The invention relates to a method for ascertaining a temperature of a substance to be measured, viz., a temperature of a measured substance conducted in a line, and to a corresponding measuring system.
US-A 2017/0074701, US-A 2017/0074730, WO-A 2017/131546, or WO-A 2015/099933 disclose measuring systems or methods for ascertaining a measured substance temperature, viz., a temperature of a measured substance, e.g., a gas, a liquid, or a dispersion, flowing in a line, e.g., a pipe, wherein a temperature of a typically metallic wall (wall temperature) surrounding the lumen of the line is detected on a surface facing away from the lumen (lateral surface) by means of one or more temperature sensors, and the measured substance temperature values representing the measured substance temperature are generated, e.g., viz., calculated, on the basis of temperature measurement signals generated therewith.
At least one of the temperature sensors of the particular measuring system is formed by means of temperature sensors, which are arranged outside the line and are therefore not contacted by the measured substance flowing in the lumen in the line during operation, and optionally also a coupling body, consisting, for example, of a thermal adhesive, which connects said temperature sensor to the wall in a thermally conductive manner. The temperature sensor is also configured to convert a wall temperature, corresponding to a temperature at a temperature measuring point formed by means of the in particular temperature sensor, into a corresponding temperature measuring signal, viz., an electrical measuring signal representing the particular wall temperature, e.g., with an electrical signal voltage dependent upon said wall temperature, and/or an electrical signal current dependent upon said wall temperature. The temperature sensor can accordingly be, for example, a platinum measuring resistor, a thermistor or a thermocouple, or also an electrical circuit formed by means of several such temperature-sensitive electrical or electronic components.
Each of the measuring systems described above further comprises measuring system electronics which are configured to receive at least one temperature measuring signal and to generate the measured substance temperature values using said temperature measuring signal. For this purpose, the measuring system electronics are typically electrically connected directly to the at least one temperature sensor by means of corresponding connecting lines. In the case of measuring systems used in industrial measuring and automation technology, the measuring system electronics are usually realized by means of one or more microprocessors, optionally also designed as digital signal processors (DSP), in such a way that the measuring system electronics determine the particular temperature measured values by numerically calculating digital sampling values obtained from the measurement signals, not least the at least one temperature measurement signal, and provide them in the form of corresponding digital values. In addition, the measuring system electronics are also typically accommodated within at least one comparatively robust, in particular impact-resistant, pressure-resistant, and/or weather-proof, electronics housing. The electronics housing can, for example, be arranged apart from the line, or can also be arranged in the immediate vicinity thereof, and possibly also fixed on the line. The particular measuring system electronics unit can also be electrically connected via corresponding electrical lines to a superordinate electronic data processing system which is arranged spatially remote from the particular measuring system and is also spatially distributed and to which the measurement values generated by the particular measuring system are passed on in a timely manner, e.g., also in real time, by means of at least one measurement value signal suitably carrying these measurement values. The data processing system can be formed, for example, by means of programmable logic controllers (PLC) and/or process control computers installed in a control room, and by means of corresponding data transmission networks—for example, a fieldbus system and/or a radio network. Further examples of measuring systems for ascertaining a measured substance temperature by means of temperature sensors arranged outside on a line conducting the measured substance are disclosed, inter alia, in EP A 919 793, US-A 2008/0127745, US-A 2008/0115577, US-A 2011/0113896, U.S. Pat. Nos. 4,768,384A, 7,040,179B, WO-A 95/08758, WO-A 01/02816, WO-A 2009/051588, WO-A 2009/134268, WO-A 2012/018323, WO-A 2012/033504, WO-A 2012/067608, or WO-A 2012/115639.
As in US-A 2017/0074701, US-A 2017/0074730, EP-A 919 793, US-A 2008/0127745, US-A 2008/0115577, US-A 2011/0113896, U.S. Pat. Nos. 4,768,384A, 7,040,179B, WO-A 95/08758, WO-A 01/02816, WO-A 2009/051588, WO-A 2009/134268, WO-A 2012/018323, WO-A 2012/033504, WO-A 2012/067608, or WO-A 2012/115639, measuring systems of the type in question can furthermore also be configured to determine at least one further measured variable of the measured substance flowing in the line which deviates from the measured substance temperature, in particular, viz., to generate measured values representing this variable. For example, such a measuring system can also be a vibronic measuring system that is useful for measuring one or more substance parameters of the measured substance, such as a density and/or a viscosity, and/or the measurement of one or more flow parameters of the measured substance, e.g., a mass and/or volume flow and/or a flow velocity, and consequently generates corresponding density measured values, viscosity measured values, mass flow measured values, volume flow measured values, and/or flow velocity during operation. The structure and mode of operation of such vibronic measuring systems, formed by means of the aforementioned measuring transducer of the vibration-type typically designed as a (metal) pipe and comprising a line—e.g., also designed as Coriolis mass-flow measuring devices, or also as Coriolis mass-flow/measuring systems, are known to a person skilled in the art and per se and are, for example, described extensively and in detail in US-B 65/133,393, U.S. Pat. Nos. 6,651,513B, 7,017,242B, 7,406,878B, 8,757,007B, 8,671,776B, or 8,924,165B or also in the mentioned US-A 2017/0074701, US-A 2017/0074730, EP-A 919 793, US-A 2008/0127745, US-A 2008/0115577, US-A 2011/0113896, U.S. Pat. Nos. 4,768,384A, 7,040,179B, WO-A 01/02816, WO-A 2009/051588, WO-A 2009/134268, WO-A 2012/018323, WO-A 2012/033504, WO-A 2012/067608, or WO-A 2012/115639. With such vibronic measuring systems, the line is also configured in particular to at least temporarily be vibrated while having the measured substance flow through for the purpose of measuring the material and/or flow parameter during operation. Typically, for this purpose, the line is actively excited to useful vibrations, viz., mechanical vibrations, about a static rest position associated with the particular line, by means of at least one vibration exciter of the measurement transducer acting thereupon in an electromechanical manner, formed for example by means of a permanent magnet affixed to the outside of the line, and by means of an exciter coil interacting therewith, especially also such mechanical vibrations as are suitable for inducing Coriolis forces in the flowing measured substance dependent upon its mass flow, and/or which are suitable for inducing frictional forces in the flowing measured substance dependent upon its viscosity, and/or which are suitable for inducing inertial forces in the flowing measured substance dependent upon its density. In order to detect mechanical vibrations of the line, and not least also their useful vibrations, the particular (vibronic) measuring system further comprises at least one, e.g., electrodynamic, vibration sensor which is configured to convert at least one vibration signal, viz., an electrical vibration measurement signal representing vibration movements of the line—for example, with an electrical signal voltage dependent upon a speed of the vibration movements of the line. The measuring system electronics of such vibronic measuring systems—not least for the above-described case in which the density measured values representing the density of the measured substance and/or viscosity measured values representing the viscosity of the measured substance can be generated—are further configured to also generate measured values using both the at least one temperature measurement signal and the at least one vibration signal, e.g., in such a way that the measuring system electronics determine density measured values and/or viscosity measured values based upon a useful frequency measured by the vibration signal, viz., a vibration frequency of the useful vibrations which is dependent upon the material parameter to be measured, and for this purpose also metrologically compensates for any dependence of the useful frequency on a momentary measuring fluid temperature. In addition to the evaluation of the temperature measurement signals and of the at least one vibration signal, the measuring system electronics of such vibronic measuring systems typically also serve to generate at least one, for example, harmonic and/or clocked driver signal for the at least one electromechanical vibration exciter. Said drive signal can, for example, be regulated with regard to a current intensity and/or a voltage level.
Further investigations have shown that measured substance temperature values determined by means of the aforementioned methods or measuring systems can differ considerably from the true or actual measured substance temperature, even at comparatively low flow velocities of the measured substance flowing in the line at about 0.1 m·s−1 and/or given comparatively low Reynolds numbers of about 100 of the measured substance flowing in the line, e.g., in such a way that measured substance temperature values, which represent a core temperature of the measured substance corresponding to a temperature of a partial volume of the measured substance in the center of the lumen, can deviate more than 4K from said core temperature; this in particular also when taking into account heat flows detected by means of two or more temperature sensors within the wall and/or within an atmosphere enclosing the line—for example, according to the cited US-A 2017/0074701, US-A 2017/0074730, US-A 2008/0127745, U.S. Pat. No. 7,040,179B, WO-A 2017/131546, or WO-A 2015/099933.
To this end, it is an object of the invention to specify a method which allows a precise determination of a measured substance temperature of a measured substance flowing in a line, not least, specifically, a core temperature of the measured substance, based upon a measured wall temperature; this in particular also in the case of flow velocities of the measured substance flowing in the line of more than 0.1 m·s−1, or in the case of Reynolds numbers of the measured substance flowing in the line of more than 100 and/or also in such a way that the determined measured substance temperature, or a measured substance temperature value representing this, deviates from the true measured substance temperature by less than 3 K, especially also less than 1 K. Moreover, a further object of the invention is to specify a measuring system suitable for executing such a method.
To achieve the object, the invention consists of a method for ascertaining a measured substance temperature TM, viz., a temperature, in particular a core temperature, of a measured substance conducted in a line, in particular a tube, wherein the line has a lumen enclosed by an, especially metallic, wall, which method comprises:
V=f(Δp, ρ, μ, λ, cp)=Pra·Ecb·ζc;
X
TM
=X
TW−(k1·XV+k2)=XTW−XΔT.
In addition, the invention also consists of a measuring system, e.g., a vibronic measuring system, which is configured to implement the method according to the invention, wherein the measuring system comprises a temperature sensor thermally coupled to a lateral surface of the wall for generating a temperature measurement signal following a change of a temperature Tw of the wall, e.g., viz., a surface temperature of a hollow cylindrical segment of the wall, with a change of at least one signal parameter, e.g., viz., an electrical temperature measurement signal, as well as measuring and operating electronics electrically connected to the temperature sensor—for example, also formed by means of at least one microprocessor.
According to a first embodiment of the method according to the invention, it is further provided that the measured substance temperature value XTM satisfy a calculation rule dependent upon both the characteristic number value XV as well as the wall temperature value XTw, and parameterized by a line-specific first coefficient k1 and a line-specific second coefficient k2:
X
TM
=X
TW−(k1·XV+k2)=XTW−XΔT
In further developing this embodiment of the invention, the first coefficient k1 and the second coefficient k2 are previously determined (calibration) constants, and/or the first coefficient k1 is not less than 0.5 K (Kelvin) and no more than 1.5 K; and/or the second coefficient k2 is not less than −0.2 K and not more than 0.2 K—for example, is equal to 0.
According to a second embodiment of the method according to the invention, it is further provided that the first exponent a be more than 0.1 and less than 0.5—for example, 0.3.
According to a third embodiment of the method according to the invention, it is further provided that the second exponent b be more than 0.8 and less than 1.2—for example, 1.
According to a fourth embodiment of the method according to the invention, it is further provided that the third exponent c be more than 0.8 and less than 1.2—for example, 1.
According to a fifth embodiment of the method according to the invention, it is further provided that the second exponent b be equal to the third exponent c—for example, viz., equal to one.
According to a sixth embodiment of the method according to the invention, it is further provided that the parameter value XV satisfy a calculation rule:
In further developing this embodiment of the invention, the second exponent b is equal to one.
According to a seventh embodiment of the method according to the invention, it is further provided that the specific heat capacity cp of the measured substance be not less than 1 kJ·kg−1·K−1 and no more than 5 kJ·kg−1·K−1.
According to an eighth embodiment of the method according to the invention, the thermal conductivity λ of the measured substance is not less than 0.1 W·m−1·K−1 and not more than 1 W·m−1·K−1.
According to a ninth embodiment of the method according to the invention, it is further provided that the viscosity μ of the measured substance be greater than 1 mPa·s—for example, greater than 10 mPa·s.
According to a tenth embodiment of the method according to the invention, it is further provided that the density ρ of the measured substance be greater than 500 kg·m−3 and/or less than 2,000 kg·m−3.
According to an eleventh embodiment of the method according to the invention, it is further provided that the measured substance flowing in the line have a flow velocity U, e.g., average or greatest, which is greater than 0.1 m·s−1—for example, greater than 1 m·s−1.
According to a twelfth embodiment of the method according to the invention, it is further provided that the measured substance flowing in the line have a mass flow {dot over (m)} greater than 0.01 kg·s−1—for example, greater than 0.1 kg·s−1.
According to a thirteenth embodiment of the method according to the invention, it is further provided that the measured substance flowing in the line have a Reynolds number Re which is greater than 100—for example, greater than 1,000.
According to a fourteenth embodiment of the method according to the invention, it is further provided that the density value Xρ deviate from the (true) density ρ of the measured substance by not more than 0.5% of the density ρ (fρ<0.5%)—for example, by more than 0.1% of the density ρ (fρ>0.1%).
According to a fifteenth embodiment of the method according to the invention, it is further provided that the pressure differential value XΔp deviate from the (true) pressure differential Δp by not more than 15% of the pressure differential Δp (fΔp<15%)—for example, by more than 5% of the pressure differential Δp (fΔp>5%).
According to a sixteenth embodiment of the method according to the invention, it is further provided that the viscosity value Xμ deviate from the (true) viscosity μ of the measured substance by not more than 15% of the viscosity μ (fμ<15%)—for example, by more than 2% of the viscosity μ (fμ>2%).
According to a seventeenth embodiment of the method according to the invention, it is further provided that the thermal conductivity value Xλ deviate from the (true) thermal conductivity λ of the measured substance by not more than 50% of the thermal conductivity λ (fλ<50%)—for example, more than 5% of the thermal conductivity λ (fλ>5%).
According to an eighteenth embodiment of the method according to the invention, it is further provided that the heat capacity value Xcp deviate from the (true) specific heat capacity cp of the measured substance by no more than 50% of the specific heat capacity cp (fcp<50%)—for example, by more than 5% of the specific heat capacity cp (fcp>5%).
According to a nineteenth embodiment of the method according to the invention, it is further provided that the measured substance temperature value XTM deviate from the (true) temperature TM, e.g., viz., the core temperature, of the measured substance by less than 2 K—for example, less than 1 K.
According to a twentieth embodiment of the method according to the invention, it is further provided that the wall temperature Tw (TM<Tw), be higher, e.g., by more than 1 K, than the temperature TM of the measured substance—for example, viz., a core temperature of the measured substance.
According to a twenty-first embodiment of the method according to the invention, it is further provided that the measured substance temperature value XTM be less than the wall temperature value XTw (XTM<XTw).
According to a twenty-second embodiment of the method according to the invention, it is further provided that the measured substance temperature value XTM represent a core temperature of the measured substance.
According to a twenty-third embodiment of the method according to the invention, it is further provided that the wall temperature value XTw represent the temperature Tw, e.g., the surface temperature, of a hollow cylindrical segment of the wall.
According to a twenty-fourth embodiment of the method according to the invention, it is further provided that, for ascertaining the at least wall temperature value XTw, a surface temperature of the wall, e.g., viz., on a hollow cylindrical segment of the wall, be ascertained.
According to a twenty-fifth embodiment of the method according to the invention, it is further provided that the wall of the line consist of metal—for example, a steel, a titanium alloy, a tantalum alloy, or a zirconium alloy.
According to a twenty-sixth embodiment of the method according to the invention, it is further provided that the wall of the line have a wall thickness which is not less than 0.5 mm, e.g., more than 1 mm, and/or no more than 5 mm—for example, less than 3 mm.
According to a twenty-seventh embodiment of the method according to the invention, it is further provided that the line for ascertaining the density value, and/or for ascertaining the viscosity value, and/or for ascertaining the pressure differential value XΔp be made to vibrate, e.g., viz., actively excited to mechanically vibrate by means of an electromechanical vibration exciter of the Coriolis mass flow/density measuring device.
According to a first embodiment of the measuring system according to the invention, the measuring and operating electronics are further configured to ascertain at least one measured substance temperature value XTM. Furthermore, the measuring and operating electronics can also be configured to ascertain the at least one wall temperature value XTw and/or the at least one characteristic number value XV for the measured substance characteristic number V.
According to a first development of the invention, the method further comprises ascertaining a flow index n of the measured substance flowing in the line.
According to a second development of the invention, the method further comprises ascertaining at least one Reynolds number value XRe representing a Reynolds number Re of the measured substance flowing in the line. Furthermore, the pressure loss coefficient value Xζ can therefore be calculated such that it satisfies a calculation rule:
X
ζ
=k41+k42·XRek43.
According to a third development of the invention, the method further comprises ascertaining at least one mass flow value X{dot over (m)} representing a mass flow {dot over (m)} of the measured substance flowing in the line.
According to a fourth development of the invention, the method further comprises both ascertaining at least one Reynolds number value XRe representing a Reynolds number Re of the measured substance flowing in the line, as well as ascertaining at least one mass flow value X{dot over (m)} representing a mass flow {dot over (m)} of the measured substance flowing in the line, and it is additionally provided that the pressure differential value XΔp satisfy a calculation rule:
and/or that the Reynolds number value XRe satisfy a calculation rule:
According to a fifth development of the invention, the method further comprises ascertaining at least one velocity value XU representing a, for example, mean or largest flow velocity U of the measured substance flowing in the line. Furthermore, the pressure loss coefficient value Xζ can therefore be calculated such that it satisfies a calculation rule:
and/or the characteristic number value XV can be calculated such that it satisfies a calculation formula:
According to a sixth development of the invention, the method further comprises using a Coriolis mass flow/density measuring device for ascertaining the density value Xρ, and/or for ascertaining the viscosity value Xμ, and/or for ascertaining the pressure differential value XΔp. The line can accordingly also be a component of the Coriolis mass flow/density measuring device, for example.
According to a seventh development of the invention, the method further comprises using a pressure differential measuring device for ascertaining the pressure differential value XΔp. The line can accordingly also be a component of the pressure differential measuring device, for example.
According to an eighth development of the invention, the method further comprises both ascertaining a first static pressure established in the flowing measured substance, and a second static pressure established in the flow direction downstream thereof in the flowing measured substance, as well as ascertaining the pressure differential value XΔp based upon the ascertained first and second static pressures.
According to a ninth development of the invention, the method further comprises both ascertaining the temperature Tw of the wall, especially a surface temperature of a hollow cylindrical segment of the wall, as well as generating an, in particular electrical, temperature measurement signal following a change in said temperature Tw with a change of at least one signal parameter.
According to a tenth development of the invention, the method further comprises using a temperature sensor thermally coupled to a lateral surface of the wall for generating the temperature measuring signal.
According to an eleventh development of the invention, the method further comprises using the temperature measurement signal for ascertaining the at least one wall temperature value XTw.
In a twelfth development of the invention, the measuring system comprises a vibration exciter for exciting mechanical vibrations of the line, as well as at least two vibration sensors for ascertaining mechanical vibrations of the line and for converting said vibrations into vibration signals. Furthermore, both the vibration exciter as well as the first and second vibration sensors can be electrically connected to the measuring system electronics, and the measuring system electronics can be configured to feed electrical power into the vibration exciter by means of an electrical excitation signal useful for causing mechanical vibrations of the line, as well as to receive and evaluate the vibration signals of the vibration sensors, e.g., viz., to digitize and/or ascertain the density value, and/or the viscosity value Xμ, and/or the pressure differential value XΔp, and/or the mass flow value X{dot over (m)}, and/or the Reynolds number value XRe on the basis of the vibration signals or on the basis of the vibration signals as well as the electrical excitation signal.
According to a thirteenth development of the invention, the measuring system comprises first and second pressure sensors for ascertaining the pressure differential which are inserted in the wall of the line at a distance from one another in the direction of flow. Furthermore, both the first pressure sensor and the second can be electrically connected to the measuring system electronics, and the measuring system electronics can be configured to ascertain the pressure differential value XΔp, e.g., viz., also the viscosity value Xμ and/or the velocity value XU, by using pressure measurement signals, including digital ones for example, generated by means of the aforementioned pressure sensors.
A basic idea of the invention is to ascertain an (additional) heating of the measured substance flowing in the line by converting kinetic energy of the flowing measured substance into thermal energy due to friction processes within the measured substance flowing through the line, or between the flowing measured substance and the wall of the line, by means of further material and flow parameters of the measured substance, viz., its density, its viscosity, its thermal conductivity, its thermal capacity as well as the pressure differential, and to accordingly take it into account when ascertaining the measured substance temperature on the basis of the wall temperature.
The invention as well as advantageous embodiments thereof are explained in more detail below based upon exemplary embodiments shown in the figures of the drawing. Identical or identically acting or identically functioning parts are provided with the same reference signs in all figures; for reasons of clarity or if it appears sensible for other reasons, reference signs mentioned before are dispensed with in subsequent figures. Further advantageous embodiments or developments, especially, combinations of partial aspects of the invention that were initially explained only separately, furthermore emerge from the figures of the drawing and/or from the claims themselves.
In particular:
To ascertain the measured substance temperature TM, the measured substance is, according to the invention, provided by the line in a predetermined flow direction, e.g., with a flow velocity U of more than 0.1 m/s, and/or with a mass flow {dot over (m)} greater than 0.01 kg·s−1, and, as shown schematically in
Unavoidable friction processes within the measured substance flowing through the line, or also between the flowing measured substance and the wall of the line, lead to the fact that kinetic energy of the flowing measured substance is converted into thermal energy, and therefore, by dissipation, (additional) heating is generated of the measured substance flowing in the line, e.g., viz., in a partial volume of the flowing measured substance located close to the wall; and this regularly in such a way that a temperature difference is established along one and the same radius of the line between the wall temperature and the measured substance temperature, and/or the wall temperature Tw is higher than the measured substance temperature TM (TM<Tw) actually to be measured. Not least for the case described above, where the measured substance temperature TM to be ascertained is a core temperature of the measured substance, the aforementioned dissipation can cause this to actually be more than 1 K less than the (measured) wall temperature Tw. The aforementioned friction processes can also be particularly pronounced, inter alia, when the measured substance flowing in the line has a flow velocity U that is greater than 0.1 m·s−1, especially greater than 1 m·s−1, and/or when the measured substance flowing in the line has a mass flow {dot over (m)} greater than 0.01 kg·s−1, e.g., also greater than 0.1 kg·s−1, and/or when the measured substance FL flowing in the line has a Reynolds number Re which is greater than 100, especially, viz., also greater than 1,000. The Reynolds number Re of the measured substance flowing in the line is a dimensionless parameter for fluids, which is known to be defined as a ratio between inertial and viscous forces in the flowing fluid and which, inter alia, also corresponds to a calculation formula that depends upon a characteristic length L or A:
Furthermore, the aforementioned friction processes could also be observed in particular with such measured substances in which a specific heat capacity cp is not less than 1 kJ·kg−1·K−1, and/or in which thermal conductivity λ is not less than 0.1 W·m−1·K−1, and/or in which a viscosity is μ greater than 1 mPa·s, especially, viz., greater than 10 mPa·s, and/or in which a density ρ is greater than 500 kg·m−3.
To ascertain the measured substance temperature TM according to the invention, taking into account the aforementioned friction processes or the associated dissipation, additionally at least one density value Xρ representing a density ρ of the measured substance flowing in the line is ascertained, along with at least one viscosity value Xμ representing a viscosity μ, especially an effective dynamic viscosity, of the measured substance flowing in the line, at least one thermal conductivity value Xλ representing the thermal conductivity λ of the measured substance, at least one heat capacity value Xcp representing a specific heat capacity cp of the the measured substance, as well as at least one pressure differential value XΔp representing a pressure differential Δp established within the measured substance flowing in the line in the flow direction, especially, viz., a differential between a first static pressure p1 established in the flowing measured substance and a second static pressure p2 established downstream of the first static pressure p1 in the flowing medium. The viscosity μ of the measured substance can generally also be defined or ascertained, e.g., as an effective viscosity μ, in such a way that it corresponds to a calculation formula depending upon a consistency K of the measured substance flowing in the line, a shear velocity {dot over (γ)} of the measured substance flowing in the line, and a flow index n of the measured substance flowing in the line:
wherein the consistency K of the measured substance flowing in the line is in turn defined as a ratio between a shear stress τ in the measured substance and a shear velocity {dot over (γ)} in the measured substance, and therefore corresponds to a calculation rule:
The aforementioned density values Xρ, viscosity values Xμ, thermal conductivity values Xλ, heat capacity values Xcp, and/or pressure differential values XΔp can for example also be digital values or digital measured values. For the aforementioned case, where the measuring system is formed by a Coriolis mass flow measuring device or is designed as a component of such a Coriolis mass flow measuring device, said Coriolis mass flow measuring device can also be configured to ascertain the aforementioned density value Xρ, and/or the Coriolis mass flow measuring device can be configured to ascertain the aforementioned viscosity value Xμ, and/or the Coriolis mass flow measuring device can be configured to ascertain the aforementioned pressure differential value XΔp. The use of such a measuring system also has, inter alia, the advantage that the density value Xρ can be determined so precisely that it deviates from the (true or actual) density ρ of the measured substance by not more than 0.5% of the density ρ (fρ<0.5%), or the pressure differential value XΔp can be ascertained so precisely that it deviates from the (true or actual) pressure differential Δp by not more than 15% of the pressure differential Δp (fΔp<15%), and/or the viscosity value Xμ deviates from the (true or actual) viscosity μ of the measured substance by not more than 15% of the viscosity μ (fμ<15%). For the other cited case in which the measuring system is formed by means of a pressure differential measuring device or is designed as a component of such a pressure differential measuring device, said pressure differential measuring device can also be used, for example, alternatively or in addition to the aforementioned Coriolis mass flow measuring device to ascertain the pressure differential value XΔp. The use of such a measuring system also has, inter alia, the advantage that the pressure differential value XΔp can be determined so precisely that it deviates from the (true or actual) pressure differential Δp by not more than 5% of the pressure differential Δp (fΔp<5%). The thermal conductivity value Xλ specific to the particular measured substance and/or heat capacity value Xcp, and optionally also the aforementioned flow index n, can, for example, also be correspondingly ascertained in advance and/or with knowledge of the existing measured substance from a specific thermal conductivity value (Xλ) or heat capacity values (Xcp), and flow indices (n) can also optionally be read out from a (value) table assigned to a particular measured substance, optionally also recurring, e.g., regularly, and/or due to a change or a replacement of the measured substance in the line.
According to the invention, the density value Xρ, the viscosity value Xμ, the pressure differential value XΔp, the thermal conductivity value, and the heat capacity value are, further, also used to ascertain at least one characteristic number value XV for a measured substance characteristic number V which characterizes a heating of the measured substance flowing in the line caused by dissipation—for example, in a partial volume of the flowing measured substance located close to the wall. To process the density value Xρ, the viscosity value Xμ, the pressure differential value XΔp, thermal conductivity value, and heat capacity value Xcp, or for calculating the characteristic number value XV, the measuring system can further comprise corresponding (measuring system) electronics 20 which, for example, generate digital measurement values and/or are formed by means of a microprocessor, which can in turn be accommodated in a separate (electronics) protective housing 200, for example. Said (electronics) protective housing 200 can, for example, be designed to be impact and/or explosion resistant, and/or can be configured to protect the (measuring system) electronics from dust and/or splash water. According to a further embodiment of the invention, the (measuring system) electronics 20 are designed in particular to ascertain the at least one measured substance temperature value XTM.
The (measuring system) electronics 20 can also have, for example, a non-volatile data memory (EEPROM) for storing digital data, especially also digital (measured) values. In a further embodiment of the invention, said data memory is configured to save the at least one thermal conductivity value Xλ and/or the at least one heat capacity value Xcp. Accordingly, the aforementioned (value) table for specific thermal conductivity values, and/or the specific heat capacity value, and/or the one for flow indices can also be stored in the data memory such that at least one specific thermal conductivity value (Xλ), and/or at least one particular specific heat capacity value (Xcp), and/or a particular flow index (n) can be assigned to an entry for a specific measured substance and read out for calculating the characteristic number value XV. Furthermore, the at least one wall temperature value XTw, the at least one density value Xρ, the at least one viscosity value Xμ, and/or the at least one pressure differential value XΔp can also be stored in the non-volatile data memory, and/or the at least one characteristic number value XV, and/or the at least one measured substance temperature value XTM can also be (intermediately) saved in the non-volatile data memory. For the aforementioned case in which a temperature sensor 21 is provided for acquiring the wall temperature Tw and for generating the temperature measurement signal θ1 representing it, the (measuring system) electronics 20 can also be electrically connected to the temperature sensor, e.g., by means of an electrical connection line, and the (measuring system) electronics 20 can also be configured to receive and evaluate said temperature measurement signal θ1, e.g., viz., to digitize and/or ascertain the wall temperature value XTw based upon temperature measurement signal θ1. For the other aforementioned case in which the measuring system is formed by a Coriolis mass flow measuring device, the (measuring system) electronics 20 can, just like the line, also be a component of said Coriolis mass flow measuring device, or, for the cited case in which the measuring system is formed by a pressure differential measuring device, the (measuring system) electronics 20 can also be part of said pressure differential measuring device.
According to the invention, the aforementioned measured substance characteristic number V corresponds to a calculation determined by an Eckert number Ec of the measured substance flowing in the line, a Prandtl number Pr of the measured substance flowing in the line, and a pressure loss coefficient ζ of the line, as well as by a line-specific first exponent a, a line-specific second exponent b, and a line-specific third exponent c:
V=f(Δp, ρ, μ, λ, cp)=Pra·Ecb·ζc (4).
Typically, the exponent a is more than 0.1 and less than 0.5, especially, viz., 0.3. The exponent b and the exponent c in turn can each be more than 0.8 and less than 1.2, e.g., viz., the same, and/or can each be 1.
Using both the aforementioned wall temperature value XTw as well as the ascertained characteristic number value XV, at least one measured substance temperature value XTM representing the temperature TM of the measured substance, e.g., viz., its core temperature, has been ascertained according to the invention; this, for example, such that the measured substance temperature value XTM satisfies the calculation rule depending, inter alia, upon both the characteristic number value XV as well as the wall temperature value XTw:
X
TM
=X
TW−(k1·XV+k2)=XTW−XΔT (5).
The aforementioned calculation rule for the wall temperature value XTw can further be parameterized by a line-specific first coefficient k1 and a line-specific second coefficient k2. For a particular measuring system, said coefficient k1, k2 can be (calibration) constants ascertained in advance, e.g., over the course of calibration under reference conditions, wherein the coefficient k1 is typically not less than 0.5 K (Kelvin) and not more than 1.5 K, and/or wherein the coefficient k2 is typically not less than −0.2 K and not more than 0.2 K, can also optionally, viz., be set to zero if desired. According to a further embodiment of the invention, the characteristic number value XV as well as the line-specific first and second coefficients k1, k2 are dimensioned such that, especially in the case of flowing measured substance and/or in the case in which the measured substance temperature value XTM represents a core temperature of the measured substance, the measured substance temperature value XTM is less than the wall temperature value XTw (XTM<XTw).
The Prandtl number Pr of the measured substance flowing in the line is a dimensionless parameter for fluids, which is known to be defined as a ratio between viscosity μ and thermal conductivity λ, and therefore corresponds to a calculation formula:
or, when using the effective viscosity, accordingly corresponds to a calculation formula:
The Eckert number Ec of the measured substance flowing in the line is also a dimensionless parameter for fluids which is defined as a ratio of kinetic energy of the flowing measured substance and an enthalpy difference established between said measured substance and the wall, or corresponds to a calculation formula:
wherein, in determining the measured substance temperature TM according to the invention, the temperature difference ΔT to be used therefor can be easily assumed to be constant, e.g., set to 1 K, so that the Eckert number Ec can also correspond to a simplified calculation formula:
for example, with k3=1 K−1. Likewise, the aforementioned pressure loss coefficient ζ of the measured substance flowing in the line is also dimensionless. In the present case, this is a measure of a pressure loss in or along the line through which the flow passes, wherein the pressure loss coefficient ζ, occasionally also referred to as the pressure loss or resistance coefficient, corresponds to a calculation formula:
Accordingly, the measured substance characteristic number V can also be defined by a calculation formula:
To determine the characteristic number value XV, according to a further embodiment of the invention, at least one velocity value XU is also determined, which represents a, for example, average or greatest flow velocity U of the measured substance flowing in the line, and the parameter value XV is ascertained based upon the aforementioned calculation formula (11), such that the characteristic number value XV satisfies a calculation rule:
wherein a line-specific third coefficient k3 corresponds with the aforementioned temperature difference ΔT (k3=ΔT−1=kEc).
For the aforementioned typical case in which the exponent b can be set to be equal to the exponent c, the measured substance key value V accordingly also corresponds to a calculation formula which is simplified in comparison to the calculation formula (11), especially, viz., independent of the flow velocity U:
for example, viz., also corresponds to a further simplified calculation formula:
or the measured substance characteristic number V can be defined by one of the simplified calculation formulas (13) or (14). Based upon this, the characteristic number value XV can therefore also be ascertained such that it satisfies a calculation rule which is simpler in comparison with the aforementioned calculation rule (12):
for example, viz.,
According to a further embodiment of the invention, it is further provided that a first static pressure p1 established in the measured substance FL flowing in the line 111 and a second static pressure p2 established in the flow direction downstream thereof in the flowing measured substance be ascertained, and in addition at least the pressure differential value XΔp, e.g., also the viscosity value Xμ and/or the aforementioned velocity value XU, be ascertained on the basis of the detected first and second static pressures. The first and second static pressures p1, p2 or the pressure differential Δp (Δp=p1−p2), as is also indicated in
As mentioned, inter alia, in the above-mentioned U.S. Pat. Nos. 8,757,007B, 8,671,776B, or 8,924,165B, the aforementioned pressure loss coefficient ζ of the measured substance flowing in the line can also correspond to a calculation formula:
ζ=k41+k42·Rek43 (18),
or the pressure differential Δp also corresponds to a calculation formula:
or, taking into account the aforementioned calculation formula (1), for example, also corresponds to a calculation formula:
Furthermore, the pressure differential value XΔp can be ascertained based upon the mass flow {dot over (m)}, the density ρ, as well as the viscosity μ and/or the Reynolds number Re of the flowing measured substance, or the measured substance characteristic number V can therefore also be defined by a calculation formula:
or, with the same exponents b and c, can also be defined by a calculation formula:
As a result, both the pressure loss coefficient ζ as well as the pressure differential Δp can therefore also be ascertained on the basis of such measured variables, which, for example, can also be measured by means of a vibronic measuring system—for example, viz., also a (conventional) Coriolis mass flow measuring device.
Accordingly, according to another embodiment of the invention, it is further provided that at least one mass flow value X{dot over (m)} representing the mass flow {dot over (m)} of the measured substance flowing in the line, and/or at least one Reynolds number value XRe representing the Reynolds number Re of the measured substance flowing in the line be ascertained. The Reynolds number value XRe can, according to the calculation formula (1), be ascertained, for example, such that it satisfies a calculation rule:
or a calculation formula:
wherein the coefficient k61 corresponds with the aforementioned characteristic length L, or the coefficient k62 corresponds with the aforementioned characteristic length A. Using the at least one Reynolds number value XRe as well as the aforementioned mass flow value X{dot over (m)} together with the density value Xρ, both the pressure loss coefficient value Xζ as well as the pressure differential value XΔp can then be calculated, for example, such that the pressure loss coefficient value Xζ satisfies a calculation rule:
X
ζ
=k41+k42·XRek43 (25)
and/or the pressure differential value XΔp satisfies a calculation rule:
If necessary, the velocity value XU can also be ascertained based upon the calculation rule using the at least one mass flow value X{dot over (m)} and the at least one density value Xρ:
The aforementioned coefficients k41, k42, k43, k51, k52, k61, k62, and k7 are in each case likewise line-specific or measuring system-specific (calibration) constants which, just like the aforementioned coefficients k1, k2, can be ascertained in advance for a particular measuring system, e.g., by calibrating the measuring system under reference conditions, e.g., viz., over the course of a calibration of the measuring system at the manufacturer and/or a (re-) calibration of the measuring system on-site.
According to a further embodiment of the invention, it is further provided that the line for ascertaining the density value Xρ, and/or for ascertaining the viscosity value Xμ, and/or for ascertaining the pressure differential value XΔp, and/or the aforementioned mass flow value and/or the predesignated Reynolds number value XRe be made to vibrate; this, for example, such that the line 111 is actively excited to useful vibrations, viz., mechanical vibrations about an associated static rest position with at least one vibration frequency which corresponds to or deviates only slightly from a resonance frequency which is immanent for the line—for example, also, viz., dependent upon the density ρ of the measured material FL flowing in the line 111. The active excitation of mechanical vibrations of the line 111, and therefore the excitation of the useful vibrations, can take place, as is also shown in
As already mentioned, a particular objective of the invention is, inter alia, also that—or the measuring system according to the invention is so suited that—greater measurement accuracy can be achieved in comparison with conventional measuring systems or measuring methods with regard to ascertaining the measured substance temperature TM; and this in particular also such that a measured substance temperature value XTM ascertained according to the invention deviates from the actual or true measured substance temperature TM by less than 3 K, especially less than 1 K, not least in the case in which said measured substance temperature value XTM represents the core temperature. The method according to the invention also has, inter alia, the advantage that the desired high measurement accuracy in ascertaining the measured substance temperature TM can also be achieved if the density value Xρ deviates from the (true or actual) density ρ of the measured substance by not more than 0.5% of the density ρ (fρ<0.5%) and/or if the pressure differential value XΔp deviates from the (true or actual) pressure differential Δp by not more than 15% of the pressure differential Δp (fΔp<15%), and/or if the viscosity value Xμ deviates from the (true or actual) viscosity μ of the measured substance by not more than 15% of the viscosity μ (fμ<15%), and/or if the thermal conductivity value Xλ deviates from the (true or actual) thermal conductivity λ of the measured substance by not more than 50% of the thermal conductivity λ (fλ<50%), and/or if the heat capacity value Xcp deviates from the (true or actual) specific heat capacity cp of the measured substance by no more than 50% of the specific heat capacity cp (fcp<50%); and this in particular also in the case in which the density value Xρ deviates from the (true or actual) density ρ of the measured substance by more than 0.1% of density ρ (fρ>0.1%), and/or the viscosity value Xμ deviates from the (true or actual) viscosity μ of the measured substance by more than 2% of the viscosity μ (fμ>2%), and/or the pressure differential value XΔp deviates from the (true or actual) pressure differential Δp by more than 5% of the pressure differential Δp (fΔp>5%), and/or the thermal conductivity value Xλ deviates from the (true or actual) thermal conductivity λ of the measured substance by more than 5% of the thermal conductivity λ (fλ>5%), and/or the heat capacity value Xcp deviates from the (true or actual) specific heat capacity cp of the measured substance by more than 5% of the specific heat capacity cp (fcp>5%). In ascertaining the measured substance temperature TM according to the invention, it can also be advantageous in this case, and not least also in the case in which the aforementioned core temperature is at issue, for the specific heat capacity cp to be no more than 5 kJ·kg−1·K−1, and/or the thermal conductivity λ of the measured substance to be no more than 1 W·m−1·K−1, and/or the density ρ of the measured substance to be less than 2,000 kg·m−3.
Number | Date | Country | Kind |
---|---|---|---|
10 2020 120 054.4 | Jul 2020 | DE | national |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/EP2021/066756 | 6/21/2021 | WO |