JP5728052B2 - Instrument electronics and method for geometric thermal compensation in flow meters - Google Patents

Description

  The present invention relates to flow meters, and more particularly to instrument electronics and methods for geometric thermal compensation in flow meters.

  Typically, a vibratory line sensor, such as a Coriolis flow meter or a vibratory density meter, is operated by detecting the movement of a vibratory pipe that contains flowing material. Properties associated with material in the pipeline, such as mass flow and density, can be determined by processing measurement signals received from motion transducers associated with the pipeline. In general, the vibration mode of a vibration system filled with material is affected by the combined mass, stiffness, and damping characteristics of the containing conduit and the material contained therein.

  A typical Coriolis flow meter includes one or more flow lines or flow tubes that are connected inline in a pipeline or other transport system and transport materials such as fluids, slurries, etc. in the system. Each pipe line is considered to have a set of natural vibration modes including, for example, a simple bending mode, a torsion mode, a radial mode, and a coupled mode. In a typical Coriolis flow measurement application, the conduit is excited in one or more vibration modes as material flows through the conduit. Typically, the excitation is provided by an actuator such as an electromechanical device such as a voice coil drive that periodically vibrates the conduit. Mass flow rate is determined by measuring the time delay or phase between motions at the transducer location. Typically, these two transducers (or pick-off sensors) are employed to measure the vibration response of the flow line and are typically placed at positions upstream or downstream of the actuator. The two pickoff sensors are connected to the electronic instrument by wiring such as two pairs of independent wires. The electronic instrument receives signals from the two pickoff sensors and processes these signals to derive mass flow measurements.

  For a set of flow meter conditions (eg, specific temperature, installation, external load, etc.), the mass flow rate is directly proportional to the time delay (Δt) between pickoff sensors. This relationship is expressed by Equation 1 below:

Given by. The FCF term is a proportionality constant and is usually called a flow compensation coefficient. The zero value is an empirically derived zero flow offset.
FCF depends primarily on the stiffness and geometry of the flow meter conduit. The geometric shape includes features such as where two measurements of phase or time are made. Stiffness depends on the material properties of the flow line and the geometry of the line. For a particular flow meter, the FCF value and the zero value are found by a calibration process performed with a calibration fluid flowing at two known mass flow rates at a particular calibration temperature.
Special table 2003-528305 gazette Special table 2003-503723 gazette

  As the stiffness or geometry of the flow meter changes during operation, the FCF also changes after the initial calibration time. For example, when the operating temperature is higher than the calibration temperature, the stiffness of the flow meter changes. To ensure accurate mass flow measurement, the FCF value and the zero value need to be approximately constant. This is extremely difficult to achieve. Instead, accurate mass flow measurement requires that a robust method be employed to compensate for changes in FCF and zero values.

Typically, a conventional flow meter is calibrated at a specific reference temperature (T ₀ ). However, in use, the flow meter often operates at a temperature different from the reference temperature. In the prior art, the flow meter is compensated for temperature changes in a relatively simple manner. Conventionally, it is known that the elastic modulus changes with temperature. As a result, in the prior art, equations for mass flow and density are added to compensate for the effect on the modulus of elasticity.

  The conventional typical mass flow equation including temperature compensation for elastic modulus or Young's modulus (E) is:

Given by. The Young's modulus term (1-φ · ΔT) defines how the FCF changes in response to changes in flow meter temperature from the reference temperature (T ₀ ).
The slope of the function φ is often referred to as FT and is typically determined through experimentation with a particular flow meter design or group of flow meters. In the prior art, FCF is usually considered to be essentially the same as the gradient of modulus of elasticity over temperature. However, the modulus of elasticity is not always linear over the entire temperature range in which the flow meter operates. To compensate for this non-linearity, higher order polynomials that better compensate for this change, eg, Equation 3 below:

Has been adopted. The high-order polynomial term (1-φ ₁ · ΔT−φ ₂ · ΔT ² ...) Defines how the FCF changes as the flow meter temperature changes. The Young's modulus term is expressed as TF _y . The (TF _y ) term includes a first order linear term or can include a polynomial.

The Coriolis flow meter can also measure the density (ρ _f ) of the process fluid in the reference vibration frame. The square of the vibration period is directly proportional to the value obtained by dividing the mass of the vibration system by the stiffness. For certain conditions of the flow line, stiffness and mass are constant and fluid density (ρ _f ) is directly proportional to the square of the period. This relationship is given by Equation 4 below:

Given by. The C ₁ term is a proportionality constant and the C ₂ term is an offset. The coefficients C ₁ and C ₂ depend on the stiffness of the flow line and on the mass and volume of the fluid in the flow meter. The coefficients C ₁ and C ₂ are determined by calibrating the flow meter with two fluids of known density.

  In the prior art, density calculations are also compensated with temperature. A typical form of density calculation including temperature compensation for the modulus of elasticity is Equation 5 below:

Given by. The (TF _y ) term defines how the square of the tube period changes with the change in temperature from the previously discussed reference temperature (T ₀ ).
The slope of the function φ is often referred to as DT and is typically determined through experimentation with a particular flow meter design or group of flow meters. As noted, higher order functions can be used to remove the effect of temperature on the density temperature compensation process, as well as at mass flow rate. Like FT, in the prior art, DT is usually considered to be the same as the gradient of modulus of elasticity over temperature. As a result, in the prior art, mass flow and density are temperature compensated in the same way.

  Near the reference temperature (ie, calibration temperature), the DT and FT temperature compensation procedures work well tolerate. However, at the extremes of temperature, the inherent inaccuracies and imperfections become prominent and become noticeable. For this reason, additional compensation and calibration processes are often required in the prior art. For example, for flow meters used at high temperatures such as 90 ° C, a new calibration process is performed at a similarly high reference temperature. This additional calibration process ensures that the flowmeter operates within the desired accuracy at temperatures near this new calibration temperature. However, if the ambient temperature is significantly reduced (or increased), the accuracy of the flow meter is adversely affected.

In accordance with an embodiment of the present invention, meter electronics for flow meter geometric thermal compensation is provided. The instrument electronics includes an interface configured to receive a flow meter sensor signal and a temperature signal (T). The meter electronics is also coupled to the interface and configured to receive the sensor signal and the temperature signal, and the temperature signal (T) is used to geometrically compensate the thermal coefficient for one or more flow lines of the flow meter. A processing system for calculating (TF _e ) is provided. A geometric thermal compensation factor (TF _e ) is used to process the first and second sensor signals.

According to an embodiment of the present invention, a method for geometric thermal compensation in a flow meter is provided. The method receives a flow meter sensor signal and a temperature signal and uses the temperature signal (T) to determine a geometric thermal compensation factor (TF _e ) for one or more flow lines of the flow meter. Including calculating. A geometric thermal compensation factor (TF _e ) is used to process the first and second sensor signals.

According to an embodiment of the present invention, a method for geometric thermal compensation in a flow meter is provided. The method receives a flow meter sensor signal and a temperature signal and uses the temperature signal (T) to determine a geometric thermal compensation factor (TF _e ) for one or more flow lines of the flow meter. Including calculating. Further, the method includes calculating both or one of the thermally compensated density and the thermally compensated mass flow rate. A geometric thermal compensation factor (TF _e ) is used to process the first and second sensor signals.

In one aspect of the aspect meter electronics, the geometric thermal compensation factor (TF _e ) comprises a linear equation.
In another aspect of the meter electronics, the geometric thermal compensation factor (TF _e ) includes a polynomial.

In yet another aspect of the meter electronics, the meter electronics further comprises a storage system configured to store a geometric thermal compensation factor (TF _e ).
In another aspect of the meter electronics, the meter electronics further comprises a storage system configured to store density and mass flow.

In yet another aspect of the meter electronics, the processing system is configured to use the temperature signal (T) to calculate a geometric thermal compensation factor (TF _e ) for one or more flow lines of the flow meter. The

In yet another aspect of the instrument electronics, the geometric thermal compensation factor includes a temperature difference (ΔT) between a reference temperature (T ₀ ) and a temperature signal (T).
In yet another aspect of the meter electronics, the processing system is configured to calculate one or more flow characteristics from the sensor signal and a geometric thermal compensation factor (TF _e ).

In yet another aspect of the meter electronics, the processing system is configured to calculate a thermally compensated density.
In yet another aspect of the meter electronics, the processing system comprises a formula

And is configured to calculate a thermally compensated density. However, the (TF _e ) term includes the primary thermal expansion coefficient α.
In yet another aspect of the meter electronics, the (TF _y ) term includes an elastic modulus thermal compensation term.

In yet another aspect of the instrument electronics, the processing system is configured to calculate a thermally compensated mass flow rate.
In yet another aspect of the meter electronics, the processing system comprises a formula

Is configured to calculate a thermally compensated mass flow rate. However, the (TF _e ) term includes the primary thermal expansion coefficient α.
In yet another aspect of the meter electronics, the (TF _y ) term includes an elastic modulus thermal compensation term.

In one aspect of the method, the geometric thermal compensation factor (TF _e ) comprises a linear equation.
In another aspect of the method, the geometric thermal compensation factor (TFe) comprises a polynomial.
In yet another aspect of the method, calculating comprises calculating a geometric thermal compensation factor (TF _e ) for the one or more flow lines using the temperature signal (T) and the primary thermal expansion coefficient α or polynomial. Further comprising.

In yet another aspect of the method, the geometric thermal compensation factor includes a temperature difference (ΔT) between a reference temperature (T ₀ ) and a temperature signal (T).
In yet another aspect of the method, the method further includes calculating one or more flow characteristics from the sensor signal and a geometric thermal compensation factor (TF _e ).

In yet another aspect of the method, the method further comprises calculating a thermally compensated density.
In yet another embodiment of the method, the method has the formula

And further calculating a thermally compensated density. However, the (TF _e ) term includes the primary thermal expansion coefficient α.
In yet another aspect of the method, the (TF _y ) term includes an elastic modulus thermal compensation term.

In yet another aspect of the method, the method further comprises calculating a thermally compensated mass flow rate.
In yet another embodiment of the method, the method has the formula

And further calculating a thermally compensated mass flow rate. However, the (TF _e ) term includes the primary thermal expansion coefficient α.
In yet another aspect of the method, the (TF _y ) term includes an elastic modulus thermal compensation term.

FIG. 2 is a diagram showing a Coriolis flow meter comprising a flow meter assembly and instrument electronics. It is a figure which shows the meter electronic device of the flowmeter which concerns on embodiment of invention. It is a flowchart of the method of operating the flowmeter which concerns on embodiment of invention.

  1-3 and its description provide specific examples that teach those skilled in the art how to make and use the best mode of the invention. For the purpose of teaching inventive principles, some conventional aspects have been simplified or omitted. As those skilled in the art will appreciate, variations on these examples are within the scope of the invention. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of the invention. As a result, the invention is not limited to the specific examples described below, but only by the claims and their equivalents.

  FIG. 1 shows a Coriolis flow meter 5 comprising a flow meter assembly 10 and a meter electronics 20. Instrument electronics 20 is connected to flow meter assembly 10 via lead 100 to provide density, mass flow, volume flow, total mass flow, temperature, and other information via path 26. As will be apparent to those skilled in the art, the present invention can be used with any type of Coriolis flow meter 5 regardless of the number of drives, pick-off sensors and flow lines and operating vibration modes. The construction of the Coriolis flow meter 5 will be described, although it will be apparent to those skilled in the art that the present invention can be implemented as a vibrating tube densimeter without the additional measurement capability provided by the Coriolis flow meter 5.

  The flow meter assembly 10 includes a pair of flanges 101, 101 ', manifolds 150, 150', a drive device 180, pick-off sensors 170L, 170R, and flow lines 130, 130 '. Drive device 180 and pickoff sensors 170L, 170R are connected to flow lines 130, 130 '.

  When the flow meter assembly 10 is inserted into a pipeline system (not shown) carrying the material to be measured, the material enters the flow meter assembly 10 through the flange 101, passes through the inlet side manifold 150, Reorient so that the entire amount of material enters the flow lines 130, 130 ', flow through the flow lines 130, 130', return to the outlet manifold 150 ', and from the flow meter assembly 10 through the flange 101'. Get out.

  The flow lines 130, 130 ′ are selected to have substantially the same mass distribution, moment of inertia and elastic modulus with respect to their respective bending axes WW, W′-W ′, and the inlet side manifold 150 and outlet side Appropriately attached to the manifold 150 '.

  The flow lines 130, 130 ′ are driven by the drive device 180 in the opposite direction with respect to the respective bending axes W, W ′ and in the so-called first out-of-phase bending mode of the flow meter 5. The drive device 180 comprises one of many known devices, such as a magnet attached to the flow line 130 and a counter coil attached to the flow line 130 '. When alternating current is passed through the opposing coil, both lines are vibrated. An appropriate drive signal is applied from the instrument electronic device 20 to the drive device 180 via the lead wire 186.

  Instrument electronics 20 receives sensor signals on leads 165L, 165R. Instrument electronics 20 generates a drive signal on lead 185, which causes drive 180 to vibrate conduits 130, 130 '. The meter electronics 20 receives a temperature signal from a resistance temperature device (RTD) 190 that performs ambient temperature measurements. A temperature signal is received from RTD 190 via lead 195. The meter electronics 20 processes the right and left temperature signals from the pickoff sensors 170L, 170R to calculate the mass flow rate. Path 26 provides an input / output means for instrument electronics 20 to interface with the operator. The description of FIG. 1 is provided merely as an example of the operation of the flow meter 5 and does not limit the teaching of the present invention.

  FIG. 2 shows the meter electronics 20 of the flow meter 5 according to an embodiment of the invention. The meter electronics 20 includes an interface 23 and a processing system 24 and can further include a storage system 25.

  Interface 23 is configured to receive signals from flow meter assembly 10 and communicate those signals to processing system 24. For example, the interface 23 is configured to receive a first sensor signal from the first pickoff sensor 170L and a second sensor signal from the second pickoff sensor 170R. The interface 23 is also configured to receive and store the temperature signal 32 from the RTD 190. The temperature signal 32 includes a measurement of the ambient temperature of the flow lines 130, 130 '.

The processing system 24 receives and stores the first and second sensor signals 31 and the temperature signal 32. The processing system 24 also includes a primary coefficient of thermal expansion (α) 33. The primary coefficient of thermal expansion (α) 33 represents the change in geometric size due to temperature, more suitably due to temperature change. Thus, the primary coefficient of thermal expansion (α) 33 can include a linear function of temperature, or can include a polynomial function of temperature. For the purposes of the invention, the temperature change is the change in temperature (T) from the reference temperature or calibration temperature (T ₀ ), ie the value T−T ₀ .

  The primary coefficient of thermal expansion (α) 33 includes a flow line eigenvalue. The primary coefficient of thermal expansion (α) 33 is selected according to at least the material of the flow lines 130, 130 ′ of the flow meter assembly 10. Further, the primary coefficient of thermal expansion (α) 33 may be selected according to other characteristics of the flow meter assembly 10, such as the shape of the tube, the thickness of the wall surface, and the like.

The primary thermal expansion coefficient (α) 33 includes an element called a geometric thermal compensation coefficient (TF _e ) 45. The geometric thermal compensation factor (TF _e ) 45 is used to perform geometric compensation due to thermal expansion and contraction of the flow meter assembly 10. Accordingly, the geometric thermal compensation factor (TF _e ) 45 may be formed according to the material and characteristics of the flow meter assembly 10. The geometric thermal compensation coefficient (TF _e ) 45 will be described in detail later.

  The processing system 24 is configured to calculate one or more flow characteristics and one or more flow measurements from the sensor signal 31. The flow measurements may include one or more of mass flow 35, density 34, etc. The flow characteristics can include one or more of the frequency (f), phase difference (Δθ), time delay (Δt), etc. used to generate the flow measurement.

In one embodiment, the processing system 24 is configured to use the temperature signal 34 to calculate a geometric thermal compensation factor (TF _e ) 45 in one or more flow lines 130, 130 ′. Is done. A geometric thermal compensation factor (TF _e ) 45 is used to process the sensor signal 31.

In some embodiments, the geometric thermal compensation factor (TF _e ) 45 can include a primary compensation factor represented, for example, as a (1 + α · ΔT) term. The first order compensation of (TF _e ) can include a first order approximation of geometric thermal expansion. In some embodiments, the primary compensation factor (TF _e ) provides sufficient accuracy. However, the geometric thermal expansion or contraction is not strictly linear, and in certain embodiments, the first order approximation does not achieve the desired accuracy. Thus, in some embodiments, the geometric thermal compensation factor (TF _e ) 45 includes a polynomial as has been done for Young's modulus (E) (see equation (3)). The multinomial compensation coefficient is expressed, for example, as a (1 + α ₁ · ΔT + α ₂ · ΔT ² + α ₃ · ΔT ³ ) term.

In one embodiment, the processing system 24 is configured to calculate a geometric thermal compensation factor (TF _e ) 45 in the one or more flow lines 130, 130 ′ using the temperature signal and The geometric thermal compensation factor (TF _e ) 45 is used to calculate the thermally compensated density. In one embodiment, the processing system 24 is configured to calculate a geometric thermal compensation factor (TF _e ) 45 in the one or more flow lines using the temperature signal, and the geometric system. A thermal compensation factor (TF _e ) 45 is used to calculate a thermally compensated mass flow rate. A geometric thermal compensation factor (TF _e ) 45 can also compensate for other flow characteristics.

The storage system 25 can store received signals and data. For example, the storage system 25 can store the received sensor signal 31 and the received temperature signal 32. The storage system 25 can store constants used for calculation. For example, the storage system 25 can store a reference temperature (T ₀ ) 36, a stiffness value (K) 38, a first constant C ₁ 39, a second constant C ₂ 40, and an FCF value 37. Storage system 25 can store calculated values including density 34, mass flow rate 35, and geometric thermal compensation factor (TF _e ) 45. If desired, additional calculated values can be stored in the storage system 25.

According to certain embodiments of the invention, thermal expansion or contraction terms are included in the density and mass flow equations for the flow meter, in addition to elastic modulus compensation. Equations 6-14 below show the derivation of the geometric thermal compensation including the geometric thermal compensation factor (TF _e ) 45. Equations 15 through 19 show how the terms are included when processing the sensor signal of the flow meter 5.

  The physical operation of the Coriolis flowmeter is well approximated by beam theory. The natural frequency of Euler Bernoulli's beam is:

Given by. The (E) term is the elastic modulus of the beam, the (I) term is the area moment of inertia of the beam, and the (M / l) term is the mass per unit length of the beam (tube) and the fluid it contains. Where the (l) term is the length of the beam and the (β _n l) ² term is a constant that depends on the boundary conditions of the beam.

  The mass per unit length (M / l) expressed using the density (ρ) and the cross-sectional area (A) is expressed by the following formula 7,

Given by. The subscript indicates a flow line or tube (t) and fluid (f).
Elastic modulus (E) varies with temperature. Equation 8 below:

Represents the modulus of elasticity as a function of temperature. This is shown to be linear, but can be represented by a higher order polynomial. The term (E ₀ ) is the elastic modulus at the reference temperature (T ₀ ). As discussed above, the (TF _y ) term is the Young's modulus, and is a linear approximation (1-φ · (T−T ₀ )) or polynomial (1−φ · ΔT−φ ₂ · ΔT ² −φ ₃ · ΔT ³ −φ ₄ · ΔT ⁴ ).

  The tube size varies with temperature due to thermal expansion. Equation 9 below:

Is the equation for the pipe length (l) as a function of temperature. Although this is shown to be linear, it can be represented by a higher order polynomial, similar to the elastic modulus.
The l ₀ term is the length at the reference temperature T ₀ and the (TF _e ) term is the geometric thermal expansion coefficient. Again, the (TF _e ) term includes a geometric thermal expansion coefficient that includes (T−T ₀ , ie ΔT) and (α) terms. The α term contains the primary coefficient of thermal expansion introduced in accordance with the present invention. The α term is introduced to thermally compensate for geometric expansion and contraction.

This relationship can be applied to other dimensions such as inner and outer diameters. The inner and outer diameters are used to calculate the cross-sectional area A _t (T) of the pipe, the cross-sectional area A _f (t) of the fluid, and the moment of inertia I (t) as shown in the following equations 10 to 12. It is done.

The term d _o is the outer diameter of the tube, and the term d _i is the inner diameter.
Since the mass of the tube does not change with temperature, its density must decrease with volume expansion. The density (ρ _t ) of the tube as a function of temperature is

Given by. The ρ _t0 term is the density of the flow line at the reference temperature (T ₀ ). The tube period (K) is expressed by the following equation 14,

As inversely proportional to the natural frequency (ω _n ).
Using Equations 6-14, the fluid density (ρ _f ) is given by Equation 15 below:

As given by the tube period (K), temperature (T), change in elastic modulus with respect to temperature (φ) and geometric thermal compensation factor (TF _e ). The C ₁ and C ₂ terms are constants that are independent of temperature and are related to the shape and material properties of the flow line at the reference temperature. The (TF _y ) and (TF _e ) terms include a (ΔT) term that includes the difference between the temperature (T) and the reference temperature (T ₀ ). Further, the (TF _e ) term includes the primary thermal expansion coefficient (α).

  The phase angle difference (Δθ) between the two points of the beam carrying the fluid due to the Coriolis force is given by

It has the shape given by The x term represents the position along the length of the beam, given by the length (l),

The term is the mass flow rate and the other variables are predefined.
The time delay (Δt) is given by Equation 17 below:

As related to the phase difference (Δθ). From Equation 6 to Equation 16, the time delay (Δt) is given by Equation 18 below:

Mass flow rate as given by

And a constant (C). The C term is a constant based on two points where the time delay (Δt) is measured.
Mass flow rate

Is:

As expressed by the time delay (Δt), temperature (T), change in elastic modulus with respect to temperature (φ), and geometric thermal compensation factor (TF _e ). The FCF term includes a substantially constant value that is independent of temperature and related to the shape and material properties of the tube at the reference temperature (T ₀ ). The (ΔT) value is the difference between the temperature (T) and the reference temperature (T ₀ ).

  The mass flow error introduced by not properly compensating for geometrical thermal expansion and contraction is not significant if all other variables are properly characterized and temperature measurements are accurate. In contrast, however, density errors are perceptible when geometrical thermal changes are not considered. Inaccuracies in mass flow and density become more pronounced as the ambient temperature moves away from the reference temperature.

A novel method for calculating mass flow and density improves the accuracy of Coriolis flow meters and vibration density meters by compensating for thermal expansion and contraction. If the density of the fluid is different from the density of water and the temperature is not near the reference temperature (T ₀ ), the advantage of density measurement accuracy is significant.

  FIG. 3 is a flow diagram 300 of a method for operating the flow meter 5 according to an embodiment of the present invention. In step 301, sensor signal 31 is received. In some embodiments, first and second sensor signals 31 are received from the flow meter.

In step 302, the meter electronics receives a temperature signal from the flow meter assembly 10. The temperature substantially includes ambient temperature. In step 303, the instrument electronics calculates a geometric thermal compensation factor (TF _e ) as previously discussed. The geometric thermal compensation factor compensates the flow characteristics for thermal expansion or contraction of the shape of the flow line. Thermal expansion or contraction includes, for example, a change in cross-sectional size and / or length of the flow line.

In step 304, one or more flow characteristics are calculated using the geometric thermal compensation factor (TF _e ). As discussed above, the compensated density value of the fluid can be calculated. As discussed above, a compensated mass flow value of the fluid can be calculated.

  Temperature compensation results in improved accuracy. Temperature compensation provides improved accuracy over substantially the entire operating temperature range of the flow meter. Temperature compensation provides more accurate compensation for mass flow measurements. Temperature compensation provides more accurate compensation of density. Temperature compensation improves the analysis of test results when the temperature varies between tests.

Claims (12)

An instrument electronics (20) for geometric thermal compensation in a vibratory flow meter (5) comprising one or more vibratory sensor signals and a temperature signal T of the vibratory flow meter (5). In an instrument electronics (20) comprising an interface (23) configured to receive:
Coupled with the interface (23) and configured to receive the one or more vibration type sensor signals and the temperature signal (T), and using the temperature signal (T), the vibration type flow meter (5 A processing system (24) for calculating a geometric thermal compensation factor (TF _e ) of one or more flow lines (130, 130 ′) of
The geometric thermal compensation factor (TF _e ) is used to process one or more vibration type sensor signals;
The geometric thermal compensation factor (TF _e) is, only contains the high-order polynomial expression,
The processing system 24 has the formula

And the (TF _e ) term includes the primary coefficient of thermal expansion (α), K is the tube period, and C ₁ and C ₂ are the calibration constants. There, [rho _f is the fluid density, TF _y is the Young's modulus, the Tf _e a geometric thermal compensation factor,
Instrument electronics. The instrument electronics of claim 1 , wherein the (TF _y ) term includes an elastic modulus thermal compensation term. An instrument electronics (20) for geometric thermal compensation in a vibratory flow meter (5) comprising one or more vibratory sensor signals and a temperature signal T of the vibratory flow meter (5). In an instrument electronics (20) comprising an interface (23) configured to receive:
Coupled with the interface (23) and configured to receive the one or more vibration type sensor signals and the temperature signal (T), and using the temperature signal (T), the vibration type flow meter (5 A processing system (24) for calculating a geometric thermal compensation factor (TF _e ) of one or more flow lines (130, 130 ′) of
The geometric thermal compensation factor (TF _e ) is used to process one or more vibration type sensor signals;
The geometric thermal compensation factor (TF _e) is, only contains the high-order polynomial expression,
The processing system (24) has the formula

, Wherein the (TF _e ) term includes a primary thermal expansion coefficient (α), FCF is a flow compensation coefficient, and ΔT is one or more Is the time delay of the vibration sensor signal, K is the tube period,

Is the mass flow rate, TF _y is the Young's modulus, Tf _e is the geometric thermal compensation factor,
Instrument electronics. The instrument electronics of claim 3 , wherein the (TF _y ) term includes an elastic modulus thermal compensation term. A method for geometric thermal compensation in a vibratory flow meter, the method comprising receiving one or more vibratory sensor signals and a temperature signal (T) of the vibratory flow meter.
Using the temperature signal (T) to calculate a geometric thermal compensation factor (TF _e ) of one or more flow lines of the vibratory flow meter;
The geometric thermal compensation factor (TF _e ) is used to process one or more vibration type sensor signals;
The geometric thermal compensation factor (TF _e) is, only contains the high-order polynomial expression,
formula

, Further comprising the step of calculating a thermally compensated density, wherein the (TF _e ) term includes a primary coefficient of thermal expansion (α), K is the tube period, and C ₁ and C ₂ are calibration constants. in and, [rho _f is the density of the fluid, TF _y is the Young's modulus, the Tf _e a geometric thermal compensation factor,
Method. The method of claim 5 , wherein the (TF _y ) term comprises an elastic modulus thermal compensation term. A method for geometric thermal compensation in a vibratory flow meter, the method comprising receiving one or more vibratory sensor signals and a temperature signal (T) of the vibratory flow meter.
Using the temperature signal (T) to calculate a geometric thermal compensation factor (TF _e ) of one or more flow lines of the vibratory flow meter;
The geometric thermal compensation factor (TF _e ) is used to process one or more vibration type sensor signals;
The geometric thermal compensation factor (TF _e) is, only contains the high-order polynomial expression,
formula

, Wherein the (TF _e ) term includes a primary coefficient of thermal expansion (α), FCF is a flow compensation factor, and ΔT is one or more. Is the time delay of the vibration type sensor signal, K is the tube period,

Is the mass flow rate, TF _y is the Young's modulus, Tf _e is the geometric thermal compensation factor,
Method. The method of claim 7 , wherein the (TF _y ) term comprises an elastic modulus thermal compensation term. A method for geometric thermal compensation in a vibratory flow meter, the method comprising receiving one or more vibratory sensor signals and a temperature signal (T) of the vibratory flow meter.
Using the temperature signal (T) to calculate a geometric thermal compensation factor (TF _e ) of one or more flow lines of the vibratory flow meter, the geometric thermal compensation factor (TF _e ) TF _e ) includes a higher order polynomial representation,
Calculating at least one of a thermally compensated density and a thermally compensated mass flow rate;
With
The geometric thermal compensation factor (TF _e ) is used to process one or more vibration type sensor signals ;
The step of calculating the thermally compensated density comprises the equation

, Further comprising the step of calculating a thermally compensated density, wherein the (TF _e ) term includes a primary coefficient of thermal expansion (α), K is the tube period, and C ₁ and C ₂ are calibration constants. in and, [rho _f is the density of the fluid, TF _y is the Young's modulus, the Tf _e a geometric thermal compensation factor,
Method. The method of claim 9 , wherein the (TF _y ) term comprises an elastic modulus thermal compensation term. A method for geometric thermal compensation in a vibratory flow meter, the method comprising receiving one or more vibratory sensor signals and a temperature signal (T) of the vibratory flow meter.
Using the temperature signal (T) to calculate a geometric thermal compensation factor (TF _e ) of one or more flow lines of the vibratory flow meter, the geometric thermal compensation factor (TF _e ) TF _e ) includes a higher order polynomial representation,
Calculating at least one of a thermally compensated density and a thermally compensated mass flow rate;
With
The geometric thermal compensation factor (TF _e ) is used to process one or more vibration type sensor signals ;
Said step of calculating the thermally compensated mass flow comprises the equation

, Wherein the (TF _e ) term includes a primary coefficient of thermal expansion (α), FCF is a flow compensation factor, and ΔT is one or more. Is the time delay of the vibration type sensor signal, K is the tube period,

Is the mass flow rate, TF _y is the Young's modulus, Tf _e is the geometric thermal compensation factor,
Method. The method of claim 11 , wherein the (TF _y ) term comprises an elastic modulus thermal compensation term.

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