NON-INVASIVE OPEN CHANNEL FLOW METER

Abstract

A method measures surface velocity of a fluid having a free surface flowing through a pipe or a channel. A microwave beam is sent by patch antenna including an emitting patch area and receiving patch areas parallel to the emitting patch area. Microwave signals reflected by the moving fluid free surface are received on the receiving patch areas separated by a predetermined distance. The patch antennae are either in horizontal or vertical planes parallel to the average fluid velocity. For each microwave signal received, a phase shift between microwave signals received by different patch areas is determined to calculate azimuth angles and azimuth position of reflectors on the fluid surface or to calculate the elevation angle corresponding to each signal received. Based on Doppler frequency shifts between the sent and received microwaves and corresponding phase shifts, lateral and/or longitudinal distribution of the surface velocity of the fluid is calculated.

Claims

1. A method for measuring surface velocity of a fluid flowing through a pipe or a channel, wherein said fluid has a free surface, comprising the steps of: sending a microwave beam by a patch antenna comprising at least one emitting patch area and at least two receiving patch areas parallel to the emitting patch area; receiving microwave signals reflected by the moving fluid free surface on the at least two receiving patch areas separated by a predetermined distance, said patch antenna being either perpendicular to the flow in horizontal planes or in vertical planes parallel to an average fluid velocity; for each microwave signal received on the patch area, determining a phase shift between the microwave signals received by the different patch area allowing calculation of azimuth angles to determine an azimuth position of reflectors on the fluid surface or allowing calculation of an elevation angle corresponding to each signal received on the receiving area; for each microwave signal received on the receiving patch area determining a Doppler frequency shift between the sent microwave beam and the received microwave signal; calculating, based on the Doppler frequency shifts and the corresponding phase shifts, lateral and/or longitudinal distribution of the surface velocity of the fluid.

2. The method according to claim 1, wherein the sent microwave beam comprises a sequence of consecutive linear frequency-modulated continuous waves and the received signal is a time delayed version of a transmitted chirp, reflector velocity being determined by evaluating the phase difference of consecutive chirps.

3. The method according to claim 2, wherein the sent microwave beam and the received signals are compared using a homodyne receiver, resulting in an intermediate frequency signal defined by a frequency difference between the transmitted and received signals, which is proportional to a signal propagation time and thereby to a distance between the microwave patch antenna and the target.

4. The method according to claim 1, wherein the sent microwave beam has an azimuth comprised between 20° and 90° and an elevation angle comprised between 10° and 30°.

5. The method according to claim 1, wherein the microwave beams have a frequency comprised between 20 GHz and 80 GHz.

6. The method according to claim 5, wherein the microwave signals have a center frequency selected from the group consisting of 24.125 GHz, 61 GHz, and 77 GHz.

7. The method according to claim 6, wherein a spacing between adjacent receiving patch area is equal to about one-half of a wavelength of a centre frequency signal.

8. The method according to claim 1, wherein the receiving patch areas are located in vertical planes parallel to the fluid flow allowing determination of individual target velocities and an azimuth of arrival.

9. The method according to claim 1, wherein the receiving patch areas are located in horizontal planes parallel to the fluid flow allowing determination of individual target velocities and a distance between the sensor and the fluid.

10. The method according to claim 7, comprising the steps of making a first complete set of measurements and calculations, rotating the antenna by 90° around a normal axis and making a second set complete set of measurements and calculations.

11. The method according to claim 1, wherein the sensor comprises: at least two microwave patch area emitters placed orthogonally to each other, the first patch area emitter being located in a vertical plane parallel to the flow and the second patch antenna emitter being located in a horizontal plane parallel to the flow, and at least two sets of receiving antennae respectively parallel to the first and second patch antennae emitters, measurement of the different phase shifts, and frequency shifts allowing determination of individual target velocities, angle of arrival and distance to the fluid.

12. A channel transporting a fluid comprising a free surface, the channel comprising a sensor for measuring surface velocities of the fluid, the sensor being located at a height above the fluid surface, and comprising: a patch antenna having a normal vector directed toward a middle of the channel and impinging the fluid surface at a predetermined elevation angle, said patch antenna comprising at least one emitter patch area and at least two receiver patch areas parallel to the emitter patch area; a microwave generator connected to the at least one emitter patch area; a homodyne receiver for determining phase and frequency shifts between a signal emitted in use by the emitting area and signals received in use by the receiving patch area; a processing unit for calculating velocity distribution of the fluid surface from the phase and frequency shift determined by the homodyne receiver.

13. The channel according to claim 12, wherein the receiving patch areas are located in vertical planes parallel to fluid flow allowing the determination of individual target velocities and the azimuth of arrival.

14. The channel according to claim 12, wherein the receiving patch areas are located in horizontal planes parallel to fluid flow allowing determination of individual target velocities and a distance between the sensor and the fluid.

15. The channel according to claim 12, wherein the patch antenna comprises at least two microwave patch area emitters placed orthogonally to each other, the first patch area emitter being located in a vertical plane parallel to the flow and the second patch antenna emitter being located in a horizontal plane parallel to the flow, and at least two sets of receiving antennae respectively parallel to the first and second patch antennae emitters.

16. A sensor for measuring velocity distribution of a fluid surface flowing in a channel, said sensor comprising: means for securing the sensor above the fluid surface at a predetermined height and angle; a patch antenna comprising at least one emitter patch area and at least two receiver patch areas parallel to the emitter patch area; a microwave generator connected to the at least one emitter patch area; a homodyne receiver for determining phase and frequency shifts between a signal emitted in use by the emitting patch area and the signals received by the at least two receiver patch areas; a processing unit for calculating velocity distribution of the fluid surface from the phase and frequency shift determined by the homodyne receiver.

17. The sensor according to claim 16, further comprising a height measurement sensor for independently determining a fluid surface level.

18. The method according to claim 1, wherein the microwave beams have a frequency comprised between 24.125 GHz and 77 GHz.

19. The method according to claim 8, comprising the steps of making a first complete set of measurements and calculations, rotating the antenna by 90° around a normal axis and making a second set complete set of measurements and calculations.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0013] FIG. 1a represents an example of a channel with a measuring velocity sensor according to the invention.

[0014] FIG. 1b represents another example of a channel with a measuring velocity sensor according to the invention.

[0015] FIG. 1c represents a combination of examples of FIGS. 1a and 1b.

[0016] FIG. 2 shows an example of channel according to the invention.

[0017] FIG. 3 represents a patch antenna (5) comprising one transmitting patch area TX 6 and two receiving patch areas 7 RX1 and RX2 separated by a distance d.

[0018] FIG. 4 represents a patch antenna 5 comprising one transmitting patch area (6) and M receiver patch areas (7) separated by a distance d.

[0019] FIG. 4b represents a patch antenna 5 comprising two orthogonal transmitting patch area 6 and two sets of M receiver patch areas 7 separated by a distance d.

[0020] FIG. 5 shows the general principle of measuring angles from phases shifts.

[0021] FIG. 6 shows the frequency up-chirps cycle used in some embodiments of the invention.

[0022] FIG. 7 shows the data space used to represents the data obtained from the sensor off the invention.

[0023] FIG. 8 presents an illustration of selected sub-matrices of the three-dimensional microwave data cube in spectral domain is shown in FIG. 8

[0024] FIG. 9. Shows selected two-dimensional sub-matrices of the three-dimensional radar data cube in a spectral domain, in which the normalized frequencies are converted to range r, angle of arrival is a, and velocity is v at a chosen angle of arrival, evaluated for all velocities.

[0025] FIG. 10 Tx and Rx patch areas of an example of patch antenna according to the invention.

[0026] FIG. 11 illustrates a range-Doppler map according to an example of the invention.

[0027] FIG. 12 shows the two-dimensional map, velocity height and amplitude of an example of the description.

[0028] FIG. 13 shows the arrangement of the channel of an example of the description.

[0029] FIG. 14 shows the two-dimensional map, velocity height and amplitude of an example of the description.

DETAILED DESCRIPTION

[0030] According to the invention, a sensor generates a microwave beam directed towards a fluid surface at a determined angle, wherein said fluid surface reflects a multitude of signals back to the senor. The system is capable of measuring the distance between the target and the radar sensor, the angles of arrival of the impinging radio frequency signal and the target velocity. The sensor has one or more transmitting patch arrays and two or more receiving patch arrays disposed at an angle to the fluid velocity. Each reflected signal is detected by the two or more receiver patch arrays. The signals from the receiving patch arrays are identical but have a phase shift due to the physical distance from the receiving patch arrays and the angle from which the reflected signals are coming. The angle of the moving reflecting fluid scatters can be calculated and the velocity profile within the angle detection can be determined.

[0031] This result can be achieved by transmitting a continuous wave signal preferably at a frequency of 24.125 GHz towards the fluid surface. The reflected signals with a Doppler frequency shift are analysed at two or more receiving elements, and the phase shift between the signals at the receiving elements is analysed.

[0032] Alternatively, a signal with consecutive up-chirps within the signal bandwith B around the centre frequency fc, which can be preferably 61, or 77 GHz, is transmitted towards the fluid surface. The reflected signals are analysed; the delayed reflected up-chirps, the phase shift between consecutive chirps and the phase shift between contiguous receiving devices, will allow calculating the distance, the speed and the impacting angle from each reflecting scatter to the microwave device.

[0033] Every single reflecting scatter will have a triple signature, the velocity at which the target moves, i.e. the angle to the axis of the transmitted beam and the distance to the microwave device. This will allow to determine the complete fluid flow surface velocity profile and the distance from the fluid flow to the microwave system using one single antenna.

[0034] The present invention uses a device 1 for measuring the surface velocity of a fluid 2 flowing through a pipe or a channel 3, said device 1 comprising a patch antenna 5 with one or more transmitting antenna(e) 6 and m receiving antennae 7 separated by a distance d, said transmitting antenna 6 generating a microwave signal preferably with a centre frequency fc of 77 GHz and said receiving antennae 7 receiving the microwave signal reflected from the surface of the fluid 2. The microwave signals received on the receiving antennae with a phase shift φ allowing the calculation of the angle α to determine the exact azimuth position of the reflector on the fluid surface 2.

[0035] According to an example of the invention, the device 1 transmits a signal, which describes a sequence of consecutive linear frequency-modulated continuous waves (up-chirps), impinging at the surface of the fluid 2 where it is reflected. The received signal is a time-delayed version of the transmitted chirp. Both signals are compared using a homodyne receiver; this results in an intermediate frequency signal defined by the frequency difference between the transmitted and received sampling signal which is proportional to the signal propagation time and thus to the distance between the microwave antenna frontend and the target. The target velocity is determined by evaluating the phase difference of consecutive chirps, and the angle of arrival of the impinging radio frequency signal is calculated by evaluating the phase difference at adjacent receiving antennae of the radar system. Hence, the velocity of the target can be determined for a specific angle and range.

[0036] In a first embodiment, a microwave patch antenna transmitter is used to direct an asymmetrical beam having a large azimuth and small elevation towards the fluid flow at a defined angle (FIG. 1A). In this multiple channel microwave module, which is using a defined transmitting frequency f, a portion of the reflected microwave signal is captured by two or more receiver antennae 7 separated from each other by a defined distance d (FIG. 3).

[0037] The Doppler frequency shift difference between the transmitted continuous-wave radar signal at frequency f from the transmitter patch area and the received signals at frequency f.sub.d (frequency with Doppler shift) from the receiving patch areas will allow to calculate the target velocity. The phase shift between the received signals at contiguous receiving patch areas will allow to calculate the angle α from which the reflected signal originates.

[0038] In a second embodiment and first arrangement positioning the transmitting and receiving patch areas orthogonal to the fluid flow movement and using a patch antenna 5 as shown in FIG. 4 an asymmetrical micro-wave beam is directed towards the fluid surface at a defined angle θ, said beam having a main lobe with large azimuth and small elevation.

[0039] The transmit signal will consist in a sequence of consecutive linear frequency-modulated continuous-waves (up-chirps), impinging at the surface of the fluid where it is reflected, generating a damped and time-delayed version of the transmitted chirp captured by the receiving patch areas, which are going to be analysed to calculate the individual target velocities as well as determining their positions on the fluid surface.

[0040] In a second embodiment and second arrangement positioning the transmitting and receiving patch areas parallel to the fluid flow movement and using a patch antenna 5 as shown in FIG. 4 an asymmetrical micro-wave beam is directed towards the fluid surface at a defined angle θ, said beam having a main lobe with small azimuth and large elevation (FIG. 1B).

[0041] The transmit signal will consist in a sequence of consecutive linear frequency-modulated continuous-waves (up-chirps), impinging at the surface of the fluid where it is reflected, generating a damped and time-delayed version of the transmitted chirp captured by the receiving patch areas, which will to be analysed to calculate the individual target velocities as well as to determine the distance from the micro-wave antenna to the fluid surface.

[0042] In a third embodiment combining the transmitting and receiving patch areas are positioned orthogonal and parallel to the fluid movement and using a patch antenna (5) as shown in FIG. 4 B, directing two asymmetrical micro-wave beams towards the fluid surface at a defined angle θ, said beams having firstly, a main lobe with large azimuth and small elevation and, secondly, a main lobe with small azimuth and large elevation as shown in FIG. 1 C.

[0043] The transmit signals will consist in a sequence of consecutive linear frequency-modulated continuous-waves (up-chirps), impinging at the surface of the fluid where they are reflected, generating damped and time-delayed versions of the transmitted chirp captured by the receiving patch areas, which are going to be analysed to calculate the individual target velocities as well as to determine their positions on the fluid surface and the distance from the micro-wave antenna to the fluid surface.

[0044] As previously mentioned in the first embodiment, a continuous wave radar signal at defined frequency f preferably at (about) 24.125 GHz is transmitted from the transmitter patch area towards the fluid surface (2) at a defined angle θ as shown in FIG. 2, said beam having a main lobe with large azimuth and small elevation. This will allow the main lobe to illuminate an ellipsoidal portion of the fluid surface (4) as shown in FIG. 1 A. The azimuth angle range can vary from 20° to 90° or more while the elevation angle will vary from 10° to 30°.

[0045] FIG. 5 shows the two receiver patch areas RX1 and RX2 receiving the same signal f.sub.d, with the same Doppler frequency shift, but if the signal is coming in at an angle α, the two Doppler carrier waves will have a phase shift 4). This phase shift 4) allows to precisely calculate the angle α as shown in FIG. 2 and FIG. 5, between the received beams and the orthogonal direction of the antenna plane. When this angle α is known, the exact position on the fluid surface from the target from which each Doppler carrier wave originates, can be calculated. By analysing all reflected beams, measuring their Doppler frequency shift and calculating the angle, the velocity distribution or surface velocity profile of the fluid flowing through the detection area 4 can be determined as shown in FIG. 1 A and FIG. 2.

[0046] As previously mentioned, in a second embodiment, using a patch antenna 5 as shown in FIG. 4 comprising one transmitting patch area 6 and M receiver patch areas 7, an asymmetrical micro-wave beam is directed towards the fluid surface at a defined angle θ, said beam having a main lobe with large azimuth and small elevation. This will allow the main lobe to illuminate an ellipsoidal portion of the fluid surface (4) as shown in FIG. 1 A. The azimuth angle range can vary from 20° to 90° or more while the elevation angle will vary from 10° to 30°.

[0047] As illustrated in FIG. 6, the transmit signal of the microwave frontend describes a sequence of K consecutive linear up-chirps specified by the centre frequency f.sub.c of 61 or 77 GHz, the sweep time T and the signal band-width B. During each cycle, N samples are acquired at each of the M receiver channels of the microwave module.

[0048] The transmit signal impinging at the surface of the fluid is reflected, generating a damped and time-delayed version of the transmitted chirp captured by the receiving patch areas. Both signals are compared using a homodyne receiver; this results in an intermediate frequency signal defined by the frequency difference between the transmitted and received sampling signal which is proportional to the signal propagation time and thus to the distance between the microwave antenna frontend and the target. The target velocity is determined by evaluating the phase difference of consecutive chirps, and the angle of arrival of the impingeing radio frequency signal is calculated by evaluating the phase difference at adjacent receiving antennae of the radar system. Hence, the velocity of the target can be determined for a specific angle and range.

[0049] This result in three distinct sampling domains called fast-time sample n, slow-time sample k and spatial sample m. Hence, the acquired intermediate frequency signal can be represented by the three-dimensional microwave data cube illustrated in FIG. 7.

[0050] The corresponding digitized intermediate frequency signal is modelled by:

s[n,m,k]=A cos(2π(ψ.sub.rn+ψ.sub.αm+ψ.sub.vk))  (1)

With the signal amplitude A. The normalized frequency ψr, in the fast-time domain, where n is the sample index with 1≤n≤N, is modeled by

[00001]$\begin{array}{cc}{\psi }_r=\frac{2\mathrm{rB}}{\mathrm{cN}}& \left(2\right)\end{array}$

[0051] Where c specifies the signal propagation velocity (speed of light) and r is the distance between the microwave module and the target. In the spatial domain, where m is the index of the receiving antenna and M the number of receiving antennae with 1≤m≤M, a normalized frequency ψα arises which is defined by

[00002]$\begin{array}{cc}{\psi }_{\alpha }=\frac{d{f}_c}{c}\sin \left(\alpha \right)& \left(3\right)\end{array}$

[0052] With d describing the spacing between adjacent receiving antennae of the microwave module, and α specifying the angle of arrival of the impinging radio frequency signal (FIG. 2).

[0053] For the slow-time domain, where k is the index of the up-chirp with 1≤k≤K, the Doppler effect caused by the movement of the target results in a normalized frequency ψv described by

[00003]$\begin{array}{cc}{\psi }_v=\frac{2{\mathrm{vf}}_{c}T}{c}\cos \left(\alpha \right)\cos \theta & \left(4\right)\end{array}$

With θ specifying the inclination angle of the microwave module (FIG. 2) and v the target velocity.

[0054] Signal Processing

[0055] According to equation (1) a normalized frequency arises for each sampling domain of the three-dimensional radar microwave data cube, resulting in a cosinusoidal intermediate frequency signal. Hence, by applying a three-dimensional discrete Fourier transform (DFT), the microwave data cube can be transformed to the spectral domain, whose dimensions correspond to the normalized frequencies ψr (fast-time domain), ψα (spatial domain), and ψv (slow-time domain).

[0056] An illustration of selected sub-matrices of the three-dimensional microwave data cube in spectral domain is shown in FIG. 8.

[0057] In FIG. 9, the normalized frequencies ψr, ψα, and ψv have been converted to range r, angle of arrival—a, and velocity v according to (2), (3), and (4), respectively.

Design Borders of the Measurement System

[0058] Since the signals are processed digitally, the sampling intervals must be selected accordingly in each dimension. With regard to the Nyquist criterion the normalized frequencies must be prevented from changing by more than ½. According to the fast-time domain, this results in a limitation of the distance r between the microwave module and the target defined by

[00004]$\begin{array}{cc}r\le \frac{cN}{4B}& \left(5\right)\end{array}$

[0059] To achieve maximum versatility of the microwave-based measurement system, the unambiguity range for the angle of arrival α of the impinging radio frequency signal should not be limited.

[0060] Thus, the microwave module must be designed such that the spacing d between adjacent receiving antennae of the microwave module is limited by

[00005]$\begin{array}{cc}d\le \frac{c}{2f_c}=\frac{\lambda }{2}& \left(6\right)\end{array}$

[0061] Where λ represents the wavelength of the radio frequency signal and d=λ/2 the distance by two adjacent receiving patch areas (FIG. 10).

[0062] Regarding the slow-time domain, a limit in the movement of the target relative to the microwave module between consecutive transmit cycles and thus of the target velocity arises with

[00006]$\begin{array}{cc}.Math.v.Math.\le \frac{c}{4f_{c}T\cos \left(\theta \right)}& \left(7\right)\end{array}$

[0063] By adjusting the number of samples N and the sweep time T, the measurement system can be setup to allow velocity measurements in accordance with the Nyquist criterion for a given scenario.

Resolution of the Measurement System

[0064] One important parameter of the radar-based fluid surface velocity measurement system is the target resolution, which describes the ability to distinguish between multiple targets that are located within the radar beam. If the targets cannot be distinctly separated, the measurement results will be significantly affected.

[0065] Basically, the problem of target resolution is a problem of resolving multiple frequencies in the output spectrum. Therefore, the achievable resolution mainly depends on the frequency measurement algorithm used. For the discrete Fourier transform, which is commonly used for frequency calculations, the frequency resolution equals approximately one DFT bin, which is the frequency difference of two adjacent lines in the discrete DFT magnitude spectrum. Our measurement system enables to distinguish multiple targets in each dimension of the three-dimensional micro-wave data cube in spectral domain. The fast time domain, enables to distinguish between objects if their distances to the radar module differ by more than

[00007]$\begin{array}{cc}{\delta }_r=\frac{c}{2B}& \left(8\right)\end{array}$

[0066] In order to be able to separate targets in special domain, their angle of arrival α of the impingeing radio frequency signals must differ by more than

[00008]$\begin{array}{cc}{\delta }_{\alpha }=\arcsin \left(\frac{c}{d{f}_{c}M}\right)& \left(9\right)\end{array}$

[0067] Strictly speaking, this is the lower limit of the resolution in special domain, which is only valid in the range of α˜0°.

[0068] Regarding the slow time domain, we can distinguish between objects if their movement Δr relative to the radar module between consecutive transmit cycles varies by more than

[00009]$\begin{array}{cc}{\delta }_{\Delta r}=\frac{c}{2f_{c}K}& \left(10\right)\end{array}$

[0069] As a note, above results are valid only if no window functions are applied to the measurement data before computing the DFT spectrum. If window functions are used, their effects have to be considered since they broaden the target spectrum, and thus degrade the achievable resolution. If model based high resolution algorithms are used, it is possible to go beyond the above-mentioned resolution limits. Nevertheless, the discrete Fourier transform is by far the most common and widest used method for frequency calculations, because it can be implemented by the fast Fourier transform algorithm which is computationally efficient and widespread available on many signal processing systems.

Test Measurement Setups and Experimental Results

[0070] In order to validate this approach(es) of measuring the fluid surface velocity distribution by a non-invasive radar measuring system as in the second embodiment and first arrangement, and measuring the velocity distribution within the illuminates area of the fluid surface and the distance from the radar device to the fluid surface in the second embodiment and second arrangement, test measurements have been conducted.

[0071] In order to evaluate the performance of the radar-based surface velocity measurement system for fluid, experiments were carried out at a channelized stream. To this end, for both types of arrangements, the radar module was positioned at a height of h=0.91 m above the surface of the water, with the radar beam pointing upstream. To allow a comparison of both arrangements, the same parameters of the radar system were chosen: [0072] f.sub.c=77 GHz [0073] B=2 GHz [0074] M=8 [0075] N=128 [0076] K=8192 [0077] T=250 μs [0078] θ=40° [0079] d=λ/2

[0080] Independently of the type of arrangement, these parameters result in a limitation of the distance between the radar module and the target r of 4.80 m, while the system was designed to provide an unambiguity range for the angle of arrival α of the impinging radio frequency signal between −180° and +180°. The following values were calculated for the center of the radar beam with α=0° wherein both arrangements yield the same limitations. In this case, the chosen parameters result in a detectable surface velocity v of +/−5.08 m/s. Regarding the ability of the radar system to distinguish between multiple targets, these parameters yield a resolution in range measurement with δ.sub.r=7.49 cm, in special domain with δ.sub.α=14.5°, and in velocity measurement with δ.sub.v=1.24 mm/s.

Second Embodiment, First Arrangement, Patch Areas Orthogonal to the Fluid Flow Direction.

[0081] Especially in open channels, the surface velocity is not constant for the cross section of the channel. Therefore, the measurement system being able to measure the surface velocity profile for the entire channel cross section would present a significant benefit. To this end, the radar system according to the present invention is positioned above the stream so that the main lobe of the transmitting antenna illuminates the fluid, while the receiving antennae are arranged orthogonal to the direction of flow. This is shown in schematic form in FIG. 1 A and FIG. 2.

[0082] The use of this measurement arrangement makes it possible to determine the movement Δr of the target relative to the radar module between consecutive transmit cycles for arbitrary angles of arrival α and ranges r within the design borders specified previously. Thus, by evaluating the estimated normalized frequency in slow time domain ψv at different ranges and angles, a surface velocity profile can be determined. Using the relationship:

Δr=υT cos(θ)cos(α)  (11)

with θ specifying the inclination angle of the radar module,
results according to (4) in the measurement of the surface velocity

[00010]$\begin{array}{cc}\hat{v}\left(\alpha \right)=\frac{\widehat{{\psi }_v}\left(r|\alpha \right)c}{2f_{c}T\cos \left(\theta \right)\cos \left(\alpha \right)}& \left(12\right)\end{array}$

at a chosen angle of arrival, evaluated for all ranges. With respect to (7), a limit for the unambiguously determinable surface velocity arises with

[00011]$\begin{array}{cc}.Math.v.Math.\le \frac{c}{4f_{c}T\cos \left(\theta \right)\cos \left(\alpha \right)}& \left(13\right)\end{array}$

and according to (10) the resolution in velocity measurement yields

[00012]$\begin{array}{cc}{\delta }_v=\frac{c}{2f_{c}TK\cos \left(\theta \right)\cos \left(\alpha \right)}& \left(14\right)\end{array}$

[0083] Obviously, especially in open channels, disturbing reflections generated by stationary or moving scatters can occur. However, they can be distinguished from the target of interest if they differ in at least one of the three dimensions of the radar data cube in spectral domain. More precisely, either the range r, the angle of arrival α or the velocity of the scatter must differ from the target of interest by more than the corresponding resolutions δ.sub.r, δ.sub.α, or δ.sub.v, respectively. Based on the same measurement data set as used in FIG. 8, an illustration of selected two-dimensional sub-matrices of the three-dimensional radar data cube in spectral domain is shown in FIG. 9, where the normalized frequencies ψr, ψα, and ψv have been converted to range r, angle of arrival a, and velocity v according to (2), (3), and (12), respectively.

Experimental Results

[0084] For the type of installation, in which the radar module is positioned above the stream so that the receiving antennae are arranged orthogonal to the direction of flow, the normalized frequencies corresponding to the position of the maximum absolute value of the radar data cube in spectral domain are determined. This yields measurements for the surface velocity with =1:64 m/s, for the distance between the radar module and the target with {circumflex over (r)}=1:46 m, and for the angle of arrival of the impingeing radio frequency signal with {circumflex over (α)}=−5:38°. These values are the basis for the selection of the two-dimensional sub-matrices shown in FIG. 9. The measured surface velocity is consistent with the results of a commercial hand-held electromagnetic current meter.

[0085] An obvious interpretation of the radar data cube in spectral domain is the evaluation at a specific angle of arrival, which corresponds to the well-known range-Doppler map illustrated in FIG. 11. In principle, based on the determined range {circumflex over (r)} and the known inclination angle θ of the radar module, the height of the measurement system above the surface of the water could also be determined.

[0086] Since the presented measurement system also estimates the angle of arrival α of the impingeing radio frequency signal, a surface velocity profile can be determined. As shown in FIG. 12. for a range of r=1:46 m, at angles α around 0° an almost constant surface velocity is observed. For higher values of α no relevant scatters are present at this distance due to the steep slope of the artificial surrounding of the stream.

Second Embodiment, Second Arrangement, Patch Areas Parallel to the Fluid Flow Direction.

[0087] It is important to measure the fluid level in addition to the velocity distribution in the part of the fluid flow illuminated by the main lobe so that the volumetric flow discharge can be calculated if the pipe or channel profile is known. To this end, the radar system is positioned above the stream so that antennae are arranged parallel to the direction of flow. This is shown in schematic format in FIG. 13.

[0088] Again, using this measurement arrangement makes it possible to determine the movement Δr of the target relative to the radar module between consecutive transmit cycles for arbitrary angles of arrival α and ranges r within the design borders specified previously. Using the relationship

Δr=υT cos(θ−α)  (15)

and

h=r sin(θ−α)  (16)

with h describing the height of the radar module above the surface of the fluid, results according to (2) in a measurement of the radar height

[00013]$\begin{array}{cc}\hat{h}\left(\alpha \right)=\frac{\widehat{{\psi }_r}\left(v|\alpha \right)\mathrm{cN}\sin \left(\theta -\alpha \right)}{2B}& \left(17\right)\end{array}$

[0089] Regarding the slow time domain, with respect to (4) the measurement of the surface velocity yields

[00014]$\begin{array}{cc}\hat{v}\left(\alpha \right)=\frac{\widehat{{\psi }_v}\left(r.Math.\alpha \right)c}{2f_{c}T\cos \left(\theta -\alpha \right)}& \left(18\right)\end{array}$

at a chosen angle of arrival, evaluated for all ranges. Thus, it is possible to measure the height h of the radar module above the surface of the fluid and the surface velocity for each angle of arrival α separately. However, since it can be assumed that the target velocity and the radar height remain unchanged for different angles of arrival, a superposition of the corresponding magnitude spectra can be performed, yielding a significant improvement of the accuracy of the measurements for velocity and radar height. According to (7), a limit for the unambiguously determinable surface velocity arises with

[00015]$\begin{array}{cc}.Math.v.Math.\le \frac{c}{4f_{c}T\cos \left(\theta -\alpha \right)}& \left(19\right)\end{array}$

and with respect to (10) the resolution in velocity measurement yields

[00016]$\begin{array}{cc}{\delta }_v=\frac{c}{2f_{c}TK\cos \left(\theta -\alpha \right)}.& \left(20\right)\end{array}$

Experimental Results

[0090] For the type of installation, in which the radar module is positioned above the stream so that the receiving antennae are arranged parallel to the direction of flow, a superposition of the magnitude spectra for the considered angels of arrivals a is performed. Determining the position of the maximum value of the resulting two-dimensional map, which is illustrated in FIG. 14, yields measurements for the surface velocity with =1:63 m/s, and for the height of the radar module above the surface of the water with ĥ=0:916 m. The measured surface velocity is consistent with the results of a commercial hand-held magnetic current meter and with the value determined using the orthogonal arrangement of the receiving antennae. The measured radar height is very close to the expected value of h=0:91 m, especially as, due to waves present at the surface of the water, the determination of the actual fluid level is inherently imprecise.