WO2004003540A2

WO2004003540A2 - Ultrasound doppler methods for determining rheological parameters of a fluid

Info

Publication number: WO2004003540A2
Application number: PCT/CH2003/000320
Authority: WO
Inventors: Boris Ouriev; Erich Josef Windhab
Original assignee: Bühler AG
Priority date: 2002-06-28
Filing date: 2003-05-19
Publication date: 2004-01-08
Also published as: AU2003223822A1; AU2003223822A8; WO2004003540A3; DE10229220A1

Abstract

The invention relates to a method for determining rheological parameters of a free-flowing fluid, especially a suspension or an emulsion, which is transported by a line, especially a pipe. The inventive method uses ultrasound Doppler methods and at least two pressure measurements to obtain information relating to the free-flowing fluid. According to the invention, said information is evaluated by determining the wall shear stress in the fluid along the flow direction of the fluid flow in the region of the fluid flow penetrated by the ultrasound waves, by determining the fluid velocity profile transversally to the flow direction of the fluid flow in the region of the fluid flow penetrated by the ultrasound waves, and by selecting and adapting a suitable (adaptable) model for the viscosity function (shear viscosity) and suitable marginal conditions for the free-flowing fluid.

Description

Ultrasonic Doppler method for determining rheological parameters of a fluid

The present invention relates to a method for determining rheological parameters of a flowing fluid, in particular a suspension or an emulsion, according to the preamble of claim 1.

Similar processes are already known. Here, the ultrasonic Doppler method is used to determine a local velocity profile transverse to the line for the fluid carrying and suspended or emulsified particles flowing in a line or a flow channel. In addition, a measurement of the static pressure upstream and downstream of the region of the determined local velocity profile determines a pressure difference along the direction of flow in the region of the local velocity profile. From the speed profile and the pressure difference assigned to it, certain rheological parameters of the examined flowing fluid, such as the viscosity function (shear viscosity), the yield point etc. are determined.

This combination of the ultrasound Doppler method (UVP, Ultrasound Velocity Profiling) and the pressure difference determination (PD, Pressure Difference), which the expert briefly calls UVP-PD, has been described in numerous publications in various versions with always minor modifications.

In the article "Velocity profile measurement by ultrasound Doppier shift method" by Y. Takeda in the International Journal of Heat and Fluid Flow ", Volume 7, No. 4, December 1986, the suitability of the EIA methodology for the determination of a one-dimensional velocity profile in Tubes or blood vessels with a diameter of only a few millimeters are confirmed. In "Rheological Study of Non-Newtonian fluid" by E. Windhab, B. Ouriev, T. Wagner and M. Drost, 1 ^st International Symposium on Ultrasonic Doppler Methods for Fluid Me- chanics and Fluid Engineering, September 1996, the initially mentioned UVP-PD method described.

A detailed description of the theoretical and apparatus-based principles of the UVP-PD method as well as its application in drag shear and pressure shear flows, in particular model suspensions and rheological fluids such as e.g. in chocolate or pasta production can be found in "Ultrasound Doppier Based In-Line Rheometry of Highly Concentrated Suspensions" by B. Ouriev, Diss. ETH No. 13523, Zurich 2000.

The UVP-PD method described here provides good results for various types of velocity profiles and for the rheological parameters of the fluids to be determined, both in laminar and in turbulent flows.

Although the method described at the outset enables the rheological parameters of numerous fluids to be determined, the experience and intuition of a rheology expert always had to be used to make sensible decisions when determining the rheological parameters of the fluid.

The invention has for its object to provide a method that enables a routine determination of the rheological parameters of a fluid even for a non-specialist with little experience in the field of rheology.

This object is achieved by the characterizing features of claim 1.

The following steps are carried out to determine the rheological parameters of the flowing fluid, in particular a suspension or emulsion which is conveyed through a flow channel, in particular a line or a pipe: a) irradiation of an ultrasound signal sent from an ultrasound transmitter with at least a predetermined first frequency f1 at an angle Θ different from 90 ° to the direction of flow into the fluid flow; b) receiving and measuring the frequency of an ultrasonic signal which is reflected / scattered by particles carried in the fluid in the respective fluid areas, with at least one second frequency f2 which is characteristic of the respective fluid area and which is shifted by a respective frequency shift Δf with respect to the frequency f1, in an ultrasound receiver; c) measuring the static pressure along the flow direction of the fluid flow in the region of the fluid flow irradiated by the ultrasonic waves at N locations; and d) evaluating the information predetermined and measured in steps a), b) and c) for determining rheological parameters of the flowing fluid,

marked by

d1) determining the wall shear stress in the fluid along the direction of flow of the fluid flow in the region of the fluid flow irradiated by the ultrasound waves; d2) determining the fluid velocity profile in the fluid transversely to the direction of flow of the fluid flow in the region of the fluid flow irradiated by the ultrasound waves; d3) selection of a suitable model for the viscosity function (shear viscosity) and suitable boundary conditions for the flowing fluid; and d4) iteratively adapting the parameters and boundary conditions of the appropriate model to the measured information.

By selecting both a suitable, that is to say adaptable to the measured data, model for the rheological properties, that is to say for the viscosity function and the boundary conditions, and then adapting this model iteratively to the measured data, it is ensured that the correct one Model is used for an optimal description of the rheological properties. The emitted ultrasound signal preferably comprises a plurality of discrete first frequencies (f1. F1 ¹ , fl ", ...) and the received ultrasound signal in each case at least a plurality of discrete second frequencies (f2, f2 \ f2", ...), which are in relation to the respective first Frequencies (fl, fl ', fl ", ...) are each shifted by a frequency shift Δf which is characteristic of the respective fluid area. This enables the determination of the fluid speed which is characteristic of a fluid area on the basis of several differences, for which at least in a first approximation f2-f1 = f2'-f1 '= f2 "-f1" = ... = Δf. The arithmetic mean of the individual differences is preferably formed in order to obtain a reliable value for Δf and thus for the respective fluid velocity of one of the field areas.

It is also advantageous if the emitted ultrasound signal has a first frequency spectrum (FS1) and the received ultrasound signal has at least one second frequency spectrum (FS2), which is shifted in relation to the first frequency spectrum (FS1) by a frequency shift Δf that is characteristic of the respective fluid range. Here, too, frequency shifts at several points in the two frequency spectra can be used for averaging the value Δf and thus for determining the respective fluid velocity of one of the fluid areas.

The emitted and the received ultrasonic signal can also be pulsed signals, each of which in particular has a constant carrier frequency. This facilitates the assignment of the respective frequency shift Δf and a respective fluid range using the respective transit time of the ultrasound signal between the time of leaving the ultrasound transmitter and the time of reception by the ultrasound receiver.

The transmitted and the received ultrasonic signal can also be continuous signals. This is particularly advantageous when using the frequency spectra FS1 and FS2 described above. The emission of the ultrasound signal radiated into the fluid and the reception of the reflected ultrasound signal expediently take place at the same location, for example by means of an ultrasound transceiver.

In some cases it is also advantageous if the emission of the ultrasound signal radiated into the fluid and the reception of the reflected ultrasound signal take place at different locations. The ultrasonic transmitter and the ultrasonic receiver can e.g. opposite, on both sides of the flowing fluid. This enables working with ultrasonic waves, which are scattered on the particles carried in the fluid, not with a reversal of direction of 180 °, but with a relatively small change in direction. This guarantees an approximately equally long transit time or an approximately equally long path in the flowing medium for all ultrasonic waves received at the opposite ultrasonic sensor. In this way, practically all of the ultrasound waves reflected / scattered between the ultrasound sensor and the ultrasound receiver via particles in different fluid areas lying between them are approximately equally attenuated by the flowing medium that has been crossed. However, care must be taken to ensure that, with an increasingly smaller deflection angle of the sound waves reflected / scattered on the moving particles, the absorption of the received sound waves is evened out, but on the one hand with a correspondingly reduced resolution when locating the respective reflecting field areas of the method according to the invention , in particular using pulsed signals, and on the other hand has to be bought through smaller frequency shifts. However, with increasing flow velocities in the fluid, the frequency shifts also increase, so that at least the effect of the small deflection angles is then compensated for.

A first ultrasound transceiver is preferably arranged in the first wall area and a second ultrasound transceiver is arranged in the second wall area. As a result, the flow can be irradiated "from left to right" and at the same time "from right to left" with ultrasound waves. In this way, "left" and "right" measurement results can be averaged. This is particularly advantageous when one is asked whether certain asymmetries in the experimentally determined velocity distribution transverse to the direction of flow are only metrological artifacts or real asymmetries of the real velocity distribution in the fluid. Such artifacts, which simulate an asymmetry in the speed distribution, can then generally be corrected by averaging the two artifact-related distributions. If the averaged result is still asymmetrical, then this indicates an actual asymmetry in the flow.

A suitable model is expediently adapted by iteratively adapting a model-based theoretical speed profile to a measured speed profile. The various rheological parameters can then be read from the adjusted theoretical speed profile.

The measured speed profiles are preferably treated before the adaptation, in particular a temporal averaging of the measured speed profiles. This gives you more reliable speed profiles for the subsequent adjustment of the models.

A statistical fluctuation variable, in particular the standard deviation, is preferably determined in each case from the determined wall shear stresses and / or from the determined speed profiles and compared with a predetermined limit value for the fluctuation variable. This comparison is preferably used as the basis for the selection of reliable measurement data.

A suitable model can be selected by checking the boundary conditions used in the model. For example, assume that the velocity of the fluid on the wall is zero, i.e. that there is wall adhesion. Depending on whether the curve fitting was successful or not, this assumption can be retained or rejected. A similar procedure can be used with the assumption that the velocity of the fluid on the wall is different from zero.

The boundary conditions can advantageously also be checked by counting unsuccessful iteration steps when attempting to adapt a model, in particular when a predetermined number of iteration steps is exceeded another model with different parameters and / or other boundary conditions is selected.

The models used are preferably selected from the following group of models:

> Power law model

> Herschel Bulkley model

> Cross model.

However, other rheological models can also be selected.

The boundary conditions used are preferably selected from the following group of boundary conditions:

> Fluid velocity on the wall is zero or there is wall adhesion

> Fluid velocity on the wall is not zero or there is wall sliding

> The yield point in one area of the fluid flow is not reached or there are grafts in the flow

> The flow limit was not exceeded in any area of the fluid flow or there was no grafting in the flow

> Flow type: laminar

> Flow type: turbulent.

A description of the models and boundary conditions used can be found in "Ultrasound Doppier Based In-Line Rheometry of Highly Concentrated Suspensions" by B. Ouriev, Diss. ETH No. 13523, Zurich 2000 or in "Rheological study of concentrated suspensions in pressure-driven shear" flow using a novel in-line ultrasound Doppier method "by B. Ouriev and EJ Windhab, Experiments in Fluids 32 (2002).

At least some of the determined rheological parameters of the fluid can also be compared with values of these parameters that were determined in a different way. This enables the results for the rheological pa parameters. The rheological parameters are preferably determined differently by measuring the viscosity in a rotary rheometer and / or in a capillary rheometer.

The statistical fluctuation variable, in particular the standard deviation, is expediently determined for the recorded speed signals of each speed channel (= location on the speed profile) and / or for the recorded pressure signals of each pressure measuring point. This information can be used, among other things, to distinguish whether the flowing fluid is in a turbulent or laminar flow state.

Further advantages, features and possible uses of the invention result from the following description of preferred exemplary embodiments which are not to be understood as restricting, wherein:

1 schematically shows a measuring arrangement known per se, with the aid of which the method according to the invention is carried out; and

2 to 6 the procedure according to the invention for processing and evaluating the measurement arrangement by. Fig. 1 schematically show the measured values obtained.

1 shows a pipe section 1, in which a fluid 2 flows. The measuring arrangement in FIG. 1 comprises an ultrasound transceiver 3 and a pressure sensor 4 downstream and a pressure sensor 5 upstream from the ultrasound transceiver 3.

According to the ultrasonic Doppler method (UVP method), an ultrasonic transceiver 3 sends a narrow ultrasonic wave US with a frequency fl (practically flat wave or parallel beam) into the flowing fluid 2 transversely to the fluid flow direction. The ultrasonic wave US is reflected or scattered by moving particles which are carried in the flowing fluid 2. The part of the ultrasonic wave US which is reflected or scattered back into the ultrasonic transmitter-receiver 3 has a shifted frequency f2 due to the movement of the particles (double Shift). This frequency shift provides information about the speed of the particles or the fluid in a certain fluid volume. The assignment of the detected different frequency shifts to the locations in the fluid at which the frequency shifting reflection or scattering takes place takes place via a transit time measurement between the time of transmission and the reception of the ultrasound wave at the ultrasound transmitter-receiver 3. Preferably, therefore, pulsed ultrasound waves are used. The smaller the temporal and thus also the spatial distances between the reflected ultrasound pulses received in succession, the greater the local resolution and the number of frequency shifts detected. The speed profile can be determined in this way.

With the two pressure sensors 4 and 5, a first static pressure P1 downstream and a second static pressure P2 upstream of the area of the fluid flow crossed by the ultrasonic waves are measured. The wall shear stress in the fluid is then determined from this.

The viscosity function (shear viscosity) of the fluid can then be determined by the combination of the fluid velocity distribution ("reaction of the fluid") transverse to the direction of flow and the fluid wall shear stress ("external influence on the fluid").

In addition to the determination of the fluid wall shear stress and the determination of the fluid velocity profile, a suitable model for the viscosity function (shear viscosity) and suitable boundary conditions for the flowing fluid are selected according to the invention.

2 schematically shows the procedure for evaluating the measured pressure information for determining the wall shear stress in the fluid. At 1) the geometry of the flow channel is entered. At 2) the first pressure P1 is entered, at 3) the second pressure P2 is entered and at 4) the Nth pressure PN is entered. So up to N different pressures P1 to PN can be entered. The entered pressure values P1 to PN are triggered by means of one at 11) in order to measure the measured pressure values in real time assign, and are filtered in a filter at 10) to achieve signal smoothing. At 5) a pressure difference is then calculated in real time, from which the wall shear stress is determined at 6) and the wall shear stress distribution at 7). From 8) the real-time pressure difference determined at 5) determines the mean value of the absolute pressure. Using the real-time pressure difference determined at 5), statistical values (eg standard deviation etc.) are generated together with the values of the signal smoothed at 10), which describe the time-varying course of the pressure values passed on at 9).

Fig. 3 shows schematically the procedure for handling the unprocessed "raw" speed profiles before curve fitting. At 1) measured unprocessed speed profiles are entered. At 2), the fluid shelling speed measured for the fluid under investigation and the specified sound frequency is entered. The values of the entered speed profiles are subjected to a temporal averaging via a trigger at 19) in order to obtain averaged speed profiles at 3). In addition, the parameters used in the ultrasonic Doppler method are entered at 18), specifically at 11) the Doppler angle, at 12) acoustic information, at 13) the initial depth, at 14) the channel spacing, at 15) that Measurement window, at 16) the pulse repetition frequency and at 17) the beam geometry used. At 4) the standard deviation for each speed channel of the speed profile is determined, which is then compared at 5) with a predetermined limit value. At 6), 7) and 8), the real starting depth, the real penetration depth and the real channel spacing are then determined from this. Based on these three values, reliable speed data are then selected at 9) for the further calculations, which are finally prepared at 10) for curve fitting.

4 schematically shows the procedure for choosing a suitable model, for selecting reliable data and for checking the boundary conditions for the flowing fluid. At 1) the speed data are prepared for curve fitting. In 2), the standard deviation SMD determined is compared with a predetermined limit value SMDL of the standard deviation. If SMD is smaller than SMDL, it is decided at 3) that SMD is used for fitting the data (curve fitting). In this case, curve fitting is carried out at 4) using the method of least squares. This is used in 5) to monitor the axial symmetry of the flow profile and in 6) to determine the maximum flow speed. If SMD is larger than SMDL, the solution to the boundary value problem is initiated at 18) and a warning signal is issued at 20). The warning signal indicates that the boundary conditions have not been met.

At 7) it is checked whether the wall speed is zero. If it is affirmed at 11) that the speed on the wall is different from zero, the power law model is loaded at 16) with the assumption of a wall sliding effect. If, however, at 11) it is denied that the speed on the wall is different from zero, this statement (speed on the wall is zero) is used as a condition at 12). At 8) it is checked whether the maximum flow rate is constant, at 9) it is checked whether the pressure fluctuations are low, that is to say whether SMD is small and at 10) it is checked whether the temperature difference along the flow channel (tube) is small or zero is.

If at 12) all of the conditions 8), 9) and 10) are answered in the affirmative and if the speed on the wall is zero, at 13) the power law model is loaded as part of the solution approach from 18). If it is determined at 14) that the flow index is greater than a given limit value, the power law model is loaded at 16) with the assumption of a wall sliding effect, and at 17) the model is loaded with the assumption of a flow limit. If, on the other hand, it is determined at 14) that the flow index is less than a given value, the power law model is loaded at 15). If, on the other hand, in 12) all of the conditions 8), 9) and 10) are negated or are not fulfilled and if the speed on the wall is different from zero, the solution is initiated in 18) with the power law model to determine the Flow index, at 19) a repetition of the measurement is initiated and at 20) a warning signal is issued. 5 schematically shows the procedure for solving the boundary value problem by curve fitting and in particular the consideration of the assumption of wall sliding during curve fitting.

With 1) it is assumed that the maximum flow rate is constant. With 2) and with the first iteration of 9) it is assumed that the speed on the wall is zero. In 3), the information from 1) and 2) is used to adapt using the power law model. At 4) the flow index n of the power law model is then set from 7) to n = 1. Based on this requirement and the requirement of 1) and the requirement of 9) that the sliding speed on the wall is zero, the theoretical speed profile for n = 1 is calculated at 5).

At 6) an adjustment of the entered data is carried out using the method of least squares. The data for this are entered at 18), 19), 20), 21) and 22), namely at 18) the real starting depth, at 19) the real penetration depth, at 20) the real channel spacing, at 21) that Exceeding the standard deviation limit by the standard deviation and at 22) information about the axial symmetry of the flow profile from the control of the axial symmetry. At 17), a data area is selected from the data entered at 18) to 22). In 12) and 13), the flow index or criteria of the adaptation quality are read from the adjustment made in 6).

At 11) a decision is made as to whether the flow index read at 12) is below a lowest limit or not. If this is not the case, the flow index is incremented at 10) in order to be used again at 3) with the power law model. One then proceeds iteratively, with the steps 10), 3), 4), 5), 6), 12) and 13) being carried out several times. However, if the other case at 11), namely that the flow index is below a lowest limit value, the solution of the boundary value problem with other models is initiated at 8).

At 7) it is assumed that the fluid slides on the wall, so that the fluid velocity on the wall is different from zero. This assumption is confirmed in 4) with the tenzgesetz model used to calculate a corresponding theoretical profile at 5). The further procedure for the iteration is then the same as in the previous paragraph.

At 16), a decision is made as to whether the criteria of the quality of adaptation read at 13) exceed predetermined limit values or not. If this is the case, a query is made at 14) whether the number of iterations exceeds a predetermined number or not. If this is the case, the sliding speed on the wall is set to zero in 9) in a first iteration step, and the iteration is started again in 5). Otherwise we continue the iteration. The further procedure for the iteration is again the same as in the two previous paragraphs. If it is decided at 16) that the criteria of the adaptation do not exceed the predetermined limit values, the arguments (e.g. flow index, sliding speed, radius of the plug, etc.) are output at 15) and the process proceeds to 23).

At 23) it is queried whether the sliding speed on the wall is zero or not. If it is zero, the volumetric flow velocity, the wall shear velocity and the shear velocity distribution are calculated from the adaptation to the velocity profile at 24), 25) and 26). If the sliding speed on the wall is not zero, the volumetric flow rate, the wall shear rate and the shear rate distribution are calculated in an analogous manner at 27), 28) and 29) from the adaptation to the speed profile assuming wall sliding. From the variables calculated at 24) to 26) or at 27) to 29), the wall shear viscosity is calculated at 32) and the shear viscosity function at 33) (e.g. their distribution along a direction transverse to the flow).

6 schematically shows the procedure for determining the flow state. With 1), 2), 3) and 4) one starts from the power law model, from the Herschel-Bulkley model, from the cross model or from other models. From this, the boundary value problem is solved again at 7) and the rheological parameters are output at 9). At 15), a decision is made as to whether the shear viscosity calculated from the shear viscosity distribution is less than a predetermined viscosity limit value entered by the user, which is carried out by reference measurements carried out off-line and / or on-line, for example using a rotary rheometer, a capillary rheometer or some other rheometer was used. If the shear viscosity is less than the limit value, it is decided that there is a turbulent flow state according to 14). If the shear viscosity is greater than or equal to the limit value, it is decided that there is a laminar flow state according to 13).

At 6) a solution for the turbulent flow state is used. This approach differs from the approach in the laminar flow state only in the adaptation model, which has a similar shape, but in which other values for the parameters, e.g. for the flow index. The "turbulent" flow index is then calculated at 6) and used at 11).

At 12) it is decided whether the flow index is below a lowest limit or not. If the flow index is below, it is decided that there is a turbulent flow state according to 14) If the flow index is equal to or greater than the lowest limit value and based on an evaluation of the large SMD, viscosity, flow index and maximum speed, it is decided that a laminar flow state according to 13) or a turbulent flow state according to 14), and 6) uses the solution for the turbulent flow.

At 10) one assumes that there is wall sliding. In 5) the solution is used taking into account wall sliding. This gives a value for the wall glide at 8) and other theological parameters at 9).

At 18) one starts from the standard deviation SMD for each speed channel. At 16) it is decided whether the SMD exceeds a maximum limit or not. If the SMD exceeds this maximum limit, a decision is again made at 12) whether or not the flow index is less than the lowest limit. If so, the turbulent state according to 14) is present. If no, the laminar flow state according to 13) is present.

At 19) one starts from the standard deviation SMD of the current nth adaptation to the unprocessed "raw" pressure signal. At 17) it is decided whether there are pressure fluctuations or not. If there are pressure fluctuations and if an assessment of the viscosity, the flow index and the maximum speed allow it, it is decided that a turbulent state according to 14) is present, and the approach for the turbulent flow is used in 6). If there are no pressure fluctuations, the decision is made for the laminar state, and the solution for the laminar flow is used in 7).

In summary, it can be said that the following types of flow can essentially be distinguished:

> laminar flow with grafting (highly viscous material, e.g. highly concentrated suspension)

> laminar flow without grafting (both with flow index n> 1, i.e. dilatant or shear thickening material, as well as with flow index n <1, i.e. pseudoplastic or shear thinning material)

> turbulent flow (low-viscosity material, e.g. weakly concentrated suspension).

The ("smoothed") global flow profile of the turbulent flow transverse to the pipe axis, in which the local speed fluctuations have been filtered out, can be analogous to the highly viscous plug flow e.g. can be described by the Herschel-Bulkley model.

Claims

claims

1. A method for determining rheological parameters of a flowing fluid, in particular a suspension or emulsion, which is conveyed through a flow channel, in particular a line or a pipe, the method comprising the following steps:

a) irradiation of an ultrasound signal sent from an ultrasound transmitter with at least one predetermined first frequency fl at an angle Θ different from 90 ° to the direction of flow into the fluid flow; b) receiving and measuring the frequency of an ultrasound signal which is reflected / scattered by particles carried in the fluid in the respective fluid areas with at least one second frequency f2 which is characteristic of the respective fluid area and which is shifted by a respective frequency shift Δf with respect to the frequency fl, in an ultrasound receiver; c) measuring the static pressure along the flow direction of the fluid flow in the region of the fluid flow irradiated by the ultrasonic waves at N locations; d) evaluating the information specified and measured in steps a), b) and c) for determining rheological parameters of the flowing fluid, e) characterized in that the following steps are carried out for evaluation under d): d1) determining the wall shear stress in the fluid along the

Flow direction of the fluid flow in the area of the fluid flow irradiated by the ultrasonic waves; d2) determining the fluid velocity profile in the fluid transversely to the direction of flow of the fluid flow in the region of the fluid flow irradiated by the ultrasound waves; d3) selection of a suitable model for the viscosity function (shear viscosity) and suitable boundary conditions for the flowing fluid; and d4) iteratively adapting the parameters and boundary conditions of the appropriate model to the measured information.

2. The method according to claim 1, characterized in that the emitted ultrasound signal has a plurality of discrete first frequencies (fl, fT, fl ", ...) and the received ultrasound signal at least in each case a plurality of discrete second frequencies (f2, f2", f2 ", ...), which are shifted from the respective first frequencies (fl, fT, fl ", ...) by a frequency shift Δf characteristic of the respective fluid range.

3. The method according to claim 1, characterized in that the emitted ultrasound signal has a first frequency spectrum (FS1) and the received ultrasound signal has at least a second frequency spectrum (FS2), each of which is characteristic of the respective fluid range compared to the first frequency spectrum (FS1) Frequency shift Δf is shifted.

4. The method according to any one of claims 1 to 3, characterized in that the transmitted and the received ultrasonic signal are each pulsed signals.

5. The method according to claim 4, characterized in that the pulsed signals each have a constant carrier frequency.

6. The method according to any one of claims 1 to 3, characterized in that the transmitted and the received ultrasonic signal are continuous signals.

7. The method according to any one of claims 1 to 6, characterized in that the transmission of the ultrasound signal radiated into the fluid and the reception of the reflected ultrasound signal at the same location ⁵ .

8. The method according to any one of claims 1 to 6, characterized in that the emission of the ultrasound signal radiated into the fluid and the reception of the reflected ultrasound signal take place at different locations.

9. The method according to any one of claims 1 to 8, characterized in that the adaptation of a suitable model is carried out by iteratively adapting a model-based theoretical speed profile to a measured speed profile.

10. The method according to claim 9, characterized in that the measured speed profiles are treated before the adaptation.

11. The method according to claim 10, characterized in that the treatment is a temporal averaging of the measured speed profiles.

12. The method according to any one of claims 1 to 11, characterized in that from the determined wall shear stresses and / or from the determined speed profiles in each case a statistical fluctuation variable, in particular the standard deviation, is determined and compared with a predetermined limit value for the fluctuation variable.

13. The method according to claim 12, characterized in that the comparison is used as the basis for the selection of reliable measurement data.

14. The method according to any one of claims 1 to 13, characterized in that the selection of a suitable model is carried out by checking the boundary conditions used in the model.

15. The method according to claim 14, characterized in that the checking of the boundary conditions by counting unsuccessful iteration steps in the attempted Adaptation of a model is done.

16. The method according to claim 15, characterized in that when a predetermined number of iteration steps is exceeded, a different model with different parameters and / or other boundary conditions is selected.

17. The method according to any one of claims 1 to 16, characterized in that the models used are selected from the following group of models:

> Power law model

> Herschel Bulkley model

> Cross model.

18. The method according to any one of claims 1 to 17, characterized in that the boundary conditions used are selected from the following group of boundary conditions:

> Fluid velocity on the wall is zero or there is wall adhesion

> Fluid velocity on the wall is not zero or there is wall sliding

> Flow state: laminar

> Flow state: turbulent.

19. The method according to any one of claims 1 to 18, characterized in that at least some of the determined rheological parameters of the fluid are compared with values of these parameters, which were determined in a different way.

20. The method according to claim 19, characterized in that the other type of determination of the rheological parameters is the measurement of viscosity in a rotary rheometer and / or in a capillary rheometer.

21. The method according to claim 12 to 20, characterized in that the statistical fluctuation variable, in particular the standard deviation, is determined for the recorded speed signals of each speed channel (= location on the speed profile) and / or for the recorded pressure signals of each pressure measuring point.