Method for measuring a fluid density or a fluid viscosity

Abstract

A method and device for estimating a density value .sub.m indicative of a true density or for estimating a viscosity value .sub.m indicative of a true viscosity of a fluid is disclosed. For this, a first resonance frequency f.sub.R of a first mechanical oscillator in a reference volume and a second resonance frequency f.sub.F of a second mechanical oscillator in contact with the fluid are measured. The estimated value .sub.m or .sub.m is then derived using these resonance frequencies f.sub.R and f.sub.F. During this derivation, at least one fluid-temperature- or fluid-pressure-dependent parameter of the fluid is used. Additionally or alternatively, the first (i.e. reference) mechanical oscillator is arranged in contact with a reference fluid. Thus, fundamental errors in the derivation of the estimated value .sub.m or .sub.m are reduced and the estimated value becomes more reliable.

Claims

1. A method for deriving an estimated value .sub.m which is indicative of a density of a fluid with a fluid temperature T.sub.F and a fluid pressure p.sub.F, the method comprising the steps of: a) measuring a first resonance frequency f.sub.R of a resonant vibration of a first mechanical oscillator, wherein said first mechanical oscillator is arranged in a reference volume and wherein said first mechanical oscillator is secluded from said fluid; b) measuring a second resonance frequency f.sub.F of a resonant vibration of a second mechanical oscillator, wherein said second mechanical oscillator is arranged in a measurement volume, wherein said measurement volume comprises said fluid, and wherein said fluid is in contact with said second mechanical oscillator; c) deriving said estimated value .sub.m using said first resonance frequency f.sub.R and said second resonance frequency f.sub.F; wherein in said step c) said fluid temperature T.sub.F and/or said fluid pressure p.sub.F and/or at least one parameter which is dependent on said fluid temperature T.sub.F and/or on said fluid pressure p.sub.F is/are used for deriving said estimated value .sub.m; wherein in said step c) a fluid-temperature-dependent viscosity function (T.sub.F) is used for deriving said estimated value .sub.m, wherein the fluid-temperature-dependent viscosity function (T.sub.F) is known, pre-measured or pre-modeled; wherein said estimated value .sub.m, which is indicative of said density of said fluid, is derived; and wherein in said step c) a fluid-temperature-dependent offset parameter C(T.sub.F) is used for deriving said estimated value .sub.m, wherein said fluid-temperature-dependent offset parameter C(T.sub.F) is indicative of a temperature-dependent frequency offset between said first and said second mechanical oscillators, and/or between a first oscillator circuit connected to and used to operate said first mechanical oscillator and a second oscillator circuit connected to and used to operate said second mechanical oscillator.

2. The method of claim 1, wherein a plurality of values of for different fluid temperatures T.sub.F are pre-stored in a lookup-table or calculated on-the-fly.

3. The method of claim 1, wherein in said step c) a fluid-pressure-dependent viscosity function (p.sub.F) is used for deriving said estimated value .sub.m, wherein a plurality of values of for different fluid pressures p.sub.F are prestored in a lookup-table or calculated on-the-fly, by fitting and/or interpolation or extrapolation algorithms.

4. The method of claim 1, wherein in said step c) a fluid-pressure-dependence of the offset parameter C(T.sub.F, p.sub.F) is also used for deriving said estimated value .sub.m.

5. The method of claim 1, wherein a reference-fluid-temperature-dependence /T.sub.F of a viscosity function (T.sub.R) of the reference fluid is equal to or differs less than 30% from a fluid-temperature-dependence /T.sub.F of the fluid-temperature-dependent viscosity function (T.sub.F) of said fluid, at least for fluid temperatures T.sub.F and reference fluid temperatures T.sub.R in a range between 170 K and 400 K.

6. The method of claim 1, wherein said estimated value .sub.m is derived according to: $.Math.f_R-f_F.Math.=.Math.A{}_m+\tilde{B}\sqrt{{}_m}\sqrt{\left(p_f,T_f\right)}+C\left(p_F,T_F\right).Math.$ $\mathrm{with}$ $A=\frac{c_{1}t}{2{}_{q}w}{f}_d$ $\mathrm{and}$ $\tilde{B}=\frac{c_2}{2{}_{q}w}\sqrt{\frac{f_d}{}}$ and with c.sub.1, c.sub.2, t, and w being oscillator-geometry-dependent constants, with .sub.q being an effective density of a material of said mechanical oscillators with (p.sub.F,T.sub.F) being a fluid-pressure- and/or fluid-temperature-dependent viscosity function of said fluid, with f.sub.d being a common design resonance frequency of said first and second mechanical oscillators, and with C(p.sub.F,T.sub.F) being a fluid-pressure- and/or fluid-temperature-dependent offset parameter which is indicative of a frequency offset between said first and said second mechanical oscillator and/or between a first oscillator circuit connected to said first mechanical oscillator and a second oscillator circuit connected to said second mechanical oscillator; wherein said reference fluid temperature T.sub.R in Kelvin is equal to or differs less than 5%, from said fluid temperature T.sub.F; and wherein a reference fluid pressure p.sub.R of a reference fluid is at most 0.1 mbar over a reference fluid temperature range of T.sub.R>200 K and T.sub.R<400 K.

7. The method of claim 1, wherein said first mechanical oscillator is in contact with a reference fluid with a reference fluid pressure p.sub.R of at least 10 mbar, over a reference fluid temperature range of T.sub.R>200 K and T.sub.R<400 K; and wherein said estimated value .sub.m is derived according to $.Math.f_R-f_F.Math.=.Math.A_F{}_m+\left({\tilde{B}}_F\sqrt{}-{\tilde{B}}_R\sqrt{{}_R}\right).Math.\sqrt{\left(p_F,T_F\right)}++D\left(p_F,T_F\right).Math.$ $\mathrm{with}$ $D\left(p_F,T_F\right)=C\left(p_F,T_F\right)-A_R{}_R$ with A.sub.F, A.sub.R, {tilde over (B)}.sub.F, and {tilde over (B)}.sub.R being oscillator-geometry-dependent constants, with subscripts R, F relating to the first and second mechanical oscillator, respectively; with .sub.R being a density of said reference fluid, wherein said density of said fluid is equal to or differs less than 50% from said density .sub.R of said reference fluid; with (p.sub.F,T.sub.F) being a fluid-pressure- and/or fluid-temperature-dependent viscosity function of said fluid, which is equal to or differs less than 50% from a reference-fluid-pressure- and/or reference-fluid-temperature-dependent viscosity function .sub.R(p.sub.R,T.sub.R) of said reference fluid; and with C(p.sub.F,T.sub.F) being a fluid-pressure- and/or fluid-temperature-dependent offset parameter which is indicative of a frequency offset between said first and said second mechanical oscillators and/or between a first oscillator circuit connected to said first mechanical oscillator and a second oscillator circuit connected to said second mechanical oscillator; wherein said first and second mechanical oscillators are selected such that said oscillator-geometry-dependent constants {tilde over (B)}.sub.F and {tilde over (B)}.sub.R are equal or differ less than 50% from each other; and wherein said reference fluid temperature T.sub.R in Kelvin is equal to or differs less than 5% from said fluid temperature T.sub.F.

8. The method of claim 1, wherein said fluid temperature T.sub.F and/or a reference fluid temperature T.sub.R and/or a temperature of said first mechanical oscillator and/or a temperature of said second mechanical oscillator is or are controlled by at least one temperature regulator.

9. The method of claim 1, wherein said first mechanical oscillator, said second mechanical oscillator, said fluid, and said reference fluid have the same temperature.

10. The method of claim 1, wherein said first mechanical oscillator is in contact with a reference fluid with a reference fluid temperature T.sub.R and a reference fluid pressure p.sub.R, and said reference volume comprises said reference fluid.

11. The method of claim 1, wherein the temperature dependence C/T of the offset parameter C is pre-measured or pre-modeled and is used for calibration of the method, or that the mechanical oscillators are selected such that the temperature dependence C/T is less than 0.1 Hz/K.

12. The method of claim 1, further comprising deriving an estimated value .sub.m indicative of a viscosity of the fluid, using said first resonance frequency f.sub.R and said second resonance frequency f.sub.F; wherein said fluid temperature T.sub.F and/or said fluid pressure p.sub.F and/or at least one parameter which is dependent on said fluid temperature T.sub.F and/or on said fluid pressure p.sub.F is/are used for deriving said estimated value .sub.m; and wherein said first mechanical oscillator is in contact with a reference fluid with a reference fluid temperature T.sub.R and a reference fluid pressure p.sub.R, said reference volume comprises said reference fluid, and said reference fluid temperature T.sub.R in Kelvin is equal to or differs less than 5% from said fluid temperature T.sub.F.

13. The method of claim 12, wherein said reference fluid pressure p.sub.R is at most 0.1 mbar over a reference fluid temperature range of T.sub.R>200 K and T.sub.R<400 K, or said reference fluid pressure p.sub.R is at least 1 mbar over a reference fluid temperature range of T.sub.R>200 K and T.sub.R<400 K.

14. The method of claim 12, further comprising the step of deriving said fluid temperature T.sub.F by said first and/or said second mechanical oscillator; and/or deriving said fluid temperature T.sub.F and/or a reference fluid temperature T.sub.R by at least one temperature sensor, a resistance temperature detector, a thermocouple, an integrated circuit temperature sensor, and/or an optical temperature sensor.

15. The method of claim 12, wherein the estimated value .sub.m which is indicative of the viscosity n of the fluid is derived by solving the equation $.Math.{}_m\left(T_F\right).Math.={\left(\frac{.Math.f_F-f_R.Math.-\left(A+C\left(T_F\right)\right)}{\tilde{B}\sqrt{}}\right)}^2$ with f.sub.R being said reference fluid temperature-dependent first resonance frequency, with f.sub.F being said fluid temperature-dependent second resonance frequency, with being a known, pre-measured, or pre-modeled density function of the fluid, with A and {tilde over (B)} being oscillator-specific constants, and with C(T.sub.F) being a fluid-temperature-dependent frequency offset parameter between the first and second mechanical oscillators and/or oscillator circuits.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention and its embodiments will be more fully appreciated by reference to the following detailed description of advantageous but nonetheless illustrative embodiments in accordance with the present invention when taken in conjunction with the accompanying drawings.

(2) FIG. 1 shows a fluid-insulated electrical apparatus 40 with a sensor 1 according to a first embodiment of the invention, wherein a fluid-temperature-dependent viscosity (T.sub.F) is used for deriving an estimated value .sub.m,

(3) FIG. 2 shows a viscosity function (T.sub.F) as a function of a fluid temperature T.sub.F for different gases,

(4) FIG. 3 shows a dependence of an estimated value .sub.m of a fluid temperature T.sub.F, wherein .sub.m is derived with different methods for comparison, and

(5) FIG. 4 shows a fluid-insulated electrical apparatus 40 with a sensor 1 according to a second embodiment of the invention, wherein a reference volume RV comprises a reference fluid R which is in contact with a first mechanical oscillator 10.

BRIEF DESCRIPTION OF THE INVENTION

Description of the Figures

(6) FIG. 1 shows a fluid-insulated electrical apparatus 40 with a sensor 1 according to a first embodiment of the invention. A fluid-temperature-dependent viscosity function (T.sub.F) is used in this embodiment for deriving an estimated value .sub.m which is indicative of a density of a fluid F (see below). The electrical apparatus 40 comprises a fluid compartment 41 which comprises an insulation fluid F (e.g. an insulation gas comprising SF.sub.6) for insulating an electrically active part 42 of the electrical apparatus 40. The insulation fluid has a fluid pressure p.sub.F=3.5 bar, a fluid temperature T.sub.F=20 C., a viscosity =14 Pa s and a density =4.09 kg/m.sup.3. A gas permeable protective mesh 104 can be arranged near a flange on the fluid compartment 41 for preventing the passage of particles and undesired chemical compounds which could damage a connected sensor 1. A connector unit 103 of a sensor 1 connects a measurement volume MV of the sensor 1 to the fluid compartment 41 of the electrical apparatus 40. In the measurement volume MV, a second mechanical oscillator (quartz tuning fork, e.g. model CFS206 from Citizen) with a design resonance frequency of f.sub.d=32.768 k Hz is arranged. This tuning fork is in contact with the fluid F. An oscillator circuit 20a induces a resonant vibration in the tuning fork, but due to interactions with the fluid F, the second resonance frequency f.sub.F=32.758 kHz slightly varies from the design resonance frequency f.sub.d. Furthermore, the second resonance frequency f.sub.F is temperature dependent due to fork-material and oscillator circuit properties. The second mechanical oscillator as well as the second oscillator circuit 20a are in thermal equilibrium with the fluid F, i.e., they have the same temperature T.sub.F. This can, e.g., be facilitated by an optional temperature regulator 105 (dotted) and/or a sensor housing with a high thermal conductivity. Optional temperature sensors 101 (dotted) and/or an optional pressure sensor 102 (dotted) can be used to measure the temperature T.sub.F and/or the pressure p.sub.F of the fluid F as well as a temperature of the first mechanical oscillator. As an alternative to using a temperature sensor 101, the deviation of the second resonance frequency f.sub.F from the design resonance frequency f.sub.d can be used to quantify the fluid temperature T.sub.F, when a constant fluid density in the measurement volume MV is assumed.

(7) In a sealed reference volume RV of the sensor 1, a first mechanical oscillator 10 is arranged (pressure p.sub.R at most 10.sup.4 mbar). The first mechanical oscillator is also a quartz tuning fork e.g. of the same type and the same design resonance frequency f.sub.d as the second mechanical oscillator 20. An oscillator circuit 10a induces a resonant vibration in the first mechanical oscillator 10, but due to the missing interactions with the fluid F, the first resonance frequency f.sub.R=32.768 kHz slightly varies from the second resonance frequency f.sub.F of the second mechanical oscillator 20. The first resonance frequency f.sub.R can also slightly vary from the design resonance frequency f.sub.d due to temperature dependencies of the first mechanical oscillator 10 and the oscillator circuit 10a. In other words, also the first resonance frequency f.sub.R is temperature dependent. The first mechanical oscillator 10 is not in contact with the fluid F, but in thermal equilibrium with the fluid F and the second mechanical oscillator 20. Therefore, also the deviation of the difference between the resonance frequencies f.sub.R and f.sub.F from the difference of the design frequencies f.sub.d,R and f.sub.d,F can be used to quantify the fluid temperature T.sub.F, while fluid and reference fluid densities are assumed to be constant.

(8) The values of f.sub.F and f.sub.R are read out by the oscillator circuits 10a and 20a and transmitted to an analysis and control unit 30 comprising a processing unit 30a and a memory 30b.

(9) Using these resonance frequencies f.sub.R and f.sub.F, the processing unit 30 derives an estimated value .sub.m which is indicative of the density of the fluid F according to

(10) $\begin{array}{cc}.Math.f_R-f_F.Math.=.Math.A{}_m+\tilde{B}\sqrt{{}_m}\sqrt{\left(T_F\right)}+C\left(T_F\right).Math.\mathrm{with}A=\frac{c_{1}t}{2{}_{q}w}{f}_d\mathrm{and}\tilde{B}=\frac{c_2}{2{}_{q}w}\sqrt{\frac{f_d}{}}& \mathrm{eq}.1\end{array}$ and with c.sub.1, c.sub.2, t, and w being tuning-fork-geometry-dependent constants. .sub.q is an effective density of the material of the second mechanical oscillator 20. f.sub.d is the design resonance frequency of the second mechanical oscillator 20.

(11) In this embodiment, a fluid-temperature-dependent viscosity function (T.sub.F) (see FIG. 2) of the fluid F is used for deriving the estimated value .sub.m. Alternatively, also a viscosity function (p.sub.F,T.sub.F) taking into account the fluid pressure p.sub.F could be used (not shown here). This function is pre-stored in the memory 30b as a lookup table for different fluid temperature values T.sub.F. Interpolation algorithms can furthermore be used. The parameter C(T.sub.F) is a fluid-temperature-dependent frequency offset parameter which is indicative of a manufacturing tolerance-induced frequency offset between said first and said second mechanical oscillators 10 and 20 and their respective oscillator circuits 10a and 20a. This parameter also describes fluid-temperature-dependences f/T of the first and second resonance frequencies f.sub.R and f.sub.F and it is also pre-stored in the memory 30b for different temperatures T. A parameter C(p.sub.R,T.sub.R) that is also pressure-dependent is also possible (not shown here).

(12) By using a fluid-temperature-dependent viscosity function (T.sub.F) and a fluid-temperature-dependent frequency offset parameter C(T.sub.F), fundamental errors in the derivation of the estimated values .sub.m (or alternatively .sub.m in a similar embodiment) can be avoided or reduced (see FIG. 3). As stated above, also a pressure dependency of (p.sub.F) and C(p.sub.F) can be taken into account. The effect of such corrections is an order of magnitude smaller than the temperature dependence, however. Specifically, the change of viscosity with pressure is approximately /p=0.5%10 bar in the range between 0.1 bar and 10 bar, while the change of viscosity with temperature is approximately /T=5%100 K in the range between 100 K and 400 K.

(13) It should be noted that resonance frequencies f.sub.R and f.sub.F of at least 1 kHz, preferably at least 30 kHz, more preferably at least 100 kHz of the mechanical oscillators also lead to reduced fundamental viscosity-induced errors in the derivation of .sub.m, because {tilde over (B)}{square root over ((T.sub.F))}{square root over (f.sub.d)}{square root over ((T.sub.F))} while Af and thus the contribution of the viscosity-dependent term becomes smaller with increasing resonance frequencies f.sub.R and f.sub.F. Zeisel et al., A precise and robust quartz sensor based on tuning fork technology for (SF.sub.6)-gas density control, Sensors and Actuators 80 (2000), 233-236 give more details on this.

(14) FIG. 2 shows a viscosity function (T.sub.F) as a function of a fluid temperature T.sub.F for different gases. Such a viscosity function (T.sub.F) is used in the first embodiment of the invention as described with regard to FIG. 1. Specifically here, diamonds show a viscosity for dry air at a pressure of 1 bar, circles show a viscosity for nitrogen at a pressure of 1 bar, and rectangles show a viscosity for SF.sub.6. All gases show a similar temperature dependence /T. Lines are 3.sup.rd order polynomial fits through the measured points. By using a fluid-temperature-dependent viscosity function (T.sub.F), fundamental errors in the derivation of the estimated values .sub.m (or .sub.m) can be avoided or reduced.

(15) FIG. 3 shows an estimated value .sub.m as a function of a fluid temperature T.sub.F as obtained from the first embodiment of the invention as described with regard to FIG. 1. Furthermore, different correction approaches are compared. Specifically, rectangles show prior-art estimated values .sub.m as obtained with a constant (i.e., non-fluid-temperature-dependent) viscosity . As it can be seen, a mis-estimation of the density of the fluid F of 2% results in a temperature range between 10 C. and +70 C. with such an approach due to a fundamental temperature error neglecting the fluid-temperature-dependence of the viscosity .

(16) In contrast, diamonds show estimated values .sub.m as obtained when taking into account a fluid-temperature dependent viscosity function (T.sub.F) as shown in FIG. 2, i.e. according to the present application. Obviously, these estimations are much closer to a true density value , the mis-estimation of the density being reduced to 0.1% over the same temperature range. The true density is shown with a dashed-dotted line. All other lines are linear fits.

(17) FIG. 4 shows a fluid-insulated electrical apparatus 40 with a sensor 1 according to a second embodiment of the invention. The second embodiment is very similar to the first embodiment described with regard to FIG. 1. Therefore, the same reference symbols are used. One difference between the first embodiment and the second embodiment is that the reference volume RV in the second embodiment comprises a reference fluid R with a reference fluid pressure p.sub.R and a reference fluid temperature T.sub.R. The reference fluid R is in contact with the first mechanical oscillator 10. Being exposed to the reference fluid R, which is the same or a similar fluid (see above, i.e. similar in terms of densities and .sub.R, similar in terms of viscosity functions (p.sub.F,T.sub.F) and .sub.R(p.sub.R,T.sub.R) and their temperature-dependences /T), the first (reference) mechanical oscillator will also respond to the same effects like the second (fluid-embedded) mechanical oscillator, provided that the fluid and the reference fluid have the same or at least similar (see above) temperatures T.sub.F and T.sub.R. This can, e.g., be facilitated by an optional temperature regulator 105 (dotted) and/or a sensor housing with a high thermal conductivity. In this second embodiment, the reference fluid pressure p.sub.R is 1 bar. Thus, pressure-dependent effects on the viscosity are similar for the fluid F and the reference fluid R. Fluid temperature T.sub.F and reference fluid temperature T.sub.R can be measured by temperature sensors 101. In this embodiment, the following equation is used for deriving the estimated value .sub.m

(18) $.Math.f_R-f_F.Math.=.Math.A_F{}_m+\left({\tilde{B}}_F\sqrt{}-{\tilde{B}}_R\sqrt{{}_R}\right).Math.\sqrt{\left(p_F,T_F\right)}++D\left(p_F,T_F\right).Math.$ with the same definitions as discussed above.

(19) By arranging the first mechanical oscillator 10 in contact with a reference fluid, fundamental errors in the derivation of the estimated values .sub.m or .sub.m can be intrinsically avoided or reduced.

(20) Definitions:

(21) The term fluid relates to a substance, such as a liquid [and/] or gas, that can flow, has no fixed shape, and offers little resistance to an external stress (from http://www.thefreedictionary.com/fluid, accessed on Sep. 11, 2011).

(22) The term high-voltage relates to voltages larger than 50 kV.

(23) The term medium-voltage relates to voltages larger than 1 kV.

(24) Note:

(25) While there are shown and described presently preferred embodiments of the invention, it is to be distinctly understood that the invention is not limited thereto but may be otherwise variously embodied and practiced within the scope of the following claims.

REFERENCE SYMBOLS

(26) 1 sensor 10 first mechanical oscillator 101 temperature sensor 102 pressure sensor 103 connector unit 104 protective mesh 105 temperature regulator 10a first oscillator circuit 20 second mechanical oscillator 20a second oscillator circuit 30 analysis and control unit 30a processing unit 30b memory 40 fluid-insulated electrical apparatus 41 fluid compartment 42 electrically active part C(T.sub.F,p.sub.F) frequency offset parameter F fluid f.sub.d design resonance frequency f.sub.R first resonance frequency f.sub.F second resonance frequency MV measurement volume p pressure p.sub.F fluid pressure p.sub.R reference fluid pressure R reference fluid RV reference volume T temperature T.sub.F fluid temperature T.sub.R reference fluid temperature (T.sub.F,p.sub.F) viscosity function of fluid .sub.m estimated value indicative of viscosity h of fluid .sub.m estimated value indicative of density of fluid /T.sub.R reference-fluid-temperature-dependence of a viscosity function (T.sub.R) /T.sub.F fluid-temperature-dependence of a viscosity function (T.sub.F) f.sub.R/T.sub.R reference-fluid-temperature-dependence of a first resonance frequency f.sub.R f.sub.F/T.sub.F fluid-temperature-dependence of a second resonance frequency f.sub.F C/T temperature dependence of C C/p pressure dependence of C .sub.R(p.sub.R,T.sub.R) reference-fluid-pressure- and/or reference-fluid-temperature-dependent viscosity function of the reference fluid .sub.R density of reference fluid