The present invention relates to a method for ascertaining a physical parameter of a gas-containing liquid by means of a measuring transducer having at least one measuring tube for guiding the gas-containing liquid, wherein the measuring tube has an inlet side end section and an outlet side end section, wherein the measuring transducer has at least one inlet side affixing apparatus and one outlet side affixing apparatus, with which the measuring tube is affixed, in each case, into a different one of the end sections, wherein the measuring tube is excitable between the two affixing apparatuses to execute oscillations, wherein mass flow and density of the gas-containing liquid are determinable from the oscillatory behavior of the measuring tube. The measured values for mass flow and density have, however, cross sensitivities to the velocity of sound and compressibility of the gas-containing liquid, which increase with increasing gas load. A compensation of these cross sensitivities is, consequently, desired.
WO 01/01086 A1 discloses a method for compressibility compensation in the case of mass flow measurement in a Coriolis mass flow meter. In such case, mass flow measurement is performed in two different modes, of which one is a bending oscillation mode and another a radial oscillation mode. A comparison of the mass flow values ascertained by means of these two modes is used. This is, however, a problematic approach, since the radial mode oscillations have considerable dependence on the flow profile and on the static pressure. Additionally, more sensors than the usual two are required, in order to be able to register both bending oscillations as well as also radial mode oscillations. Equally, a more complex exciter structure is required.
It is, consequently, an object of the present invention to provide a measuring method with a more robust and at the same time simpler compensation of cross sensitivities for compressibility and velocity of sound. The object of the invention is achieved by the method of the independent claim.
The method of the invention is a method for ascertaining a physical parameter of a gas-containing liquid by means of a measuring transducer having at least one measuring tube for guiding the gas-containing liquid, wherein the gas is present especially in the form of bubbles suspended in the liquid, wherein the measuring tube has an inlet side end section and an outlet side end section, wherein the measuring transducer has at least one inlet side affixing apparatus and one outlet side affixing apparatus, with which the measuring tube is, in each case, affixed into a different one of the end sections, wherein the measuring tube is excitable between the two affixing apparatuses to execute bending oscillations of various modes with different eigenfrequencies, of which an f1-mode has no oscillation nodes between the affixing apparatuses, and wherein an f3-mode has two oscillation nodes between the affixing apparatuses, wherein the method comprises steps as follows: ascertaining the eigenfrequencies of the f1-mode and the f3-mode; ascertaining a first preliminary density value for the gas-containing liquid guided in the measuring tube based on the eigenfrequency of the f1-mode; ascertaining a second preliminary density value for the gas-containing liquid guided in the measuring tube based on the eigenfrequency of the f3-mode; ascertaining a value for the velocity of sound of the gas-containing liquid guided in the measuring tube, and/or ascertaining, as a function of the velocity of sound and the eigenfrequency of a mode, at least one correction term and/or density error for the preliminary density value, which was ascertained based on the eigenfrequency of the mode, for determining a corrected density measured value; and/or ascertaining a correction term for a preliminary mass flow value for determining a corrected mass flow measured value based on the first preliminary density value, the second preliminary density value, the eigenfrequency of the f1-mode and the eigenfrequency of the f3-mode.
Suspended bubbles are especially bubbles, whose size is no greater than three times a penetration depth, which depends on the kinematic viscosity of the liquid and the eigenfrequency of the f1-mode.
To a first approximation, the formula for a preliminary density value ρi of a gas-containing liquid as a function of eigenfrequency fi of an fi-mode can be of the following form:
wherein c0i, c1i, and c2i, are mode dependent coefficients.
The above approximation does not, however, take into consideration the influences of the oscillating gas-containing liquid in the measuring tube. The closer the resonant frequency of the oscillating gas-containing liquid is to the eigenfrequency of a bending oscillation mode, the greater is the influence of the eigenfrequency. Since the resonant frequency of the gas-containing liquid lies, usually, above the eigenfrequency of the measuring tubes, the influence on the f3-bending oscillation mode is greater than influence on the f1-bending oscillation mode. This leads to different preliminary mode specific density values, wherein the ratio between the preliminary density values provides the opportunity to ascertain and to correct the influence of the oscillating gas-containing liquid.
The resonant frequency of the oscillating gas-containing liquid depends on its velocity of sound. In a further development of the invention, a mode specific correction term Ki for a preliminary density value is, consequently, a function of a quotient of the velocity of sound of the gas-containing liquid and the eigenfrequency of the mode, with which the preliminary density measured value was ascertained.
In a further development of the invention, the velocity of sound c of the gas-containing liquid is determined by searching for that sound velocity value, in the case of which the quotient of the first correction term for the first preliminary density value divided by the second correction term for the second preliminary density value equals the quotient of the first preliminary density value divided by the second preliminary density value. Which mathematical procedure is used, in such case, is of lesser importance.
In a further development of the invention, the correction term Ki for the preliminary density values ρi as a function of the eigenfrequency of the fi-mode has the following form:
wherein r and g are gas independent constants, c is the velocity of sound of the gas-containing liquid, fi is the eigenfrequency of the fi-mode, ρcorr the corrected density, and b a scaling constant, wherein especially: r/b<1, especially r/b<0.9, and/or b=1.
In a further development of the invention, g in the above equation is a proportionality factor between a resonant frequency fres of the gas-containing liquid and the velocity of sound of the gas-containing liquid and depends on the diameter of the measuring tube, wherein:
f
res
=g·c
In a further development of the invention, the preliminary density values are determined based on the eigenfrequency of the fi-mode by means of a polynomial in 1/fi, especially in (1/fi)2, wherein the coefficients of the polynomial are mode dependent.
In a further development of the invention, there holds for a density error Eρi of a preliminary density value based on the eigenfrequency of the fi-mode:
E
ρi
:=K
i−1,
wherein a mass flow error Em of a preliminary mass flow value is proportional to the density error Eρi of the first preliminary density value as follows:
E
m
:=k·E
ρ1,
wherein the proportionality factor k is not less than 1.5, for example, not less than 1.8 and especially not less than 1.9, wherein the proportionality factor k is no greater than 3, for example, no greater than 2.25 and especially no greater than 2.1. In a currently preferred embodiment of the invention, the proportionality factor k=2.
A correction term Km for the mass flow is:
Km:=1+Em,
wherein the corrected mass flow {dot over (m)}corr is ascertained as
and
wherein {dot over (m)}v is the preliminary mass flow value.
In a further development of the invention, the method additionally includes steps as follows:
determining a deviation between the first preliminary density value based on the eigenfrequency of the f1-mode and the second preliminary density value based on the eigenfrequency of the f3-mode; testing whether the deviation is greater than a reference value; and, when this is the case, ascertaining, and, in given cases, outputting, a value for the velocity of sound.
In a further development of the invention, the reference value for the deviation of the density values is so selected that the velocity of sound can be determined with a statistical error of no greater than 10%, especially no greater than 5% and preferably no greater than 2%.
In a further development of the invention, the reference value is not less than 0.2 kg/m3 especially not less than 0.4 kg/m3, wherein the reference value is also no greater than 2 kg/m3, for example, no greater than 1 kg/m3, and especially no greater than 0.6 kg/m3.
In a further development of the invention, the method is especially applied when the gas-containing liquid oscillating in the measuring tube has a resonant frequency, which is no greater than 20 times the eigenfrequency of the f1-mode of the measuring tube.
In a further development of the invention, the method is applied when the suspended bubbles have a radius r, which is no greater than five times, especially no greater than three times, a penetration depth δ, wherein
δ=(v/(π*f1))1/2,
wherein v is the kinematic viscosity of the liquid and f1 the eigenfrequency of the f1-mode.
The penetration depth δ describes the range of a flow field due to relative movements of a bubble suspended by its surrounding liquid. In the case of small radii, suspended bubbles essentially affect the compressibility, while in the case of radii, which significantly exceed the penetration depth, additional effects occur, which degrade the accuracy of the corrections of the invention.
The invention will now be explained in greater detail based on the example of an embodiment presented in the drawing, the figures of which show as follows:
The example of an embodiment of a method 100 of the invention shown in
Based on the ascertained eigenfrequencies fi, in a step 120, preliminary density values ρ1 and ρ3 are determined using the formula:
wherein c0i, c1i, and c2i, are mode dependent coefficients. In a step 130, which is explained in greater detail below based on
Finally in a step 140, a corrected density value is determined by means of the correction term.
As shown in
wherein r is, for instance, 0.84, b=1 and g is a measuring tube dependent proportionality factor between velocity of sound and resonant frequency, which can assume, for example, a value of 10/m.
Based on the ascertained velocity of sound, then in step 133 of the method in
The preliminary density value ρi is, finally, used in step 140 of the method in
The preliminary density value ρi is thus divided by the correction term Ki, in order to obtain the corrected density value ρcorr.
Shown in
Shown in
The correction terms for a preliminary mass flow measured value of a Coriolis mass flow measurement device can be determined from the correction terms for density by first determining the density error Eρ1 , from the correction terms Ki for density:
E
ρi
:=K
i−1,
The mass flow error Em for correction of a preliminary mass flow value is especially twice the first preliminary density error Eρ1, thus:
E
m:=2·Eρ1.
Equally, the mass flow error Em can be calculated as:
For a correction term Km for the mass flow, the following holds:
K
m:=1+Em,
wherein the corrected mass flow {dot over (m)}corr is ascertained as
and
wherein {dot over (m)}v is a previous mass flow value, which results from the phase difference between the signals of two oscillation sensors arranged symmetrically on the measuring tube and a calibration factor.
Number | Date | Country | Kind |
---|---|---|---|
10 2015 122 661.8 | Dec 2015 | DE | national |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/EP2016/077942 | 11/17/2016 | WO | 00 |