Method for determining a measured viscosity value, and coriolis mass flowmeter for carrying out the method

Abstract

A method (100) serves for determining a measured viscosity value of a medium by means of a Coriolis mass flowmeter with a measuring tube and comprises: exciting (110) a measuring-tube vibration; ascertaining (122) a measured eigenfrequency value f of the measuring-tube vibration; ascertaining (124) a measured damping value Dm; ascertaining (126) a measured flow-rate value,formula (I) of the medium; ascertaining (128) a measured density value ρ of the medium; and ascertaining (130) a measured viscosity value (130) ηm as a function of a viscosity-relevant damping coefficient D η, on the basis of the above measured values; wherein the said damping coefficient is obtained from the measured damping value Dm by subtraction of an eigen damping coefficient D0 of the measuring tube and a flow-dependent damping coefficient Df, which can be represented by a model function MD which is proportional to a product of a power of a Reynolds number and a power of a Stokes number, formula (II), wherein the Reynolds number Re and the Stokes number St each include a provisional viscosity value, wherein the following applies for the exponents: 1.8 > ERe > 1.3; 4.0 > ESt > 3.4 and 2.8 > ES / ER > 2.2, wherein the measured viscosity value ηm is ascertained with an algorithm which ascertains the viscosity-relevant damping coefficient D η by the flow-dependent damping coefficient Df being ascertained in relation to the measured damping value Dm by means of the model function MD or by means of a routine which approximates the behaviour of the model function MD and wherein the measured viscosity value is determined as a function of the viscosity-relevant damping coefficient D η.

Description

[0001] Method for determining a viscosity measurement value and Coriolis mass flow meter for carrying out the method

[0002] The present invention relates to a method for determining a viscosity measurement value of a medium by means of a Coriolis mass flowmeter and to a Coriolis mass flowmeter for carrying out the method.

[0003] A generic determination of a viscosity measurement value is usually carried out by measuring the damping of a measuring tube oscillation of a Coriolis mass flowmeter.

[0004] Publication WO 2021 037 492 A1 discloses that viscosity measurement exhibits cross-sensitivity to the flow rate or flow velocity, since a flow-dependent damping contribution occurs, particularly at high flow rates, without which the viscosity is overestimated. However, an inaccurate viscosity measurement leads to an incorrect Reynolds number, which has a correspondingly detrimental effect on a Reynolds number correction of the flow measurement value.

[0005] The determination of a correction factor for the flow rate or density as a function of the Reynolds number is the subject of patent DE 10 2021 202 464 B3. This patent teaches a saturated curve of the correction factor with a tanh function of the logarithm of the Reynolds number around the point of the steepest slope of the correction factor as a function of the logarithm of the Reynolds number. While this is a pragmatic approach, it does not adequately account for the diversity of factors influencing damping and flow measurement. Therefore, the object of the present invention is to remedy this situation.

[0006] The object is achieved according to the invention by the method according to independent patent claim 1 and the Coriolis mass flowmeter according to independent patent claim 13.

[0007] The method according to the invention is used to determine a viscosity measurement value of a medium by means of a Coriolis mass flowmeter with at least one measuring tube in which the medium is guided, wherein the measuring tube is to be excited by an exciter to oscillate in a bending vibration useful mode, wherein the oscillation experiences a damping D which depends on the viscosity and the density of the medium, as well as the mass flow rate of the medium and the natural frequency of the bending vibration useful mode of the measuring tube, wherein the method comprises the following steps: exciting an oscillation of the measuring tube in a bending vibration useful mode; determining a natural frequency measurement value f of the bending vibration useful mode; determining a damping measurement value Dm of the bending vibration useful mode; determining a flow rate measurement value m of the medium; determining a density measurement value p of the medium;and determining a viscosity measurement value r|m for the medium, based on the damping measurement value Dm, the density measurement value p, the natural frequency measurement value f and the flow rate measurement value m, wherein the viscosity measurement value r|m is a function of a viscosity-relevant damping contribution D; n which is determined from the damping measured value Dm by subtracting a self-damping contribution Do of the measuring tube and a flow-dependent damping contribution Df, i.e.:

[0008] Dr) = Dm _ do _ D f , where the flow-dependent damping contribution Df can be represented by a model function MD which is proportional to a product of a power of a preliminary Reynolds number and a power of a preliminary Stokes number

[0009] D f = A f ■ Re ERe ■ St Est, where a provisional viscosity value is included in the provisional Reynolds number Re and the provisional Stokes number St, where the following applies to the exponent of the Reynolds number Re: ER6> 1.3; where the following applies to the exponent of the Reynolds number Re: ER6< 1.8; where the following applies to the exponents of the stroke number St: Est > 3.4; where the following applies to the exponents of the stroke number St: Est < 4.0; where the quotient of the exponents ES / ER > 2.2; where the quotient of the exponents ES / ER < 2.8; where the viscosity measurement value r|m is determined using an algorithm which calculates the viscosity-relevant damping contribution D n determined by determining and subtracting the flow-dependent damping contribution Df from the damping measured value Dm using the model function MD or by means of a routine that approximates the behavior of the model function MD, and where the viscosity measured value is determined as a function of the viscosity-relevant damping contribution D nis determined, whereby in particular in the case of approximation the routine approximates the behavior of the model function MD in such a way that a viscosity-relevant damping contribution D determined using the approximated flow-dependent damping contribution Df v for actual viscosities of not less than 10 cP by not more than 3 % of a flow-dependent damping contribution Df determined using the model function v deviates from the latter.

[0010] In a further development of the invention, the following applies to the exponent of the Reynolds number Re: ER6> 1.4; where the following applies to the exponent of the Reynolds number Re: ER6< 1.7; where the following applies to the exponents of the stroke number St: Est > 3.5; where the following applies to the exponents of the stroke number St: Est < 3.9; where the quotient of the exponents is ES / ER > 2.3; and where the quotient of the exponents is ES / ER < 2.65.

[0011] In a further development of the invention, a provisional viscosity value is included in the provisional Reynolds number Re and the provisional Stokes number St; the provisional Reynolds number is given as: where the preliminary Stokes number is given as:

[0012] St = i . pE , dj j 2-rrf where di is the inner diameter of the measuring tube, where n r the number of

[0013] measuring tubes, and where nv is the preliminary viscosity value.

[0014] In a further development of the invention, the viscosity measurement value is determined on the basis of a

[0015] Damping measurement value is determined iteratively in N iteration steps, whereby to determine the viscosity measurement value in the j+1-th iteration, the viscosity measurement value after the j-th iteration is used as a preliminary viscosity value in the calculation of the preliminary Reynolds number and the preliminary Stokes number, where 0 < j < N.

[0016] In a further development of the invention, a first preliminary viscosity value is determined on the basis of the damping measurement value Dm under the assumption that the flow-dependent damping contribution Df is zero, or a first preliminary viscosity value is a literature value.

[0017] In a further development of the invention, the natural frequency measured value f is not more than 600 Hz, for example not more than 400 Hz and in particular not more than 200 Hz.

[0018] In a further development of the invention, a first preliminary viscosity value o is to be estimated on the basis of the damping measurement value Dm and the self-damping contribution Do with a first estimate according to: no = H ■ f ■ p ■ (1 - V1 - E(f, p) ■ (D m - D o )) , where E(f, p) is a device-specific prefactor depending on the natural frequency measured value and the density,

[0019] E(f. p) = ; where G is a device-specific constant, and where H is a device-specific constant, where the viscosity measurement value m is a function of the viscosity-relevant damping contribution D n to be estimated with a second estimate according to: wherein the algorithm performs or approximates the first estimate and the second estimate, wherein in particular in the case of approximating the estimates the approximated viscosity measurement value does not deviate from the latter by more than the maximum of 1 cP and 5% of the value according to the estimates, in particular not more than 2% of the value according to the estimates.

[0020] In one embodiment of this further development of the invention, a viscosity output value r|A is determined which is the minimum of the first preliminary viscosity value o and the viscosity measurement value m: A = min (no, m) wherein, in particular in the case of the approximation of the estimates, the viscosity output value nA does not deviate from the latter by more than the maximum of 1 cP and 5% of the viscosity output value nA according to the estimates, in particular by not more than 2% of the viscosity output value nA according to the estimates.

[0021] In a further development of the invention, the viscosity measurement value nm is a function of the viscosity-relevant damping contribution D n with an estimate iteratively in N iterations according to: where E(f, p) is a device-specific prefactor depending on the natural frequency measured value and the density,

[0022] E(f. p) = ; where G is a device-specific constant, and where H is a device-specific constant, where ry+i is the viscosity value after the j+1-th iteration, where D ,j is the viscosity-relevant damping contribution after the j-th iteration, which can be determined as where Df is the flow-dependent damping contribution after the j-th iteration, which can be determined as

[0023] Df = A f ■ Rej ERe ■ Stj Est where the Reynolds number Rei and the Stokes number Sti can be determined after the j-th iteration as where j is the index of the iteration steps with 0 < j < N where the algorithm performs or approximates the estimation, wherein in particular in the case of approximation the approximated viscosity measurement value does not deviate from the value of the estimate by more than the maximum of 1 cP and 5% of the value of the estimate, in particular not more than 2% of the value of the estimate of the value of the estimate of the value of the estimate.

[0024] In the iterative process, a viscosity value of zero or the value from the previously described refinement can be used as the first value of a preliminary viscosity. In fact, the starting value is not critical in the iterative process. Only the number of required iterations decreases the more accurate the first preliminary viscosity value is. In a refinement of the invention, a Reynolds number and / or a Stokes number is determined based on the measured viscosity value.

[0025] In a further development of the invention, the viscosity output value and / or the viscosity measured value for actual viscosities between 1 cP and 300 cP and flow velocities between 0 m / s and 5 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter deviates by no more than the maximum of 10% of the actual viscosity and 1 cP from the actual viscosity upwards or downwards, and / or the viscosity output value and / or the viscosity measured value for actual viscosities between 1 cP and 300 cP and flow velocities between 5 m / s and 10 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter deviates by no more than the maximum of 25% of the actual viscosity and 2.5 cP from the actual viscosity upwards or downwards.

[0026] In a further development of the invention, the viscosity output value and / or the viscosity measured value for actual viscosities between 300 cP and 1000 cP and flow velocities between 0 m / s and 3 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter deviates by no more than the maximum of 10% of the actual viscosity and 1 cP from the actual viscosity upwards or downwards, and / or the viscosity output value and / or the viscosity measured value deviates for actual viscosities between 300 cP and 1000 cP and flow velocities between 3 m / s and 6 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter by no more than the maximum of 25% of the actual viscosity and 2.5 cP from the actual viscosity upwards or downwards.

[0027] In a further development of the invention, the damping measured value is determined on the basis of a ratio between an oscillation amplitude of the oscillation of the measuring tube in the bending oscillation useful mode and the amplitude of the associated excitation current, or on the basis of a width of a resonance curve Af / f of the bending oscillation useful mode, or on the basis of a decay time of the oscillation in the bending oscillation useful mode with the excitation power switched off, or reduced or increased.

[0028] The Coriolis mass flowmeter according to the invention is equipped with: at least one measuring tube for conducting a flowable medium; an exciter for exciting an oscillation of the measuring tube in a bending oscillation useful mode; two oscillation sensors for detecting the oscillation of the measuring tube in a bending oscillation useful mode; and a measuring and operating circuit configured to carry out the method according to one of the preceding claims.

[0029] The invention will now be explained in more detail with reference to the exemplary embodiments illustrated in the drawings. It shows:

[0030] Fig. 1 : a schematic representation of an embodiment of a Coriolis mass flow meter according to the invention;

[0031] Fig. 2a: a schematic diagram for uncorrected viscosity measurements and viscosity measurements corrected according to the invention as a function of the flow rate for a high viscosity and a low Stokes number;

[0032] Fig. 2b: a schematic diagram for uncorrected viscosity measurements and viscosity measurements corrected according to the invention as a function of the flow rate for a high viscosity and a high Stokes number;

[0033] Fig. 2c: a schematic diagram for uncorrected viscosity measurements and viscosity measurements corrected according to the invention as a function of the flow rate for a low viscosity and a low Stokes number;

[0034] Fig. 2d: a schematic diagram for uncorrected viscosity measurements and viscosity measurements corrected according to the invention as a function of flow rate for a low viscosity and a high Stokes number; Fig. 3a: a diagram for a sequence of viscosity values ​​for a first

[0035] Embodiment of the method according to the invention; and

[0036] Fig. 3b: a diagram for a sequence of viscosity values ​​for a second

[0037] Embodiment of the method according to the invention;

[0038] Fig. 4a: a flow chart for an embodiment of the method according to the invention;

[0039] Fig. 4b: a detailed flowchart with substeps of a

[0040] Method step of the embodiment of the method according to the invention from Fig. 4a; and

[0041] Fig. 4c: a detailed flowchart with substeps of another

[0042] Method step of the embodiment of the method according to the invention from Fig. 4a.

[0043] The exemplary embodiment of a Coriolis mass flowmeter 1 according to the invention shown in Fig. 1 comprises an oscillator 10 which comprises a pair of parallel, oscillatable measuring tubes 14 which extend between an inlet-side flange 11 and an outlet-side flange 12, wherein the flanges each comprise a flow divider or collector into which the measuring tubes 14 open. The flow dividers are connected to one another by a rigid housing 15, so that vibrations of the flow dividers accommodating the measuring tubes in the range of vibration frequencies of useful bending vibration modes of the oscillator are effectively suppressed. The measuring tubes 10 are rigidly connected to an inlet-side node plate 20 and an outlet-side node plate 21, wherein the node plates define vibration nodes of the oscillator 10 formed by the two measuring tubes 14, and thus largely determine the frequencies of the useful bending vibration modes.The oscillator 10 is excited to oscillate by an electrodynamic exciter 17 acting between the two measuring tubes 14, wherein the oscillations are detected by two vibration sensors 18, 19 that detect relative movements of the measuring tubes 14. The exciter 17 is operated by a measuring and operating circuit 30, which also detects and evaluates the signals from the vibration sensors to determine a natural frequency of the bending vibration useful mode, a density measurement value, a mass flow measurement value, and a damping measurement value. According to the invention, the measuring and operating circuit 30 is also configured to carry out the method according to the invention, as explained further below.

[0044] The measuring and operating circuit 30 can, unlike the one shown in Fig. 1, also comprise several spatially separated modules. Thus, the calculation of the damping and viscosity measurements can also be performed in a remote computing unit, to which the required raw data is transmitted, for example, wirelessly.

[0045] Furthermore, the Coriolis mass flowmeter according to the invention can also have a different number of measuring tubes, for example, four measuring tubes, each of which forms an oscillator in pairs, or a single measuring tube. Suitable Coriolis mass flowmeters for implementing the invention are offered by the applicant, for example, under the designations Promass F, Promass X, Promass Q, Promass E, Promass A, Promass S, and Promass I.

[0046] The schematic diagrams shown in Figs. 2a to 2d show uncorrected viscosity measurements (solid lines) and viscosity measurements corrected according to the invention (dash-dotted lines) as a function of flow velocity in a supply line to a Coriolis mass flowmeter according to the invention, wherein the supply line has a diameter that corresponds to the nominal diameter of the Coriolis mass flowmeter. The uncorrected viscosity measurements are uncorrected in that the damping of the measuring tube oscillation, which increases with increasing flow velocity, is interpreted entirely as being caused by the viscosity of the medium, thus neglecting a flow-dependent damping contribution Df as the cause of the increasing damping.The present invention now makes it possible to identify this flow-dependent damping contribution Df and to subtract it from a determined damping measurement value Dm in addition to the self-damping contribution Do, i.e. the expression.

[0047] Dr) = Dm _ do _ D f (I), and based on the viscosity-relevant damping contribution D thus obtained n to determine a correct viscosity measurement.

[0048] Investigations in connection with the present invention have shown that the flow-dependent damping contribution Df can be represented as proportional to a product of a power of a preliminary Reynolds number and a power of a preliminary Stokes number, i.e.:

[0049] D f = A f ■ Re ERe ■ St Est (II).

[0050] The preliminary Reynolds number Re is given as: (III), and the preliminary Stokes number is given as: s t = £ d;. JE 2iZräf ( 'iv) '

[0051] The Stokes number and the Reynolds number are provisional in that they themselves depend on the viscosity of the medium. Therefore, plausible preliminary values ​​for the viscosity are required to obtain a reasonable preliminary Reynolds number Re and a reasonable preliminary Stokes number St. This can be done, for example, with an estimate in which the flow-dependent damping contribution is assumed to be zero. The following applies to the exponent of the Reynolds number Re: 1.8 > ER6 > 1.3. The following applies to the exponent of the Strokes number St: 4.0 > Est > 3.4. The quotient of the exponents is 2.8 > ES / ER > 2.2.

[0052] For a given Coriolis mass flowmeter, the flow-dependent damping contribution Df can be determined experimentally, for example, by recording damping values ​​Dm for some media as a function of the flow rate and calculating the differences to the damping at zero flow. Based on these differences, the parameters of the function from equation (II) can be determined by regression calculation: D m (m) - D m (0) = D f (m) = A f ■ Re E R« ■ St E st. (V)

[0053] If the pre-factor Af has been determined for a specific measuring device and, if necessary, a fine-tuning of the exponents has been carried out within the limits given above, a basis is given to determine the flow-dependent damping contribution during ongoing measuring operation, with the help of which the viscosity-specific damping contribution can then be determined based on a damping measured value, which ultimately forms the basis for determining the viscosity measured value.

[0054] The effectiveness of the method according to the invention is evident from the diagrams in Figs. 2a-2d. The flow velocity range shown in the diagrams extends from 0 m / s to approximately 10 m / s. The Reynolds number in the measuring tube(s) of the Coriolis mass flowmeter increases proportionally to the flow velocity in the supply line.

[0055] The actual viscosity of the medium for the curves in Figs. 2a and 2b is a few 10 mPas. The actual viscosity of the medium for the curves in Figs. 2c and 2b is only a few mPas. Accordingly, the flow-dependent damping contribution in the diagrams in Figs. 2a and 2b increases even at lower velocities compared to the situation in Figs. 2c and 2d. This initially appears counterintuitive since the viscosity is in the denominator of the above defining equation for the velocity-proportional Reynolds number. However, the viscosity is in the numerator of the defining equation for the Stokes number, so that because the exponent of the Stokes number is more than a factor of 2 larger, the flow-dependent damping contribution Df increases with viscosity. The curves in Figs.Figures 2a and 2c are characteristic of a Coriolis mass flowmeter with stiffer measuring tubes, thus higher natural frequencies compared to the measuring tubes of the Coriolis mass flowmeter, for which the curves in Figs. 2b and 2d are characteristic. Therefore, the curves in Figs. 2b and 2d represent a situation with a larger Stokes number, which leads to larger uncorrected viscosity values ​​than in Figs. 2a and 2c. Having described above how the individual damping contributions are to be determined, the following explains how a viscosity value can be determined from a damping contribution.

[0056] The relationship between damping D and viscosity r| can be modeled as: where E(f, p) is a device-specific prefactor dependent on the natural frequency measured value and the density, for which the following applies:

[0057] E(f. p) = ; where G and H are device-specific constants, where f is the natural frequency of a bending vibration mode whose damping D is evaluated, and where p is a density measurement value of a medium causing the damping D, whose viscosity is to be determined.

[0058] By applying equation (VI), a first preliminary value rjo for the viscosity can be determined, which must be inserted into equations (III) and (IV) to obtain a preliminary Reynolds number and a preliminary Stokes number.

[0059] Neglecting the flow effect, the first preliminary value for the viscosity is to be determined according to:

[0060] 2 o = H ■ f ■ p ■ (1 - Vl - E(f, p) - (D m - D0)) (VII),

[0061] Subsequently, a flow-dependent damping contribution Df and viscosity-relevant damping contribution D nby means of equations (I) and (II), the latter determining the determination of a viscosity measurement value r|m, for example according to: 2 m = H ■ f ■ p ■ (1 - Vl - E(f, P ) - D (VIII).

[0062] The results of this calculation lead to the curves of the corrected viscosity measurements in the diagrams of Figs. 2a - 2d.

[0063] The accuracy of determining viscosity measurements depends on the flow rate and the actual viscosity.

[0064] The determination of the viscosity measurement value has a certain iterative character, as explained below with reference to Figs. 3a and 3b.

[0065] In the example described above, the preliminary viscosity value rjo was calculated based on the measured damping value Dm, assuming a stationary medium. Thus, the total damping, less the inherent damping Do of the measuring tube, was assigned to the viscosity. For a flowing medium, this not surprisingly leads to an excessively high preliminary viscosity value rio, which is shown in Fig. 3a in relation to the actual viscosity value iqt. With this somewhat excessive preliminary value, which is included in the preliminary Reynolds number and the preliminary Stokes number, the flow-dependent damping contribution according to equation (II) is naturally also somewhat too high, which can lead to the viscosity-relevant damping contribution being determined to be somewhat too low. As a result, the measured viscosity value would therefore be too low.However, by choosing suitable parameters, in particular the constant Af, it can be achieved that this viscosity measurement value rp determined after the first iteration already agrees sufficiently well with the actual viscosity measurement value, so that further iterations can be dispensed with.

[0066] Fig. 3b, however, shows a general case of an estimation with the viscosity measurement value r|m as a function of the viscosity-relevant damping contribution D T1 in N iterations according to: where r|j+i is the viscosity value after the j+1-th iteration, where D ,j is the viscosity-relevant damping contribution after the j-th iteration, which can be determined as D m - D o - D f j. Df is the flow-dependent damping contribution after the j-th iteration, which can be determined as D f j = A f ■ Rej ERe ■ Stj Est, where the Reynolds number Rei and the Stokes number Sti can be determined after the j J-th iteration as Re: = 4 |m| and St J Trdi nRT|j J

[0067] , where j is the index of the iteration steps with 0 < j < N.

[0068] For example, the iteration can be stopped if the viscosity measurement value does not change by more than 2% from one iteration step to the next;

[0069] For example, rjo = 0 can be chosen as the starting value for the viscosity. With the same coefficients as in the example in Fig. 3a, this would lead to the starting value after the first iteration. With other coefficients, which actually better reflect the actual relationship between damping and viscosity, it would take several iterations until the viscosity measurement converges, as shown in Fig. 3b.

[0070] The accuracy of determining viscosity measurements depends on the flow rate and viscosity. Accordingly, the tolerance intervals outlined in Figs. 2a to d vary depending on the flow rate range, with the dotted lines representing absolute tolerance values ​​and the solid lines representing relative ones.

[0071] As a result, various mathematical approaches are possible to implement the principle of the invention. The aforementioned functions can be calculated explicitly, approximated by other functions, such as polynomials, or their values ​​can be stored in lookup tables and thus read out. Interpolation can be performed between the support points stored in the tables.

[0072] The essential steps of the method 100 according to the invention are illustrated in Fig. 4a to Fig. 4c and will be explained in summary below. The method 100 requires the excitation 110 of an oscillation of at least one measuring tube in a bending oscillation mode. Based on the oscillation behavior of the measuring tube, input variables for determining the measured viscosity value are determined 120. This is followed by the determination 130 of a measured viscosity value r|m for the medium based on the input variables.

[0073] Determining 120 the input variables comprises determining 122 a natural frequency measured value f of the useful bending vibration mode; determining 124 a damping measured value Dm of the useful bending vibration mode, for example by determining the ratio between the excitation current amplitude for exciting the useful bending vibration mode and a vibration amplitude achieved thereby; determining 126 a flow rate measured value m of the medium; and determining 128 a density measured value p of the medium based on the natural frequency measured value.

[0074] Determining 130 a viscosity measurement value r|m for the medium based on the damping measurement value Dm, the density measurement value p, the natural frequency measurement value f and the flow rate measurement value m comprises determining 132 a flow-dependent damping contribution in the manner described above, determining 134 a viscosity-relevant damping contribution, in particular by subtracting a natural damping contribution and the flow-dependent damping contribution from the damping measurement value and determining 136 the viscosity measurement value based on the viscosity-relevant damping contribution.

Claims

Patent claims 1. A method for determining a viscosity measurement value of a medium by means of a Coriolis mass flowmeter having an oscillator with at least one measuring tube in which the medium is guided, wherein the measuring tube is to be excited by an exciter to oscillate in a bending vibration useful mode, wherein the oscillation experiences a damping D which depends on the viscosity and density of the medium, as well as the mass flow rate of the medium and the natural frequency of the bending vibration useful mode of the measuring tube, the method comprising the following steps: Excitation of an oscillation of the measuring tube in a bending vibration useful mode; Determining a natural frequency measurement value f of the useful bending vibration mode; Determining a damping measurement value Dm of the bending vibration useful mode; Determining a flow rate measurement value m of the medium; Determining a density measurement value p of the medium; and Determining a viscosity measurement value r|m for the medium, based on the damping measurement value Dm, the density measurement value p, the natural frequency measurement value f and the flow rate measurement value m, where the viscosity measurement value r|m is a function of a viscosity-relevant damping contribution D v which is determined from the damping measured value Dm by subtracting a self-damping contribution Do of the measuring tube and a flow-dependent damping contribution Df, i.e.: D v - D m - D Q - Df , where the flow-dependent damping contribution Df can be represented by a model function MD which is proportional to a product of a power of a preliminary Reynolds number and a power of a preliminary Stokes number D f = A f ■ Re ERe ■ St Est, where a provisional viscosity value is included in the provisional Reynolds number Re and the provisional Stokes number St, where the following applies to the exponent of the Reynolds number Re: ER6> 1.3; where the following applies to the exponent of the Reynolds number Re: ER6< 1.8; where the following applies to the exponents of the stroke number St: Est > 3.4; where the following applies to the exponents of the stroke number St: Est < 4.0; where the quotient of the exponents ES / ER > 2.2; where the quotient of the exponents ES / ER < 2.8; where the viscosity measurement value r|m is determined using an algorithm which calculates the viscosity-relevant damping contribution D vdetermined by determining the flow-dependent damping contribution Df to the damping measured value Dm by means of the model function MD or by means of a routine that approximates the behavior of the model function MD, and wherein the viscosity measured value is determined as a function of the viscosity-relevant damping contribution D, wherein in particular in the case of approximation the routine approximates the behavior of the model function MD in such a way that a viscosity-relevant damping contribution D determined using the approximated flow-dependent damping contribution Df v for actual viscosities of not less than 10 cP by not more than 3% of a flow rate determined using the model function. dependent damping contribution Df determined viscosity-relevant damping contribution D v deviates from the latter.

2. The method according to claim 1, wherein the preliminary Reynolds number Re and the preliminary Stokes number St each include a preliminary viscosity value; wherein the preliminary Reynolds number is given as: , and where the preliminary Stokes number is given as: where di is the inner diameter of the measuring tube, where n r is the number of measuring tubes, where r|v is the preliminary viscosity value.

3. Method according to one of the preceding claims, wherein the viscosity measurement value is determined iteratively on the basis of a damping measurement value in N iteration steps, wherein to determine the viscosity measurement value in the j+1-th iteration, the viscosity measurement value after the j-th iteration is included as a preliminary viscosity value in the calculation of the value of the preliminary Reynolds number and the preliminary Stokes number, where 0 < j < N.

4. Method according to one of the preceding claims, wherein a first preliminary viscosity value is determined on the basis of the damping measurement value Dm under the assumption that the flow-dependent damping contribution Df is zero, or wherein a first preliminary viscosity value is a literature value.

5. Method according to claim 1, wherein the natural frequency measured value f is not more than 600 Hz, for example not more than 400 Hz and in particular not more than 200 Hz.

6. Method according to one of the preceding claims: wherein a first preliminary viscosity value rjo is to be estimated on the basis of the damping measurement value Dm and the self-damping contribution Do with a first estimate according to: where E(f,p) is a device-specific prefactor depending on the natural frequency measured value and the density, where G is a device-specific constant, and where H is a device-specific constant, where the viscosity measurement value r|m is a function of the viscosity-relevant damping contribution D T1 to be estimated with a second estimate according to: wherein the algorithm performs or approximates the first estimate and the second estimate, wherein in particular in the case of approximating the estimates the approximated viscosity measurement does not deviate from the latter by more than the maximum of 1 cP and 5% of the value according to the estimates.

7. The method according to claim 6, wherein a viscosity output value r|A is determined which is the minimum of the first preliminary viscosity value o and the viscosity measurement value m: A = min (0, r|m)> wherein in particular in the case of approximation of the estimates the viscosity output value nA does not deviate from the latter by more than the maximum of 1 cP and 5% of the viscosity output value nA according to the estimates.

8. Method according to one of claims 1 to 5, wherein the viscosity measurement value nm is determined as a function of the viscosity-relevant damping contribution D T1 with an estimate iteratively in N iterations is to be estimated according to: where r|j+i is the viscosity value after the j+1 -th iteration, where E(f, p) is a device-specific prefactor depending on the natural frequency measured value and the density, E(f. p) = ; where G is a device-specific constant, and where H is a device-specific constant, where Dnj is the viscosity-relevant damping contribution after the j-th iteration, which can be determined as where Df is the flow-dependent damping contribution after the j-th iteration, which can be determined as D fJ = A f - Rej ERe ■ Stj Est where the Reynolds number Rei and the Stokes number Sti can be determined after the j-th iteration as where j is the index of the iteration steps with 0 < j < N, where N > 1 , in particular N>2, in particular the iteration is stopped if the viscosity measurement value does not change by more than 2% from one iteration step to the next; wherein the algorithm performs or approximates the estimation, in particular, in the case of approximation, the approximated viscosity measurement value does not deviate from the value of the estimate by more than the maximum of 1 cP and 5% of the value of the estimate.

9. Method according to one of the preceding claims, wherein a Reynolds number and / or a Stokes number is determined on the basis of the determined viscosity measurement value.

10. The method according to any one of the preceding claims, wherein the viscosity output value and / or the viscosity measurement value for actual viscosities between 1 cP and 300 cP and flow velocities between 0 m / s and 5 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter does not deviate from the actual viscosity by more than the maximum of 10% and 1 cP upwards or downwards, and / or wherein the viscosity output value and / or the viscosity measurement value for actual viscosities between 1 cP and 300 cP and flow velocities between 5 m / s and 10 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter does not deviate from the actual viscosity by more than the maximum of 25% and 2.5 cP upwards or downwards.

11. Method according to one of claims 1 to 9, wherein the viscosity output value and / or the viscosity measurement value for actual viscosities between 300 cP and 1000 cP and flow velocities between 0 m / s and 3 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter does not deviate from the actual viscosity by more than the maximum of 10% of the actual viscosity and 1 cP upwards or downwards, and / or wherein the viscosity output value and / or the viscosity measurement value for actual viscosities between 300 cP and 1000 cP and flow velocities between 3 m / s and 6 m / s in a feed line to the Coriolis mass flowmeter with its nominal diameter does not deviate from the actual viscosity by more than the maximum of 25% and 2.5 cP above or below the actual viscosity.

12. Method according to one of the preceding claims, wherein the damping measured value is determined on the basis of a ratio between an oscillation amplitude of the oscillation of the measuring tube in the bending oscillation useful mode and the amplitude of the associated excitation current, or on the basis of a width of a resonance curve Af / f of the bending oscillation useful mode, or on the basis of a decay time of the oscillation in the bending oscillation useful mode with the excitation power switched off, or reduced or increased.

13. Method according to one of the preceding claims, wherein the following applies to the exponent of the Reynolds number Re: ER6> 1.4; wherein the following applies to the exponent of the Reynolds number Re: ER6< 1.7; wherein the following applies to the exponents of the stroke number St: Est > 3.5; wherein the following applies to the exponents of the stroke number St: Est < 3.9; wherein the quotient of the exponents ES / ER > 2.3; and wherein the quotient of the exponents ES / ER < 2.

65.

14. A Coriolis mass flowmeter comprising: an oscillator having at least one measuring tube for conveying a flowable medium; an exciter for exciting an oscillation of the measuring tube in a bending oscillation useful mode; two oscillation sensors for detecting the oscillation of the measuring tube in a bending oscillation useful mode; and a measuring and operating circuit configured to carry out the method according to one of the preceding claims.

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