ00)  (5)

Equation (5) is rewritten into the following equation:

In this case, if equation (6) is mapped on the complex coordinate plane with reference to ω0·t, a real axis component Ex and an imaginary axis component Ey are given by

In addition, Ex and Ey represented by equations (7) and (8) are transformed into a complex vector Ec represented by

The inter-electrode electromotive force Ec represented by equation (9) which is transformed into complex coordinates becomes an inter-electrode electromotive force which originates from only a temporal change in magnetic field and is irrelevant to the flow velocity. In equation (9), rk·ω0·b1·exp{j·(π/2+θ1+θ00)} is a complex vector having a length rk·ω0·b1and an angle π/2+θ1+θ00with respect to the real axis.

In addition, the proportion coefficient rk and angle θ00described above can be transformed into a complex vector kc to obtain the following equation:

In equation (10), rk is the magnitude of the vector kc, and θ00is the angle of the vector kc with respect to the real axis.

An inter-electrode electromotive force originating from the flow velocity of a fluid to be measured will be described next. Letting V (V≠0) be the magnitude of the flow velocity of the fluid, since a component v×Ba originating from a flow velocity vector v of the fluid is generated in a generated eddy current in addition to the eddy current I when the flow velocity is 0, an eddy current Iv generated by the flow velocity vector v and the magnetic field Ba is directed as shown inFIG. 3. Therefore, the direction of an inter-electrode electromotive force Ev generated by the flow velocity vector v and the magnetic field Ba becomes opposite to the direction of the inter-electrode electromotive force E generated by the temporal change, and the direction of Ev is defined as the positive direction.

In this case, as indicated by the following equation, the inter-electrode electromotive force Ev originating from the flow velocity is the value obtained by multiplying the magnetic field B1by a proportion coefficient rkv, and substituting θ1+θ01into the phase θ1(rkv and θ1are associated with a magnitude V of the flow velocity, the conductivity and permittivity of the fluid to be measured, and the structure of the measuring tube1including the arrangement of the electrodes2aand2b):
Ev=rkv·{b1·cos(ω0·t−θ1−θ01)}  (11)

Equation (11) is rewritted into

In this case, when mapping equation (12) on the complex coordinate plane with reference to ω0·t, a real axis component Evx and an imaginary axis component Evy are given by
Evx=rkv·b1·{cos(θ1+θ01)}  (13)
Evy=rkv·b1·{sin(θ1+θ01)}  (14)

In addition, Evx and Evy represented by equations (13) and (14) are transformed into a complex vector Evc represented by

The inter-electrode electromotive force Evc represented by equation (15) which is transformed into complex coordinates becomes an inter-electrode electromotive force which originates from the flow velocity of the fluid to be measured. In equation (15), rkv·b1·exp{j·(θ1+θ01)} is a complex vector having a length rkv·b1and an angle θ1+θ01with respect to the real axis.

In addition, the proportion coefficient rkv and θ01described above can be transformed into a complex vector kvc to obtain the following equation:

In equation (16), rkv is the magnitude of the vector kvc, and θ01is the angle of the vector kvc with respect to the real axis. In this case, rkv is equivalent to the value obtained by multiplying the proportional coefficient rk (see equation (10)) described above by the magnitude V of the flow velocity and a proportion coefficient γ. That is, the following equation holds:
rkv=γ·rk·V(17)

An inter-electrode electromotive force Ea1cas a combination of inter-electrode electromotive force Ec originating from a temporal change in magnetic field and an inter-electrode electromotive force Evc originating from the flow velocity of the fluid is expressed by the following equation upon combining equation (9) and an equation obtained by substituting equation (17) into equation (15).

As is obvious from equation (18), an inter-electrode electromotive force Ea1cis written by two complex vectors, i.e., the ∂A/∂t component rk·ω0·b1·exp{j·(π/2+θ1+θ00)} and the v×B component γ·rk·V·b1·exp{j·(θ1+θ01)}. The length of the resultant vector obtained by combining the two complex vectors represents the amplitude of the output (the inter-electrode electromotive force Ea1c), and an angle φ of the resultant vector represents the phase difference (phase delay) of the inter-electrode electromotive force Ea1cwith respect to the phase ω0·t of the input (exciting current).

The angle θ00is the angle of the vector kc with respect to the real axis, and the angle θ01is the angle of the vector kvc with respect to the real axis. These definitions can be rephrased such that θ00is the angle of the ∂A/∂t component with respect to the imaginary axis, and θ01is the angle of the v×B component with respect to the real axis. Assume that the inter-electrode electromotive force Ea1cis represented by E10in a state wherein the relationship between the angles θ00and θ01is defined as θ01=θ00+Δθ01. In this case, the inter-electrode electromotive force E10is represented by the following equation:

Assuming that the ∂A/∂t component in the resultant vector represented by equation (19) is given by a product Va10obtained by multiplying a constant term Ka=ext(j·π/2) in the ∂A/∂t component, a term B1c=b1·exp{j·θ1) associated with the magnetic field, a term C=rk·exp(j·θ00) associated with the characteristic or state of the fluid, and the angular frequency ω0, the first term of the right side of equation (19) is represented by equation (20).
Va10=Ka·B1c·C·ω0  (20)

Assuming that the v×B component in the resultant vector is given by a product Vb10obtained by multiplying a constant term Kb=γ·exp(j·Δθ01) in the v×B component, a term B1c=b1·exp(j·θ1) associated with the magnetic field, a term C=rk·exp(j·θ00) associated with the characteristic or state of the fluid, and the magnitude V of the flow velocity, the second term of the right side of equation (19) is represented by equation (21).
Vb10=Kb·B1c·C·V(21)

FIG. 4is a graph showing the vector Va10, vector Vb10, and resultant vector (flow velocity V) Va10+Vb10. When extracting only Va10from the resultant vector Va10+Vb10, and extracting the variation factor C dependent on the characteristic or state of the fluid, a change in the characteristic or state of the fluid or the state in the measuring tube can be known independently of the flow velocity. A method of extracting the ∂A/∂t component from the resultant vector will be generally described.

FIG. 5is a block diagram for explaining the second principle of a state detection device of the present invention. This state detection device includes a measuring tube1, electrodes2aand2b, and first and second exciting coils3aand3bwhich apply, to a fluid to be measured, time-changing magnetic fields asymmetric on the front and rear sides of the measuring tube1which are bordered on a plane PLN which is perpendicular to the direction of a measuring tube axis PAX and includes the electrodes2aand2b, when the plane PLN serves as a boundary of the measuring tube1. The first exciting coil3ais placed at a position spaced apart from the plane PLN by an offset distance d1to, for example, the downstream side. The second exciting coil3bis placed at a position spaced apart from the plane PLN by an offset distance d2to, for example, the upstream side.

The state detection device shown inFIG. 5is obtained by adding one exciting coil to the state detection device shown inFIG. 1. If the second exciting coil3bto be newly added is placed on the same side as the existing first exciting coil3a, the resultant arrangement is a redundant arrangement of that shown inFIG. 1. Therefore, the second exciting coil3bneeds to be placed on a side different from that of the first exciting coil3athrough the plane PLN including the electrodes2aan2b. With this arrangement, if a v×B component originating from a magnetic field Bb generated from the first exciting coil3aand the flow velocity and a v×B component originating from a magnetic field Bc generated from the second exciting coil3band the flow velocity, which are detected by the electrodes2aand2b, are directed in the same direction, a ∂A/∂t component originating from a change in the magnetic field Bb generated by the first exciting coil3aand a ∂A/∂t component originating from a change in the magnetic field Bc generated by the second exciting coil3bare directed in opposite directions. Using this principle makes it possible to efficiently extract a ∂A/∂t component.

Of the magnetic field Bb generated from the first exciting coil3a, a magnetic field component (magnetic flux density) B1orthogonal to both an electrode axis EAX connecting the electrodes2aand2band the measuring tube axis PAX on the electrode axis EAX, and of the magnetic field Bc generated from the second exciting coil3b, a magnetic field component (magnetic flux density) B2orthogonal to both the electrode axis EAX and the measuring tube axis PAX on the electrode axis EAX are given by
B1=b1·cos(ω0·t−θ1)  (22)
B2=b2·cos(ω0·t−θ2)  (23)

In equations (22) and (23), b1and b2are the amplitudes of the magnetic flux densities B1and B2, ω0is an angular frequency, and θ1and θ2are phase differences (phase lags) between the magnetic flux densities B1and B2and ω0·t. The magnetic flux densities B1and B2will be respectively referred to as the magnetic fields B1and B2hereinafter.

Since the electromotive force originating from a change in magnetic field depends on a time derivative dB/dt of the magnetic field, the magnetic field B1generated by the exciting coil3aand the magnetic field B2generated by the second exciting coil3bare differentiated by

If the flow velocity of the fluid to be measured is 0, a generated eddy current is only a component originating from a change in magnetic field. An eddy current I1based on the magnetic field Bb and an eddy current I2based on the magnetic field Bc are directed as shown inFIG. 6. Therefore, an inter-electrode electromotive force E1which is generated by a change in the magnetic field Bb and is irrelevant to the flow velocity and an inter-electrode electromotive force E2which is generated by a change in the magnetic field Bc and is irrelevant to the flow velocity are directed opposite to each other as shown inFIG. 6within a plane including the electrode axis EAX and the measuring tube axis PAX.

At this time, an overall inter-electrode electromotive force E as the sum of the inter-electrode electromotive forces E1and E2is the value obtained by multiplying the difference (−dB1/dt+dB2/dt) between time derivatives dB1/dt and dB2/dt of a magnetic field by a proportional coefficient rk and replacing the phase differences θ1and θ2with θ1+θ00and θ2+θ00, respectively (rk and θ00are associated with a conductivity and permittivity of the fluid to be measured and the structure of the measuring tube1including the positions of the electrodes2aand2b) according to the following equation:

If the magnitude of the flow velocity of the fluid to be measured is V (V≠0), components v×Bb and v×Bc originating from a flow velocity vector v of the fluid to be measured are generated in the generated eddy currents in addition to eddy currents I1and I2generated when the flow velocity is 0. For this reason, an eddy current Iv1originating from the flow velocity vector v and the magnetic field Bb and an eddy current Iv2originating from the flow velocity vector v and the magnetic field Bc are directed as shown inFIG. 7. Consequently, an inter-electrode electromotive force Ev1generated by the flow velocity vector v and the magnetic field Bb and an inter-electrode electromotive force Ev2generated by the flow velocity vector v and the magnetic field Bc are directed in the same direction.

An overall inter-electrode electromotive force Ev obtained by adding the inter-electrode electromotive forces Ev1and Ev2is the value obtained by multiplying the sum of the magnetic fields B1and B2by a proportional coefficient rkv and replacing the phase differences θ1and θ2with θ1+θ01and θ2+θ01, respectively (rkv and θ01are associated with the magnitude V of the flow velocity, the conductivity and permittivity of the fluid to be measured, and the structure of the measuring tube1including the positions of the electrodes2aand2b) according to the following equation:

Considering the directions of the inter-electrode electromotive forces described with reference toFIGS. 6 and 7, of an overall inter-electrode electromotive force obtained by combining the electromotive force obtained by converting the inter-electrode electromotive force originating from a temporal change in magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force originating from the flow velocity of the fluid to be measured into a complex vector, a component Ea2cwith an angular frequency ω0is expressed by applying the equation (17) to the equations (26) and (27).

Assume that a state wherein θ2=θ1+Δθ2represents the relationship between a phase lag θ1of the magnetic field B1with respect to ω0·t and a phase lag θ2of the magnetic field B2with respect to ω0·t, and θ01=θ00+Δθ01represents the relationship between the angle θ00of the ∂A/∂t component with respect to the imaginary axis and the angle θ01of the v×B component with respect to the real axis. Such state is defined as an excitation state ST1. In this case, letting E20be the inter-electrode electromotive force Ea2cin the excitation state ST1, the inter-electrode electromotive force E20is given by

Assume that a state (θ2=π+θ1+Δθ2) wherein the phase difference between the magnetic fields B1and B2has changed from that in the excitation state ST1by a constant value π, and θ01=θ00+Δθ01holds is given as ST2. In this case, letting E20R be the inter-electrode electromotive force Ea2cin the excitation state ST2, the inter-electrode electromotive force E20R is represented by the following equation according to equation (29).

The sum of the first term of the right side of equation (29) and the first term of the right side of equation (30) represents the overall ∂A/∂t component obtained by combining a ∂A/∂t component originating from a change in the magnetic field generated from the first exciting coil3aand a ∂A/∂t component originating from a change in the magnetic field generated from the second exciting coil3b. The sum of the second term of the right side of equation (29) and the second term of the right side of equation (30) represents the overall v×B component obtained by combining a v×B component originating from the magnetic field generated from the first exciting coil3aand the flow velocity of the fluid and a v×B component originating from the magnetic field generated from the first exciting coil3band the flow velocity of the fluid.

In this case, if the distance d1from the plane PLN, which is perpendicular to the measuring tube axis PAX and includes the electrodes2aand2b, to the first exciting coil3ais almost equal to the distance d2from the plane PLN to the second exciting coil3b(d1≈d2), b1≈b2and Δθ2≈0. In this case, equations (29) and (30) are rewritten as follows:

That is, since the inter-electrode electromotive force E20is almost only the electromotive force based on the v×B component, and the inter-electrode electromotive force E20R is almost only the electromotive force based on the ∂A/∂t component, it is obvious that keeping the phase difference between the magnetic field generated from the first exciting coil3aand the magnetic field generated from the second exciting coil3bat almost π makes it possible to efficiently extract a ∂A/∂t component.

Assume that, of the ∂A/∂t component in the resultant vector represented by equation (29), the portion originating from the magnetic field generated from the first exciting coil3ais represented by a product Va10of constant term Ka=exp(j·π/2) in the ∂A/∂t component, term B1c=b1·exp(j·θ1) associated with the magnetic field generated from the first exciting coil3a, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the angular frequency ω0. In this case, Va10is represented by equation (33), and the ∂A/∂t component in equation (30) is also represented by Va10.
Va10=Ka·B1c·C·ω0  (33)

Assume that, of the v×B component in the resultant vector represented by equation (29), the portion originating from the magnetic field generated from the first exciting coil3ais represented by a product Vb10of constant term Kb=γ·exp(j·Δθ01) in the v×B component, term B1c=b1·exp(j·θ1) associated with the magnetic field generated from the first exciting coil3a, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the magnitude V of the flow velocity. In this case, Vb10is represented by equation (34), and the v×B component in equation (30) is also represented by Vb10.
Vb10=Kb·B1c·C·V(34)

FIG. 8is a graph showing a resultant vector (flow velocity V) Va10+Vb10of the vector Va10and the vector Vb10. Referring toFIG. 8, Re is a real axis, and Im is an imaginary axis.

Assume that, of the ∂A/∂t component in the resultant vector represented by equation (29), the portion originating from the magnetic field generated from the second exciting coil3bis represented by a product Va20of constant term −Ka=−exp(j·π/2) in the ∂A/∂t component, term B2c=b2·exp{j·(θ1+Δθ2)} associated with the magnetic field generated from the second exciting coil3b, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the angular frequency ω0. In this case, Va20is represented by equation (35).
Va20=−Ka·B2c·C·ω0  (35)

Since the excitation state ST2represented by equation (30) shifts in the phase of the magnetic field from the excitation state ST1represented by equation (29) by π, the direction of the magnetic field reverses, and the term associated with the magnetic field generated from the second exciting coil3bbecomes −B2c=−b2·exp{j·(θ1+Δθ2)}. If, therefore, the portion originating from the magnetic field generated from the second exciting coil3b, of the ∂A/∂t component in the resultant vector represented by equation (30), is represented by a product Va20R of constant term −Ka in the ∂A/∂t component, term −B2cassociated with the magnetic field generated from the second exciting coil3b, term C associated with a characteristic or state of the fluid, and the angular frequency ω0, Va20R is represented by equation (36).
Va20R=−Ka·(−B2c)·C·ω0  (36)

Assume that, of the v×B component in the resultant vector represented by equation (29), the portion originating from the magnetic field generated from the second exciting coil3bis represented by a product Vb20of constant term Kb=γ·exp(j·Δθ01) in the v×B component, term B2c=b2·exp{j·(θ1+Δθ2)} associated with the magnetic field generated from the second exciting coil3b, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the magnitude V of the flow velocity. In this case, Vb20is represented by equation (37).
Vb20=Kb·B2c·C·V(37)

FIG. 9is a graph showing a resultant vector (flow velocity V) Va20+Vb20of the vector Va20and the vector Vb20.FIG. 10is a graph showing a resultant vector (flow velocity V) Vas0+Vbs0of the vector Vas0and the vector Vbs0. The vector Vas0represents a ∂A/∂t component vector Va10+Va20=Ka·(B1c−B2c)·C·ω0obtained when performing excitation by using the first and second exciting coils3aand3b. The vector Vbs0represents a v×B vector Vb10+Vb20=Kb·(B1c+B2c)·C·V obtained when performing excitation by using the first and second exciting coils3aand3b.

Since the excitation state ST2shifts in the phase of the magnetic field from the excitation state ST1by π, a term associated with the magnetic field generated from the second exciting coil3bbecomes −B2c. If, therefore, the portion originating from the magnetic field generated from the second exciting coil3b, of the v×B component in the resultant vector represented by equation (30), is represented by a product Vb20R of constant term Kb in the v×B component, term −B2cassociated with the magnetic field generated from the second exciting coil3b, term C associated with a characteristic or state of the fluid, and the magnitude V of the flow velocity, Vb20R is represented by equation (38).
Vb20R=Kb·(−B2c)·C·V(38)

FIG. 11is a graph showing a resultant vector (flow velocity V) Va20R+Vb20R of the vector Va20R and the vector Vb20R.FIG. 12is a graph showing a resultant vector (flow velocity V) Vas0R+Vbs0R of the vector Vas0R and the vector Vbs0R. The vector Vas0R represents a ∂A/∂t component vector Va10+Va20R=Ka·(B1c+B2c)·C·ω0obtained when performing excitation by using the first and second exciting coils3aand3b. The vector Vbs0R represents a v×B vector Vb10+Vb20R=Kb·(B1c−B2c)·C·V obtained when performing excitation by using the first and second exciting coils3aand3b.

According to equations (33), (34), (36), and (38), a ∂A/∂t component Va10+Va20R (the first term of the right side of equation (30)) and a v×B component Vb10+Vb20R (the second term of the right side of equation (30)) which are detected by the electrodes2aand2bin the excitation state ST2are given by
Va10+Va20R=Ka·(B1c+B2c)·C·ω0  (39)
Vb10+Vb20R=Kb·(B1c−B2c)·C·V(40)

Extracting only the ∂A/∂t component Va10+Va20R from the resultant vector E20R (=Va10+Va20R+Vb10+Vb20R) of the ∂A/∂t component and v×B component and extracting the variation factor C due to a characteristic or state of the fluid make it possible to know a change in the characteristic or state of the fluid or a state in the measuring tube independently of the flow velocity. A method of extracting a ∂A/∂t component from a resultant vector will be generalized and described later.

FIG. 13is a block diagram for explaining the third principle of the state detection device of the present invention. This state detection device includes a measuring tube1, first electrodes2aand2band second electrodes2cand2dwhich are arranged in the measuring tube1to be perpendicular to both a magnetic field applied to a fluid to be measured and a measuring tube axis PAX and face each other so as to be come into contact with the fluid to be measured, and detect the electromotive force generated by the magnetic field and the flow of the fluid to be measured, and an exciting coil3which applies, to the fluid to be measured, a time-changing magnetic field which is asymmetric on the front and rear sides of the measuring tube1which are bordered on a plane PLN1and a time-changing magnetic field which is asymmetric on the front and rear sides of the measuring tube1which are bordered on a plane PLN2, when a plane which is perpendicular to the measuring tube axis PAX and includes the first electrodes2aand2bserving as the plane PLN1and a plane which is perpendicular to the measuring tube axis PAX and includes the second electrodes2cand2dserves as the plane PLN2. The first electrodes2aand2bare placed at a position spaced apart from a plane PLN3which includes the axis of the exciting coil3and is perpendicular to the direction of the measuring tube axis PAX by an offset distance d3to, for example, the upstream side. The second electrodes2cand2dare placed at a position spaced apart from the plane PLN3by an offset distance d4to, for example, the downstream side.

The state detection device shown inFIG. 13is obtained by adding one pair of electrodes to the state detection device shown inFIG. 1. If the second electrodes2cand2dto be newly added are placed on the same side as the first electrodes2aand2b, the resultant arrangement is a redundant arrangement of that shown inFIG. 1. Therefore, the second electrodes2cand2dneed to be placed on a side different from that of the first electrodes2aand2bthrough the exciting coil3. With this arrangement, a v×B component originating from the magnetic field generated from the exciting coil3and the flow velocity and detected by the first electrodes2aand2band a v×B component originating from the magnetic field generated from the exciting coil3and the flow velocity and detected by the second electrodes2cand2dare directed in the same direction. In contrast, a ∂A/∂t component originating from a change in the magnetic field generated from the exciting coil3, which is detected by the first electrodes2aand2b, and a ∂A/∂t component originating from a change in the magnetic field generated by the exciting coil3, which is detected by the second electrodes2cand2d, are directed in opposite directions. Using this principle makes it possible to efficiently extract a ∂A/∂t component.

Of a magnetic field Bd generated from the first exciting coil3, a magnetic field component (magnetic flux density) B3orthogonal to both an electrode axis EAX1connecting the electrodes2aand2band the measuring tube axis PAX on the electrode axis EAX1, and of the magnetic field Bd generated from the exciting coil3, a magnetic field component (magnetic flux density) B4orthogonal to both an electrode axis EAX2and the measuring tube axis PAX on the electrode axis EAX2are given by
B3=b3·cos(ω0·t−θ3)  (41)
B4=b4·cos(ω0·t−θ4)  (42)

Note, however, that since B3and B4are generated from the single exciting coil3, b3and b4, and θ3and θ4have some relationships with each other and are not independent variables. In equations (41) and (42), b3and b4are the amplitudes of the magnetic flux densities B3and B4, ω0is an angular frequency, and θ3and θ4are phase differences (phase lags) between the magnetic flux densities B3and B4and ω0·t. The magnetic flux densities B3and B4will be respectively referred to as the magnetic fields B3and B4hereinafter.

Since the electromotive force originating from a change in magnetic field depends on a time derivative dB/dt of the magnetic field, the magnetic fields B3and B4of the magnetic field Bd generated from the exciting coil3are differentiated according to

If the flow rate of the fluid to be measured is 0, a generated eddy current is only a component originating from a change in magnetic field. An eddy current I due to a change in the magnetic field Bd is directed as shown inFIG. 14. Therefore, a first inter-electrode electromotive force E1which is generated between the electrodes2aand2bby a change in the magnetic field Bd and is irrelevant to the flow velocity within a plane including the electrode axis EAX1and the measuring tube axis PAX and a second inter-electrode electromotive force E2which is generated between the electrodes2cand2dby a change in the magnetic field Bd and is irrelevant to the flow velocity within a plane including the electrode axis EAX2and the measuring tube axis PAX are directed opposite to each other as shown inFIG. 14.

At this time, the first and second inter-electrode electromotive forces E1and E2are the values obtained such that time derivatives (−dB3/dt and dB4/dt) of magnetic fields to which the directions of electromotive forces are added are multiplied by a proportional coefficient rk and the phase differences θ3and θ4are replaced with θ3+θ00and θ4+θ00, respectively (rk and θ00are associated with the conductivity and permittivity of the fluid to be measured and the structure of the measuring tube1including the positions of the electrodes2a,2b,2c, and2d) according to the following equations:

If the magnitude of the flow velocity of the fluid to be measured is V (V≠0), a component v×Bd originating from a flow velocity vector v of the fluid to be measured is generated in the generated eddy current in addition to an eddy currents I generated when the flow velocity is 0. For this reason, an eddy current Iv originating from the flow velocity vector v and the magnetic field Bd is directed as shown inFIG. 15. Consequently, a first inter-electrode electromotive force Ev1generated by the flow velocity vector v and the magnetic field Bd and a second inter-electrode electromotive force Ev2generated by the flow velocity vector v and the magnetic field Bd are directed in the same direction.

At this time, the first and second inter-electrode electromotive forces Ev1and Ev2are the values obtained such that magnetic fields (B3and B4) to which the directions of electromotive forces are added are multiplied by a proportional coefficient rkv and the phase differences θ3and θ4are replaced with θ3+θ01and θ4+θ01, respectively (rkv and θ01are associated with the magnitude V of the flow velocity, the conductivity and permittivity of the fluid to be measured, and the structure of the measuring tube1including the positions of the electrodes2a,2b,2c, and2d) according to the following equation:

Considering the directions of the inter-electrode electromotive forces described with reference toFIGS. 14 and 15, a first inter-electrode electromotive force Ea3cbetween the electrodes2aand2bwhich is obtained by combining the electromotive force obtained by converting the inter-electrode electromotive force originating from a temporal change in magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force originating from the flow velocity of the fluid to be measured into a complex vector is represented by the following equation according to equation (18) using equation (17).
Ea3c=rk·ω0·b3·exp{j·(π/2+θ3+θ00)}+γ·rk·V·b3·exp{j·(θ3+θ01)}  (49)

In addition, a second inter-electrode electromotive force Ea4cbetween the electrodes2cand2dwhich is obtained by combining the electromotive force obtained by converting the inter-electrode electromotive force originating from a temporal change in magnetic field into a complex vector and the electromotive force obtained by converting the inter-electrode electromotive force originating from the flow velocity of the fluid to be measured into a complex vector is represented by the following equation according to equation (18) using equation (17).

Assume that θ4=θ3+Δθ4represents the relationship between a phase lag θ3of the magnetic field B3with respect to ω0·t and a phase lag θ4of the magnetic field B4with respect to ω0·t, and θ01=θ00+Δθ01represents the relationship between an angle θ00of the ∂A/∂t component with respect to the imaginary axis and an angle θ01of the v×B component with respect to the real axis. If E301is a value obtained by substituting θ01=θ00+Δθ01into the first inter-electrode electromotive force Ea3cgiven by equation (49), and E302is a value obtained by substituting θ4=θ3+Δθ4and θ01=θ00+Δθ01into the second inter-electrode electromotive force Ea4cgiven by equation (50), the first and second inter-electrode electromotive forces E301and E302are represented as follows:

A sum E30sand a difference E30dof the first and second inter-electrode electromotive forces E301and E302are represented by

The first term of the right side of equation (53) represents a ∂A/∂t component in the sum of the electromotive force detected by the first electrodes2aand2band the electromotive force detected by the second electrodes2cand2d. The second term of the right side of equation (53) represents a v×B component in the sum of the electromotive force detected by the first electrodes2aand2band the electromotive force detected by the second electrodes2cand2d. The first term of the right side of equation (54) represents a ∂A/∂t component in the difference between the electromotive force detected by the first electrodes2aand2band the electromotive force detected by the second electrodes2cand2d. The second term of the right side of equation (54) represents a v×B component in the difference between the electromotive force detected by the first electrodes2aand2band the electromotive force detected by the second electrodes2cand2d.

In this case, if the distance d3from the plane PLN3including the axis of the exciting coil3to the electrode axis EAX1connecting the electrodes2aand2bis almost equal to the distance d4from the plane PLN3to the electrode axis EAX2connecting the electrodes2cand2d(d3≈d4), then b3≈b4and Δθ4≈0. In this case, equations (53) and (54) are rewritten as follows:

That is, since the sum E30sof first and second inter-electrode electromotive forces is almost only the electromotive force based on the v×B component, and the difference E30dbetween the first and second inter-electrode electromotive forces is almost only the electromotive force based on the ∂A/∂t component, it is obvious that obtaining the difference between the first and second inter-electrode electromotive forces makes it possible to efficiently extract a ∂A/∂t component.

Assume that a ∂A/∂t component in the resultant vector of the first inter-electrode electromotive force E301of equation (51) is represented by a product Va30of constant term Ka=exp(j·π/2) in the ∂A/∂t component, term Bc3=b3·exp(j·θ3) associated with the magnetic field generated from the exciting coil3, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the angular frequency ω0. In this case, Va30is represented by equation (57).
Va30=Ka·Bc3·C·ω0  (57)

Assume that a v×B component in the resultant vector of the first inter-electrode electromotive force E301of equation (51) is represented by a product Vb30of constant term Kb=γ·exp(j·Δθ01) in the v×B component, term Bc3=b3·exp(j·θ3) associated with the magnetic field generated from the exciting coil3, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the magnitude V of the flow velocity. In this case, Vb30is represented by equation (58).
Vb30=Kb·Bc3·C·V(58)

Assume that a ∂A/∂t component in the resultant vector of the second inter-electrode electromotive force E302of equation (52) is represented by a product Va40of constant term −Ka=−exp(j·π/2) in the ∂A/∂t component, term Bc4=b4·exp{j·(θ3+Δθ4)} associated with the magnetic field generated from the exciting coil3, term C=rk·exp(j·θ00) associated with the characteristic or state of the fluid, and the angular frequency ω0. In this case, Va40is represented by equation (59).
Va40=−Ka·Bc4·C·ω0  (59)

Considering that (E301−E302) when the difference between the first inter-electrode electromotive force E301and the second inter-electrode electromotive force E302is to be obtained, the equation obtained by reversing the sign of Va40of equation (59) is defined as Va40R (Va40R=−Va40) represented by equation (60):
Va40R=Ka·Bc4·C·ω0  (60)

Assume that a v×B component in the resultant vector of the second inter-electrode electromotive force E302of equation (52) is represented by a product Vb40of constant term Kb=γ·exp(j·Δθ01) in the v×B component, term Bc4=b4·exp{j·(θ3+Δθ4)} associated with the magnetic field generated from the exciting coil3, term C=rk·exp(j·θ00) associated with a characteristic or state of the fluid, and the magnitude V of the flow velocity. In this case, Vb40is represented by equation (61).
Vb40=Kb·Bc4·C·V(61)

Considering that (E301−E302) when the difference between the first inter-electrode electromotive force E301and the second inter-electrode electromotive force E302is to be obtained, the equation obtained by reversing the sign of Vb40of equation (61) is defined as Vb40R (Vb40R=−Vb40) represented by equation (62):
Vb40R=−Kb·Bc4·C·V(62)

According to equations (57), (58), (60), and (62), in the electromotive force difference E30drepresented, a ∂A/∂t component Va30+Va40R (the first term of the right side of equation (54)) originating from a change in the magnetic field generated from the exciting coil3and a v×B component Vb30+Vb40R (the second term of the right side of equation (54)) originating from the magnetic field generated from the exciting coil3and the flow velocity are given by
Va30+Va40R=Ka·(Bc3+Bc4)·C·ω0  (63)
Vb30+Vb40R=Kb·(Bc3−Bc4)·C·V(64)

Extracting only the ∂A/∂t component (Va30+Va40R) from the resultant vector E30R (=Va30+Va40R+Vb30+Vb40R) of the ∂A/∂t component and v×B component and extracting the variation factor C due to a characteristic or state of the fluid make it possible to know a change in the characteristic or state of the fluid or the state in the measuring tube independently of the flow velocity.

A method of extracting a ∂A/∂t component from a resultant vector will be described next. A characteristic or state of a target fluid and a state in a measuring tube will be referred to as parameters hereinafter.

As an extraction method which can be applied to the three arrangements shown inFIGS. 1,5, and13, the first extraction method will be described. The first extraction method is a method using the phenomenon that although a ∂A/∂t component varies depending on the frequency, a v×B component does not vary. Note that in the first extraction method, a component C which varies depending on the value of a parameter needs to be associated with only the value of the parameter, and have no frequency characteristic.

First of all, in the arrangement shown inFIG. 1, when an exciting current with the angular frequency ω0is supplied to the exciting coil3, the electromotive force detected by the electrodes2aand2bcorresponds to the resultant vector Va10+Vb10of the vector Va10of the ∂A/∂t component and the vector Vb10of the v×B component according to the following equations.
Va10=Ka·B1c·C·ω0  (65)
Vb10=Kb·B1c·C·V(66)

In consideration of the fact that a ∂A/∂t component is a vector irrelevant to the magnitude V of the flow velocity and a v×B component is a vector which changes in magnitude in proportion to the magnitude V of the flow velocity, taking the difference between a resultant vector obtained with an exciting angular frequency ω2different from ω0and a resultant vector obtained with the exciting angular frequency ω0cancels out the v×B component. As a consequence, the ∂A/∂t component is left.

A v×B component obtained with the exciting angular frequency ω2is equal to that in equation (66). A ∂A/∂t component obtained with the exciting angular frequency ω2is given by the equation obtained by replacing ω0with ω2in equation (65) as follows:
Va12=Ka·B1c·C·ω2  (67)

Subtracting the resultant vector Va12+Vb10obtained with the exciting angular frequency ω2from the resultant vector Va10+Vb10obtained with the exciting angular frequency ω0cancels out the v×B component, and becomes equal to Va10−Va12. The ∂A/∂t component Va10−Va12irrelevant to the flow velocity can therefore be extracted by using the output difference between different frequency components.FIG. 16is a graph showing the processing of extracting the ∂A/∂t component Va10−Va12in the form of a complex vector.

In the arrangement shown inFIG. 5, as described above, keeping the phase difference between the magnetic field generated from the first exciting coil3aand the magnetic field generated from the second exciting coil3bat almost n makes it possible to efficiently extract a ∂A/∂t component. Assume that the first exciting current having the angular frequency ω0is supplied to the first exciting coil3a, and the second exciting current having the angular frequency ω0with a phase difference Δθ2+π with respect to the first exciting current is supplied to the second exciting coil3b. In this case, letting Vas0R be the vector Va10+Va20R of the ∂A/∂t component in equation (39) and Vbs0R be the vector Vb10+Vb20R of the v×B component in equation (40), the electromotive force detected by the electrodes2aand2bcorresponds to a resultant vector Vas0R+Vbs0R given below:
Vas0R=Ka·(B1c+B2c)·C·ω0  (68)
Vbs0R=Kb·(B1c−B2c)·C·V(69)

As shown inFIG. 1, a v×B component obtained when the exciting angular frequency is set to ω2becomes equal to equation (69). In addition, a vector Vas2R of a ∂A/∂t component obtained when the exciting angular frequency is set to ω2becomes equal to the value obtained by replacing ω0with ω2in equation (68) according to the following equation:
Vas2R=Ka·(B1c+B2c)·C·ω2  (70)

Subtracting the resultant vector Vas2R+Vbs0R obtained with the exciting angular frequency ω2from the resultant vector Vas0R+Vbs0R obtained with the exciting angular frequency ω0cancels out the v×B component, and becomes equal to Vas0R−Vas2R. The ∂A/∂t component Vas0R−Vas2R irrelevant to the flow velocity can therefore be extracted by using the output difference between different frequency components.FIG. 17is a graph showing the processing of extracting the ∂A/∂t component Vas0R−Vas2R in the form of a complex vector.

In the arrangement shown inFIG. 13, the method of extracting a ∂A/∂t component from a resultant vector is the same as that in the arrangement shown inFIG. 5. The extraction method described in the case of the state detection device shown inFIG. 5may be made to correspond to the state detection device shown inFIG. 13by replacing the electromotive force originating from the influence of the magnetic field generated from the first exciting coil3awith the electromotive force detected by the first electrodes2aand2b, replacing the electromotive force originating from the influence of the magnetic field generated from the second exciting coil3bwith the electromotive force detected by the second electrodes2cand2d, replacing the electromotive force detected in the excitation state ST1with an electromotive force sum, and replacing the electromotive force detected in the excitation state ST2with an electromotive force difference.

The second extraction method will be described as an extraction method which can be applied to the arrangements shown inFIGS. 5 and 13of the three arrangements shown inFIGS. 1,5, and13. The second extraction method is a method of canceling v×B components by using the phenomenon that v×B components are directed in the same direction on the front and rear sides in the tube axis direction with respect to a plane which includes the exciting coil and is perpendicular to the tube axis direction, but ∂A/∂t components are directed in opposite directions.

In the case of the arrangement shown inFIG. 5, as described above, keeping the phase difference between the magnetic field generated from the first exciting coil3aand the magnetic field generated from the second exciting coil3bat almost n makes it possible to efficiently extract a ∂A/∂t component. The ∂A/∂t component vector Vas0R is extracted from the resultant vector Vas0R+Vbs0R in the same manner as in the first extraction method. If Vas0R>>Vbs0R, then Vbs0R≈0, thus approximately extracting the ∂A/∂t component vector Vas0R.

In the initial state (at the time of calibration), if the magnetic field B1generated from the first exciting coil3aand the magnetic field B2generated from the second exciting coil3bare set to be equal in advance, the differences between the magnetic fields B1and B2and those in the initial state decrease. As a consequence, the condition represented by the following expression holds.
|b1+b2·exp(j·Δθ2)|>>|b1−b2·exp(j·Δθ2)|  (71)

Since ω0>γ·V holds, the following condition holds for the inter-electrode electromotive force E20R given by equation (30) in consideration of the condition represented by equation (71).
|ω0·exp(j·π/2)·{b1+b2·exp(j·Δθ2)}|>>|γ·V·exp(j·Δθ01)·{b1−b2·exp(j·Δθ2)}|  (72)

Letting Vas0R′ be the electromotive force obtained by approximating the inter-electrode electromotive force E20R given by equation (30) by using the condition represented by expression (72), the inter-electrode electromotive force Vas0R′ is represented by

Obviously, therefore, using the phase difference between the magnetic field generated from the first exciting coil3aand the magnetic field generated from the second exciting coil3bmakes it possible to extract the ∂A/∂t component vector Vas0R in the resultant vector Vas0R+Vbs0R.

In the arrangement shown inFIG. 13, a method of extracting the ∂A/∂t component from the resultant vector is the same as that in the arrangement shown inFIG. 5as described in the first extraction method. In the arrangement shown inFIG. 13, using the output difference between the first electrodes2aand2band the second electrodes2cand2dmakes it possible to extract the ∂A/∂t component vector Vas0R from the resultant vector Vas0R+Vbs0R.

A method of extracting the above-described parameter from the extracted ∂A/∂t component will be described next. The parameter in the ∂A/∂t component includes the first parameter whose variation factor is irrelevant to the frequency (i.e., the influence of the frequency can be ignored), and the second parameter whose variation factor is relevant to the frequency.

The ∂A/∂t component extracted in the arrangement shown inFIG. 1by the first extraction method is a vector Va10−Va12. The ∂A/∂t component extracted in the arrangement shown inFIG. 5is a vector Vas0R−Vas2R. Since the extracted ∂A/∂t component is irrelevant to the flow velocity V, the characteristic or state of the fluid or a state in the measuring tube, other than the flow velocity, can be measured by using the ∂A/∂t component. Since it is possible to extract the first parameter in either of the vectors Va10−Va12and Vas0R−Vas2R by the same method as described above, a case wherein the first parameter is extracted from the vector Vas0R−Vas2R will be exemplified.

In the vector Vas0R−Vas2R, C=rk·exp(j·θ00) represents the variation factor which changes depending on the target first parameter. A proportional coefficient rk and the angle θ00of the ∂A/∂t component with respect to an imaginary axis are represented as functions of the first parameter p, i.e., rk[p] and θ00[p], respectively. If the variation factor C is Cp when the first parameter is p, the variation factor Cp is given by
Cp=rk[p]·exp(j·θ00[p])  (75)

According to equations (68) and (70), the vector Vas0R−vas2R is expressed by
Vas0R−Vas2R=Ka·(B1c+B2c)·Cp·(ω0−ω2)  (76)

According to equation (76), the variation factor Cp which changes depending on the target first parameter is expressed by
Cp={Vas0R−Vas2R}/{Ka·(B1c+B2c)·(ω0−ω2)}  (77)

In this case, when a magnetic field whose amplitude or phase does not vary is to be generated by using a proper exciting coil, terms B1cand B2cassociated with the magnetic field in a ∂A/∂t component become values which can be checked at the time of calibration, and the magnitude of {Vas0R−Vas2R}/{Ka·(B1c+B2c)·(ω0−ω2)} and the angle of {Vas0R−Vas2R}/{Ka·(B1c+B2c)·(ω0−ω2)} with respect to the real axis are respectively represented by rk[p] and θ00[p]. Therefore, storing the relationship between the first parameter p and the proportional coefficient rk[p] or the relationship between the first parameter p and the angle θ00[p] in advance at the time of calibration makes it possible to obtain the first parameter p by calculating the magnitude or phase of {Vas0R−Vas2R}/{Ka·(B1c+B2c)·(ω0−ω2)}. Since the first parameter p does not change depending on the frequency, the first parameter p can be obtained by using an arbitrary frequency.

The ∂A/∂t component extracted in the arrangement shown inFIG. 5by the second extraction method is a vector Vas0R in equation (68). Since the extracted ∂A/∂t component is irrelevant to the flow velocity V, the characteristic or state of the fluid or a state in the measuring tube, other than the flow velocity, can be measured by using the ∂A/∂t component. In the vector Vas0R in equation (68), C=rk·exp(j·θ00) represents the variation factor which changes depending on the target second parameter. A proportional coefficient rk and the angle θ00of the ∂A/∂t component with respect to an imaginary axis are represented as functions of the second parameter p and angular frequency ω, i.e., rk[p,ω] and θ00[p,ω], respectively. If the variation factor C is Cp when the second parameter is p, and the angular frequency is ω0, the variation factor Cp0is given by
Cp0=rk[p,ω0]·exp(j·θ00[p,ω0])  (78)

According to equation (68), the vector Vas0R is expressed by
Vas0R=Ka·(B1c+B2c)·Cp0·ω0  (79)

According to equation (79), the variation factor Cp0which changes depending on the target second parameter is expressed by
Cp0=Vas0R/{Ka·(B1c+B2c)·ω0}  (80)

In this case, when a magnetic field whose amplitude or phase does not vary is to be generated by using a proper exciting coil, terms B1cand B2cassociated with the magnetic field in a ∂A/∂t component become values which can be checked at the time of calibration, and the magnitude of Vas0R/{Ka·(B1c+B2c)·ω0} and the angle of Vas0R/{Ka·(B1c+B2c)·ω0} with respect to the real axis are respectively represented by rk[p,ω0] and θ00[p,ω0]. Therefore, storing the relationship between the second parameter p and the proportional coefficient rk[p,ω0] or the relationship between the second parameter p and the angle θ00[p,ω0] with the exciting angular frequency ω0in advance at the time of calibration makes it possible to obtain the second parameter p by calculating the magnitude or phase of Vas0R/{Ka·(B1c+B2c)·ω0}.

When the exciting frequency is fixed to one level, a method of obtaining the second parameter is the same as that of the first parameter. Hence, a case wherein the value of the second parameter is output in consideration of variation of the magnetic field will be exemplified as a case wherein the exciting frequency is not fixed to one level. In this case, the variation factor of the magnetic field can be removed, and the value of the second parameter with a small error can be output by obtaining the ∂A/∂t components with a plurality of frequencies.

In the vector Vas2R in equation (70), when the value of the variation factor C with the exciting angular frequency ω2is Cp2, the variation factor Cp2and vector Vas2R are expressed by the following equation according to equations (78) and (79).
Cp2=rk[p,ω2]·exp(j·θ00[p,ω2])  (81)
Vas2R=Ka·(B1c+B2c)·Cp0·ω2  (82)

According to equation (82), the variation factor Cp2which changes depending on the target second parameter is expressed by the following equation.
Cp2=Vas2R{Ka·(B1c+B2c)·ω2}  (83)

When Cp0≠Cp2holds, and the ratio between the variation factors Cp0and Cp2is Cn, the ratio Cn is expressed by the following equation according to equations (78), (80), (81), and (83).

According to equation (84), the ratio Cn does not have the variation factor of the magnetic field, and the second parameter p can be obtained by reducing the error factor. At the time of calibration, storing the relationship among the exciting angular frequencies ω0and ω2, the second parameter p, and {rk[p,ω2]/rk[p,ω0]}, or storing the relationship among the exciting angular frequencies ω0and ω2, the second parameter p, and (θ00[p,ω2]−θ00[p,ω0]) makes it possible to obtain the second parameter p without the variation factor of the magnetic field (e.g., the shift of the magnetic field) by calculating the magnitude or phase of (Vas2R/Vas0R)·(ω0/ω2).

A case wherein the plurality of second parameter values are obtained will be described next. When the frequency characteristics of the parameters depending on the parameters are different from each other, obtaining the ∂A/∂t components with the plurality of exciting angular frequencies makes it possible to obtain the plurality of second parameter values. In this case, two second parameter values are obtained. Of the two parameters, one is the third parameter, and the other is the fourth parameter.

In the vector Vas0R in equation (68), C=rk·exp(j·θ00) represents the variation factor which changes depending on the target second parameter. A proportional coefficient rk and the angle θ00of the ∂A/∂t component with respect to an imaginary axis are represented as functions of the third parameter p, the fourth parameter q, and the angular frequency ω, i.e., rk[p,q,ω] and θ00[p,q,ω], respectively. If the variation factor C is Cpq0when the third parameter is p, the fourth parameter is q, and the angular frequency is ω, the variation factor Cpq0is given by
Cpq0=rk[p,q,ω0]·exp(j·θ00[p,q,ω0])  (85)

According to equation (68), the vector Vas0R is expressed by
Vas0R=Ka·(B1c+B2c)·Cpq0·ω0  (86)

According to equation (86), the variation factor Cpq0which changes depending on the target third and fourth parameters is expressed by
Cpq0=Vas0R/{Ka·(B1c+B2c)·ω0}  (87)

If the value of the variation factor C is Cpq2when the third parameter is p, the fourth partaker is q, and the angular frequency is ω2, the variation factor Cpq2and the vector Vas2R are expressed by the following equations according to equations (85) and (86).
Cpq2=rk[p,q,ω2]·exp(j·θ00[p,q,ω2])  (88)
Vas2R=Ka·(B1c+B2c)·Cpq2·ω2  (89)

According to equation (89), the variation factor Cpq2which changes depending on the target third and fourth parameters is expressed by following equation.
Cpq2=Vas2R/{Ka·(B1c+B2c)·ω2}  (90)

In this case, when a magnetic field whose amplitude or phase does not vary is to be generated by using a proper exciting coil, terms B1cand B2cassociated with the magnetic field in a ∂A/∂t component become values which can be checked at the time of calibration, and the magnitude of Vas0R/{Ka·(B1c+B2c)·ω0} and the angle of Vas0R/{Ka·(B1c+B2c)·ω0} with respect to the real axis are respectively represented by rkg[p,q,ω0] and θ00[p,q,ω0], and the magnitude of Vas2R/{Ka·(B1c+B2c)·ω2} and the angle of Vas2R/{Ka·(B1c+B2c)·ω2} with respect to the real axis are respectively represented by rkg[p,q,ω2] and θ00[p,q,ω2].

Therefore, storing the relationship among the third parameter p, the fourth parameter q, and the proportional coefficient [p,q,ω0] obtained with the exciting angular frequency ω0, and the relationship among the third parameter p, the fourth parameter q, and the proportional coefficient [p,q,ω2] obtained with the exciting angular frequency ω2make it possible to obtain the third parameter p and the fourth parameter q by calculating the magnitudes of Vas0R/{Ka·(B1c+B2c)·ω0} and Vas2R/{Ka·(B1c+B2c)·ω2}.

Storing the relationship among the third parameter p, the fourth parameter q, and the angle θ00[p,q,ω0] obtained with the exciting angular frequency ω0, and the relationship among the third parameter p, the fourth parameter q, and the angle θ00[p,q,ω2] obtained with the exciting angular frequency ω2in advance at the time of calibration make it possible to obtain the third and fourth parameters p and q by calculating the phases of Vas0R/{Ka·(B1c+B2c)·ω0} and Vas2R/{Ka·(B1c+B2c)·ω2}.

Points of concern to be raised at the time of implementation will be described next. In order to obtain the value of the parameter p from the proportional coefficient rk[p] and rk[p,ω] obtained from a measured value, it is necessary to generate a table for inversion in advance. The proportional coefficient rk[p] and angle θ00[p] will be representatively expressed by a function f[p], the proportional coefficient rk[p,ω] and angle θ00[p,ω] will be representatively expressed by a function f[p,ω] (when a plurality of parameters are used, a function f[p,q,ω]), and inversion and a table will be described. There are two methods of generating a table for inversion, i.e., a method (to be referred to as the first generating method hereinafter) of generating a table by interpolation from a measurement result at the time of calibration, and a method (to be referred to as the second generating method hereinafter) of directly generating a table from a theoretical formula.

The first generating method for a table (to be referred to as the first table hereinafter) for the extraction of the first parameter will be described first. As shown inFIG. 18, assuming that f[p1]=y1was obtained as a measurement result when the value of the first parameter was p1at the time of calibration, and f[p2]=y2was obtained as a measurement result when the value of the first parameter was p2, the first parameter p is represented by the following equation by linear approximation between two points:
p=(p2−p1)/(y2−y1)·(f[p]−y1)+p1  (91)

The first table can be generated by equation (91). Using the first table makes it possible to obtain the first parameter p from the function f[p] (the proportional coefficient rk[p] or angle θ00[p]) obtained at the time of actual measurement after calibration. Although the linear approximation has been exemplified, a polynomial also allows inversion in the same manner as described above.

The second generating method for the first table will be described next. If the relationship between the first parameter p and y=f[p] is obtained as a theoretical formula at the time of design, and there is an inverse function f−1(y), the first parameter p is represented by
p=f−1(f[p])  (92)

FIG. 19shows the relationship represented by equation (92). Storing equation (92) as the first table in advance makes it possible to obtain the first parameter p from the function f[p] obtained at the time of actual measurement after calibration.

The first generating method for a table (to be referred to as the second table hereinafter) for the extraction of one second parameter will be described next. As shown inFIG. 20, assuming that the ratio ry1between f[p1,ω0] with the exciting angular frequency ω0and f[p1,ω2] with the exciting angular frequency ω2is obtained as a measurement result when the value of the second parameter was p1at the time of calibration, and the ratio ry2between f[p2,ω0] with the exciting angular frequency ω0and f[p2,ω2] with the exciting angular frequency ω2is obtained as a measurement result when the value of the second parameter was p2, the second parameter p is represented by the following equation by linear approximation between two points:

The second table can be generated by equation (93). Using the second table makes it possible to obtain the second parameter p from the ratio f[p,ω2]/f[p,ω0] of the functions obtained at the time of actual measurement after calibration. The function f[p,ω2] means the proportional coefficient rk[p,ω2] or angle θ00[p,ω2], and the function f[p,ω0] means the proportional coefficient rk[p,ω0] or angle θ00[p,ω0]. Although the linear approximation has been exemplified, a polynomial also allows inversion in the same manner as described above.

The second generating method for the second table will be described next. If the relationship between the second parameter p and y=f[p,ω] with the exciting angular frequency G) is obtained as a theoretical formula at the time of design, and the ratio f[p,ω0]/f[p,ω2] of the function is represented by ry=g[p], when there is an inverse function g−1(p), the second parameter p is represented by
p=g−1(g[p])  (94)

FIG. 21shows the relationship represented by equation (94). Storing equation (94) as the second table in advance makes it possible to obtain the second parameter p from the ratio f[p,ω2]/f[p,ω0] of the function obtained at the time of actual measurement after calibration.

The first generating method for a table (to be referred to as the third table hereinafter) for the extraction of a plurality of second parameters will be described next. In this case, the values of two second parameters are obtained. Of the two second parameters, one is the third parameter, and the other is the fourth parameter. As shown inFIG. 22, assume that, with the exciting angular frequency ω0at the time of calibration, f[p1,q1,ω0]=z11is obtained as a measurement result when the third parameter is p1and the fourth parameter is q1, f[p1,q2,ω0]=z12is obtained as a measurement result when the third partaker is p1and the fourth parameter is q2, f[p2,q1,ω0]=z21is obtained as a measurement result when the third parameter is p2and the fourth parameter is q1, and f[p2,q2,ω0]=z22is obtained as a measurement result when the third parameter is p2and the fourth parameter is q2. In this case, a plane including arbitrary three points out of the measurement results z11, z12, z21, and z22is expressed by the following equation.
p/a0+q/b0+f[p,q,ω0]/c0=1  (95)

As shown inFIG. 23, assume that, with the exciting angular frequency ω2at the time of calibration, f[p1,q1,ω2]=z11′ is obtained as a measurement result when the third parameter is p1and the fourth parameter is q1, f[p1,q2,ω2]=z12′ is obtained as a measurement result when the third parameter is p1and the fourth parameter is q2, f[p2,q1,ω2]=z21′ is obtained as a measurement result when the third parameter is p2and the fourth parameter is q1, and f[p2,q2,ω2]=z22′ is obtained as a measurement result when the third parameter is p2and the fourth parameter is q2. In this case, a plane including arbitrary three points out of the measurement results z11′, z12′, z21′, and z22′ is expressed by the following equation.
p/a2+q/b2+f[p,q,ω2]/c2=1  (96)

Storing the equations (95) and (96) of the plane as the third table makes it possible to define the third parameter p and the fourth parameter q as an intersection of the following two lines from the functions f[p,q,ω0]=z and f[p,q,ω2] obtained at the time of actual measurement after calibration.
p/a0+q/b0+z0/c0=1  (97)
p/a2+q/b2+z2/c2=1  (98)

FIG. 24shows an example of the lines expressed by equations (97) and (98). For example, the solutions of the third parameter p and the fourth parameter q can be obtained by the Gaussian elimination method using simultaneous equations of equations (97) and (98). Although approximation is performed by using a plane, inverse transformation can also be performed by using a curved plane.

The second generating method for the third table will be described next. When the relationship among the third parameter p, the fourth parameter q, z0=f[p,q,ω0] with the exciting angular frequency ω0, and z2=f[p,q,ω2] with the exciting angular frequency ω2is obtained as a theoretical formula at the time of design, a curved plane equation can be obtained as the third table. Storing the third table makes it possible to obtain two curved line equations from the functions f[p,q,ω0] and f[p,q,ω2] obtained at the time of actual measurement after calibration. The third parameter p and the fourth parameter q are obtained as the intersection of the two curved lines. An example of two curved lines is shown inFIG. 25.

FIRST EMBODIMENT

The first embodiment of the present invention will be described in detail next. This embodiment uses the first principle described above. A state detection device according to this embodiment includes one exciting coil and a pair of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 1except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 1. This embodiment uses the first extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the first parameter irrelevant to an exciting frequency. An example of the first parameter is the level of a fluid or the deposited state of a substance adhering to the inside of a measuring tube.

When an exciting current with an angular frequency ω0is supplied to an exciting coil3, and the first parameter is p1, an inter-electrode electromotive force E110is represented by the following equation according to equations (19), (65), and (75).

When an exciting current with an angular frequency ω2is supplied to the exciting coil3, and the first parameter is p1, an inter-electrode electromotive force E112is represented by the following equation according to equations (19), (67), and (75).

Letting EdA1be the difference between the inter-electrode electromotive forces E110and E112, the electromotive force difference EdA1is given by

According to equation (101), it is obvious that a ∂A/∂t component in a resultant vector can be extracted by using the output difference between different frequency components. Equation (101) is irrelevant to a magnitude V of the flow velocity, and hence is only the component generated by ∂A/∂t. Using the electromotive force difference EdA1, therefore, makes it possible to measure a state of the fluid or a state in the measuring tube other than the flow velocity.

When a variation factor dependent on the first parameter is Cp1, Cp1=rk[p1]·exp(j·θ00[p1]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cp1is represented by equation (101).
Cp1=EdA1/[b1·exp{j·(π/2+θ1)}·(ω0−ω2)]  (102)

According to equation (102), a magnitude rk[p1] of the variation factor Cp1and an angle θ00[p1] thereof from the real axis are represented by
rk[p1]=|EdA1|/{b1·(ω0−ω2)}  (103)
θ00[p1]=∠EdA1−(π/2+θ1)  (104)

The first parameter p1can be obtained from the relationship between the first parameter p1and rk[p1], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the first parameter p1and the angle θ00[p1].

The specific arrangement and operation of the state detection device according to this embodiment will be described next.FIG. 26is a block diagram showing the arrangement of the state detection device according to this embodiment. The same reference numerals as inFIG. 26denote the same components inFIG. 1. The state detection device of this embodiment includes a measuring tube1, electrodes2aand2b, the exciting coil3placed at a position spaced apart by an offset distance d in the axial direction from a plane PLN which includes the electrodes2aand2band is perpendicular to the direction of a measuring tube axis PAX, a power supply unit4which supplies an exciting current to the exciting coil3, and a state quantifying unit8.

The exciting coil3and the power supply unit4constitute an exciting unit which applies a time-changing magnetic field asymmetric to the plane PLN to the fluid to be measured.

The state quantifying unit8includes a signal conversion unit5which obtains the amplitudes and phases of two frequency components with the first and second angular frequencies ω0and ω2of the resultant electromotive forces detected by the electrodes2aand2b, extracts an electromotive force difference between the two angular frequency components as a ∂A/∂t components on the basis of the amplitudes and the phases, and extracts, from the ∂A/∂t components, the magnitude or phase of the variation factor dependent on the first parameter and independent of the frequency, a state storage unit6(equivalent to the above-described first table) which stores in advance the relationship between the first parameter and the magnitude or phase of the variation factor dependent on the first parameter, and a state output unit7which obtains the first parameter corresponding to the magnitude or phase of the extracted variation factor based on the relationship stored in the state storage unit6.

The power supply unit4repeats, in a T-sec cycle, the operation of continuing the first excitation state for T1 sec in which an exciting current with a first angular frequency ω0is supplied to the exciting coil3and then continuing the second excitation state for T2 sec in which an exciting current with a second angular frequency ω2is supplied to the exciting coil3. That is, T=T1+T2.

FIG. 27is a flowchart showing the operations of the state quantifying unit8. First of all, the signal conversion unit5obtains an amplitude r110of the electromotive force E110of a component with the angular frequency ω0of the electromotive force between the electrodes2aand2b, and also obtains a phase difference φ110between the real axis and the electromotive force E110by using a phase detector (not shown) (step101inFIG. 27).

Subsequently, in the second excitation state, the signal conversion unit5obtains an amplitude r112of the electromotive force E112of a component with the angular frequency ω2of the electromotive force between the electrodes2aand2b, and also obtains a phase difference φ112between the real axis and the electromotive force E112by using the phase detector (step102).

The signal conversion unit5then calculates a real axis component E110xand imaginary axis component E110yof the inter-electrode electromotive force E110, and a real axis component E112xand imaginary axis component E112yof the inter-electrode electromotive force E112according to the following equations (step103):
E110x=r110·cos(φ110)  (105)
E110y=r110·sin(φ110)  (106)
E112x=r112·cos(φ112)  (107)
E112y=r112·sin(φ112)  (108)

After the calculation of equations (105) to (108), the signal conversion unit5obtains the magnitude and angle of the electromotive force difference EdA1between the inter-electrode electromotive forces E110and E112(step104). The processing in step104corresponds to the processing of obtaining a ∂A/∂t component, and is equivalent to the calculation of equation (101). The signal conversion unit5calculates a magnitude |EdA1| of the electromotive force difference EdA1according to the following equation:
|EdA1|={(E110x−E112x)2+(E110y−E112y)2}1/2(109)

The signal conversion unit5then calculates an angle ∠EdA1of the electromotive force difference EdA1with respect to the real axis according to the following equation:
∠EdA1=tan−1{(E110y−E112y)/(E110x−E112x)}  (110)

With the above operation, the processing in step104is complete.

The signal conversion unit5then calculates the magnitude rk[p1] of the variation factor Cp1dependent on the first parameter p1and the angle θ00[p1] with respect to the real axis from the electromotive force difference EdA1according to the following equations (step105):
rk[p1]=|EdA1|/{b1·(ω0−ω2)}  (111)
θ00[p1]=∠EdA1−(π/2+θ1)  (112)

The amplitude b1of the magnetic field B1generated from the exciting coil3and the phase difference θ1between the magnetic field B1and ω0·t are constants which can be obtained in advance by calibration or the like.

The relationship between the first parameter p1and the magnitude rk[p1] of the variation factor Cp1or the relationship between the first parameter p1and the angle θ00[p1] of the variation factor Cp1is registered in advance in the state storage unit6in the form of a mathematical expression or table. In step106, the state output unit7calculates the value of the first parameter p1corresponding to rk[p1] or θ00[p1] by referring to the state storage unit6on the basis of the magnitude rk[p1] or angle θ00[p1] of the variation factor Cp1calculated by the signal conversion unit5(or acquires it from the state storage unit6).

The state quantifying unit8performs the processing in steps101to106described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step107). Note that the processing in steps102to106is performed in the second excitation state for a duration of T2 sec.

As described above, this embodiment is configured to extract the electromotive force difference EdA1(∂A/∂t component) from the inter-electrode electromotive forces E110and E112in the two excitation states with different exciting frequencies, extract the magnitude or phase of the variation factor Cp1dependent on the characteristic or state of the fluid or a state in the measuring tube (the first parameter p1) from the electromotive force difference EdA1, and obtain the first parameter p1on the basis of the magnitude or phase of the variation factor Cp1. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

In this embodiment, the components of the state quantifying unit8, except for the detecting units of the inter-electrode electromotive forces E110and E112, can be implemented by a computer comprising a CPU, storage unit, and interface and programs which control the hardware resources. In this embodiment, for example, the v×B component can be extracted by E110−EdA1·{(ω0−ω2)/ω0}. There is known a technique of calculating the flow rate of the fluid from the v×B component in the field of a general electromagnetic flowmeter, which can be easily implemented by a computer included in the state quantifying unit8. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitude rk[p1] or angle θ00[p1] of the variation factor Cp1from the electromotive force difference EdA1. However, the first parameter p1can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude rk[p1] or the angle θ00[p1] which has a higher sensitivity and obtain the first parameter p1on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the first parameter p1at higher speed. For example, it suffices to use the magnetic field represented by the following equation instead of equation (3).
B1=b1·cos(ω0·t−θ1)+b1·cos(ω2·t−θ1)  (113)

The following description will explain a specific example of the state detection device of this embodiment which detects the deposited state (a change in the inner diameter of the measuring tube) of a substance in the measuring tube. As shown inFIG. 28, this example uses capacitive coupling type electrodes which do not come into contact with a fluid to be measured in consideration of the deposition of a substance in the measuring tube1. When the electrodes2aand2bare of the capacitive coupling type, they are coated with a lining10made of ceramic, Teflon, or the like formed on the inner wall of the measuring tube1.

As shown inFIG. 28, as a substance11is deposited on the inner wall of the measuring tube1, the inner diameter of the measuring tube1changes, and the value of the magnitude rk[p1] of the variation factor Cp1varies.FIG. 29shows an example of the relationship between the thickness (first parameter p1) of the substance11and the magnitude rk[p1] of the variation factor Cp1. Obtaining this relationship by a theoretical formula at the time of design or by measurement at the time of calibration and storing it in the state storage unit6in advance can obtain the thickness of the substance11in step106on the basis of the magnitude rk[p1] of the variation factor Cp1obtained in step105inFIG. 27.

SECOND EMBODIMENT

The second embodiment of the present invention will be described next. This embodiment is the same as the first embodiment except that one exciting coil is added to the state detection device, and uses the above-described second principle. That is, the state detection device of this embodiment includes two exciting coils and a pair of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 5except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 5. If the second exciting coil to be newly added is placed on the same side as the first exciting coil, the resultant arrangement is a redundant arrangement of the first embodiment. Therefore, the second exciting coil needs to be placed on a side different from that of the first exciting coil through a plane including the electrodes. This embodiment uses the first extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the first parameter irrelevant to the exciting frequency.

Assume that the first exciting current having an angular frequency ω0is supplied to a first exciting coil3a, the second exciting current having the angular frequency ω0with a phase difference Δθ2+π with respect to the first exciting current is supplied to a second exciting coil3b, and the first parameter is p2. In this case, an inter-electrode electromotive force E220is represented by the following equation according to equations (30), (68), and (75).

Assume that the first exciting current having an angular frequency ω2is supplied to the first exciting coil3a, the second exciting current having the angular frequency ω2with the phase difference Δθ2+π with respect to the first exciting current is supplied to the second exciting coil3b, and the first parameter is p2. In this case, an inter-electrode electromotive force E222R is represented by the following equation according to equations (30), (70), and (75).

In this case, if a distance d1from a plane PLN, which is perpendicular to a measuring tube axis PAX and includes electrodes2aand2b, to the first exciting coil3ais almost equal to a distance d2from the plane PLN to a second exciting coil3b(d1≈d2), then b1≈b2and Δθ2≈0. In this case, equations (114) and (115) are rewritten as follows:

That is, since the inter-electrode electromotive forces E220R and E222R are almost only the electromotive forces based on the ∂A/∂t components, computation errors in the extraction of a ∂A/∂t component can be reduced. This point is a difference in terms of technical significance between the first and second embodiments. Note, however, that the subsequent theoretical development will be made assuming that b1≠b2and Δθ2≠0.

Letting EdA2be the difference between the inter-electrode electromotive forces E220R and E222R, the electromotive force difference EdA2is given by

According to equation (118), it is obvious that a ∂A/∂t component in a resultant vector can be extracted by using the output difference between different frequency components. Equation (118) is irrelevant to a magnitude V of the flow velocity, and hence is only the component generated by ∂A/∂t. Using the electromotive force difference EdA2, therefore, makes it possible to measure a state of the fluid or a state in the measuring tube other than the flow velocity.

When a variation factor dependent on the first parameter is Cp2, Cp2=rk[p2]·exp(j·θ00[p2]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cp2is represented by the following equation according to equation (118).

Letting m2band θ2bbe the magnitude and angle of [exp{j·(π/2+θ1)}·{b1+b2·exp(j·Δθ2)}] in equation (119), m2band θ2bare represented by
m2b={b12+b22+b1·b2·cos(Δθ2)}1/2(120)
θ2b=tan−1[{b2·sin(Δθ2)}/{b1+b2·cos(Δθ2)}]−(π/2+θ1)  (121)

According to equations (119) to (121), the magnitude rk[p2] of the variation factor Cp2and the angle θ00[h2] with respect to the real axis are represented by
rk[p2]=|EdA1|/{m2b·(ω0−ω2)}  (122)
θ00[p2]=∠EdA1−θ2b(123)

The first parameter p2can be obtained from the relationship between the first parameter p2and rk[p2], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the first parameter p2and the angle θ00[p2].

The specific arrangement and operation of the state detection device according to this embodiment will be described next.FIG. 30is a block diagram showing the arrangement of the state detection device according to this embodiment. The same reference numerals as inFIG. 5denote the same components inFIG. 1. The state detection device of this embodiment includes a measuring tube1, electrodes2aand2b, the first and second exciting coils3aand3b, a power supply unit4which supplies exciting currents to the first and second exciting coils3aand3b, and a state quantifying unit8a.

The first and second exciting coils3aand3band the power supply unit4aconstitute an exciting unit which applies a time-changing magnetic field asymmetric to a plane PLN to the fluid to be measured.

The state quantifying unit8aincludes a signal conversion unit5awhich obtains the amplitudes and phases of two frequency components with the first and second angular frequencies ω0and ω2of the resultant electromotive forces detected by the electrodes2aand2b, extracts an electromotive force difference between the two angular frequency components as a ∂A/∂t components on the basis of the amplitudes and the phases, and extracts, from the ∂A/∂t components, the magnitude or phase of the variation factor dependent on the first parameter and independent of the frequency, a state storage unit6a(equivalent to the above-described first table) which stores in advance the relationship between the first parameter and the magnitude or phase of the variation factor dependent on the first parameter, and a state output unit7awhich obtains the first parameter corresponding to the magnitude or phase of the extracted variation factor based on the relationship stored in the state storage unit6a.

In this embodiment, as described above, the distance d1from the plane PLN to the first exciting coil3ais almost equal to the distance d2from the plane PLN to the second exciting coil3b.

The power supply unit4arepeats, in a T-sec cycle, the operation of continuing the first excitation state for T1 sec in which the first exciting current with the first angular frequency ω0is supplied to the first exciting coil3aand at the same time the second exciting current with a phase difference Δθ2+π with respect to the first exciting current and the angular frequency ω0is supplied to the second exciting coil3b, and continuing the second excitation state for T2 sec in which the frequencies of the first and second exciting currents have been changed with respect to the first excitation state to the second angular frequency ω2. That is, T=T1+T2.

Although the operation of the exciting unit is different from that in the first embodiment, the processing of the state quantifying unit8ais the same as that in the first embodiment, and hence the operation of the state quantifying unit8awill be described by using the reference numerals inFIG. 27. First of all, the signal conversion unit5aobtains an amplitude r220R of the electromotive force E220R of a component with the angular frequency ω0of the electromotive force between the electrodes2aand2bin the first excitation state, and obtains a phase difference φ220R between the real axis and the inter-electrode electromotive force E220R by using a phase detector (not shown) (step101inFIG. 27).

The signal conversion unit5athen obtains an amplitude r222R of the electromotive force E222R of a component with the angular frequency ω2of the electromotive force between the electrodes2aand2bin the second excitation state, and obtains a phase difference φ222R between the real axis and the inter-electrode electromotive force E222R by using the phase detector (step102).

The signal conversion unit5athen calculates a real axis component E220Rx and imaginary axis component E220Ry of the inter-electrode electromotive force E220R, and a real axis component E222Rx and imaginary axis component E222Ry of the inter-electrode electromotive force E222R according to the following equations (step103):
E220Rx=r220R·cos(φ220R)  (124)
E220Ry=r220R·sin(φ220R)  (125)
E222Rx=r222R·cos(φ222R)  (126)
E222Ry=r222R·sin(φ222R)  (127)

After the calculation of equations (124) to (127), the signal conversion unit5aobtains the magnitude and angle of the electromotive force difference EdA2between the inter-electrode electromotive forces E220R and E222R (step104). The processing in step104corresponds to the processing of obtaining a ∂A/∂t component, and is equivalent to the calculation of equation (118). The signal conversion unit5acalculates a magnitude |EdA2| of the electromotive force difference EdA2according to the following equation:

The signal conversion unit5athen calculates an angle ∠EdA2of the electromotive force difference EdA2with respect to the real axis according to the following equation:

With the above operation, the processing in step104is complete.

The signal conversion unit5athen calculates the magnitude rk[p2] of the variation factor Cp2dependent on the first parameter p2and the angle θ00[p2] with respect to the real axis from the electromotive force difference EdA2according to the following equations (step105):
rk[p2]=|EdA2|/(m2b·ω0−ω2)  (130)
θ00[p2]=∠EdA2−θ2b(131)

Note that m2band θ2b(the amplitude b1of the magnetic field B1generated from the first exciting coil3a, the amplitude b2of the magnetic field B2generated from the second exciting coil3b, the phase difference θ1between the magnetic field B1and ω0·t, and θΔ2) are constants which can be obtained in advance by calibration or the like.

The relationship between the first parameter p2and the magnitude rk[p2] of the variation factor Cp2or the relationship between the first parameter p2and the angle θ00[p2] of the variation factor Cp2is registered in advance in the state storage unit6ain the form of a mathematical expression or table. In step106, the state output unit7acalculates the value of the first parameter p2corresponding to rk[p2] or θ00[p2] by referring to the state storage unit6aon the basis of the magnitude rk[p2] or angle θ00[p2] of the variation factor Cp2calculated by the signal conversion unit5a(or acquires it from the state storage unit6a). The state quantifying unit8aperforms the processing in steps101to106described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step107).

As described above, this embodiment is configured to obtain the inter-electrode electromotive force E220R in the first excitation state in which the magnetic field B1with angular frequency ω0is applied from the first exciting coil3ato the fluid to be measured, and the magnetic field B2having the frequency ω0with the phase difference Δθ2+π with respect to the magnetic field B1is applied from the second exciting coil3bto the fluid to be measured, obtain the inter-electrode electromotive force E222R in the second excitation state in which the exciting frequency with respect to the first excitation state changes to ω2, extract the electromotive force difference EdA2(∂A/∂t component) from the inter-electrode electromotive forces E220and E222, extract the magnitude or phase of the variation factor Cp2dependent on the characteristic or state of the fluid or a state in the measuring tube (the first parameter p2) from the electromotive force difference EdA2, and obtain the first parameter p2on the basis of the magnitude or phase of the variation factor Cp2. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

In this embodiment, the components of the state quantifying unit8a, except for the detecting units of the inter-electrode electromotive forces E220R and E222R, can be implemented by a computer comprising a CPU, storage unit, and interface and programs which control the hardware resources. In this embodiment, for example, the v×B component can be extracted by E220R−EdA2·{(ω0−ω2)/ω0}. There is known a technique of calculating the flow rate of the fluid from the v×B component in the field of a general electromagnetic flowmeter, which can be easily implemented by a computer included in the state quantifying unit8a. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, adjusting the distance d1from the plane PLN including the electrodes2aand2bto the first exciting coil3aand the distance d2from the plane PLN to the second exciting coil3ballows the inter-electrode electromotive forces E220R and E220R to be almost only electromotive forces based on ∂A/∂t components. With this processing, this embodiment can extract a ∂A/∂t component more effectively, and can reduce computation errors more than the first embodiment.

In this embodiment, it suffices to extract either the magnitude rk[p2] or angle θ00[p2] of the variation factor Cp2from the electromotive force difference EdA2. However, the first parameter p2can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude rk[p2] or the angle θ00[p2] which has a higher sensitivity and obtain the first parameter p2on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting angular frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the first parameter p2at higher speed. For example, it suffices to use the magnetic field represented by the following equation instead of equations (22) and (23).
B1=b1·cos(ω0·t−θ1)+b1·cos(ω2·t−θ1)  (132)
B2=b2·cos(ω0·t−θ2)+b2·cos(ω2·t−θ2)  (133)

The following description will explain a specific example of the state detection device of this embodiment which detects a level or sectional area of the fluid. In this case, considering that a level h varies, as shown inFIGS. 31 and 32, the first and second exciting coils3aand3bare arranged in a direction horizontal to the measuring tube1, and the electrode2ais placed under the measuring tube1. When only one electrode is to be used in this manner, it suffices if an earth ring (not shown) for grounding the potential of the fluid F is provided on the measuring tube1, and an electromotive force (a potential difference from the ground potential) generated at the electrode2ais detected by the signal conversion unit5a.

As the level h (sectional area S) of the fluid F varies, the value of the magnitude rk[p2] of the variation factor Cp2also varies.FIG. 33shows an example of the relationship between the level h or sectional area S (first parameter p2) of the fluid F and the magnitude rk[p2] of the variation factor Cp2. The relationship shown inFIG. 33changes depending on the shape or the like of the measuring tube1. Therefore, obtaining this relationship by a theoretical formula at the time of design or measurement at the time of calibration and storing it in the state storage unit6ain advance make it possible to obtain the level h or sectional area S of the fluid F in step106on the basis of the magnitude rk[p2] of the variation factor Cp2obtained in step105and to obtain the level h or sectional area S of the fluid F in step106.

THIRD EMBODIMENT

The third embodiment of the present invention will be described next. A state detection device according to this embodiment includes two exciting coils and a pair of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 5except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 5. This embodiment uses the second extraction method as a method of extracting a ∂A/∂t component from a resultant vector to obtain the first parameter irrelevant to an exciting frequency.

Assume that the first exciting current having an angular frequency ω0is supplied to a first exciting coil3a, the second exciting current having the angular frequency ω0with a phase difference Δθ2+π with respect to the first exciting current is supplied to a second exciting coil3b, and the first parameter is p3. In this case, an inter-electrode electromotive force E320R is represented by the following equation according to equations (30), (68), and (75).

From equations (71) and (72), the following approximate expression holds in equation (134):
|b1+b2·exp(j·Δθ2)|>>|b1−b2·exp(j·Δθ2)|  (135)
|ω0·exp(j·π/2)·{b1+b2·exp(j·Δθ2)}|>>|γ·V·exp(j·Δθ01)·{b1−b2·exp(j·Δθ2)}  (136)

The following expressions represent an electromotive force EdA3which approximates the inter-electrode electromotive force E320R in equation (134) by using the condition of expression (136).

In equation (138), the ∂A/∂t component in the resultant vector can be extracted by using the phase difference between the magnetic fields generated from the first and second exciting coils3aand3b. Equation (138) is irrelevant to the magnitude V of the flow velocity, and hence is only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using the inter-electrode electromotive force EdA3.

When a variation factor dependent on the first parameter is Cp3, Cp3=rk[p3] exp(j·θ00[p3]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cp3is represented by equation (138).

Letting m2bbe the magnitude of [exp{j·(π/2+θ1)}·{b1+b2·exp(j·Δθ2)}] in equation (139), and letting θ2bbe the angle, m2band θ2bare represented by equations (120) and (121).

Upon applying equations (120) and (121) to equation (139), a magnitude rk[p3] of the variation factor Cp3and an angle θ00[p3] thereof from the real axis are represented by
rk[p3]=|EdA3|/(m2b·ω0)  (140)
θ00[p3]=∠EdA3−θ2b(141)

The first parameter p3can be obtained from the relationship between the first parameter p3and rk[p3], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the first parameter p3and the angle θ00[p3].

The specific arrangement and operation of the state detection device according to this embodiment will be described next. The state detection device of this embodiment has the same arrangement as that in the second embodiment, and will therefore be described by using reference numerals inFIG. 30. The state detection device of this embodiment includes a measuring tube1, electrodes2aand2b, the first and second exciting coils3aand3b, a power supply unit4, and a state quantifying unit8a.

The state quantifying unit8aincludes a signal conversion unit5awhich obtains the amplitudes and phases of the resultant electromotive forces detected by the electrodes2aand2b, extracts a ∂A/∂t component, and extracts, from the ∂A/∂t component, the magnitude or phase of the variation factor dependent on the first parameter and independent of the frequency, a state storage unit6a(equivalent to the above-described first table) which stores in advance the relationship between the first parameter and the magnitude or phase of the variation factor dependent on the first parameter, and a state output unit7awhich obtains the first parameter corresponding to the magnitude or phase of the extracted variation factor based on the relationship stored in the state storage unit6a.

The power supply unit4asupplies the first exciting current with the angular frequency ω0to the first exciting coil3a, and simultaneously supplies the second exciting current having the angular frequency ω0with a phase difference Δθ2+π with respect to the first exciting current to the second exciting coil3b. The phase difference between the magnetic field generated from the first exciting coil3aand the magnetic field generated from the second exciting coil3bis made almost π(Δθ02≈0).

FIG. 34is a flowchart showing the operations of the state quantifying unit8aof this embodiment. First of all, the signal conversion unit5aobtains an amplitude r320R of the electromotive force E320R of a component with the angular frequency ω0of the electromotive force between the electrodes2aand2b, and obtains a phase difference φ320R between the real axis and the inter-electrode electromotive force E320R by using a phase detector (not shown) (step201inFIG. 34).

Next, the signal conversion unit5aobtains the magnitude and angle of the electromotive force EdA3which approximates the inter-electrode electromotive force E320R (step202). The processing in step202corresponds to the processing of obtaining the ∂A/∂t component, and is equivalent to the calculation of equation (138). The signal conversion unit5acalculates a magnitude |EdA3| of the electromotive force EdA3which approximates the inter-electrode electromotive force E320R according to the following equation:
|EdA3|=r320R(142)

The signal conversion unit5athen calculates an angle ∠EdA3of the inter-electrode electromotive force EdA3with respect to the real axis according to the following equation:
∠EdA3=φ320R  (143)

With the above operation, the processing in step202is complete.

The signal conversion unit5athen calculates the magnitude rk[p3] of the variation factor Cp3dependent on the first parameter p3and the angle θ00[p3] with respect to the real axis from the electromotive force difference EdA3according to the following equations (step203):
rk[p3]=|EvA3|/(m2b·ω0)  (144)
θ00[p3]=∠EdA3−θ2b(145)

Note that m2band θ2b(the amplitude b1of the magnetic field B1generated from the first exciting coil3a, the amplitude b2of the magnetic field B2generated from the second exciting coil3b, the phase difference θ1between the magnetic field B1and ω0·t, and Δθ2) are constants which can be obtained in advance by calibration or the like.

The relationship between the first parameter p3and the magnitude rk[p3] of the variation factor Cp3or the relationship between the first parameter p3and the angle θ00[p3] of the variation factor Cp3is registered in advance in the state storage unit6ain the form of a mathematical expression or table. In step204, the state output unit7acalculates the value of the first parameter p3corresponding to rk[p3] or θ00[p3] by referring to the state storage unit6aon the basis of the magnitude rk[p3] or angle θ00[p3] of the variation factor Cp3calculated by the signal conversion unit5a(or acquires it from the state storage unit6a). The state quantifying unit8aperforms the processing in steps201to204described above in a predetermined cycle until, for example, the operator designates the end of the measurement (YES in step205).

As described above, according to this embodiment, note that when the magnitudes of the magnetic fields B1and B2are equal to each other in a state wherein the phase difference between the magnetic fields B1and B2generated from the first and second exciting coils3aand3bis almost π, the inter-electrode electromotive force E320R can be approximately extracted as the ∂A/∂t component. This embodiment is configured to extract the magnitude or phase of the variation factor Cp3dependent on the characteristic or state of the fluid or a state in the measuring tube (the first parameter p3) from the approximately extracted ∂A/∂t component, and obtain the first parameter p3based on the magnitude or phase of the variation factor Cp3. Therefore, the characteristic or state of the fluid or the state in the measuring tube can be accurately detected regardless of the flow velocity of the fluid

As in the second embodiment, the components of the state quantifying unit8aof this embodiment, except for the detecting unit of the inter-electrode electromotive force E320R, can be implemented by a computer and program. In this embodiment, assume that the first exciting current having an angular frequency ω0is supplied to the first exciting coil3a, the second exciting current having the angular frequency ω0with the phase difference Δθ2with respect to the first exciting current is supplied to the second exciting coil3b, and the first parameter is p3. In this case, an inter-electrode electromotive force E320is obtained by reversing the sign of b2in equation (134). As a result, the inter-electrode electromotive force E320can be handled as the v×B component. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitude rk[p3] or angle θ00[p3] of the variation factor Cp3from the inter-electrode electromotive force EdA3. However, the first parameter p3can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude rk[p3] or the angle θ00[p3] which has a higher sensitivity and obtain the first parameter p3on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

Fourth Embodiment

The fourth embodiment of the present invention will be described next. A state detection device according to this embodiment includes two exciting coils and a pair of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 5except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 5. This embodiment uses the second extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the second parameter for a variation factor having a frequency characteristic. For example, the second parameter is a fluid impedance, and the conductivity and permittivity of the fluid.

Assume that the first exciting current having an angular frequency ω0is supplied to a first exciting coil3a, the second exciting current having the angular frequency ω0with the phase difference Δθ2+π with respect to the first exciting current is supplied to a second exciting coil3b, and the second parameter is p4. In this case, an inter-electrode electromotive force E420R is represented by the following equation according to equations (30), (78), and (79).

From equations (71) and (72), the following approximate expression holds in equation (146):
|b1+b2·exp(j·Δθ2)|>>|b1−b2·exp(j·Δθ2)|  (147)
|ω0·exp(j·π/2)·{b1+b2·exp(j·Δθ2)}|>>|γ·V·exp(j·Δθ01)·{b1−b2·exp(j·Δθ2)}|  (148)

The following expressions represent an electromotive force EdA40which approximates the inter-electrode electromotive force E420R in equation (146) by using the condition of expression (148).

Assume that the first exciting current having an angular frequency ω2is supplied to the first exciting coil3a, the second exciting current having the angular frequency ω2with a phase difference Δθ2+π with respect to the first exciting current is supplied to the second exciting coil3b, and the second parameter is p4. In this case, an inter-electrode electromotive force E422R is represented by the following equation according to equations (30), (81) and (82).

Since ω2>γ·V holds, the following condition holds for the inter-electrode electromotive force E422R given by equation (151) in consideration of the condition represented by equation (147).
|ω2·exp(j·π/2)·{b1+b2·exp(j·Δθ2)}|>>|γ·V·exp(j·Δθ01)·{b1−b2·exp(j·Δθ2)}|  (152)

The following expressions represent the inter-electrode electromotive force EdA42which approximates the inter-electrode electromotive force E422R in equation (151) by using the condition of expression (152).

In equations (150) and (154), the ∂A/∂t component in the resultant vector can be extracted by using the phase difference between the magnetic fields generated from the first and second exciting coils3aand3b. Equations (150) and (154) are irrelevant to the magnitude V of the flow velocity, and hence are only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using this electromotive force difference.

Letting m2band θ2bbe the magnitude and angle of [exp{j·(π/2+θ1)}·{b1+b2·exp(j·Δθ2)}] in equations (155) and (156), m2band θ2bare represented by equations (120) and (121).

Upon applying equations (120) and (121) to equation (155), a magnitude rk[p4,ω0] of the variation factor Cp40and an angle θ00[p4,ω0] thereof from the real axis are represented by
rk[p4,ω0]=|EdA40|/(m2b·ω0)  (157)
θ00[p4,ω0]=∠EdA40−θ2b(158)

Upon applying equations (120) and (121) to equation (156), a magnitude rk[p4,ω2] of the variation factor Cp42and an angle θ00[p4,ω2] thereof from the real axis are represented by
rk[p4,ω2]=|EdA42|/(m2b·ω2)  (159)
θ00[p4,ω2]=∠EdA42−θ2b(160)

When the ratio between the variation factors Cp42and Cp40is Cn4, the ratio Cn4is represented by the following equation.

In this case, the magnitude (rk[p4,ω2]/rk[p4,ω0]) of the ratio Cn4and the angle (θ00[p4,ω2]−θ00[p4,ω0]) with respect to the real axis are represented by the following equations.

According to equations (161) to (163), it is obvious that the ratio Cn4does not include the variation factor of the magnetic field, and the value of the second parameter p4can be obtained by reducing error factors.

The second parameter p4can be obtained from the relationship between the second parameter p4and (rk[p4,ω2]/rk[p4,ω0]), which is checked in advance by measurement or the like at the time of calibration, or the relationship between the second parameter p4and (θ00[p4,ω2]−θ00[p4,ω0]).

The specific arrangement and operation of the state detection device according to this embodiment will be described next. The state detection device according to this embodiment has the same arrangement as that of the state detection device in the second embodiment. Hence, the same reference numerals as inFIG. 30denote the same components in this embodiment. The state detection device of this embodiment includes a measuring tube1, electrodes2aand2b, first and second exciting coils3aand3b, a power supply unit4, and a state quantifying unit8a.

The state quantifying unit8aincludes a signal conversion unit5awhich obtains the amplitudes and phases of two frequency components with the first and second angular frequencies ω0and ω2of the resultant electromotive forces detected by the electrodes2aand2b, extracts ∂A/∂t components with angular frequencies ω0and ω2, and extracts, from the ratio between the ∂A/∂t components with angular frequencies ω0and ω2, the magnitude or phase of the ratio between the variation factors dependent on the second parameter and frequency, a state storage unit6a(equivalent to the above-described second table) which stores in advance the relationship between the second parameter and the magnitude or phase of the ratio between the variation factors, and a state output unit7awhich obtains the second parameter corresponding to the magnitude or phase of the ratio between the extracted variation factors based on the relationship stored in the state storage unit6a.

The power supply unit4arepeats, in a T-sec cycle, the operation of continuing the first excitation state for T1 sec in which the first exciting current having the first angular frequency ω0is supplied to the first exciting coil3aand at the same time the second exciting current having the angular frequency ω0with the phase difference Δθ2+π with respect to the first exciting current is supplied to the second exciting coil3b, and continuing the second excitation state for T2 sec in which the frequencies of the first and second exciting currents in the first excitation state has been changed to the second angular frequency ω2. That is, T=T1+T2. Assume that the phase difference between the magnetic fields generated from the first and second exciting coils3aand3bis almost π(Δθ2≈0) in the first and second excitation states.

FIG. 35is a flowchart showing the operation of the state quantifying unit8aaccording to this embodiment. First of all, the signal conversion unit5aobtains an amplitude r420R of the electromotive force E420R with the angular frequency ω0component of the electromotive force between the electrodes2aand2bin the first excitation state, and obtains a phase difference φ420R between the real axis and the inter-electrode electromotive force E420R by using a phase detector (not shown) (step301inFIG. 35).

Subsequently, the signal conversion unit5aobtains an amplitude r422R of the electromotive force E422R with the angular frequency ω2component of the electromotive force between the electrodes2aand2bin the second excitation state, and obtains a phase difference φ422R between the real axis and the inter-electrode electromotive force E422R by using the phase detector (step302).

Next, the signal conversion unit5acalculates the magnitude |EdA40| and an angle ∠EdA40with respect to the real axis of the electromotive force EdA40which approximates the inter-electrode electromotive force E420R (step303) according to the following equation (step303):
|EdA40|=r420R(164)
∠EdA40=φ420R  (165)

The signal conversion unit5athen calculates the magnitude |EdA42| and an angle ∠EdA42with respect to the real axis of the electromotive force EdA42which approximates the inter-electrode electromotive force E422R according to the following equation (step304):
|EdA42|=r422R(166)
∠EdA42=φ422R  (167)

The processing in steps303and304corresponds to the processing of obtaining the ∂A/∂t component, and is equivalent to the calculation of equations (150) and (154).

The signal conversion unit5aextracts the variation factor Cp40dependent on the second parameter p4from the inter-electrode electromotive force EdA40, extracts the variation factor Cp42dependent on the second parameter p4from the inter-electrode electromotive force EdA42, and obtains the magnitude and angle of the ratio Cn4between the variation factors Cp42and Cp40(step305). The signal conversion unit5acalculates the magnitude (rk[p4,ω2]/rk[p4,ω0]) of the ratio Cn4as follows:

The signal conversion unit5acalculates the angle (θ00[p4,ω2]−θ00[p4,ω0]) with respect to the real axis of the ratio Cn4as follows:
θ00[p4,ω2]−θ00[p4,ω0]=∠EdA42−∠EdA40  (169)

With the above operation, the processing in step305is complete.

The relationship between the second parameter p4and the magnitude (rk[p4,ω2)]/rk[p4,ω0]) of the ratio Cn4or the relationship between the second parameter p4and the angle (θ00[p4,ω2]−θ00[p4,ω0]) of the ratio Cn4is registered in advance in the state storage unit6ain the form of a mathematical expression or table. In step306, the state output unit7acalculates the value of the second parameter p4corresponding to rk[p4,ω2]/rk[p4,ω0]) or (θ00[p4,ω2]−θ00[p4,ω0]) by referring to the state storage unit6aon the basis of the magnitude (rk[p4,ω2]/rk[p4,ω0]) or angle (θ00[p4,ω2]−θ00[p4,ω0]) of the ratio Cn4calculated by the signal conversion unit5a(or acquires it from the state storage unit6a).

The state quantifying unit8aperforms the processing in steps301to306described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step307). Note that the processing in steps302to306is performed in the second excitation state for a duration of T2 sec.

As described above, according to this embodiment, note that when the magnitudes of the magnetic fields B1and B2are equal to each other in a state wherein the phase difference between the magnetic fields B1and B2generated from the first and second exciting coils3aand3bis almost π, the inter-electrode electromotive forces E420R and E422R can be approximately extracted as the ∂A/∂t components when the exciting angular frequencies are ω0and ω2, respectively. This embodiment is configured to extract the variation factors Cp40and Cp42dependent on the characteristic or state of the fluid or a state in the measuring tube (the second parameter p4) from the approximately extracted two ∂A/∂t components, and obtain the second parameter p4on the basis of the magnitude or phase of the ratio between the variation factors Cp42and Cp40. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

As in the second embodiment, the components of the state quantifying unit8aof this embodiment, except for the detecting unit of the inter-electrode electromotive forces E420R and E422R, can be implemented by a computer and program. In this embodiment, assume that the first exciting current having an angular frequency ω0is supplied to the first exciting coil3a, the second exciting current having the angular frequency ω0with the phase difference Δθ2with respect to the first exciting current is supplied to the second exciting coil3b, and the second parameter is p4. In this case, an inter-electrode electromotive force E420is obtained by reversing the sign of b2in equation (146). As a result, the inter-electrode electromotive force E420can be handled as the v×B component. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitude (rk[p4,ω2]/rk[p4,ω0]) or angle (θ00[p4,ω2]−θ00[p4,ω0]) of the ratio Cn4between the variation factors. However, the second parameter p4can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude (rk[p4,ω2]/rk[p4,ω0]) or the angle (θ00[p4,ω2]−θ00[p4,ω0]) which has a higher sensitivity and obtain the second parameter p4on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the second parameter p4at higher speed. For example, it suffices to use the magnetic field represented by equations (132) and (133) instead of equations (22) and (23).

An operation of detecting the resistance component of a fluid impedance will be described below as the specific example of the state detection device according to this embodiment. Upon performing excitation by using an angular frequency ω, assume that Ee2[ω] represents the electromotive force to be extracted from the electrodes2aand2bwhen the input impedance of the state detection device is Zin (=Rin/(1+j·ω·Rin·Cin)) and the fluid impedance is Zf (=Rf), and Ee1[ω] represents the electromotive force to be extracted when the input impedance is infinite. In this case, the relationship between the electromotive forces Ee2[ω] and Ee1[ω] have the following relation.

FIG. 36shows the relationship among the input impedance Zin, fluid impedance Zf, and the electromotive forces Ee2[ω] and Ee1[ω] in the form of an equivalent circuit. When the resistance component Rin is 100 and the capacitive component is 0.5 of the input impedance, the relationship between the magnitude of Ee2[ω]/Ee1[ω] and the frequency is shown inFIG. 37. Upon applying the detection of the fluid impedance to the fourth embodiment, the following equations (171) to (174) hold.

The ratio Ee2[ω2]/Ee2[ω0] between the electromotive forces Ee2[ω2] and Ee2[ω0] is represented by the following equation.

The ratio Ee1[ω2]/Ee1[ω0] between the electromotive forces Ee1[ω2] and Ee1[ω0] is represented by the following equation.
Ee1[ω2]/Ee1[ω0]=ω2/ω1  (176)

The following equation can be obtained from the relational expression Ee2[ω]=Ee1[ω]·Rin/{(Rin+Rf)+j·ω·Cin·Rin·Rf}.

Assume that the value of the resistance component Rf (second parameter p4) of the fluid impedance is obtained on the basis of the ratio of the magnitudes.FIG. 38shows the relationship between the resistance component Rf and the magnitude |rk[Rf,ω2]/rk[Rf,ω0]| of the ratio between the variation factors when ω0=0.1 and ω2=10. Obtaining this relationship by a theoretical formula at the time of design or measurement at the time of calibration, and storing it in the state storage unit6amake it possible to obtain the resistance component Rf of the fluid impedance in step306on the basis of the magnitude |rk[Rf,ω2]/rk[Rf,ω0]| of the ratio between the variation factors obtained in step305. For example, when the ratio between the variation factors is 0.009996136860, the value of the resistance component Rf is 1 with reference toFIG. 38.

Fifth Embodiment

The fifth embodiment of the present invention will be described next. A state detection device according to this embodiment includes two exciting coils and a pair of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 5except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 5. This embodiment uses the second extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the second parameter for a variation factor having a frequency characteristic. In this embodiment, two second parameter values are obtained. Of the two second parameters, one is the third parameter, and the other is the fourth parameter.

Assume that the first exciting current having an angular frequency ω0is supplied to a first exciting coil3a, the second exciting current having the angular frequency ω0with the phase difference Δθ2+π with respect to the first exciting current is supplied to a second exciting coil3b, the third parameter is p5, and the fourth parameter is q5. In this case, an inter-electrode electromotive force E520R is represented by the following equation according to equations (30), (85), and (86).

From equations (71) and (72), equations (147) and (148) hold in equation (178). The following expressions represent an electromotive force EdA50which approximates the inter-electrode electromotive force E520R in equation (178) by using the condition of expression (148).

Assume that the first exciting current having an angular frequency ω2is supplied to the first exciting coil3a, the second exciting current having the angular frequency ω2with a phase difference Δθ2+π with respect to the first exciting current is supplied to the second exciting coil3b, the third parameter is p5, and the fourth parameter is q5. In this case, an inter-electrode electromotive force E522R is represented by the following equation according to equations (30), (88) and (89).

Since ω2>γ·V holds, equation (152) holds for the inter-electrode electromotive force E522R given by equation (181) in consideration of the condition represented by equation (147). The following expressions represent the inter-electrode electromotive force EdA52which approximates the inter-electrode electromotive force E522R in equation (181) by using the condition of expression (152).

In equations (180) and (183), the ∂A/∂t component in the resultant vector can be extracted by using the phase difference between the magnetic fields generated from the first and second exciting coils3aand3b. Equations (180) and (183) are irrelevant to the magnitude V of the flow velocity, and hence are only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using this electromotive force difference.

When a variation factor dependent on the third and fourth parameters is Cpq50in equation (180), Cpq50=rk[p5,q5,ω0]·exp(j·θ00[p5,q5,ω0]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cpq50is represented by equation (180).

When a variation factor dependent on the third and fourth parameters is Cpq52in equation (183), Cpq52=rk[p5,q5,ω2]·exp(j·θ00[p5,q5,ω2]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cpq52is represented by equation (183).

Letting m2band θ2bbe the magnitude and angle of [exp{j·(π/2+θ1)}·{b1+b2·exp(j·Δθ2)}] in equations (184) and (185), m2band θ2bare represented by equations (120) and (121).

Upon applying equations (120) and (121) to equation (184), a magnitude rk[p5,q5,ω0] of the variation factor Cpq50and an angle θ00[p5,q5,ω0] thereof from the real axis are represented by
rk[p5,q5,ω0]=|EdA50|/(m2b·ω0)  (186)
θ00[p5,q5,ω0]=∠EdA50−θ2b(187)

Upon applying equations (120) and (121) to equation (185), a magnitude rk[p5,q5,ω2] of the variation factor Cpq52and an angle θ00[p5,q5,ω2] thereof from the real axis are represented by
rk[p5,q5,ω2]=|EdA52|/(m2b·ω2)  (188)
θ00[p5,q5,ω2]=∠EdA52−θ2b(189)

The parameters p5and q5can be obtained from the relationship between the parameters p5and q5and rk[p5,q5,ω0] and rk[p5,q5,ω2], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the parameters p5and q5and θ00[p5,q5,ω0] and θ00[p5,q5,ω2].

The specific arrangement and operation of the state detection device according to this embodiment will be described next. The state detection device according to this embodiment has the same arrangement as that of the state detection device in the second embodiment. Hence, the same reference numerals as inFIG. 30denote the same components in this embodiment. The state detection device of this embodiment includes a measuring tube1, electrodes2aand2b, first and second exciting coils3aand3b, a power supply unit4, and a state quantifying unit8a.

The state quantifying unit8aincludes a signal conversion unit5awhich obtains the amplitudes and phases of a plurality of frequency components of the resultant electromotive forces detected by the electrodes2aand2b, extracts ∂A/∂t components with the plurality of frequency components, and extracts, from the extracted ∂A/∂t components, the magnitudes or phases of the variation factors dependent on the plurality of second parameters and frequencies, a state storage unit6a(equivalent to the above-described third table) which stores in advance the relationship between the plurality of second parameters and the magnitudes or phases of the variation factors with the plurality of frequency components, and a state output unit7awhich obtains the plurality of second parameters corresponding to the magnitudes or phases of the extracted variation factors based on the relationship stored in the state storage unit6a.

The operation of the power supply unit4ais the same as that in the fourth embodiment.FIG. 39is a flowchart showing the operation of the state quantifying unit8aaccording to this embodiment. First of all, the signal conversion unit5aobtains an amplitude r520R of the electromotive force E520R with the angular frequency ω0component of the electromotive force between the electrodes2aand2bin the first excitation state in which the exciting angular frequency is ω0, and obtains a phase difference φ520R between the real axis and the inter-electrode electromotive force E520R by using a phase detector (not shown) (step401inFIG. 39).

Subsequently, the signal conversion unit5aobtains an amplitude r522R of the electromotive force E522R with the angular frequency ω2component of the electromotive force between the electrodes2aand2bin the second excitation state in which the exciting angular frequency is ω2, and obtains a phase difference φ522R between the real axis and the inter-electrode electromotive force E522R by using the phase detector (step402).

Next, the signal conversion unit5acalculates the magnitude |EdA50| and an angle ∠EdA50with respect to the real axis of the electromotive force EdA50which approximates the inter-electrode electromotive force E520R according to the following equation (step403):
|EdA50|=r520R(190)
∠EdA50=φ520R  (191)

The signal conversion unit5athen calculates the magnitude |EdA52| and an angle ∠EdA52with respect to the real axis of the electromotive force EdA52which approximates the inter-electrode electromotive force E522R according to the following equation (step404):
|EdA52|=r522R(192)
∠EdA52=φ522R  (193)

The processing in steps403and404corresponds to the processing of obtaining the ∂A/∂t component, and is equivalent to the calculation of equations (180) and (183).

The signal conversion unit5acalculates, from the inter-electrode electromotive force EdA50, the magnitude rk[p5,q5,ω0] of the variation factor Cpq50dependent on the third and fourth parameters p5and q5and the angle θ00[p5,q5,ω0] with respect to the real axis as follows (step405):
rk[p5,q5,ω0]=|EdA50|/(m2b·ω0)  (194)
θ00[p5,q5,ω0]=∠EdA50−θ2b(195)

The signal conversion unit5aalso calculates, from the inter-electrode electromotive force EdA52, the magnitude rk[p5,q5,ω2] of the variation factor Cpq52dependent on the third and fourth parameters p5and q5and the angle θ00[p5,q5,ω2] with respect to the real axis as follows (step406):
rk[p5,q5,ω2]=|EdA52|/(m2b·ω2)  (196)
θ00[p5,q5,ω2]=∠EdA52−θ2b(197)

Note that m2band θ2b(the amplitude b1of the magnetic field B1generated from the first exciting coil3a, the amplitude b2of the magnetic field B2generated from the second exciting coil3b, the phase difference θ1between the magnetic field B1and ω0·t, and Δθ2) are constants which can be obtained in advance by calibration or the like.

The relationship between the third and fourth parameters p5and q5and the magnitudes rk[p5,q5,ω0] and rk[p5,q5,ω2] of the variation factors Cpq50and Cpq52or the relationship between the parameters p5and q5and the angles θ00[p5,q5,ω0] and θ00[p5,q5,ω2] of the variation factors Cpq50and Cpq52is registered in advance in the state storage unit6ain the form of a mathematical expression or table.

The state output unit7acalculates the values of the third and fourth parameters p5and q5corresponding to the magnitudes rk[p5,q5,ω2] and rk[p5,q5,ω0]) or angles θ00[p5,q5,ω0] and θ00[p5,q5,ω2] by referring to the state storage unit6aon the basis of the magnitudes rk[p5,q5,ω0] and rk[p5,q5,ω2]) or angles θ00[p5,q5,ω0] and θ00[p5,q5,ω2]) of the variation factors Cpq50and Cpq52calculated by the signal conversion unit5a(step407).

The state quantifying unit8aperforms the processing in steps401to407described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step408). Note that the processing in steps402to407is performed in the second excitation state for a duration of T2 sec.

As described above, according to this embodiment, note that when the magnitudes of the magnetic fields B1and B2are equal to each other in a state wherein the phase difference between the magnetic fields B1and B2generated from the first and second exciting coils3aand3bis almost n, the inter-electrode electromotive forces E520R and E522R can be approximately extracted as the ∂A/∂t components when the exciting angular frequencies are (o0and o2, respectively. This embodiment is configured to extract the variation factors Cp50and Cp52dependent on the characteristic or state of the fluid or a state in the measuring tube (the third and fourth parameters p5and q5) from the approximately extracted two ∂A/∂t components, and obtain the third and fourth parameters p5and q5on the basis of the magnitude or phase of the variation factors Cp52and Cp50. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

As in the second embodiment, the components of the state quantifying unit8aof this embodiment, except for the detecting unit of the inter-electrode electromotive forces E520R and E522R, can be implemented by a computer and program. In this embodiment, assume that the first exciting current having an angular frequency ω0is supplied to the first exciting coil3a, the second exciting current having the angular frequency ω0with the phase difference Δθ2with respect to the first exciting current is supplied to the second exciting coil3b, the third parameter is p5, and the fourth parameter is q5. In this case, an inter-electrode electromotive force E520is obtained by reversing the sign of b2in equation (178). As a result, the inter-electrode electromotive force E520can be handled as the v×B component. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitudes rk[p5,q5,ω0] and rk[p5,q5,ω2]) or angles θ00[p5,q5,ω0] and θ00[p5,q5,ω2] of the variation factors Cpq50and Cpq52. However, the third and fourth parameters p5and q5can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitudes rk[p5,q5,ω0] and rk[p5,q5,ω2] or the angles θ00[p5,q5,ω0] and θ00[p5,q5,ω2] which has a higher sensitivity and obtain the third and fourth parameters p5and q5on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the parameters p5and q5at higher speed. For example, it suffices to use the magnetic field represented by equations (132) and (133) instead of equations (22) and (23).

An operation of detecting the resistance component and capacitive component of a fluid impedance will be described below as the specific example of the state detection device according to this embodiment. Upon performing excitation by using an angular frequency ω, assume that Ee2[ω] represents the electromotive force to be extracted from the electrodes2aand2bwhen the input impedance of the state detection device is Zin (=Rin/(1+j·ω·Rin·Cin)) and the fluid impedance is Zf (=Rf/(1+j·ω·Rf·Cf)), and Ee1[ω] represents the potential to be extracted when the input impedance is infinite. In this case, the relationship between the electromotive forces Ed2[ω] and Ee1[ω] is represented by the following equation.
Ee2[ω]=Ee1[ω]·Zf[ω]/(Zin[ω]+Zf[ω])  (198)

FIG. 40is a view showing the relationship among the input impedance Zin, fluid impedance Zf, and the electromotive forces Ed2[ω] and Ee1[ω] in the form of an equivalent circuit. When the resistance component Rin=10 and the capacitive component=0.5 in the input impedance, and ω=0.1, the relationship between the magnitude of Ee2[0.1]/Ee1[0.1] and the resistance component Rf and capacitive component Cf of the fluid impedance is shown inFIG. 41. Similarly, when Rin=10, Cin=0.5, and ω2=0.01, the relationship between the magnitude of Ee2[0.01]/Ee1[0.01] and the resistance component Rf and capacitive component Cf of the fluid impedance is shown inFIG. 42. Upon applying the detection of the fluid impedance to the fifth embodiment, the following equations (199) to (202) hold.

As a result, the magnitudes rk[p5,q5,ω0] and rk[p5,q5,ω2] and the angles θ00[p5,q5,ω0] and θ00[p5,q5,ω2] of the variation factors Cpq50and Cpq52can be obtained according to equations (194) to (197). The following equations can be obtained from the relation Ee2[ω]/Ee1[ω]=Zf/(Zin+Zf).

Assume that the values of the resistance component Rf (third parameter p5) and capacitive component Cf (fourth parameter q5) of the fluid impedance are obtained based on the magnitude rk. In this case, if rk[Rf,Cf,ω0]=Ee2[0.1]/Ee1[0.1]=0.8595658805 when Rin=10, Cin=0.5, and ω0=0.1, the solutions Rfα and Cfα of Rf and Cf can be obtained as the intersections of the curved plane shown inFIG. 41and a plane Ee2[0.1]/Ee1[0.1]=0.8595658805 (FIG. 43).

If rk[Rf,Cf,ω2]=Ee2[0.01]/Ee1[0.01]=0.6759189546 when Rin=10, Cin=0.5, and ω2=0.01, the solutions Rfβ and Cfβ of Rf and Cf can be obtained as the intersections of the curved plane shown inFIG. 42and a plane Ee2[0.01]/Ee1[0.01]=0.6759189546 (FIG. 44). Referring toFIGS. 43 and 44, Rf=5 and Cf=5 can hold as the solutions which satisfy both the exciting frequency ω0and ω2.

Obtaining the relationship shown inFIGS. 41 and 42by a theoretical formula at the time of design or by measurement at the time of calibration and storing it in the state storage unit6ain advance make it possible to obtain the resistance component Rf and capacitive component Cf of the fluid impedance in step407on the basis of the magnitude rk[p5,q5,ω0] of the variation factor Cpq50obtained in step405and the magnitude rk[p5,q5,ω2] of the variation factor Cpq52obtained in step406.

Note that candidates of solutions of the parameters p5and q5are actually obtained as curved lines on the basis of the value of the magnitude rk[p5,q5,ω0] of the variation factor Cpq50with the exciting angular frequency ω0, and the curved plane shown inFIG. 41stored in the state storage unit6a. Furthermore, candidates of solutions of the parameters p5and q5are obtained as curved lines on the basis of the value of the magnitude rk[p5,q5,ω2] of the variation factor Cpq52with the exciting angular frequency ω2, and the curved plane shown inFIG. 42stored in the state storage unit6a. Hence, the intersections between the candidates of the solutions obtained from equations of the curved planes shown inFIGS. 41 and 42are solutions of the parameters p5and q5.

More specifically, the curved line is subdivided, and equations of the two straight lines hold in the neighborhood of the solutions as represented by equations (95) and (96).
p5/a0+q5/b0+z0/c0=1  (205)
p5/a2+q5/b2+z2/c2=1  (206)

FIG. 45shows an example of the straight line obtained from equations (205) and (206). Selecting a section having an intersection of two subdivided lines, and solving two simultaneous equations by, e.g., the program of the Gaussian elimination method make it possible to obtain the solutions of the parameters p5and q5. Even when two or more second parameters are used, the solutions can be obtained using the same scheme. This calculation can be easily implemented by a computer.

Sixth Embodiment

The sixth embodiment of the present invention will be described next. A state detection device of this embodiment is obtained by adding one electrode to that in the first embodiment, using the above-described third principle. The state detection device according to this embodiment includes one exciting coils and two pairs of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 13except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 13. If the second electrode to be newly added is placed on the same side as the existing first electrode, the resultant arrangement is a redundant arrangement of that shown in the first embodiment. Therefore, the second electrode needs to be placed on a side different from that of the first electrode through the exciting coil. This embodiment uses the first extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the first parameter irrelevant to the exciting frequency.

Assume that the exciting current having an angular frequency ω0is supplied to an exciting coil3, and the first parameter is p6. In this case, the difference E630dbetween the first inter-electrode electromotive force between electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2dis represented by the following equation according to equations (54), (68), and (75).

Assume that the exciting current having an angular frequency θ2is supplied to the exciting coil3, and the first parameter is p6. In this case, the difference E632dbetween the first inter-electrode electromotive force between the electrodes2aand2band the second inter-electrode electromotive force between the electrodes2cand2dis represented by the following equation according to equations (54), (70) and (75).

In this case, if a distance d3from a plane PLN3including the axis of the exciting coil3to the electrode axis EAX1connecting the electrodes2aand2bis almost equal to a distance d4from the plane PLN3to the electrode axis EAX2connecting the electrodes2cand2d(d3≈d4), then b3≈b4and Δθ4≈0. In this case, equations (207) and (208) are rewritten as follows:

That is, since the electromotive force differences E630dand E632dare almost only the electromotive forces based on the ∂A/∂t components, computation errors in the extraction of the ∂A/∂t component can be reduced. This point is a difference in terms of technical significance between the first and sixth embodiments. Note, however, that the subsequent theoretical development will be made assuming that b3≠b4and Δθ4≠0.

Letting EdA6be the difference between the electromotive force differences E630dand E632d, the difference EdA6is given by

In equation (211), the ∂A/∂t component in the resultant vector can be extracted by using the output difference between different frequency components. Equation (211) is irrelevant to the magnitude V of the flow velocity, and hence is only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using the difference EdA6.

When a variation factor dependent on the first parameter is Cp6, Cp6=rk[p6]·exp(j·θ00[p6]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cp6is represented by equation (211).

Letting m3band θ3bbe the magnitude and angle of [exp{j·(π/2+θ3)}·{b3+b4·exp(j·Δθ4)}] in equation (212), m3band θ3bare represented by the following equation.
m3b={b32+b42+b3·b4·cos(Δθ4)}1/2(213)

According to equations (212) to (214), the magnitude rk[p6] of the variation component Cp6and the angle θ00[p6] with respect to the real axis are represented by
rk[p6]=|EdA1|/(m3b·(ω0−ω2)}  (215)
θ00[p6]=∠EdA1−θ3b(216)

The first parameter p6can be obtained from the relationship between the first parameter p6and rk[p6], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the first parameter p6and the angle θ00[p6].

The specific arrangement and operation of the state detection device according to this embodiment will be described next.FIG. 46is a block diagram showing the arrangement of the state detection device according to this embodiment. The same reference numerals as inFIG. 13denote the same components in this embodiment. The state detection device of this embodiment includes a measuring tube1, first electrodes2aand2b, second electrodes2cand2d, an exciting coil3, a power supply unit4b, and a state quantifying unit8b.

The state quantifying unit8bincludes a signal conversion unit5bwhich obtains the amplitudes and phases of the first resultant electromotive forces detected by the first electrodes2aand2band the second resultant electromotive forces detected by the electrodes2cand2d, obtains the electromotive force differences having the same frequency component of the first and second resultant electromotive forces with the first and second angular frequencies ω0and ω2, extracts the difference between the electromotive force differences with the first and second angular frequencies ω0and ω2as a ∂A/∂t component, and extracts, from the ∂A/∂t component, the magnitude or phase of the variation factor dependent on the first parameter but independent of the frequency, a state storage unit6b(equivalent to the above-described first table) which stores in advance the relationship between the first parameter and the magnitude or phase of the variation factors dependent on the first parameter, and a state output unit7bwhich obtains the first parameter corresponding to the magnitudes or phases of the extracted variation factors based on the relationship stored in the state storage unit6b.

The power supply unit4brepeats, in a T-sec cycle, the operation of continuing the first excitation state for T1 sec in which the exciting current having the first angular frequency ω0is supplied to the exciting coil3, and continuing the second excitation state for T2 sec in which the exciting current having the second angular frequency ω2is supplied to the exciting coil3. That is, T=T1+T2.

FIG. 47is a flowchart showing the operation of the state quantifying unit8b. First of all, the signal conversion unit5bobtains an amplitude r630dof the difference E630dbetween the electromotive force of a component with the angular frequency ω0of the first inter-electrode electromotive force between the electrodes2aand2band the electromotive force with the angular frequency of a component with the angular frequency ω0of the second inter-electrode electromotive force between the electrodes2cand2d, and obtains a phase difference φ630dbetween the real axis and the electromotive force difference E630dby using a phase detector (not shown) (step501inFIG. 47).

Subsequently, the signal conversion unit5bobtains an amplitude r632dof the difference E632dbetween the electromotive force with the angular frequency ω2component of the first inter-electrode electromotive force and the electromotive force with the angular frequency ω0component of the second inter-electrode electromotive force, and obtains a phase difference φ632dbetween the real axis and the electromotive force difference E632dby using the phase detector (step502).

The signal conversion unit5bthen calculates a real axis component E630dxand imaginary axis component E630dyof the electromotive force difference E630d, and a real axis component E632dxand imaginary axis component E632dyof the electromotive force difference E632daccording to the following equations (step503):
E630dx=r630d·cos(φ630d)  (217)
E630dy=r630d·sin(φ630d)  (218)
E632dx=r632d·cos(φ632d)  (219)
E632dy=r632d·sin(φ632d)  (220)

After the calculation of equations (217) to (220), the signal conversion-unit5bobtains the magnitude and angle of the difference EdA6between the electromotive force differences E630dand E632d(step504). The processing in step504corresponds to the processing of obtaining a ∂A/∂t component, and is equivalent to the calculation of equation (211). The signal conversion unit5bcalculates a magnitude |EdA6| of the difference EdA6according to the following equation:

The signal conversion unit5bthen calculates an angle ∠EdA6of the difference EdA6with respect to the real axis according to the following equation:

With the above operation, the processing in step504is complete.

The signal conversion unit5bthen calculates the magnitude rk[p6] of the variation component Cp6dependent on the first parameter p6and the angle θ00[p6] with respect to the real axis from the difference EdA6according to the following equations (step505):
rk[p6]=|EdA6|/{m3b·(ω0−ω2)  (223)
θ00[p6]=∠EdA6−θ3b(224)

Note that m3band θ3b(the amplitudes b3and b4of the magnetic fields B3and B4generated from the first exciting coil3, and the phase differences θ3and θ4between the magnetic field B3and ω0·t, and θΔ4) are constants which can be obtained in advance by calibration or the like.

The relationship between the first parameter p6and the magnitude rk[p6] of the variation factor Cp6or the relationship between the first parameter p6and the angle θ00[p6] of the variation factor Cp6is registered in advance in the state storage unit6bin the form of a mathematical expression or table. In step506, the state output unit7bcalculates the value of the first parameter p6corresponding to rk[p6] or θ00[p6] by referring to the state storage unit6bon the basis of the magnitude rk[p6] or angle θ00[p6] of the variation factor Cp6calculated by the signal conversion unit5b(or acquires it from the state storage unit6b).

The state quantifying unit8bperforms the processing in steps501to506described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step507). Note that the processing in steps502to506is performed in the second excitation state for a duration of T2 sec.

As described above, according to this embodiment, note that this embodiment is configured to obtain the difference E630dbetween the angular frequency ω0component of the first inter-electrode electromotive force and the angular frequency ω0component of the second inter-electrode electromotive force, obtain the difference E632dbetween the angular frequency ω2component of the first inter-electrode electromotive force and the angular frequency ω2component of the second inter-electrode electromotive force, extract the difference EdA6(∂A/∂t component) between the electromotive force differences E630dand E632d, extract the magnitude or phase of the variation factor Cp6dependent on the characteristic or state of the fluid or a state in the measuring tube (the first parameter p6) from the electromotive force difference EdA6, and obtain the first parameter p6on the basis of the magnitude or phase of the variation factor Cp6. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

In this embodiment, the components of the state quantifying unit8b, except for the detecting units of the electromotive force differences E630dand E632d, can be implemented by a computer comprising a CPU, storage unit, and interface and programs which control the hardware resources. In this embodiment, for example, the v×B component can be extracted by E630d−EdA6·{(ω0−ω2)/ω0}. There is known a technique of calculating the flow rate of the fluid from the v×B component in the field of a general electromagnetic flowmeter, which can be easily implemented by a computer included in the state quantifying unit8b. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, adjusting the distance d3from the plane PLN3including the axis of the exciting coil3to the first electrodes2aand2band the distance d4from the plane PLN3to the second electrodes2cand2dallows the electromotive force differences E630dand E632dto be almost only electromotive forces based on ∂A/∂t components. With this processing, this embodiment can extract a ∂A/∂t component more effectively, and can reduce computation errors more than the first embodiment.

In this embodiment, it suffices to extract either the magnitude rk[p6] or angle θ00[p6] of the variation factor Cp6from the difference EdA6. However, the first parameter p6can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude rk[p6] or the angle θ00[p6] which has a higher sensitivity and obtain the first parameter p6on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the first parameter p6at higher speed. For example, it suffices to use the magnetic field represented by following equations instead of equations (41) and (42).
B3=b3·cos(ω0·t−θ3)+b3·cos(ω2·t−θ3)  (225)
B4=b4·cos(ω0·t−θ4)+b4·cos(ω2·t−θ4)  (226)

In this embodiment, the electromotive force differences E630dand E632dare extracted from the first and second inter-electrode electromotive forces, and the difference between the electromotive force differences E630dand E632dis extracted as the ∂A/∂t component. However, the present invention is not limited to this. the electromotive force sum of the first and second inter-electrode electromotive forces may be extracted for each of the exciting angular frequencies ω0and ω2, and the difference between the two electromotive force sums may be extracted as the ∂A/∂t components.

The following description will explain a specific example of the state detection device of this embodiment which detects a level or sectional area of the fluid. In this case, considering that a level h varies, as shown inFIGS. 48 and 49, the exciting coil is arranged in a direction horizontal to the measuring tube1, and the electrodes2aand2care placed under the measuring tube1. When one first electrode and one second electrode are to be used in this manner, it suffices if an earth ring (not shown) for grounding the potential of the fluid F is provided on the measuring tube1, the potential difference between the electrode2aand the ground potential is set to the first inter-electrode electromotive force, and the signal conversion unit5adetects the potential difference between the electrode2cand the ground potential as the second inter-electrode electromotive force.

As the level h (sectional area S) of the fluid F varies, the value of the magnitude rk[p6] of the variation component Cp6also varies.FIG. 50is a graph showing an example of the relationship between the level h or sectional area S (first parameter p6) of the fluid F and the magnitude rk[p6] of the variation factor Cp6. The relationship shown inFIG. 50changes depending on the shape or the like of the measuring tube1. Therefore, obtaining this relationship by a theoretical formula at the time of design or measurement at the time of calibration and storing it in the state storage unit6bin advance make it possible to obtain the level h or sectional area S of the fluid F in step506on the basis of the magnitude rk[p6] of the variation factor Cp6obtained in step505.

Seventh Embodiment

The seventh embodiment of the present invention will be described next. A state detection device according to this embodiment includes one exciting coils and two pairs of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 13except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 13. This embodiment uses the second extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the first parameter irrelevant to an exciting frequency.

Assume that the exciting current having an angular frequency ω0is supplied to an exciting coil3, and the first parameter is p7. In this case, a difference between the first inter-electrode electromotive force between electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2dis represented by the following equation according to equations (54), (68), and (75).

If the magnetic fields B3and B4generated from the exciting coil3are set to be equal to each other in the initial state (at the time of calibration), the difference between the magnetic fields B3and B4decreases afterward. The following condition holds in the following equation:
|b3+b4·exp(j·Δθ4)|>>|b3−b4·exp(j·Δθ4)|  (228)

Since ω0>γ·V holds, the following condition holds for the electromotive force difference E730dgiven by equation (227) in consideration of the condition represented by equation (228).
|ω0·exp(j·π/2)·{b3+b4·exp(j·Δθ4)}|>>|γ·V·exp(j·Δθ01)·{b3−b4·exp(j·Δθ4)}|  (229)

The following expressions represent the electromotive force difference EdA7which approximates the electromotive force difference E730din equation (227) by using the condition of expression (229).

In equation (231), the ∂A/∂t component in the resultant vector can be extracted by using the difference between the inter-electrode electromotive forces. Equation (231) is irrelevant to the magnitude V of the flow velocity, and hence is only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using the electromotive force difference EdA7.

When a variation factor dependent on the first parameter is Cp7, Cp7=rk[p7]·exp(j·θ00[p7]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cp7is represented by equation (231).

Letting m3band θ3bbe the magnitude and angle of [exp{j·(π/2+θ3)}·{b3+b4·exp(j·Δθ4)}] in equation (232), m3band θ3bare represented by equations (213) and (214). Upon applying equations (213) and (214) to equation (232), a magnitude rk[p7] of the variation factor Cp7and an angle θ00[p7] thereof from the real axis are represented by
rk[p7]=|EdA7|/(m3b·ω0)  (233)
θ00[p7]=∠EdA7−θ3b)  (234)

The first parameter p7can be obtained from the relationship between the first parameter p7and rk[p7], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the first parameter p7and angle θ00[p7].

The specific arrangement and operation of the state detection device according to this embodiment will be described next. The state detection device according to this embodiment has the same arrangement as that of the state detection device in the sixth embodiment. Hence, the same reference numerals as inFIG. 46denote the same components in this embodiment. The state detection device of this embodiment includes a measuring tube1, first electrodes2aand2b, second electrodes2cand2d, an exciting coil3, a power supply unit4, and a state quantifying unit8a.

The state quantifying unit8bincludes a signal conversion unit5bwhich obtains the amplitudes and phases of the first resultant electromotive force detected by the first electrodes2aand2band the second resultant electromotive force detected by the second electrodes2cand2d, extracts a ∂A/∂t component from the electromotive force difference between the first and second resultant electromotive forces on the basis of the amplitudes and phases, and extracts, from the ∂A/∂t component, the magnitudes or phases of the variation factors dependent on the first parameter but independent of the frequency, a state storage unit6b(equivalent to the above-described first table) which stores in advance the relationship between the first parameter and the magnitude or phase of the variation factor dependent on the first parameter, and a state output unit7bwhich obtains the first parameter corresponding to the magnitude or phase of the extracted variation factor based on the relationship stored in the state storage unit6b.

The power supply unit4bsupplies the exciting current having the angular frequency ω0to the exciting coil3.FIG. 51is a flowchart showing the operation of the state quantifying unit8baccording to this embodiment. First of all, the signal conversion unit5bobtains an amplitude r730dof the difference E730dbetween the electromotive force with the angular frequency ω0component of the first inter-electrode electromotive force between the electrodes2aand2band the electromotive force with the angular frequency ω0component of the second inter-electrode electromotive force between the electrodes2cand2d, and obtains a phase difference φ730dbetween the real axis and the electromotive force difference E730dby using a phase detector (not shown) (step601inFIG. 51).

Subsequently, the signal conversion unit5bobtains the magnitude and angle of the electromotive force difference EdA7which approximates the electromotive force difference E730d(step602). The processing in step602corresponds to the processing of obtaining the ∂A/∂t component, and is equivalent to the calculation of equation (231). The signal conversion unit5bcalculates a magnitude |EdA7| of the electromotive force difference EdA7according to the following equation:
|EdA7|=r730d(235)

The signal conversion unit5bthen calculates an angle ∠EdA7with respect to the real axis of the electromotive force difference EdA7according to the following equation:
∠EdA7=φ730d  (236)

With the above operation, the processing in step602is complete.

The signal conversion unit5bcalculates, from the electromotive force difference EdA7, the magnitude rk[p7] of the variation factor Cp7dependent on the first parameter p7and the angle θ00[p7] with respect to the real axis as follows (step603):
rk[p7]=|EdA7|/(m3b·ω0)  (237)
θ00[p7]=∠EdA7−θ3b(238)

Note that m3band θ3b(the amplitudes b3and b4generated from the exciting coil3, the phase difference θ3and θ4between the magnetic field B3and ω0·t, and Δθ4) are constants which can be obtained in advance by calibration or the like.

The relationship between the first parameter p7and the magnitude rk[p7] of the variation factor Cp7or the relationship between the first parameter p7and the angle θ00[p7] of the variation factor Cp7is registered in advance in the state storage unit6bin the form of a mathematical expression or table. In step604, the state output unit7bcalculates the value of the first parameter p7corresponding to rk[p7] or θ00[p7] by referring to the state storage unit6bon the basis of the magnitude rk[p7] or angle θ00[p7] of the variation factor Cp7calculated by the signal conversion unit5b(or acquires it from the state storage unit6b). The state quantifying unit8bperforms the processing in steps601to604described above in a predetermined cycle until, for example, the operator designates the end of the measurement (YES in step605).

As described above, according to this embodiment, note that when the magnitudes of the magnetic fields B3and B4generated from the exciting coil3are equal to each other, the electromotive force difference E730dcan be approximately extracted as the ∂A/∂t components. This embodiment is configured to extract the magnitude or phase of the variation factor Cp7dependent on the characteristic or state of the fluid or a state in the measuring tube (the first parameter p7) from the approximately extracted ∂A/∂t component, and obtain the first parameter p7on the basis of the magnitude or phase of the variation factor Cp7. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

As in the sixth embodiment, the components of the state quantifying unit8bof this embodiment, except for the detecting unit of the electromotive force difference E730d, can be implemented by a computer and program. In this embodiment, assume that the exciting current having an angular frequency ω0is supplied to the exciting coil3, and E730srepresents a sum of the first inter-electrode electromotive force between electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2d. In this case, an inter-electrode electromotive force E730sis obtained by reversing the sign of b4in equation (227). As a result, the inter-electrode electromotive force E730scan be handled as the v×B component. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitude rk[p7] or angle θ00[p7] of the variation factor from the electromotive force difference EdA7. However, the first parameter p7can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude rk[p7] or the angle θ00[p7] which has a higher sensitivity and obtain the first parameter p7on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

Eighth Embodiment

The eighth embodiment of the present invention will be described next. A state detection device according to this embodiment includes one exciting coils and two pairs of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 13except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 13. This embodiment uses the second extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the second parameter for a variation factor having a frequency characteristic.

Assume that the exciting current having an angular frequency ω0is supplied to an exciting coil3, and the first parameter is p8. In this case, a difference E830dbetween the first inter-electrode electromotive force between electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2dis represented by the following equation according to equations (54), (78), and (79).

From equations (228) and (229), the following approximate expression holds in equation (239):
|b3+b4·exp(j·Δθ4)|>>|b3−b4·exp(j·Δθ4)|  (240)
|ω0·exp(j·π/2)·{b3+b4·exp(j·Δθ4)}|>>|γ·V·exp(j·Δθ01)·{b3−b4·exp(j·Δθ4)}|  (241)

The following expressions represent an electromotive force difference EdA80which approximates the electromotive force difference E830din equation (239) by using the condition of expression (241).

Assume that the exciting current having an angular frequency ω2is supplied to the exciting coil3, and the first parameter is p8. In this case, the difference between the first inter-electrode electromotive force between the electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2dis represented by the following equation according to equations (54), (81) and (82).

Since ω2>γ·V holds, the following condition holds for the electromotive force difference E832dgiven by equation (244) in consideration of the condition represented by equation (240).
|ω2·exp(j·π/2)·{b3+b4·exp(j·Δθ4)}|>>|γ·V·exp(j·Δθ01)·{b3−b4·exp(j·Δθ4)}|  (245)

The following expressions represent the electromotive force difference EdA82which approximates the electromotive force difference E832din equation (244) by using the condition of expression (245).

In equations (243) and (247), the ∂A/∂t component in the resultant vector can be extracted by using the difference between the inter-electrode electromotive forces. Equations (243) and (247) are irrelevant to the magnitude V of the flow velocity, and hence are only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using this electromotive force difference.

Letting m3band θ3bbe the magnitude and angle of [exp{j·(π/2+θ3)}·{b3+b4·exp(j·Δθ4)}] in equations (248) and (249), m3band θ3bare represented by equations (213) and (214). Upon applying equations (213) and (214) to equation (248), a magnitude rk[p8,ω0] of the variation factor Cp80and an angle θ00[p8,ω0] thereof from the real axis are represented by
rk[p8,ω0]=|EdA80|/(m3b·ω0)  (250)
θ00[p8,ω0]=∠EdA80−θ3b(251)

Upon applying equations (213) and (214) to equation (249), a magnitude rk[p8,ω2] of the variation factor Cp82and an angle θ00[p8,ω2] thereof from the real axis are represented by
rk[p8,ω2]=|EdA82|/(m3b−ω2)  (252)
θ00[p8,ω2]=∠EdA82−θ3b(253)

When the ratio between the variation factors Cp82and Cp80is Cn8, the ratio Cn8is represented by the following equation.

In this case, the magnitude (rk[p8,ω2]/rk[p8,ω0]) of the ratio Cn8and the angle (θ00[p8,ω2]−θ00[p8,ω0]) with respect to the real axis are represented by the following equations.
rk[p8,ω2]/rk[p8,ω0]=(|EdA82|/|EdA80|)·(ω0/ω2)  (255)
θ00[p8,ω2]−θ00[p8,ω0]=∠EdA82−∠EdA80  (256)

According to equations (254) to (256), it is obvious that the ratio Cn8does not include the variation factor of the magnetic field, and the value of the second parameter p8can be obtained by reducing error factors.

The second parameter p8can be obtained from the relationship between the second parameter p8and (rk[p8,ω2]/rk[p8,ω0]), which is checked in advance by measurement or the like at the time of calibration, or the relationship between the second parameter p8and (θ00[p8,ω2]−θ00[p8,ω0]).

The specific arrangement and operation of the state detection device according to this embodiment will be described next. The state detection device according to this embodiment has the same arrangement as that of the state detection device in the sixth embodiment. Hence, the same reference numerals as inFIG. 46denote the same components in this embodiment. The state detection device of this embodiment includes a measuring tube1, first electrodes2aand2b, second electrodes2cand2d, exciting coil3, a power supply unit4, and a state quantifying unit8a.

The state quantifying unit8bincludes a signal conversion unit5bwhich obtains the amplitudes and phases of the first resultant electromotive forces detected by the first electrodes2aand2band the second resultant electromotive forces detected by the electrodes2cand2d, obtains the electromotive force differences having the same frequency component of the first and second resultant electromotive forces with the first and second angular frequencies ω0and ω2, extracts, from the electromotive force differences, the ∂A/∂t components with the first and second angular frequencies ω0and ω2, and extracts the magnitude or phase of the ratio between the variation factors dependent on the second parameter and frequency from the ratio between the ∂A/∂t components with the first and second angular frequencies ω0and ω2, a state storage unit6b(equivalent to the above-described second table) which stores in advance the relationship between the second parameter and the magnitude or phase of the ratio between the variation factors, and a state output unit7bwhich obtains the second parameter corresponding to the magnitude or phase of the ratio between the extracted variation factors based on the relationship stored in the state storage unit6b.

The power supply unit4brepeats, in a T-sec cycle, the operation of continuing the first excitation state for T1 sec in which the exciting current having the first angular frequency ω0is supplied to the exciting coil3, and continuing the second excitation state for T2 sec in which the exciting current having the second angular frequency ω2is supplied to the exciting coil3. That is, T=T1+T2.

FIG. 52is a flowchart showing the operation of the state quantifying unit8baccording to this embodiment. First of all, the signal conversion unit5bobtains an amplitude r830dof the difference E830dbetween the electromotive force with the angular frequency ω0component of the first inter-electrode electromotive force between the electrodes2aand2band the electromotive force with the angular frequency ω0component of the second inter-electrode electromotive force between the electrodes2cand2din the first excitation state, and obtains a phase difference φ830dbetween the real axis and the electromotive force difference E830dby using a phase detector (not shown) (step701inFIG. 52).

Subsequently, the signal conversion unit5bobtains an amplitude r832dof the difference E832dbetween the electromotive force with the angular frequency ω2component of the first inter-electrode electromotive force and the electromotive force with the angular frequency ω2component of the second inter-electrode electromotive force, and obtains a phase difference φ832dbetween the real axis and the electromotive force difference E832dby using the phase detector (step702).

Next, the signal conversion unit5bcalculates the magnitude |EdA80| and an angle ∠EdA80with respect to the real axis of the electromotive force EdA80which approximates the electromotive force difference E830daccording to the following equation (step703):
|EdA80|=r830d(257)
∠EdA80=φ830d  (258)

The signal conversion unit5bthen calculates the magnitude |EdA82| and an angle ∠EdA82with respect to the real axis of the electromotive force difference EdA82which approximates the electromotive force difference E832daccording to the following equation (step704):
|EdA82|=r832d(259)
∠EdA82=φ832d  (260)

The processing in steps703and704corresponds to the processing of obtaining the ∂A/∂t component, and is equivalent to the calculation of equations (243) and (247).

The signal conversion unit5bextracts the variation factor Cp80dependent on the second parameter p8from the electromotive force difference EdA80, extracts the variation factor Cp82dependent on the second parameter p8from the electromotive force difference EdA82, and obtains the magnitude and angle of the ratio Cn8between the variation factors Cp82and Cp80(step705). The signal conversion unit5bcalculates the magnitude (rk[p8,ω2]/rk[p8,ω0]) of the ratio Cn8as follows:
rk[p8,ω2]/rk[p8,ω0]=(|EdA82|/|EdA80|)·(ω0/ω2)  (261)

The signal conversion unit5bcalculates the angle (θ00[p8,ω2]−θ00[p8,ω0]) with respect to the real axis of the ratio Cn8as follows:
θ00[p8,ω2]−θ00[p8,ω0]=∠EdA82−∠EdA80  (262)

With the above operation, the processing in step705is complete.

The relationship between the second parameter p8and the magnitude (rk[p8,ω2]/rk[p8,ω0]) of the ratio Cn8or the relationship between the second parameter p8and the angle (θ00[p8,ω2]−θ00[p8,ω0]) of the ratio Cn8is registered in advance in the state storage unit6bin the form of a mathematical expression or table. In step706, the state output unit7bcalculates the value of the second parameter p8corresponding to (rk[p8,ω2]/rk[p8,ω0]) or (θ00[p8,ω2]−θ00[p8,ω0]) by referring to the state storage unit6bon the basis of the magnitude (rk[p8,ω2]/rk[p8,ω0]) or angle (θ00[p8,ω2]−θ00[p8,ω0]) of the ratio Cn8calculated by the signal conversion unit5b(or acquires it from the state storage unit6b).

The state quantifying unit8bperforms the processing in steps701to706described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step707). Note that the processing in steps702to706is performed in the second excitation state for a duration of T2 sec.

As described above, according to this embodiment, note that when the magnitudes B3and B4generated from the exciting coil3are equal to each other, the electromotive force differences E830dand E832dcan be approximately extracted as the ∂A/∂t components when the exciting angular frequencies are ω0and ω2, respectively. This embodiment is configured to extract the variation factors Cp80and Cp82dependent on the characteristic or state of the fluid or a state in the measuring tube (the second parameter p8) from the approximately extracted two ∂A/∂t components, and obtain the second parameter p8on the basis of the magnitude or phase of the ratio between the variation factors Cp82and Cp80. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

As in the sixth embodiment, the components of the state quantifying unit8bof this embodiment, except for the detecting unit of the electromotive force differences E830dand E832d, can be implemented by a computer and program. In this embodiment, assume that the exciting current having an angular frequency ω0is supplied to the exciting coil3, and E830srepresents a sum of the first inter-electrode electromotive force between electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2d. In this case, an inter-electrode electromotive force E830sis obtained by reversing the sign of b4in equation (239). As a result, the inter-electrode electromotive force E830scan be handled as the v×B component. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitude (rk[p8,ω2]/rk[p8,ω0]) or angle (θ00[p8,ω2]−θ00[p8,ω0]) of the ratio Cn8between the variation factors. However, the second parameter p8can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitude (rk[p8,ω2]/rk[p8,ω0]) or the angle (θ00[p8,ω2]−θ00[p8,ω0]) which has a higher sensitivity and obtain the second parameter p8on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the second parameter p8at higher speed. For example, it suffices to use the magnetic field represented by equations (225) and (226) instead of equations (41) and (42).

Ninth Embodiment

The ninth embodiment of the present invention will be described next. A state detection device according to this embodiment includes one exciting coil and two pairs of electrodes, and has the same arrangement as that of the state detection device shown inFIG. 13except for the signal processing system. The principle of this embodiment will therefore be described by using reference numerals inFIG. 13. This embodiment uses the second extraction method as a method of extracting a ∂A/∂t component from a resultant vector, and obtains the second parameter for a variation factor having a frequency characteristic. In this embodiment, two second parameter values are obtained. Of the two second parameters, one is the third parameter, and the other is the fourth parameter.

Assume that the exciting current having an angular frequency ω0is supplied to an exciting coil3, the third parameter is p9, and the fourth parameter is q9. In this case, the difference E930dbetween the first inter-electrode electromotive force between electrodes2aand2band the second inter-electrode electromotive force between electrodes2cand2dis represented by the following equation according to equations (54), (85), and (86).

From equations (228) and (229), equations (240) and (241) hold in equation (263). The following expressions represent an electromotive force difference EdA90which approximates the electromotive force difference E930din equation (263) by using the condition of expression (241).

Assume that the exciting current having an angular frequency ω2is supplied to the exciting coil3, the third parameter is p9, and the fourth parameter is q9. In this case, the difference E932dbetween the first inter-electrode electromotive force between the electrodes2aand2band the second inter-electrode electromotive force between the electrodes2cand2dis represented by the following equation according to equations (54), (88) and (89).

Since ω2>γ·V holds, equation (245) holds for the electromotive force difference E932dgiven by equation (266) in consideration of the condition represented by equation (240). The following expressions represent the electromotive force difference EdA92which approximates the electromotive force difference E932din equation (266) by using the condition of expression (245).

In equations (265) and (268), the ∂A/∂t component in the resultant vector can be extracted by using the difference between the inter-electrode electromotive forces. Equations (265) and (268) are irrelevant to the magnitude V of the flow velocity, and hence are only the component generated by ∂A/∂t. The fluid state except for the flow velocity, and the state in the measuring tube can be measured by using this electromotive force difference.

When a variation factor dependent on the third and fourth parameters is Cpq90in equation (265), Cpq90=rk[p9,q9,ω0]·exp(j·θ00[p9,q9,ω0]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cpq90is represented by equation (265).

When a variation factor dependent on the third and fourth parameters is Cpq92in equation (268), Cpq92=rk[p9,q9,ω2]·exp(j·θ00[p9,q9,ω2]) holds, and the remaining portion is a constant which is provided at the time of calibration. The variation factor Cpq92is represented by equation (268).

Letting m3band θ3bbe the magnitude and angle of [exp{j·(π/2+θ3)}·{b3+b4·exp(j·Δθ4)}] in equations (269) and (270), m3band θ3bare represented by equations (213) and (214). Upon applying equations (213) and (214) to equation (269), a magnitude rk[p9,q9,ω0] of the variation factor Cpq90and an angle θ00[p9,q9,ω0] thereof from the real axis are represented by
rk[p9,q9,ω0]=|EdA90|/(m3b·ω0)  (271)
θ00[p9,q9,ω0]=∠EdA90−θ3b(272)

Upon applying equations (120) and (121) to equation (270), a magnitude rk[p9,q9,ω2] of the variation factor Cpq92and an angle θ00[p9,q9,ω2] thereof from the real axis are represented by
rk[p9,q9,ω2]=|EdA92|/(m3b·ω2)  (273)
θ00[p9,q9,ω2]=∠EdA92−θθ3b(274)

The parameters p9and q9can be obtained from the relationship between the parameters p9and q9and rk[p9,q9,ω0] and rk[p9,q9,ω2], which is checked in advance by measurement or the like at the time of calibration, or the relationship between the parameters p9and q9, and θ00[p9,q9,ω0] and θ00[p9,q9,ω2].

The specific arrangement and operation of the state detection device according to this embodiment will be described next. The state detection device according to this embodiment has the same arrangement as that of the state detection device in the sixth embodiment. Hence, the same reference numerals as inFIG. 46denote the same components in this embodiment. The state detection device of this embodiment includes a measuring tube1, first electrodes2aand2b, second electrodes2cand2d, an exciting coil3, a power supply unit4, and a state quantifying unit8b.

The state quantifying unit8bincludes a signal conversion unit5bwhich obtains the amplitudes and phases of the first resultant electromotive force detected by the first electrodes2aand2band the second resultant electromotive force detected by the second electrodes2cand2d, obtains the electromotive force differences having the same frequency component of the first and second resultant electromotive forces with the first and second angular frequencies ω0and ω2based on the amplitudes and phases, extracts, from the electromotive force differences, ∂A/∂t components with the plurality of frequency components, and extracts, from the extracted ∂A/∂t components, the magnitude or phase of the variation factors dependent on the plurality of second parameters and frequencies, a state storage unit6b(equivalent to the above-described third table) which stores in advance the relationship between the plurality of second parameters and the magnitude or phase of the variation factors with the plurality of frequency components, and a state output unit7bwhich obtains the plurality of second parameters corresponding to the magnitude or phase of the extracted variation factors based on the relationship stored in the state storage unit6b.

The operation of the power supply unit4bis the same as that in the eighth embodiment.FIG. 53is a flowchart showing the operation of the state quantifying unit8baccording to this embodiment. First of all, the signal conversion unit5bobtains an amplitude r930dof the difference between the electromotive force with the angular frequency ω0component of the first inter-electrode electromotive force between the electrodes2aand2band the electromotive force with the angular frequency ω0component of the second inter-electrode electromotive force between the electrodes2cand2din the first excitation state, and obtains a phase difference φ930dbetween the real axis and the electromotive force difference E930dby using a phase detector (not shown) (step801inFIG. 53).

Subsequently, the signal conversion unit5bobtains an amplitude r932dof the difference between the electromotive force with the angular frequency ω2of the inter-electrode electromotive force and the electromotive force with the frequency ω2of the second inter-electrode electromotive force in the second excitation state wherein the exciting angular frequency is ω2, and obtains a phase difference φ932dbetween the real axis and the electromotive force difference E932dby using the phase detector (step802).

Next, the signal conversion unit5bcalculates the magnitude |EdA90| and an angle ∠EdA90with respect to the real axis of the electromotive force EdA90which approximates the electromotive force difference E930daccording to the following equation (step803):
|EdA90|=r930d(275)
∠EdA90=φ930d  (276)

The signal conversion unit5bthen calculates the magnitude |EdA92| and an angle ∠EdA92with respect to the real axis of the electromotive force difference EdA92which approximates the electromotive force difference E932daccording to the following equation (step804):
|EdA92|=r932d(277)
∠EdA92=φ932d  (278)

The processing in steps803and804corresponds to the processing of obtaining the ∂A/∂t component, and is equivalent to the calculation of equations (265) and (268).

The signal conversion unit5bcalculates, from the electromotive force difference EdA90, the magnitude rk[p9,q9,ω0] of the variation factor Cpq90dependent on the third and fourth parameters p9and q9and the angle θ00[p9,q9,ω0] with respect to the real axis as follows (step805):
rk[p9,q9,ω0]=|EdA90|/(m3b·ω0)  (279)
θ00[p9,q9,ω0]=∠EdA90−θ3b(280)

The signal conversion unit5balso calculates, from the electromotive force difference EdA92, the magnitude rk[p9,q9,ω2] of the variation factor Cpq92dependent on the third and fourth parameters p9and q9and the angle θ00[p9,q9,ω2] with respect to the real axis as follows (step806):
rk[p9,q9,ω2]=|EdA92|/(m3b·ω2)  (281)
θ00[p9,q9,ω2]=∠EdA92−θ3b(282)

Note that m3band θ3bare constants which can be obtained in advance by calibration or the like.

The relationship between the third and fourth parameters p9and q9and the magnitudes rk[p9,q9,ω0] and rk[p9,q9,ω2] of the variation factors Cpq90and Cpq92or the relationship between the parameters p9and q9and the angles θ00[p9,q9,ω0] and θ00[p9,q9,ω2] of the variation factors Cpq90and Cpq92is registered in advance in the state storage unit6bin the form of a mathematical expression or table.

The state output unit7bcalculates the values of the third and fourth parameters p9and q9corresponding to the magnitudes rk[p9,q9,ω0] and rk[p9,q9,ω2]) or angles θ00[p9,q9,ω0] and θ00[p9,q9,ω2] by referring to the state storage unit6bon the basis of the magnitudes rk[p9,q9,ω0] and rk[p9,q9,ω2]) or angles θ00[p9,q9,ω0] and θ00[p9,q9,ω2]) of the variation factors Cpq90and Cpq92calculated by the signal conversion unit5b(step807).

The state quantifying unit8bperforms the processing in steps801to807described above in a cycle T until, for example, the operator designates the end of the measurement (YES in step808). Note that the processing in steps802to807is performed in the second excitation state for a duration of T2 sec.

As described above, according to this embodiment, note that when the magnitudes B3and B4generated from the exciting coil3are equal to each other, the electromotive force differences E930dand E932dcan be approximately extracted as the ∂A/∂t components when the exciting angular frequencies of the electromotive force differences E930dand E932dare ω0and ω2, respectively. This embodiment is configured to extract the variation factors Cp90and Cp92dependent on the characteristic or state of the fluid or a state in the measuring tube (the third and fourth parameters p9and q9) from the approximately extracted two ∂A/∂t components, and obtain the third and fourth parameters p9and q9on the basis of the magnitude or phase of the variation factors Cp90and Cp92. This makes it possible to accurately detect the characteristic or state of the fluid or the state in the measuring tube regardless of the flow velocity of the fluid.

As in the sixth embodiment, the components of the state quantifying unit8bof this embodiment, except for the detecting unit of the electromotive force differences E930dand E932d, can be implemented by a computer and program. In this embodiment, assume that the exciting current having an angular frequency ω0is supplied to the exciting coil3, the third parameter is p9, and the fourth parameter is q9. In this case, when E930srepresents a sum of the first inter-electrode electromotive force between the electrodes2aand2band the second inter-electrode electromotive force between the electrodes2cand2d, the inter-electrode electromotive force E930sis obtained by reversing the sign of b4in equation (263). As a result, the inter-electrode electromotive force E930scan be handled as the v×B component. Therefore, according to this embodiment, the characteristic or state of the fluid or the state in the measuring tube can be detected by using basically the same hardware arrangement as that of an electromagnetic induction type flowmeter.

In this embodiment, it suffices to extract either the magnitudes rk[p9,q9,ω0] and rk[p9,q9,ω2]) or angles θ00[p9,q9,ω0] and θ00[p9,q9,ω2] of the variation factors Cpq90and Cpq92. However, the third and fourth parameters p9and q9can be obtained by extracting both the magnitude and angle of the component. In this case, it suffices to select either the magnitudes rk[p9,q9,ω0] and rk[p9,q9,ω2] or the angles θ00[p9,q9,ω0] and θ00[p9,q9,ω2] which has a higher sensitivity and obtain the third and fourth parameters p9and q9on the basis of the selected magnitude or angle. This makes it possible to improve the detection sensitivity.

In addition, this embodiment has exemplified the case wherein the exciting frequency is switched to ω0or ω2. However, performing excitation using exciting currents containing components with the angular frequencies ω0and ω2makes it unnecessary to switch the exciting frequencies. This can calculate the parameters p9and q9at higher speed. For example, it suffices to use the magnetic field represented by equations (225) and (226) instead of equations (41) and (42).

Furthermore, each of the first to ninth embodiments uses the pair of electrodes2aand2bas the first electrodes, and the pair of electrodes2cand2das the second electrodes. However, the present invention is not limited to this, and may use one each of the first and second electrodes. If only one electrode is to be used, since a ground ring or a ground electrode for grounding the potential of a fluid to be measured is provided on the measuring tube1, it suffices to detect an electromotive force (a potential difference from the ground potential) generated at the single electrode by using the signal conversion unit5,5a, or5b. When a pair of electrodes are to be used, an electrode axis is defined as a straight line connecting the pair of electrodes. Assume that only one electrode is to be used. In this case, assuming that a virtual electrode is placed at a position to face the real electrode through the measuring tube axis PAX on the plane PLN including the single real electrode, the electrode axis is defined as a straight line connecting the real electrode and the virtual electrode.

INDUSTRIAL APPLICABILITY

The present invention can be applied to a state detection device which detects a characteristic or state of a fluid or a state in a measuring tube through which the fluid flows.