Vibronic measuring system for measuring a mass flow rate

Abstract

A measuring system comprises a measuring and operation electronic unit (ME) and a transducer device electrically coupled thereto. The transducer device has two tubes through which a fluid flows and causes to vibrate, a vibration exciter, two vibration sensors on the inlet and outlet sides, respectively, for generating vibration signals, and an inlet-side temperature sensor coupled to a wall of the tube for thermal conduction and an outlet-side temperature sensor coupled to a wall of the tube for generating temperature measurement signals. The measuring and operation electronic unit feeds electrical power into the vibration exciter in order to effect mechanical vibrations of the tube. Furthermore, the ME generates a mass flow sequence, by means of each of the vibration signals and each of the temperature measurement signals in such a way that mass flow measurement values are independent of the temperature difference.

Claims

1. A vibronic measuring system for measuring a mass flow rate of a fluid, said measuring system comprising: a measuring and operation electronics unit; and a transducer device electrically coupled to said measuring and operation electronics unit, wherein the transducer device includes: a first tube comprising a lumen surrounded by a wall and extending from an inlet-side first end to an outlet-side second end, said first tube adapted to be flowed through at least by a partial volume of the fluid from the first end toward the second end and in the process is caused to vibrate; a second tube comprising a lumen surrounded by a wall extending from an inlet-side first end to an outlet-side second end, said second tube adapted to be flowed through by fluid from the first end toward the second end and in the process to be caused to vibrate simultaneously with or mirror-invertedly to the first tube; a first temperature sensor which is coupled thermally conductively to the wall of the first tube, wherein said first temperature sensor is positioned less far from the first end of the first tube than from the second end of said first tube, and wherein said first temperature sensor is adapted to sense a first measuring point temperature, which is a temperature of the wall of the first tube at an inlet-side first temperature measuring point, and to convert the first measuring point temperature into a first temperature measurement signal representing the first measuring point temperature; a second temperature sensor which is thermally conductively coupled to the wall of the second tube, wherein said second temperature sensor is positioned less far from the second end of the second tube than from the first end of said second tube, and and wherein said second temperature sensor is adapted to sense a second measuring point temperature, which is a temperature of the wall of the second tube at a second temperature measuring point remote from the first temperature measuring point and/or on the outlet side, and to convert the second measuring point temperature into a second temperature measurement signal representing the second measuring point temperature; at least one vibration exciter configured to excite and maintain mechanical vibrations of both the first tube and second tube about an associated static rest position; a first vibration sensor configured to detect vibration movements of the first and second tubes and positioned less far from the first end of the first tube than from the second end of said first tube, and wherein said first vibration sensor is adapted to detect the vibration movements at an inlet-side first vibration measuring point and to generate a first vibration signal representing the vibration movements; and a second vibration sensor configured to detect the vibration movements of the first and second tubes and positioned less far from the second end of the first tube than from the first end of said first tube wherein said second vibration sensor is adapted to detect the vibration movements at an outlet-side second vibration measuring point and to generate a second vibration signal representing said vibration movements such that between the first vibration signal and said second vibration signal exists a phase difference which depends on both the mass flow rate and a temperature difference defined between a temperature of the first vibration sensor and a temperature of said second vibration sensor, wherein the first temperature sensor is positioned at the same distance from the first vibration sensor as the second temperature sensor from the second vibration sensor, and wherein the temperature of the first vibration sensor is calculated based on the first temperature measurement signal and the temperature of the second vibration sensor is calculated based on the second temperature measurement signal, wherein the measuring and operation electronics unit is electrically connected to each of the first and second vibration sensors, to each of the first and second temperature sensors and to the at least one vibration exciter, wherein the measuring and operation electronics unit is adapted to feed electrical power into the at least one vibration exciter via an electrical exciter signal to effect mechanical vibrations of both the first tube and the second tube, and wherein the measuring and operation electronics unit is adapted to generate, using each of the first and second vibration signals and each of the first and second temperature measurement signals, a mass flow sequence defined by a series of temporally successive mass flow measurement values respectively instantaneously representing the mass flow rate of the fluid such that the mass flow measurement values, at least for a reference mass flow rate defining a specified mass flow rate of a reference fluid flowing through the transducer device, are independent of the temperature difference.

2. The vibronic measuring system according to claim 1, wherein the measuring and operation electronics unit is adapted: to determine the mass flow measurement values such that a mass flow measurement value determined for the reference mass flow rate satisfies a condition: $x_{m,\mathrm{ref}}=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(\right)}^j=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(1-2\right)}^j\mathrm{with}j=0,1,2,\mathrm{.Math.}N;$ and/or to determine the mass flow measurement values such that, in case of a transducer device through which no fluid flows or a first tube through which no fluid flows, temporally successively determined mass flow measurement values satisfy a condition: $C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(\right)}^j=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(1-2\right)}^j<0\text{.}01\mathrm{kg}/h\mathrm{with}j=0,1,2,\mathrm{.Math.}N;$ and/or to generate, using at least one of the first and second vibration signals and at least one of the first and second temperature measurement signals, a density measurement value which represents a density of the fluid; and/or to generate, using at least one of the first and second vibration signals and at least one of the first and second temperature measurement signals, a viscosity measurement value which represents a viscosity of the fluid; and/or to generate, using both the first temperature measurement signal and the second temperature measurement signal, a measurement fluid temperature measurement value representing a temperature of a fluid flowing through the first tube.

3. The vibronic measuring system according to claim 1, wherein the reference fluid is water.

4. The vibronic measuring system according to claim 3, wherein the reference mass flow is, depending on a magnitude of a nominal width of the transducer device given in the SI base unit for length, less than 10000 kg/h.

5. The vibronic measuring system according to claim 1, wherein the reference fluid is an oil.

6. The vibronic measuring system according to claim 1, wherein the reference fluid is a gas.

7. The vibronic measuring system according to claim 6, wherein the reference mass flow rate is, depending on a magnitude of a nominal width of the transducer device given in the SI base unit for length, less than 1000 kg/h.

8. The vibronic measuring system according to claim 1, wherein the temperature difference is greater in the case of an inside, facing the lumen, of a wall with an undesired deposition than in the case of an intact first tube.

9. The vibronic measuring system according to claim 1, wherein the measuring and operation electronics unit is adapted to generate, using both the first temperature measurement signal and the second temperature measurement signal, a temperature difference sequence defined by a series of temporally successive temperature difference measurement values respectively representing the temperature difference.

10. The vibronic measuring system according to claim 9, wherein the measuring and operation electronics unit is adapted to generate the mass flow sequence using both the temperature difference sequence and a phase difference sequence defined by a series of temporally successive phase difference measurement values respectively representing the phase difference generated using both the first vibration signal and the second vibration signal.

11. The vibronic measuring system according to claim 9, wherein the measuring and operation electronics unit is adapted to monitor, using the temperature difference sequence, a functionality of the transducer device.

12. The vibronic measuring system according to claim 1, wherein the measuring and operation electronics unit is adapted to generate, using both the first vibration signal and the second vibration signal, a phase difference sequence defined by a series of temporally successive phase difference measurement values respectively representing the phase difference.

13. The vibronic measuring system according to claim 1, wherein the first temperature sensor and the second temperature sensor are identical in design; and/or wherein the first temperature sensor is mechanically coupled to the wall of the first tube in the same way as the second temperature sensor; and/or wherein the transducer device has no other temperature sensor contacting the wall of the first tube than the first temperature sensor; and/or wherein the transducer device has no other temperature sensor contacting the wall of the second tube than the second temperature sensor; and/or wherein the first temperature sensor is coupled thermally conductively to the wall of the first tube in the same way as the second temperature sensor.

14. The vibronic measuring system according to claim 1, wherein a vibration sensor arrangement of the first vibration sensor and the second vibration sensor is mirror-symmetric with respect to at least one imaginary symmetry axis, which imaginarily intersects the transducer device; and/or wherein the first vibration sensor is thermally conductively coupled to the wall of the first tube and/or the wall of the second tube in the same way as the second vibration sensor.

15. The vibronic measuring system according to claim 1, wherein the first tube is mirror-symmetric with respect to at least one imaginary symmetry axis, which imaginarily intersects the tube; and/or wherein a temperature sensor arrangement of the first temperature sensor and the second temperature sensor is axially symmetric with respect to at least one imaginary symmetry axis, which imaginarily intersects the transducer device; and/or wherein the first tube is curved; or wherein the first tube is straight; and/or wherein the wall of the first tube consists at least partially of a material of which a specific thermal conductivity is more than 10 W/(m.Math.K) and of which a specific heat capacity is less than 1000 J/(kg.Math.K); and/or wherein the wall of the first tube consists of metal; and/or wherein an unwound tube length of the first tube is more than 300 mm; and/or wherein the reference fluid has a specific heat capacity of more than 1 kJ.Math.kg.sup.1.Math.K.sup.1 and/or less than 4.2 kJ.Math.kg.sup.1.Math.K.sup.1; and/or wherein the first tube shows a caliber which is more than 0.1 mm (millimeters).

16. The vibronic measuring system according to claim 1, further comprising: an inlet-side first flow divider and an outlet-side second flow divider, wherein both the first tube and second tube, forming fluidically parallel connected flow paths, are connected to the first and second flow dividers such that the first tube opens with its first end into a first flow opening of the first flow divider and with its second end into a first flow opening of the second flow divider, and such that the second tube opens with its first end into a second flow opening of the first flow divider and with its second end into a second flow opening of the second flow divider.

17. The vibronic measuring system according to claim 16, wherein both the first flow divider and the second flow divider are respectively an integral component of the transducer housing.

18. The vibronic measuring system according to claim 1, further comprising: a transducer housing including a cavity surrounded by a wall, wherein at least the first tube is arranged within the cavity of the transducer housing such that an intermediate space is formed between an inner surface, facing the cavity, of the wall of the transducer housing and a lateral surface, facing the cavity, of the wall of the first tube, and wherein the transducer housing and the first tube are adapted to hold in the intermediate space a fluid, forming a fluid volume surrounding the first tube, such that the lateral surface, forming an interface between a fluid and a solid phase, is contacted.

19. The vibronic measuring system according to claim 1, further comprising: an inlet-side first connecting flange serving in particular to connect the transducer device to a line segment of a process line supplying the fluid; and an outlet-side second connecting flange configured to connect the transducer device to a line segment of a process line discharging the fluid again.

20. The vibronic measuring system according to claim 19, wherein each of the connecting flanges respectively comprises a sealing surface for the fluid-tight or leak-free connection of the transducer device to a respectively corresponding line segment of a process line, and wherein a shortest distance between said sealing surfaces defines an installation length of the transducer device, said installation length amounting to more than 250 mm and/or less than 3000 mm.

21. The vibronic measuring system according to claim 20, wherein a tube length to installation length ratio of the transducer device, defined by a ratio of an unwound tube length of the first tube to the installation length, of the transducer device is more than 1.2.

22. The vibronic measuring system according to claim 1, wherein the first temperature sensor includes a first temperature probe and a first coupling body coupling said first temperature probe thermally conductively to the wall of the first tube, and wherein the second temperature sensor includes a second temperature probe and a second coupling body coupling said second temperature probe thermally conductively to the wall of the second tube.

23. The vibronic measuring system according to claim 22, wherein the first temperature probe and the second temperature probe are identical in design; and/or wherein the first coupling body and the second coupling body are identical in design; and/or wherein the first coupling body is formed of a plastic, which is placed between the wall of the first tube and the first temperature probe, and wherein the second coupling body is formed of a plastic, which is placed between the wall of the second tube and the second temperature probe.

24. The vibronic measuring system according to claim 1, wherein the measuring and operation electronics unit comprises a multiplexer including at least two signal inputs and at least one signal output, said multiplexer adapted to optionally switch one of its signal inputs through to the signal output such that a signal applied to the respectively switched-through signal input is passed to the signal output, and wherein the measuring and operation electronics unit comprises an analog-to-digital converter with at least one signal input and at least one signal output, which analog-to-digital converter is designed to convert an analog input signal applied to said signal input with a sampling rate and with a digital resolution into a digital output signal representing said input signal and to provide it at the signal output.

25. The vibronic measuring system according to claim 24, wherein the at least one signal output of the multiplexer and the at least one signal input of the analog-to-digital converter are electrically coupled to each other, and wherein the first temperature sensor and the second temperature sensor are respectively electrically connected to the multiplexer such that the temperature measurement signal is applied to a first signal input of the multiplexer and that the temperature measurement signal is applied to a second signal input of the multiplexer.

26. The vibronic measuring system according to claim 24, wherein the output signal of the analog-to-digital converter temporarily represents exactly one of the two temperature measurement signals.

27. The vibronic measuring system according to claim 26, wherein the measuring and operation electronics unit is adapted to generate the mass flow measurement value using the output signal, representing one of the two temperature measurement signals, of the analog-to-digital converter.

28. The vibronic measuring system according to claim 1, wherein the measuring and operation electronics unit is adapted to generate, using both the first temperature measurement signal and the second temperature measurement signal, a transducer temperature measurement value, which represents a transducer device temperature, which deviates both from the first measuring point temperature and from the second measuring point temperature such that the a magnitude of said transducer temperature measurement value corresponds to an arithmetic mean of the first and second measuring point temperatures and/or to a weighted average of the first and second measuring point temperatures and/or represents an average tube wall temperature of the first tube.

29. The vibronic measuring system according to claim 28, wherein the measuring and operation electronics unit is adapted to generate, using the first temperature measurement signal although not the second temperature measurement signal, an auxiliary temperature measurement value which at least approximately represents the measurement fluid temperature; and/or wherein the measuring and operation electronics unit is adapted to generate, using the second temperature measurement signal although not the first temperature measurement signal, an auxiliary temperature measurement value which at least approximately represents the measurement fluid temperature.

30. Use of a measuring system according to claim 1 to measure at least one physical measurement variable of a flowing fluid.

31. The vibronic measuring system according to claim 1, wherein the reference mass flow rate amounts not more than 1 kg/h; and/or wherein the reference mass flow rate is kept constant; and/or wherein the reference fluid shows a Reynolds number of less than 1000; and/or wherein the reference fluid shows a specific heat capacity of more 1 kJ.Math.kg.sup.1.Math.K.sup.1 and/or less than 4.2 kJ.Math.kg.sup.1.Math.K.sup.1.

32. The vibronic measuring system according to claim 1, wherein the mass flow measurement values respectively instantaneously representing the mass flow rate of the fluid such that the mass flow measurement values are independent of the temperature difference at least for the reference mass flow rate such that mass flow measurement values temporally successively determined for at least one reference mass flow rate, which is not zero although constant, deviate from each other by no more than 0.01% of said reference mass flow rate, including for temperature differences of more than 1 K and/or less than 10 K and/or temperature differences spreading over time with a range of more than 1 K and/or temperature differences changing over time with a rate of change of more than 0.05 K/s.

33. The vibronic measuring system according to claim 1, wherein the mass flow measurement values respectively instantaneously representing the mass flow rate of the fluid such that the mass flow measurement values are independent of the temperature difference at least for the reference mass flow rate such that mass flow measurement values representing a zero scale mark of the measuring and operation electronics unit, including mass flow measurement values temporally successively respectively determined in the case of a transducer device through which no fluid flows or respectively for a reference mass flow rate of zero, are less than 0.01 kg/h or deviate from each other by less than 0.01 kg/h, including for temperature differences of more than 1 K and/or less than 10 K and/or temperature differences spreading over time with a range of more than 1 K and/or less than 10 K and/or temperature differences changing over time with a rate of change of more than 0.05 K/s.

34. The vibronic measuring system according to claim 1, wherein the measuring and operation electronics unit is adapted to determine the mass flow measurement values such that a mass flow measurement value determined for the reference mass flow rate satisfies a condition: $x_{m,\mathrm{ref}}=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(\right)}^j\mathrm{with}N3,$ wherein x.sub.m,ref is the reference mass flow rate.

Description

(1) The invention as well as other advantageous embodiments thereof are explained in more detail below using exemplary embodiments shown in the figures of the drawing. The same parts are labeled with the same reference signs in all figures; for reasons of clarity or if it appears sensible for other reasons, reference signs used before are not repeated in the subsequent figures. Further advantageous embodiments or developments, in particular combinations of partial aspects of the invention that were originally explained separately may be derived from the figures in the drawing and from the sub-claims themselves. The figures show in detail:

(2) FIG. 1 a measuring system, in particular a measuring system suitable for use in industrial measurement and automation technology, with a transducer device having a transducer housing and with a measuring and operation electronics unit accommodated in an electronics housing, in this case fastened directly to the transducer housing;

(3) FIG. 2 a schematic illustration of an exemplary embodiment of a measuring system according to FIG. 1;

(4) FIG. 3a, 3b perspective side views of a transducer device suitable for a measuring system according to FIG. 1 or 2;

(5) FIG. 4 a sectional side view of a transducer device suitable for a measuring system according to FIG. 1 or 2;

(6) FIG. 5a, 5b different sectional side views of further exemplary embodiments for temperature sensors, in particular temperature sensors suitable for a transducer device according to FIGS. 3a, 3b or a measuring system according to FIG. 1;

(7) FIG. 6 a schematic illustration of another exemplary embodiment of a measuring system according to FIG. 1; and

(8) FIG. 7 a resistor network formed by means of a plurality of discrete heat resistors in the manner of an equivalent circuit and serving to explain heat flows flowing in a transducer device according to FIGS. 2, 3 or corresponding temperature drops within said transducer device.

(9) FIG. 1 shows a schematic illustration of a vibronic measuring system for measuring a mass flow rate m of the flowing fluid FL1 (measurement fluid), optionally having a temporally and/or spatially changing measurement fluid temperature .sub.FL1, such as a gas, a liquid or a flowable dispersion, or for recurrently determining of mass flow measurement values x.sub.m instantaneously representing said mass flow rate m. The measuring system may also be designed to determine at least one further measurement variable, namely, for example, a material parameter, of the fluid FL. Said further measurement variable may, for example, be a density , a viscosity or else a measurement fluid temperature .sub.FL1 of the fluid flowing, for example, through a pipeline.

(10) For this purpose, the measuring system comprises a transducer device MW for generating measurement signals serving at least to measure the mass flow rate and a measuring and operation electronics unit ME, which is electrically connected to said transducer device MW, is in particular supplied with electrical energy during operation by an external energy storage device via a connecting cable and/or by means of an internal energy storage device, for generating the measurement values representing the measurement variable(s) sensed by the transducer device or for sequentially outputting such measurement values x.sub.m as a respectively currently valid measurement value x.sub.x (x.sub.m.fwdarw.x.sub.x) of the measuring system to a corresponding measurement output, for example also in the form of digital measurement values and/or in real time.

(11) As shown schematically in FIG. 2 or as can be seen from a combination of FIGS. 1 and 2, the transducer device of the measuring system serves in particular to guide or to be flowed through by a partial volume of the fluid FL1 to be respectively measured during operation and to provide various measurement signals for physical measurement variables to be respectively sensed by means of the transducer device and for measuring point temperatures prevailing at various measuring points within the transducer device. For this purpose, the transducer device is equipped with a first tube 11, which comprises a lumen 11 surrounded by a wall and which is, for example, at least in sections curved and/or at least in sections straight, and a second tube 12, which comprises a lumen 11 surrounded by a wall and which is, for example, at least in sections curved and/or at least in sections straight. Said tube 12 may, for example, as also indicated in FIG. 2, 3a or 3b, or as readily apparent in the combination, be identical in design to the first tube 11 and/or be arranged parallelly to the first tube 11. The wall of the tube 11 or of the tube 12 can, as is common in transducer devices of the type in question, be metallic, namely, for example, at least partially consist of titanium, zirconium or tantalum or, for example, also of stainless steel. Each of the at least like [sic] tubes 11, 12 respectively extends, as inter alia indicated in FIG. 2, from an inlet-side first end 11a or 12a to an outlet-side second end 11b or 12b and is respectively designed to be flowed through by a fluid from the respective inlet-side first end 11a or 12a toward the outlet-side second end 11b or 12b and in the process is caused to vibrate, namely also such that the tubes 11, 12 vibrate simultaneously and/or mirror-invertedly.

(12) Furthermore, each of the tubes 11, 12, which are, for example, identical in design, of the transducer device according to the invention can be at least in sections straight, consequently in sections (hollow) cylindrical, namely, for example, circular cylindrical, and/or at least in sections curved, namely, for example, in a circular arc. Both the tube 11 and the tube 12 can furthermore respectively be designed to be mirror-symmetric with respect to at least one respective imaginary symmetry axis which imaginarily intersects the respective tube, namely, for example, coinciding with a main axis of inertia of said tube, namely, for example, to be V-shaped or U-shaped. A further embodiment of the invention furthermore provides for the wall of the tube 11 and/or the wall of the tube 12 to consist at least partially, for example also predominantly or entirely, of a material, a specific thermal conductivity 10 of which is more than 10 W/(m.Math.K) and a specific heat capacity cp10 of which is less than 1000 J/(kg.Math.K).

(13) In the transducer device according to the invention or the measuring system formed therewith, each of the tubes 11, 12 is provided or designed to be respectively flowed through by a partial volume of the fluid FL1 in a flow direction, namely, for example, starting from the end 11a toward the end 11b or starting from the end 12a toward the end 12b, and in the process is caused to vibrate; this in particular such that each of the tubes 11, 12 is respectively allowed to carry out useful vibrations, namely mechanical vibrations about an associated static rest position, which are suitable for inducing in the fluid flowing through, Coriolis forces dependent at least on the mass flow rate m of the fluid. In addition, the useful vibrations carried out by the tube 11 or tube 12 can also be suitable for effecting in the fluid, frictional forces dependent on the viscosity of the fluid and/or inertial forces dependent on the density of the fluid. The transducer device may accordingly, for example, also be designed as a transducer of the vibration type serving as a component of a vibronic measuring system, for example of a Coriolis mass flow measuring device, of a density measuring device and/or of a viscosity measuring device.

(14) As already indicated, said wall may, for example, consist of a metal or a metal alloy, namely, for example, titanium, zirconium or tantalum or a corresponding alloy thereof, a steel or a nickel-based alloy. Another embodiment of the invention furthermore provides that the wall of each of the tubes 11, 12 respectively has a wall thickness s which is more than 0.5 mm and/or an inner diameter which is more than 0.5 mm. Alternatively or additionally, each of the tubes may further be dimensioned such that it has an inner diameter to wall thickness ratio, defined as a ratio of an inner diameter of the respective tube to a wall thickness s of the wall of said tube, which is less than 25:1. A further embodiment of the invention furthermore provides for the wall thickness of each of the tubes to be less than 10 mm and/or for the inner diameter to be less than 200 mm or for each of the tubes 11, 12 to respectively be dimensioned in such a way that the inner diameter to wall thickness ratio is more than 5:1.

(15) As is quite common in the transducer devices of the type in question, the tubes 11, 12 may be accommodated in a transducer housing 100 of the transducer device such that, as also shown in FIG. 4 or easily apparent from a combination of FIGS. 1, 2 and 4, each of the tubes 11, 12 is respectively arranged within one and the same cavity of the transducer housing, which cavity is surrounded by a wall of the transducer housing, for example a metallic wall and/or a wall serving as outer protective cover, and that between an inner surface 100+, facing said cavity, of the wall of the transducer housing 100, a lateral surface 11# of the wall of the tube 11, namely an outer surface, facing the cavity, of the wall of the tube 11 and a lateral surface 12# of the wall of the tube 12, namely an outer surface, facing the cavity, of the wall of the tube 12, an intermediate space 100 is formed. The tubes 11, 12 as well as said transducer housing are in this case also designed to hold in the intermediate space 100, a fluid FL2, for example a fluid having a specific thermal conductivity of less than 1 W/(m(K), namely, for example, air or an inert gas, forming a fluid volume surrounding both the tube 11 and the tube 12, such that the lateral surface 11#, facing the intermediate space, of the wall of the tube 11, forming a first interface II11 of the first type, namely an interface between a fluid and a solid phase, and the lateral surface 12#, facing the intermediate space, of the wall of the tube 12, forming an interface II12 of the first type, are contacted by fluid FL2 held in the intermediate space 100.

(16) The at least two tubes 11, 12 may, for example, be connected fluidically to each other so as to form serial flow paths such that the tube 11 with its second end 11b is connected to the first end 12a of the tube 12. However, as is quite common in transducer devices of the type in question, the tubes 11, 12 can also be connected fluidically to each other so as to form two parallel flow paths. To this end, the transducer device according to another embodiment of the invention furthermore comprises an inlet-side first flow divider 20.sub.1 and an outlet-side second flow divider 20.sub.2, wherein both the second tube 11 and the tube 12, forming fluidically parallelly connected flow paths, are connected to the flow dividers 20.sub.1, 20.sub.2, which are, for example, identical in design, such that the tube 11 opens with its end 11a into a first flow opening 20.sub.1A of the flow divider 20.sub.1 and with its end 11b into a first flow opening 20.sub.2A of the flow divider 20.sub.2, and that the tube 12 opens with its end 12a into a second flow opening 20.sub.1B of the flow divider 20.sub.1 and with its end 12b into a second flow opening 20.sub.2B of the flow divider 20.sub.2. For the aforementioned case, in which the tubes 11, 12 are accommodated within a transducer housing 100, both the flow divider 20.sub.1 and the flow divider 20.sub.2 can respectively be an integral component of said transducer housing, for example such that, as also illustrated schematically in FIG. 2, a first end of the transducer housing is formed by means of the flow divider 20.sub.1 and a second end of the transducer housing remote from the first end of the transducer housing is formed by means of the flow divider 20.sub.2.

(17) As indicated in FIG. 2, the transducer device MW may furthermore be designed to be inserted, namely, for example, detachably mounted with the process line, in the course of a process line which conducts the fluid and which is, for example, designed as a rigid pipeline. For this purpose, a first connecting flange 13 serving to connect the transducer device to a line segment of the process line conducting the fluid FL1 can be provided on the inlet side of the transducer device and a second connecting flange 14 serving to connect to a line segment of the process line discharging the fluid again can be provided on the outlet side of the transducer device. As is quite common in the transducer device of the type in question, or as indicated in FIG. 2, the connecting flanges 13, 14 can optionally also be integrated at the end into the aforementioned transducer housing 100, namely be designed as an integral component of the transducer housing. A further embodiment of the invention furthermore provides that each of the connecting flanges 13, 14 respectively has a sealing surface for the fluid-tight or leak-free connection of the transducer device to a respectively corresponding line segment of a process line and that a shortest distance between said sealing surfaces moreover defines an installation length L.sub.MW of the transducer device; this in particular such that said installation length L.sub.MW is more than 250 mm and/or less than 3000 mm and/or such that a tube length to installation length ratio L.sub.11/L.sub.MW of the transducer device, defined by a ratio of an unwound tube length L.sub.11 of the first tube 11 to the aforementioned installation length L.sub.MW, is more than 1.2, for example also more than 1.4. The aforementioned unwound tube length L.sub.11 of the tube 11 and/or an unwound tube length L.sub.12 of the tube 12 can also be more than 300 mm, for example.

(18) The measuring and operation electronics unit ME formed, for example, by means of at least one microprocessor and/or by means of a digital signal processor (DSP) can in turn, as indicated in FIG. 2, be accommodated, for example, in a single, optionally also compartmentalized, electronics housing 200 of the measuring system. Said electronics housing 200 may, depending on the requirement for the measuring system, also be designed to be impact-resistant and/or explosion-proof and/or hermetically sealed, for example. The measuring device electronics unit ME can, as also shown schematically in FIG. 2 in the manner of a block diagram, have a measuring and evaluation circuit C, which processes measurement signals of the transducer device MW and which is, for example, formed by means of a microprocessor and which during operation generates corresponding measurement values for the measurement variable to be sensed by means of the measuring system. The measuring and evaluation circuit C of the measuring and operation electronics unit ME may, for example, be realized by means of a microcomputer comprising at least one microprocessor and/or one digital signal processor (DSP). The program codes to be executed by this microcomputer as well as operating parameters serving to control the respective measuring system, such as setpoint values for controllers or controller algorithms implemented by means of the measuring and operation electronics unit, can, as also schematically illustrated in FIG. 2, be stored persistently, for example in a non-volatile data memory EEPROM of the measuring and operation electronics unit ME, and loaded into a volatile data memory RAM, which is, for example, integrated into the microcomputer, when the measuring and operation electronics unit ME starts.

(19) Incidentally, the measuring and operation electronics unit ME can also be designed such that it substantially corresponds in terms of the circuitry design to one of the measuring and operation electronics units known from the aforementioned prior art, such as US-B 63 11 136, or, for example, to a measuring transducer of a Coriolis mass flow/density measuring device offered by the applicant under the name PROMASS 83F, for example.

(20) The measurement values x.sub.x (x.sub.m, x.sub.p, x.sub., x.sub.248, . . . ) generated by means of the measuring and operation electronics unit ME can in the case of the measuring system shown here be displayed on site, namely directly at the measuring point formed by means of the measuring system. In order to on site visualize measurement values generated by means of the measuring system and/or system status messages internally generated by the measuring device where appropriate, such as an error messaging signaling increased measurement inaccuracy or measurement unreliability or an alarm signaling a fault in the measuring system itself or at the measuring point formed by means of the measuring system, the measuring system can, as also indicated in FIG. 2, for example, have a display and operating element HMI, which communicates with the measuring and operation electronics unit and is optionally also portable, such as an LCD, OLED, or TFT display placed in the electronics housing 200 behind a window provided therein accordingly, and an appropriate input keyboard and/or a touch screen. In a favorable way, the measuring and operation electronics unit ME, which can, for example, also be (re)programmed or remotely parameterized, can also be designed such that it can exchange measurement and/or other operating data, such as current measurement values, system diagnosis values, system status messages, or setting values serving to control the measuring system, during operation of the measuring system with an electronic data processing system, which is superordinate to the measuring system, for example a programmable logic controller (PLC), a personal computer (PC) and/or a workstation via a data transmission system, for example a field bus system, such as FOUNDATION FIELDBUT, PROFIBUS, and/or wirelessly via radio. Furthermore, the measuring and operation electronics unit ME can be designed such that it can be supplied by an external power supply, for example via the aforementioned field bus system. For this purpose, the measuring and operation electronics unit ME can have, for example, an internal power supply circuit NRG for providing internal supply voltages U.sub.N, which internal power supply circuit is supplied during operation via the aforementioned field bus system by an external power supply provided in the aforementioned data processing system. In this case, the measuring system can, for example, be designed as a so-called four-wire device in which the internal power supply circuit of the measuring device electronics unit ME can be connected by means of a first pair of lines to an external power supply, and the internal communication circuit of the measuring and operation electronics unit ME can be connected by means of a second pair of lines to an external data processing circuit or an external data transmission system. However, the measuring and operation electronics unit may also be designed such that, as inter alia also shown in the aforementioned US-A 2006/0161359, it can be electrically connected by means of a two-wire connection, which is, for example, configured by means of a 4-20 mA current loop, to the external electronic data processing system and is supplied with electrical power via this connection and can transmit measurement values to the data processing system, optionally also using HART Multidrop. For the typical case, in which the measuring system is provided for coupling to a field bus or another electronic communication system, the measuring and operation electronics unit ME, which can, for example, also be (re)programmed on site and/or via the communication system, can moreover have a corresponding communication interface COM, for example a communication interface compliant with the relevant industry standards, such as IEC 61158/IEC 61784, for a data communication, for example for sending measurement and/or operating data, thus the measurement values representing the respective measurement variable, to the aforementioned programmable logic controller (PLC) or a superordinate process control system and/or for receiving setting data for the measuring system. The electrical connection of the transducer device to the measuring and operation electronics unit can take place by means of corresponding connecting lines which are guided out of the electronics housing 200, for example via cable feedthrough, into the transducer housing 100 and are also laid within the transducer housing 100 at least in sections. In this case, the connecting lines can be formed at least partially as conductor wires enveloped at least in sections by an electrical insulation, for example in the form of twisted pair lines, ribbon cables and/or coaxial cables. Alternatively or additionally, the connecting lines can also be formed at least in sections by means of conductor tracks of a printed circuit board, which is optionally also coated, for example a flexible or partially rigid and partly flexible printed circuit board, cf. also the aforementioned WO-A 96/07081.

(21) In order to excite and maintain mechanical vibrations of both the tube 11 and the tube 12 about a respectively associated static rest position, namely in particular mechanical vibrations of the tube 11 and the tube 12 about a respective imaginary axis of vibration imaginarily connecting the respective first end to the respective second end or the aforementioned useful vibrations, the transducer device further comprises an electromechanical exciter arrangement E formed by means of at least one vibration exciter 41, which is, for example, electrodynamic and in particular formed by means of a plunger coil or realized as a voice coil.

(22) In order to sense mechanical vibrations of at least the tube 11, namely in particular of the at least two tubes 11, 12, the transducer device furthermore comprises a sensor arrangement S formed by means of at least one first vibration sensor 51, which is, for example, electrodynamic and/or identical in design to the vibration exciter, and by means of a second vibration sensor 52, which is, for example, electrodynamic and/or identical in design to the vibration sensor 51. The vibration sensor 51 is designed to sense vibration movements at least of the tube 11, for example also of each of the at least two tubes 11, 12, at an inlet-side first vibration measuring point formed by means of said vibration sensor 51 and to generate a first vibration signal s1 representing said vibration movements, while the vibration sensor 52 is provided or designed to sense vibration movements at least of the tube 11, for example also of each of the at least two tubes 11, 12, at an outlet-side second vibration measuring point formed by means of said vibration sensor 52 and to generate a second vibration signal s2 representing said vibration movements; this in particular such that a phase difference (co-)dependent inter alia also on a mass flow rate of the fluid flowing through the tube 11 exists between the vibration signal s1 and the vibration signal s2. For this purpose, as also indicated in FIG. 2, the vibration sensor 51, thus the first vibration measuring point formed therewith, is positioned less far from the end 11a of the tube 11 than from the end 11b, and the vibration sensor 52, thus the second vibration measuring point formed therewith, is positioned less far from the end 11b of the tube 11 than from the end 11a, in particular such that the vibration sensor 51 is positioned at the same distance from the end 11a as the vibration sensor 52 from the end 11b. The vibration sensor arrangement thus formed by means of the two vibration sensors 51, 52 can, as is quite common in a transducer device of the type in question, also, for example, be mirror-symmetric with respect to at least one imaginary symmetry axis imaginarily intersecting the transducer device, namely, for example, with respect to a symmetry axis parallel both to a main axis of inertia of the tube 11 and to a main axis of inertia of the tube 12. According to another embodiment of the invention, the vibration sensor 51 is thermally conductively coupled to the wall of the tube 11 and/or the wall of the tube 12 in the same way as the vibration sensor 12, in particular such that a heat resistor counteracting a heat flow flowing from the wall of the tube 11 to the vibration sensor 51 and further to an atmosphere surrounding the vibration sensor 51 is equal to a heat resistor counteracting a heat flow flowing from the wall of the tube 11 to the vibration sensor 52 and further to an atmosphere surrounding the vibration sensor 52 and/or that a heat resistor counteracting a heat flow flowing from the wall of the tube 12 to the vibration sensor 51 and further to an atmosphere surrounding the vibration sensor 51 is equal to a heat resistor counteracting a heat flow flowing from the wall of the tube 12 to the vibration sensor 52 and further to an atmosphere surrounding the vibration sensor 52.

(23) In order to sense measuring point temperatures prevailing within the transducer device and to convert them into a respective temperature measurement signal, not least to compensate a dependence of the aforementioned phase difference on a temperature gradient respectively established in the flow direction within the wall of the tube 11 and/or the wall of the tube 12 or on a temperature difference L which is established between a temperature of the vibration sensor 51 and a temperature of the vibration sensor 52 and which changes over time, for example at least temporarily, with a rate of change of more than 0.05 K/s, the transducer device according to the invention furthermore comprises, as shown in FIG. 2, 3a, 3b or 4, a first temperature sensor 71 coupled mechanically although thermally conductively to the wall of the first tube 11 and a second temperature sensor 72 coupled mechanically although thermally conductively to the wall of the second tube 12. Said temperature difference L can occur in the case of an intact transducer device or intact tubes 11, 12 or, as also discussed in the aforementioned WO-A 2009/134268, particularly also in the case of an inside, facing the lumen, of a wall of at least one of the tubes 11, 12 with an undesired deposition. In the latter case, the temperature difference is designed to be routinely greater in the case of intact tubes 11, 12, in particular with walls without deposition, and otherwise the same boundary conditions.

(24) The temperature sensors 71, 72 are also electrically connected to the measuring and operation electronics unit ME, for example by respectively two of the aforementioned electrical connecting lines. As also respectively shown in FIG. 2 or 3a, the temperature sensor 71 is positioned less far from the first end 11a of the tube 11 than from the second end 11b of said tube 11, while the temperature sensor 72, as also illustrated in FIG. 2 or FIG. 3b is positioned less far from the second end 12b of the tube 12 than from the first end 12a of said tube 12; this in particular such that the temperature sensor 71 is positioned at the same distance from the end 11a of the tube 11 as the temperature sensor 72 from the end 12b or that the temperature sensor 71 is positioned at the same distance from the end 11b of the tube 11 as the temperature sensor 72 from the end 12a. Alternatively or additionally, the temperature sensor 71 may, for example, also be positioned at the same distance from a center of the tube 11 as the temperature sensor 72 from a center of the tube 12. Alternatively or additionally, the temperature sensor 71 may, for example, also be positioned at the same distance from a center of the tube as the temperature sensor 72 from a center of the tube 12. Moreover, the two temperature sensors 71, 72 can furthermore also be positioned such that the temperature sensor 71 and the temperature sensor 72, as also indicated in FIG. 4 or readily apparent in a combination of FIGS. 2 and 4, are azimuthally, namely, for example, in a projection onto an imaginary cross-sectional surface comprising said longitudinal axis L as surface normal, diametrically opposed to each other with respect to an imaginary longitudinal axis L of the transducer device, which longitudinal axis corresponds, for example, to a main flow direction of the transducer device. The two temperature sensors 71, 72 can also, in particular, furthermore be positioned or arranged such that a temperature sensor arrangement of the transducer device formed by means of said temperature sensors 71, 72 is axially symmetric with respect to at least one imaginary symmetry axis imaginarily intersecting the transducer device, namely, for example, an imaginary symmetry axis parallel both to a main axis of inertia of the tube 11 and to a main axis of inertia of the tube 12. In addition, the temperature sensor 71, as also indicated in FIG. 2, can, for example, also be positioned at the same distance from the vibration sensor 51 as the second temperature sensor 72 from the vibration sensor 52. According to a further embodiment of the invention, the transducer device has no other temperature sensor contacting the wall of the tube 11 than the first temperature sensor 71 and/or the transducer device has no other temperature sensor contacting the wall of the tube 72 than the second temperature sensor 72.

(25) The temperature sensor 71 is in particular provided or designed to sense a first measuring point temperature 1, namely a temperature at a first temperature measuring point formed by means of said temperature sensor 71, and to convert it into a first temperature measurement signal 1, namely a first electrical measurement signal representing the first measuring point temperature 1. In addition, the temperature sensor 72 is provided or designed to sense a second measuring point temperature 2, namely a temperature at a second temperature measuring point formed by means of said temperature sensor 72 and to convert it into a second temperature measurement signal 2, namely a second electrical measurement signal representing the second measuring point temperature 2. Each of the temperature measurement signals 1, 2 may, for example, be designed such that it has an electrical signal voltage dependent on the respective measuring point temperature 1 or 2 and/or an electrical signal current dependent on said measuring point temperature. According to a further embodiment of the invention, the temperature sensor 71 is coupled thermally conductively to the wall of the first tube 11 in the same way as the temperature sensor 72 to the wall of the second tube 12; this, for example, also such that a heat resistor counteracting a heat flow flowing from the wall of the tube 11 to the temperature sensor 71 and further to an atmosphere surrounding said temperature sensor 71 is equal to a heat resistor counteracting a heat flow flowing from the wall of the tube 12 to the temperature sensor 72 and further to an atmosphere surrounding the temperature sensor 72. It is furthermore provided that the temperature sensor 71 is mechanically coupled to the wall of the tube 11 in the same way as the temperature sensor 72 to the wall of the tube 12. According to a further embodiment of the invention, as is also schematically illustrated in FIG. 4, the temperature sensor 71 is formed by means of a first temperature probe 711 arranged within the intermediate space 100 and by means of a first coupling body 712 which couples said temperature probe 711 thermally conductively to the wall of the tube 11. Analogously, the temperature sensor 72 can be formed by means of a second temperature probe 721, which is also arranged within the intermediate space 100 and which is, for example, identical in design to the aforementioned temperature probe 711, and by means of a second coupling body 722 which couples said temperature probe 721 thermally conductively to the wall of the tube 12 and which is, for example, also identical in design to the aforementioned coupling body 712. Each of the two temperature probes 711, 721, which carry out the actual conversion of the (measuring point) temperature to be sensed into the respective measurement signal, can, for example, respectively be formed by means of a platinum measuring resistor, a thermistor or a thermocouple. Furthermore, each of the temperature probes 711, 721 can be connected to the respectively associated coupling body 712 or 722 by means of a suitable integral connection, namely, for example, an adhesive connection or a soldering or welding connection, and/or by embedding into the respective coupling body 712 or 722.

(26) In order to achieve a mechanically stable and durable yet thermally conductive connection between the wall of the tube 11 and the temperature sensor 71, the latter is integrally connected according to another embodiment of the invention to the lateral surface 11# of the wall of the tube 11, namely, for example, adhesively or by means of a soldering or welding connection. In order to produce such an integral connection between the tube 11 and the temperature sensor 71, a thermal adhesive, thus a plastic based on epoxy resin or based on silicone, namely, for example, silicone elastomer or a one-component or two-component silicone rubber, such as the company DELO Industrie Klebstoffe GmbH & Co KGaA, 86949 Windach, Germany, inter alia sells under the name DELO-GUM 3699, can be used, for example. The plastic used to connect the temperature sensor 71 and the tube 11 can also be mixed with metal oxide particles in order to achieve as good a thermal conduction as possible. It is furthermore also possible to, partially or entirely, produce the aforementioned coupling body 712 from plastic, for example also such that a plastic molded part, which is placed between the temperature probe 711 and the wall or which contacts both the lateral surface 11# of the wall and the temperature probe 711 and which is, where applicable, also monolithic, serves as coupling body 712 or the entire coupling body 712 consists of plastic, for example a plastic applied in one or more layers to the wall of the tube 11 and thus placed between the wall of the tube 11 and the first temperature probe 711. In addition, the temperature sensor 72 can also be likewise integrally connected to the lateral surface 12# of the wall of the tube 12, namely, for example, adhesively or by means of a soldering or welding connection. For this purpose, the coupling body 722 consists according to another embodiment of the invention at least partially, for example also predominantly, of a metal; thus, the coupling body 722 can be produced from a material, a specific thermal conductivity A2 of which is greater than 10 W/(m.Math.K) or and/or a specific heat capacity cp722 of which is less than 1000 J/(kg.Math.K), namely, for example, of the same material as the coupling body 712. The two aforementioned coupling bodies 712, 722 may furthermore be readily formed by appropriately selecting the materials actually used for their respective production such that the specific thermal conductivity A722 of a material of the second coupling body 722 is equal to a specific thermal conductivity A712 of a material of the coupling body 712 and/or the specific heat capacity cp722 of the material of the coupling body 722 is equal to a specific heat capacity cp712 of the material of the first coupling body 712.

(27) According to another embodiment of the invention, the second coupling body 722 of the temperature sensor 72 is also at least partially produced from a plastic or formed by means of a plastic body correspondingly placed between the temperature probe 721 and the wall of the tube 12. Alternatively or additionally, a further embodiment of the present invention provides that the coupling body 721 of the temperature sensor 71, as also indicated in FIG. 5a, is formed by means of a disk, which is placed between the wall of the tube 11 and the temperature probe 721 and which consists of a metal or a metal alloy, for example steel, and that the coupling body 722 of the temperature sensor 72, as also indicated in FIG. 5b, is formed by means of such a disk, which is placed between the wall of the tube 12 and the temperature probe 721 and which consists of a metal or a metal alloy, for example steel. Each of the two aforementioned disks can be designed as a disk which is, for example, substantially annular or substantially rectangular, as also shown in 5a or 5b, and which has a through-opening respectively correspondingly adapted to the lateral surface of the wall of the tube 11 or to the lateral surface of the wall of the tube 12 and which is respectively pushed onto the tube 11 or the tube 12 such that the disk surrounds the associated tube 11 or 12 or at least partially contacts an inner surface, facing the lateral surface of the wall of the tube 11 or 12, of the through-opening of the respective lateral surface. Each of the two aforementioned disks can, for example, respectively also serve both as coupling body 712 or 722 of the temperature sensor 71 or 72 or as part thereof and as a gusset plate inducing inlet-side or outlet-side vibration nodes from mechanical vibrations of the tube 11, 12 or, for example, as a holder of the mentioned vibration sensor 51 or the also provided vibration sensor 52.

(28) As schematically respectively shown in FIG. 4, each of the two temperature sensors is coupled thermally to the respective tube 11 or 12 in that the coupling body 712 of the temperature sensor 71 contacts the lateral surface 11# of the wall of the tube 11, forming a first interface II21 of the second type, namely an interface between two solid phases, and the coupling body 722 of the temperature sensor 72 contacts the lateral surface 12# of the wall of the tube 12, forming an interface II22 of the second type. Each of the two interfaces II21, II22 respectively has a surface area which is defined, thus predetermined, by the specific design of the respective coupling body 712 or 722. Accordingly, as also illustrated in a simplified manner in FIG. 7 by means of an equivalent circuit diagram for a resistor network formed by means of a plurality of discrete heat resistors, a first heat resistor R1 (R1=T1/Q1), which in particular in this case is predominately determined by the thermal conduction and which is thermally conductively connected to the first temperature measuring point counteracts a heat flow Q1, which results from a temperature difference T1 prevailing between the interface II21 of the second type and the first temperature measuring point and which nevertheless entirely passes through said interface II21 and flows further to the first temperature measuring point, and a second heat resistor R2 (R2=T2/Q2), which is also predominately determined by the thermal conduction and which is thermally conductively connected to the second temperature measuring point counteracts a heat flow Q2, which results from a temperature difference T2 prevailing between the interface II22 of the second type and the second temperature measuring point and which nevertheless entirely passes through said interface II22 and flows further to the second temperature measuring point. In order to achieve the best possible thermal coupling of the temperature sensor 71 to the wall of the tube 11 and of the temperature sensor 72 to the wall of the tube 12, each of the heat resistors R1 and R2 or each of the temperature sensors 71, 72 is dimensioned according to a further embodiment of the invention such that each of the heat resistors R1 and R2 is respectively smaller than 1000 K/W, for example smaller than 25 K/W. According to a further embodiment of the invention, the two aforementioned heat resistors R1, R2 are furthermore dimensioned such that overall a condition R1=R2 is met, namely that both heat resistors R1, R2 are designed to be of the same size.

(29) In order to achieve that each of the temperature sensors 71, 72, as also assumed in the (static) calculation model underlying the equivalent circuit diagram shown in FIG. 7, respectively has only a comparatively low, thus negligible thermal inertia or each of the two measuring point temperatures 1, 2 can respectively rapidly follow any changes of in each case a first tube wall temperature ail, namely a local temperature assumed by the wall of the tube 11, or a second tube wall temperature 12, namely a local temperature assumed by the wall of the tube 12, or that vice versa, each of the two measuring point temperatures does not depend or in any case depends only slightly on a rate of change of the tube wall temperature ail, namely a rate at which the tube wall temperature .sub.11 changes over time, or on a rate of change of the tube wall temperature .sub.12, namely a rate at which the tube wall temperature .sub.12 changes over time, a further embodiment of the invention furthermore provides that each of the coupling bodies 712 and 722 is respectively designed such that both the coupling body 712 and the coupling body 722 ultimately respectively has a heat capacity C1 or C2, which is less than 2000 J/K; this advantageously furthermore such that the heat capacity C1 of the first coupling body 712 and the heat capacity C2 of the second coupling body 722 satisfy a condition

(30) $\frac{1}{1000}<\frac{C1}{C2}1$
and/or that at least the coupling body 712 has a specific heat capacity that is less than 200 J/(kg.Math.K) but possibly also less than 100 J/(kg.Math.K). Due to the compact design typically desired for the temperature sensor of the type in question and due to the typically used, namely thermally conductive, materials, a close relation between the heat resistor and the heat capacity of the respective temperature sensor moreover exists such that the respective heat capacity, thus also the aforementioned heat capacity C1 or C2, is designed to be the lower, the lower the respective heat resistor is selected. Accordingly, dimensioning the heat resistors R1, R2 of the coupling bodies 712 or 722 in the aforementioned manner can thus at the same time also achieve that each of the temperature sensors 71, 72 respectively also has only a comparatively low thermal inertia with respect to the respective tube wall temperature .sub.11 or .sub.12 or that each of the two measuring point temperatures 1, 2 can, as desired, respectively rapidly follow any changes of the respective tube wall temperature or vice versa, that each of the two measuring point temperatures 1, 2 does not depend or in any case depends only slightly on a rate of change of the tube wall temperature, namely a rate at which the respective tube wall temperature changes over time.

(31) The intermediate space 100 formed between the inner surface 100+ of the wall of the transducer housing 100 and the lateral surfaces 11#, 12# of the walls of the tube 11 or of the tube 12 is furthermore, as is quite common in transducer devices of the type in question and as respectively schematically indicated in FIG. 4 by dotted hatching, filled with a fluid FL2, which, for example, has a specific thermal conductivity F of less than 1 W/(m.Math.K), to form a fluid volume surrounding the tubes 11, 12. The fluid FL2 held in the intermediate space 100 or the fluid volume formed therewith has a fluid temperature which is hereinafter referred to as tube ambient temperature .sub.FL2 and which optionally also changes over time and which at least temporarily deviates from the measurement fluid temperature .sub.FL1 by more than 1 K (Kelvin), in particular at least temporarily by more than 5 K. Accordingly, the transducer housing and the tubes 11, 12 according to another embodiment of the invention are designed to hold said fluid FL2 in the intermediate space 100 such that the lateral surface 11#, facing the intermediate space 100, of the wall of the tube 11, forming a third interface II13 of the first type, is contacted by the fluid FL2 held in the intermediate space and the lateral surface 12#, facing the intermediate space 100, of the wall of the tube 12, forming a fourth interface II14 of the first type, is contacted by the fluid FL2 held in the intermediate space; each of the tubes 11, 12 is thus respectively thermally coupled to the fluid volume formed in the intermediate space 100. Air or an inert gas, such as nitrogen, or a noble gas, namely in particular helium, for example, can serve as fluid FL2. As a result, an outer surface, facing the intermediate space 100, of the temperature sensor 71 is also contacted by the fluid FL2 held in the intermediate space, forming a fifth interface II15 of the first type (interface between a fluid and a solid phase), and an outer surface, also facing the intermediate space 100, of the temperature sensor 72 is contacted by the fluid FL2 held in the intermediate space, forming a sixth interface 1116 of the first type, or both the temperature sensor 71 and the temperature sensor 72 are thermally coupled to the fluid volume formed in the intermediate space 100 such that, as also schematically illustrated in FIG. 4, a third heat resistor R3 (R3=T3/Q3), which in particular is in this case defined by heat conduction and by the heat flow (convection) occurring at the interface II15 and which is thermally conductively connected to the first temperature measuring point, counteracts a heat flow Q3, which results from a temperature difference T3 prevailing between the interface II15 of the first type and the first temperature measuring point, which in particular entirely flows from the first temperature measuring point to the interface II15, thus entirely passes through said interface II15, and a fourth heat resistor R4 (R4=T4/Q4), which in particular is in this case also defined by heat conduction and by the heat flow occurring at the interface II16 and which is thermally conductively connected to the second temperature measuring point, counteracts a heat flow Q4, which results from a temperature difference T4 prevailing between the interface II16 of the first type and the second temperature measuring point, which in particular entirely flows from the second temperature measuring point to the interface 1116, thus entirely passes through said interface 1116. Each of the heat resistors R3 and R4 is advantageously dimensioned to be less than 20,000 K/W, in particular less than 10,000 K/W. In order to achieve a thermal coupling of the temperature sensor 71 or the temperature sensor 72 to the fluid volume formed in the intermediate space 100, which is weaker in comparison to the thermal coupling to the tube 11, not least in order to also achieve that the measuring point temperature 1 or 2 respectively sensed therewith is as immune as possible against rapid temporal changes, which may also be spatially different, of the tube ambient temperature .sub.FL2 or that the temperature sensors 71, 72 preferably have a greater thermal inertia with respect to the tube ambient temperature .sub.FL2 than with respect to the tube wall temperature .sub.11 or .sub.12, the temperature sensor 71 or the temperature sensor 72 is furthermore designed according to a further embodiment of the invention such that the heat resistor R3 or the heat resistor R4 is more than 500 K/W, in particular more than 5000 K/W. According to a further embodiment of the invention, the two aforementioned heat resistors R3, R4 are furthermore dimensioned such that overall a condition R3=R4 is met, namely that both heat resistors R3, R4 are designed to be of the same size.

(32) In order to also be able to predetermine the heat resistor R3 as easily as possible on the one hand but to also design said heat resistor R3 on the other hand such that its respective examples also have as small a spread as possible from transducer device to transducer device within a lot or a series of industrially manufactured transducer devices of the type in question, that the transducer device is thus well reproducible overall, the temperature sensor 71 can furthermore have a third coupling body, which couples the temperature probe 711 of said temperature sensor thermally to the fluid volume formed in the intermediate space and which contacts said fluid volume, forming the third interface II15 of the first type. Said coupling body can consist at least partially, namely in particular predominantly or entirely, of a material, a specific thermal conductivity of which is greater than the specific thermal conductivity F of the fluid FL2 held in the intermediate space and/or is greater than 0.1 W/(m.Math.K) and a specific heat capacity of which is smaller than a specific heat capacity cpF of the fluid FL2 held in the intermediate space and/or less than 2000 J/(kg.Math.K). Advantageously, the material of the aforementioned coupling body can also be selected to match the fluid FL2 held in the intermediate space such that a ratio of the specific thermal conductivity of said material to the thermal conductivity F of the fluid FL2 held in the intermediate space is greater than 0.2, and/or that a ratio of the specific heat capacity of said material to the heat capacity cpF of the fluid FL2 held in the intermediate space is less than 1.5. The third coupling body may be formed, for example also entirely, by means of a plastic, such as an epoxy resin or a silicone, which is applied to the temperature probe 711 of the temperature sensor 71 and which is, for example, also mixed with metal oxide particles. Alternatively or additionally, said third coupling body can be formed, where appropriate also entirely, by means of a fabric tape applied to the temperature sensor 711, for example a fiberglass fabric tape, or by means of a metal sheet applied to the temperature probe 711, such as a sheet metal strip of stainless steel. In the same way, the temperature sensor 72 can also be formed by means of a further fourth coupling body, which in particular couples the temperature probe 721 of said temperature sensor 72 thermally to the fluid volume formed in the intermediate space and which contacts the fluid volume formed in the intermediate space 100, forming the sixth interface 1116 of the first type. In addition, the fourth coupling body can advantageously be identical in design to the aforementioned third coupling body of the temperature sensor 71 which couples the temperature probe 711 thermally to the fluid volume formed in the intermediate space 100. Correspondingly, a seventh interface of the first type is also formed within the tube 11, namely on the inner surface 11+, facing its lumen and thus contacted by the fluid FL1 conducted in the lumen, of the wall of said tube and an eighth interface of the first type is also formed within the tube 12, namely on the inner surface 12+, facing its lumen and thus contacted by the fluid FL1 conducted in the lumen, of the wall of said tube, as a result of which the tube wall temperature .sub.11 of the tube 11 or the tube wall temperature .sub.12 of the tube 12 is also co-determined by the measurement fluid temperature .sub.FL1 of the fluid FL1 currently located in the lumen of the tube 11 or in the lumen of the tube 12.

(33) As already mentioned, each of the aforementioned heat resistors R1, R2, R3 and R4 is respectively significantly or completely defined by material characteristic values, such as a specific thermal conductivity , and dimensions of the respective coupling body or the wall of the respective tube 11, 12, such as a respective effective length L.sub.th of the respective coupling body for the respective heat flow flowing through and a surface area A.sub.th of a respective effective cross-sectional area of the respective coupling body for said heat flow, namely, for example, the surface area of the respective interfaces II21, II22, and/or by corresponding material characteristic values of the wall of the respective tube 11 or 12 and of the fluid FL2 held in the intermediate space 100, thus solely by parameters that are at least approximately known in advance and at the same time substantially unchanging over a longer operating period. Thus, each of the heat resistors R1, R2, R3, R4 can be sufficiently precisely determined in advance by means of said parameters (, A.sub.th, L.sub.th), for example by experimental measurements and/or by calculations. For example, based on the known relation:

(34) $\begin{array}{cc}{R}_{\mathrm{th}}=\frac{L_{\mathrm{eff}}}{.Math.A_{\mathrm{eff}}}& \left(1\right)\end{array}$
a thermal resistivity, which co-determines the heat resistor R1 or R2 and which in particular represents a temperature drop related to a heat flow due to heat conduction processes, can in particular be quantified, namely, for example, be calculated for a unit K/W (Kelvin per Watt). Knowing the material characteristic values of the materials actually respectively used to produce the temperature sensors and the actual shape and dimension of the aforementioned interfaces II13, II14, II21, II22 formed by means of the temperature sensors, the resistance values for the aforementioned heat transfer resistances respectively co-determining the heat resistors R1, R2, R3, R4 can also be sufficiently precisely specified or sufficiently precisely determined in advance. Alternatively or additionally, the heat resistors R1, R2, R3, R4 or corresponding heat resistance ratios can also, for example, be experimentally determined by means of calibration measurements taken at the respective transducer device.

(35) In order to on the one hand provide the temperature sensor 71 with as low a thermal inertia as possible with respect to temporal changes of the tube wall temperature of the tube 11 but to on the other hand also achieve as good a thermal coupling of the temperature sensor 71 to the wall of the tube 11 as possible with as compact a design as possible, the coupling body 712 according to a further embodiment of the invention is produced at least partially, for example also predominantly or entirely, from a material, namely, for example, a thermally adhesive one, a specific thermal conductivity 712 of which is greater than a specific thermal conductivity F of the fluid FL2 held in the intermediate space and/or greater than 1 W/(m.Math.K). Advantageously, the material of the coupling body 712 is in this case furthermore selected such that a ratio 712/F of the specific thermal conductivity 712 of said material of the coupling body 712 to the specific thermal conductivity F of the fluid FL2 held in the intermediate space is greater than 2, and/or a ratio cp712/cpF of a specific heat capacity cp712 of said material of the coupling body 712 to the heat capacity cpF of the fluid FL2 held in the intermediate space is less than 1.5, in particular such that the specific heat capacity cp712 is less than a specific heat capacity cpF of the fluid held in the intermediate space. In addition, the coupling body 722 of the temperature sensor 72 can also at least partially (or entirely) be produced from the same material as the coupling body 712 of the temperature sensor 71 in order to provide an equally low thermal inertia of the temperature sensor 72 with respect to temporal changes of the tube wall temperature of the tube 12 and in order to achieve an equally good thermal coupling of the temperature sensor 72 to the wall of the tube 12. A further embodiment of the invention furthermore provides that the first temperature sensor and the second temperature sensor are identical in design, namely that both the temperature sensors and coupling bodies respectively used for this purpose and the thermal coupling of the aforementioned components to one another or to the tube and the fluid held in the intermediate space are essentially the same.

(36) For the purpose of processing or evaluation of the aforementioned measurement signals generated by means of the transducer device, the measuring and operation electronics unit ME is, as also schematically shown in FIG. 3, respectively electrically connected both to each of the at least two vibration sensors 51, 52 and to each of the two temperature sensors 71, 72 and to the at least one vibration exciter 41, for example in each case by means of corresponding connecting wires. In order to reduce the expenditure for the electrical connection of the temperature sensors of the transducer device to the measuring and operation electronics unit ME or in order to allow an easy cabling of the measuring and operation electronics unit ME to said temperature sensors, the measuring and operation electronics unit ME according to a further embodiment of the invention has, as also shown in FIG. 6, a multiplexer with at least two signal inputs and at least one signal output as well as an analog-to-digital converter ADC, which has a, for example nominal, resolution of more than 16 bits and/or is clocked with a sampling rate of more than 1000 s.sup. and has at least one signal input and at least one signal output. Said multiplexer MUX is in particular designed to, optionally, namely, for example, cyclically, switch one of its signal inputs through to the signal output such that a signal applied to the respectively switched-through signal input is passed to the signal output, while the analog-to-digital converter ADC is designed to convert an analog input signal applied to said signal input into a digital output signal representing said input signal using a sampling rate f.sub.A of, for example, in particular more than 1000 s.sup. and a digital resolution N of, for example, more than 16 bits and to provide the output signal at the signal output. As also indicated in FIG. 6, the at least one signal output of the multiplexer and the at least one signal input of the analog-to-digital converter are moreover electrically coupled to each other, and the temperature sensor 71 and the temperature sensor 72 are respectively electrically connected to the multiplexer MUX such that the temperature measurement signal 1 is applied to a first signal input of the multiplexer MUX and that the temperature measurement signal 2 is applied to a second signal input of the multiplexer MUX. As a result, the output signal of the analog-to-digital converter ADC temporarily represents exactly one of the two temperature measurement signals 1, 2 during operation. Furthermore, the measuring and operation electronics unit ME may furthermore be designed to generate the transducer temperature measurement value using said output signal of the analog-to-digital converter ADC representing one of the two temperature measurement signals 1, 2.

(37) The measuring and operation electronics unit ME is also designed to generate an exciter signal e1, which drives the exciter arrangement E, namely, for example, its at least one vibration exciter 41 and which is, for example, adjusted to a predetermined voltage level and/or to a predetermined current intensity and/or to a predetermined frequency, and which has an excitation frequency, namely a signal frequency corresponding to the useful frequency, or to feed electrical power into the at least one vibration exciter 41 in order to effect mechanical vibrations of the at least two tubes 11, 12 by means of said electrical exciter signal e1. Said exciter signal e1 serves in particular to feed at least the electrical power required for exciting or maintaining the useful vibrations to the at least one vibration exciter in a controlled manner and can accordingly have a signal frequency corresponding to an (instantaneous) resonant frequency of the useful mode, thus to the useful frequency. For example, the exciter signal e can simultaneously also have a multiplicity of sinusoidal signal components having different signal frequencies from one another, of which one signal component, for example a signal component dominating at least temporarily with respect to signal power, has the signal frequency corresponding to the useful frequency.

(38) In addition, the exciter arrangement E is designed to excite or maintain mechanical vibrations of the tubes 11, 12 when driven by said exciter signal e1. In the process, the at least one vibration exciter converts an electrical excitation power fed by means of the electrical exciter signal into excitation forces, which are, for example, pulsating or harmonic, namely essentially sinusoidal, and which act accordingly on the tube 11 or 12 and thus actively excite the desired useful vibrations. The excitation forces ultimately generated by converting electrical excitation power fed into the vibration exciter can be generated accordingly in a manner known per se to the person skilled in the art, namely by means of a driver circuit which is provided in the measuring and operation electronics unit ME and which adjusts the exciter signal on the basis of signal frequency and signal amplitude of the at least one sensor signal and provides it via an output channel. In order to determine the instantaneous resonant frequency of the useful mode or to adjust the signal frequency corresponding to the useful frequency for the exciter signal, a digital phase-locked loop (PLL) can, for example, be provided in the driver circuit, while a current intensity of the exciter signal, which determines a magnitude of said excitation forces, can, for example, be appropriately adjusted by means of a corresponding current controller of the driver circuit. The measuring device electronics unit ME can in this case, for example, also be designed to control the exciter signal such that the useful vibrations have a constant amplitude, which is thus also largely independent of the density p or the viscosity of the medium to be respectively measured. In order to generate the aforementioned exciter signal, a corresponding driver circuit Exc, namely, for example, a driver circuit designed as an independent electronics module, can furthermore be provided in the measuring and operation electronics unit ME, as is quite common in such measuring and operation electronics units or as also indicated in FIG. 2. The design and the use of so-called phase-locked loops to actively excite vibration elements of the type in question at an instantaneous resonant frequency is, for example, comprehensively described in U.S. Pat. No. 4,801,897. Other driver circuits which are suitable for adjusting the excitation energy or the excitation power and which are known per se to the person skilled in the art, for example also from the aforementioned U.S. Pat. Nos. 4,801,897, 5,024,104, or6,311,136, can naturally also be used.

(39) The measuring and operation electronics unit ME is furthermore also designed to receive and process the two vibration measurement signals s1, s2 and the two temperature measurement signals 1, 2 and to generate, using each of the two vibration signals s1, s2 and each of the temperature measurement signals 1, 2, a mass flow measurement value X.sub.m, namely a measurement value (x.sub.x.fwdarw.x.sub.m) representing the aforementioned mass flow rate m or a mass flow rate of the fluid FL1 flowing through the transducer device, or a mass flow sequence X.sub.m, namely a series of temporally successive mass flow measurement values x.sub.m,i respectively instantaneously representing the mass flow rate m of the fluid. For this purpose, as is quite common for such measuring and operation electronics units or as also indicated in FIG. 2, a corresponding measuring and evaluation circuit C, which may, optionally, also be electrically connected to the aforementioned driver circuit Exc and which is, for example, also designed as an independent electronics module and/or comprises at least one microprocessor, can furthermore be provided in the measuring and operation electronics unit ME. In the measuring system according to the invention, the measuring and operation electronics unit ME is in particular provided or designed to generate the aforementioned mass flow measurement values x.sub.m,i such that, at least for one reference mass flow rate m.sub.ref, namely a predetermined mass flow rate of a reference fluid flowing through the transducer device, namely, for example, a liquid or a gas, the mass flow measurement values x.sub.m,i (x.sub.m,i.fwdarw.x.sub.m,ref) are independent of the aforementioned temperature difference between the two temperature measuring points; this in particular such that in particular for at least one reference mass flow rate m.sub.ref, which is not zero although constant, temporally successively determined mass flow measurement values x.sub.m,i(x.sub.m,i.fwdarw.x.sub.m,ref) deviate from each other by no more than 0.01% of said reference mass flow rate m.sub.ref even in the case of various temperature differences , namely in particular temperature differences of more than 1 K and/or less than 10 K and/or temperature differences spreading over time with a range of more than 1 K and/or temperature differences changing over time with a rate of change of more than 0.05 K/s, and/or that in particular respectively in the case of a transducer device through which no fluid flows, temporally successively determined mass flow measurement values x.sub.m,i(x.sub.m,i.fwdarw.x.sub.m,ref) are less than 0.01 kg/h or deviate from each other by less than 0.01 kg/h even in the case of various temperature differences, namely in particular temperature differences of more than 1 K and/or less than 10 K and/or temperature differences spreading over time with a range of more than 1 K and/or less than 10 K and/or temperature differences changing over time with a rate of change of more than 0.05 K/s.

(40) The aforementioned reference mass flow rate m.sub.ref can, for example, be adjusted during a (wet) calibration of the measuring system with the reference fluid using a calibrated reference measuring system, for example before its delivery on a manufacturer's calibration system and/or also, as also shown inter alia in the aforementioned WO-A 02/097379, in the installation position on site. For the aforementioned case in which the reference fluid mi flows through the transducer device with a reference mass flow rate m.sub.ref not equal to zero, the fluid flow can advantageously be designed to be laminar, not least in order to establish the aforementioned temperature difference, or the reference fluid can advantageously flow through the tube 11 and/or through the tube 12 or the transducer device formed therewith with a Reynolds number (Re) of less than 1000. The aforementioned reference mass flow rate m.sub.ref can accordingly, for example, be a mass flow rate of no more than 1 kg/h and/or a mass flow rate kept constant. However, the reference mass flow rate m.sub.ref can also be zero so that the mass flow measurement values x.sub.m,i(x.sub.m,i.fwdarw.x.sub.m,ref.fwdarw.x.sub.m,ZERO) determined for it represent a zero scale mark of the measuring and operation electronics unit ME. Not least in order to establish the aforementioned temperature difference, the reference fluid may advantageously be, for example, a gas or a liquid having a specific heat capacity c.sub.p,ref of more than 1 kJ.Math.kg.sup.1.Math.K.sup.1 and/or less than 4.2 kJ.Math.kg.sup.1.Math.K.sup.1 and/or a fluid which is introduced into the tubes 11, 12 or the transducer device formed therewith with a fluid temperature of no less than 20 C. The reference fluid can thus, for example, be an oil, in particular an oil having a viscosity of more than 10.sup.2 Pa.Math.s (pascal seconds). Particularly pronounced temperature differences can in this case be determined if the respective reference mass flow rate m.sub.ref is, depending on a magnitude |D| of the nominal width of the transducer device given in the SI base unit for length (m=meters), less than |D|.Math.10000 kg/h. However, the reference fluid can, for example, also be water or, for example, also air, wherein considerable temperature differences can already be established in this case for reference mass flow rates m.sub.ref of less than |D|.Math.1000 kg/h.

(41) According to a further embodiment of the invention, the measuring and operation electronics unit ME is designed to determine the mass flow measurement values x.sub.m,i based on the following polynomial function containing in particular N temperature difference coefficients

(42) $\begin{array}{cc}{x}_{m,\mathrm{ref}}=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(\right)}^j=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(1-2\right)}^j\mathrm{with}j=0,1,2,\mathrm{.Math.}N,& \left(2\right)\end{array}$
or to determine the mass flow measurement values x.sub.m,i such that a mass flow measurement value x.sub.m,ref determined for the reference mass flow rate m.sub.ref satisfies at least one condition corresponding to said polynomial function. The measuring and operation electronics unit ME may in particular be designed to determine the aforementioned mass flow measurement values x.sub.m,i such that in the case of a transducer device through which no fluid flows or tubes 11, 12 through which no fluid flows, temporally successively determined mass flow measurement values x.sub.m,i(x.sub.m,i.fwdarw.x.sub.m,ZERO) respectively representing in particular a zero scale mark x.sub.m,ZERO of the measuring and operation electronics unit ME corresponding to a mass flow rate m of zero (m.sub.ref=0) satisfy a condition:

(43) $\begin{array}{cc}{C}_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(\right)}^j=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(1-2\right)}^{j}0\text{.}01\mathrm{kg}/h\mathrm{with}j=0,1,2,\mathrm{.Math.}N,& \left(3\right)\end{array}$
namely in particular a condition:

(44) $\begin{array}{cc}{C}_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(\right)}^j=C_0.Math.+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(1-2\right)}^{j}0& \left(4\right)\end{array}$

(45) Said temperature difference coefficients K.sub.j can be experimentally determined in advance for the respective measuring system, for example within the course of the aforementioned (wet) calibration of the measuring system by calibrating the respective measuring system at various temperature differences and/or various (reference) mass flow rates and/or by means of computer-based simulations, for example, by adapting the polynomial function or its temperature difference coefficients K.sub.j to experimentally determined measurement and/or simulation data, for example in accordance with the least squares method (LS method). Further studies in this respect have shown that for numerous applications, the number of temperature difference coefficients in the aforementioned polynomial function can easily be limited to N3 or a polynomial order can accordingly be limited to two or one. It could moreover be found that it can be sufficient for most transducer devices or transducer device types to transfer the temperature coefficients K.sub.j of the polynomial function, which were initially experimentally determined representatively for a single transducer device, to other identically designed transducer devices so that said identically designed transducer devices do not need to be recalibrated with respect to the polynomial function, significantly reducing the calibration effort.

(46) Not least in order to implement the aforementioned polynomial function, the measuring and operation electronics unit ME according to a further embodiment of the invention is furthermore designed to generate, using both the temperature measurement signal 1 and the temperature measurement signal 2, a temperature difference sequence namely a series of temporally successive temperature difference measurement values x.sub.,i respectively representing the temperature difference , and/or the measuring and operation electronics unit ME is designed to generate, using both the vibration signal s1 and the vibration signal s2 in a manner known per se to the person skilled in the art, a phase difference sequence x.sub.,i namely a series of temporally successive (conventional) phase difference measurement values x.sub.,i respectively representing the phase difference . Using both the phase difference sequence X.sub.,i and the temperature difference sequence X.sub.,i, the aforementioned mass flow sequence X.sub.m can be generated continuously, for example based on a calculation rule corresponding to the aforementioned polynomial function:

(47) $\begin{array}{cc}{x}_{m,i}=C_0.Math.x_{,i}+\underset{j=0}{\overset{N}{.Math.}}{K}_j.Math.{\left(x_j\right)}^j\mathrm{with}j=0,1,2,\mathrm{.Math.}& \left(5\right)\end{array}$

(48) The calculation of the respective (instantaneous) temperature difference measurement value x.sub. can, for example, take place such that both a first measuring point temperature measurement value representing the measuring point temperature 1 is generated based on the temperature measurement signal 1 and a second measuring point temperature measurement value representing the measuring point temperature 2 is generated based on the temperature measurement signal 2 by means of the measuring and operation electronics unit ME at time intervals and that said temperature difference measurement value x.sub. corresponds to a simple numerical subtraction of said two currently determined measuring point temperature measurement values.

(49) Additionally, the measuring and operation electronics unit ME can furthermore also be designed to monitor, using the temperature difference sequence X.sub.,i, a functionality of the transducer device, namely in particular a functionality of the tube 11 and/or the tube 12; for example, it can be diagnosed by means of the measuring and operation electronics unit, using the temperature difference sequence X.sub.,i, whether or that at least one of the tubes 11, 12 or the transducer device formed therewith has a flow resistance which is changed in comparison to an original flow resistance or, optionally, to generate, using the temperature difference sequence X.sub.,i, an alarm, which signals an only limited functionality of the transducer device, namely, for example, as a result of the aforementioned changed flow resistance of the tube 11 and/or the tube 12.

(50) According to a further embodiment of the invention, the measuring and operation electronics unit ME is furthermore designed to (recurrently) generate, using both the temperature measurement signal 1 and the temperature measurement signal 2, a transducer temperature measurement value X.sub., which represents a transducer device temperature .sub.MW, which deviates both from the measuring point temperature 1 and from the measuring point temperature 2 such that the transducer temperature measurement value X.sub. corresponds to a weighted average

(51) $\frac{.Math.1+.Math.2}{+}$
of the measuring point temperatures 1, 2.

(52) The calculation of the temperature measurement value X.sub. can, for example, take place such that first both a first measuring point temperature measurement value X.sub.1 representing the measuring point temperature 1 is generated based on the temperature measurement signal 1 and a second measuring point temperature measurement value X.sub.2 representing the measuring point temperature 2 is generated based on the temperature measurement signal 2 by means of the [ . . . ] and that said transducer temperature measurement value is determined according to a calculation rule dependent on the measuring point temperature measurement values X.sub.1, X.sub.2 and on previously determined numerical fixed values , stored in the measuring and operation electronics unit ME:

(53) $\begin{array}{cc}{X}_{}=.Math.X_1+.Math.X_2\mathrm{or}& \left(6\right)\\ X_{}=\frac{.Math.X_1+.Math.X_2}{+}& \left(7\right)\end{array}$

(54) If only two measuring point temperature measurement values determined based on the temperature measurement signals are used, the fixed values , contained in the aforementioned condition can advantageously also be selected such that the condition +a =1 is satisfied as a result; this in particular also such that the condition ==0.5 is satisfied, the measuring point temperatures 1, 2 thus having the same weight in the measurement result or the transducer temperature measurement value X.sub. thus corresponding to an arithmetic mean 0.5.Math.(1+2) of the measuring point temperatures 1, 2. For the mentioned case, in which both the two tubes 11, 12 and the two temperature sensors 71, 72 are identical in design and in which the design of the temperature sensor arrangement of the transducer device is axially symmetric with respect to the aforementioned imaginary symmetry axis, the transducer temperature temperature measurement value X.sub. accordingly represents [sic] results as the arithmetic mean of a tube wall temperature in the center of the tube 11, and a tube wall temperature in the center of the tube 12 and/or an average tube wall temperature which results at least approximately as the arithmetic mean 0.5.Math.(.sub.11+.sub.12) of an average tube wall temperature .sub.11 of the tube 11 and an average tube wall temperature .sub.12 of the tube 12. However, if necessary, the fixed values , can also be defined for this purpose, modifying the aforementioned condition ==0.5, in such a waynamely, for example, be finely adjusted based on corresponding calibration measurements at the transducer devicethat the thereby ultimately determined transducer temperature measurement value at least actually more precisely corresponds to said average tube wall temperature than when said condition ==0.5 is applied.

(55) According to a further embodiment of the invention, the measuring and operation electronics unit ME is furthermore designed to generate the at least one measurement value X.sub.x, namely, for example, the aforementioned density measurement value X.sub. and/or the aforementioned mass flow measurement value X.sub.m, using both the first temperature measurement signal 1 generated by means of the transducer device and at least the second temperature measurement signal 2 generated by means of the transducer device. That is to say, the measuring and operation electronics unit ME is in particular furthermore designed to generate, using both the transducer temperature temperature measurement value and the frequency measurement value X.sub.f, a density measurement value, namely a measurement value representing a density of the fluid and/or a viscosity measurement value, namely a measurement value representing a viscosity of the fluid.

(56) For the other mentioned case, in which the measuring system is furthermore also provided to measure the measurement fluid temperature .sub.FL1, the measuring and operation electronics unit ME is furthermore designed to occasionally also determine, based on the two temperature measurement signals 1, 2, a measurement fluid temperature measurement value X.sub.,FL, which represents said measurement fluid temperature .sub.FL1. The measurement fluid temperature measurement value X.sub.,FL can, for example, be determined easily using a calculation rule that is changed in comparison to one of the aforementioned calculation rules (1), (2) only by a coefficient K.sub.FL, which is, for example, firmly specified:

(57) $\begin{array}{cc}{X}_{,\mathrm{FL}}=.Math.X_1+.Math.X_2+K_{\mathrm{FL}}\mathrm{or}& \left(8\right)\\ X_{,\mathrm{FL}}=\frac{.Math.X_1+.Math.X_2}{+}+K_{\mathrm{FL}}& \left(9\right)\end{array}$
wherein said coefficient K.sub.FL represents a temperature difference between the measured transducer device temperature .sub.MW and the simultaneously occurring measurement fluid temperature .sub.FL1, in particular a steady temperature difference which always arises when the transducer device is in a thermal equilibrium and which can thus be determined in advance.

(58) As already discussed in US-A 2011/0113896 mentioned above, a particular risk in the case of transducer devices with parallel flow paths can inter alia also consists in that one of the tubes forming said flow paths is partly or completely blocked during operation and thus has a flow resistance that is changed in comparison to the original flow resistance, while at least another of the tubes is largely intact and continues to have fluid flow through it and thus has a flow resistance that deviates from the aforementioned flow resistance. Said change of the flow resistance can, for example, result from a solid particle being jammed in one of the tubes or from a deposition forming on the tube wall of the respective tube. Nevertheless, according to US-A 2011/0113896 or WO-A 2009/134268, a diagnosis relating to such impairment of the functionality of the transducer device can, for example, also be carried out based on measuring point temperatures that are sensed during operation of the respective transducer device or of the measuring system formed therewith at various temperature measuring points established at the respective tubes. For example, on the basis of an excessive deviation between such measuring point temperatures, any change in the flow resistance of one of the tubes can be detected. Further investigations have also surprisingly revealed that such a detection can also be reliably realized using the aforementioned temperature sensor arrangement. Accordingly, the measuring and operation electronics unit ME according to another embodiment of the invention is furthermore designed to generate, using both the temperature measurement signal 1 and the temperature measurement signal 2, a temperature deviation measurement value, which represents a, for example absolute or relative, deviation between the measuring point temperature 1 and the measuring point temperature 2. In addition, the measuring and operation electronics unit ME is furthermore also designed to, using said temperature deviation measurement value X.sub., monitor a functionality of the transducer device, namely, for example, a functionality of the tube 11 and/or a functionality of the tube 12, and optionally to diagnose that the transducer device has a flow resistance which is changed in comparison to an original flow resistance, i.e. that at least one of the tubes of the transducer device has a flow resistance which is changed in comparison to an original flow resistance and/or that the tube 11 has a flow resistance that deviates from a flow resistance of the tube 12. For example, the measuring and operation electronics unit ME may also be designed to generate, using the temperature deviation measurement value X.sub., an alarm which signals an only limited functionality of the transducer device, for example as a result of the aforementioned changes in the flow resistance.

(59) According to another embodiment of the invention, the measuring and operation electronics unit ME is furthermore designed to generate, using the temperature measurement signal 1 although not the temperature measurement signal 2 or using the temperature measurement signal 2 although not the temperature measurement signal 1, an auxiliary temperature measurement value .sub.x,MW*, which at least approximately represents the transducer device temperature. As a result, even, for example, for the case that precisely one of the two temperature sensors 71, 72 is defective and/or is disconnected from the measuring and operation electronics unit ME, for example as a result of a failure of one of the aforementioned connecting lines, a measurement value for the transducer device temperature can nevertheless be determined and be output as an alternative to the transducer temperature measurement value X.sub., MW. In addition, the measuring and operation electronics unit ME can furthermore also be designed to generate, using the temperature measurement signal 1 although not the temperature measurement signal 2 or using the temperature measurement signal 2 although not the temperature measurement signal 1, a (further) auxiliary temperature measurement value X.sub.,FL*, which at least approximately represents the measurement fluid temperature, and to optionally output said auxiliary temperature measurement value X.sub.,FL* as an alternative to the measurement fluid temperature measurement value X.sub.,FL. Alternatively or additionally, the measuring and operation electronics unit ME can also be designed to detect the aforementioned defect of one of the temperature sensors 71, 72 or the aforementioned disconnection of one of the temperature sensors 71, 72 from the measuring and operation electronics unit ME and to optionally report it, for example in the form of a maintenance message.

(60) In addition, as already mentioned, the measuring system can also furthermore be designed to measure a density and/or a viscosity of the medium based on a useful signal component at least of one of the vibration signals and/or based on the exciter signal, for example. For this purpose, the measuring and operation electronics unit ME according to a further embodiment of the invention is furthermore designed to recurrently generate, using at least one of the vibration signals s1, s2, a frequency measurement value x.sub.f, which represents a frequency of the mechanical vibrations of the tubes 11, 12; this in particular such that, using the vibration signal, a useful frequency, namely a vibration frequency of the useful vibrations dependent on the measurement variable to be measured, is determined and the frequency measurement value x.sub.f represents said useful frequency. As already mentioned and as is quite common in vibronic measuring systems of the type in question, as useful frequency can be selected one of the resonant frequencies respectively inherent in the fluid-carrying tubes, namely, for example, a resonant frequency of a bending vibration mode of the tubes. In addition, the measuring and operation electronics unit ME according to another embodiment of the invention is designed to generate at least one further measurement value using at least the frequency measurement value. Said measurement value generated by means of the frequency measurement value x.sub.f can, for example, be a density measurement value x.sub. representing the density of the fluid FL1 and/or a viscosity measurement value x.sub. representing the viscosity of the fluid FL1. The measuring and operation electronics unit ME according to another embodiment of the invention is furthermore designed to also generate the at least one density measurement value X.sub. and/or the at least one viscosity measurement value x.sub. using both the temperature measurement signal 1 generated by means of the transducer device and at least the temperature measurement signal 2 generated by means of the transducer device.