Ultrasound Doppler system for two-dimensional flow mapping in liquid metals

Flow Measurement and Instrumentation 21 (2010) 402–409

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Ultrasound Doppler system for two-dimensional flow mapping in liquid metals Sven Franke a,∗ , Lars Büttner a , Jürgen Czarske a , Dirk Räbiger b , Sven Eckert b a

Technische Universität Dresden, Faculty of Electrical Engineering and Information Technology, Laboratory for Measurements and Testing Technologies, Helmholtzstrasse 18, 01069, Dresden, Germany b

Forschungszentrum Dresden-Rossendorf, Institute Safety Research, Department Magnetohydrodynamics, Bautzner Landstrasse 128, 01328, Dresden, Germany

article

info

Article history: Received 12 November 2009 Received in revised form 29 April 2010 Accepted 2 May 2010 Keywords: Ultrasound Doppler velocimetry Flow field measurements Ultrasound sensor array Liquid metals Magnetohydrodynamics Rotating magnetic field

abstract A novel ultrasound Doppler measurement system for investigating liquid metal flows is presented. It employs an array of 25 transducer elements allowing a fast electronic traversing with concurrently high spatial resolution and therefore overcomes the limitations of commercially available ultrasound Doppler devices. For a high temporal resolution investigations were performed to parallelize the measurements as much as possible. Their results proved this parallel processing technique allowing a four times higher measurement rate compared to a serial processing for our specific ultrasound Doppler system. Therewith, a first two-dimensional one-componential flow mapping of liquid metal flows driven by a rotating magnetic field was successfully performed. In objective, this measurement system will be extended to a two-componential flow mapping. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Magnetohydrodynamics (MHD) provides manifold possibilities for electromagnetic flow control in industrial processes. The purpose is to manipulate flows of liquid metals, semiconductors or electrolytes in fields of metallurgy, crystal pulling and electrochemistry by means of magnetic forces, in order to optimize production processes and to improve product qualities. Particularly the impact of magnetic fields on convection, mass transport, heat transmission and solidification of liquid metals and the resulting material properties are determined [1–3]. One area of application can be found at the fabrication of monocrystalline semiconductor crystals according to the Czochralski process [4–6]. One aim is to grow silicon monocrystals with a wafer diameter of 450 mm for the next generation of semiconductor fabrication technology [6,7]. A further example for the exertion of electromagnetic flow control is to optimize continuous casting at steel fabrication by the damping of turbulent flows in the region of the mold [8–10]. In the field of magnetohydrodynamics still exists the exigency of fundamental researches in order to understand the interaction of liquid metal flows with Lorentz forces. The applied magnetic fields used for the generation of electromagnetic forces do not include only homogeneous continuous fields but particularly the

∗

Corresponding author. Tel.: +49 351 46339811; fax: +49 351 46337716. E-mail address: [email protected] (S. Franke).

0955-5986/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2010.05.001

combination of continuous and temporally as well as spatially varying fields [2]. Besides ongoing numerical simulations [11] a comprehensive understanding of the interaction between liquid metal flows and different kinds of applied magnetic fields requires detailed experimental investigations, too. Reliable and precise data about the velocity structure are necessary for a validation of the theoretical models implemented in the numerical computer codes. Model experiments using low melting point liquid metals (e.g. the eutectic GaInSn alloy) are considered as an important tool to investigate the flow structure and related transport processes in liquid metal flows [1]. For the evaluation of such model experiments an adequate non-invasive, multidimensional, multi-component measurement system for flow fields is desired. Due to the opaqueness, the high temperatures or the chemical aggressiveness of the fluid, the instrumentation of respective experiments appears to be very difficult. Powerful optical methods like Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA) [12] as used for measurements in transparent liquids will fail in opaque melts. Ultrasound Doppler velocimetry (UDV) offers an attractive noninvasive possibility to measure flow velocities in opaque fluids [13,14]. The method is based on the pulsed echo technique (‘‘pulsed wave Doppler’’) which applies the repetitive emission of short ultrasound bursts. Thereby, in most cases the ultrasound sensor serves as both a transmitter for the ultrasound pulse as well as a receiver for the echo signal. The echo signals from micro particles suspended in the liquid deliver the relevant information

S. Franke et al. / Flow Measurement and Instrumentation 21 (2010) 402–409

2,5 mm

403

2.1. Basic design considerations

active pair of piezo elements

In pulsed wave Doppler measurement systems the axial resolution is expressed by [15]:

5 mm 1

2

3

4

5

6

7

8

9

23

24

25

sensitive array length: 70 mm Fig. 1. Design of the linear ultrasound array.

for the reconstruction of a velocity profile. Provided that the sound velocity of the liquid is known the spatial position along the sound propagation axis can be determined from the detected time delay between the burst emission and its reception. The movement of an ensemble of scattering particles inside a given measuring volume will result in a small time shift of the signal structure between two consecutive bursts from which the velocity is obtained. Only few commercial ultrasound Doppler devices are available on the market. Apart from measurements of single velocity profiles, these instruments provide two-dimensional flow field measurings of one velocity component (2d–1c), however only with a low number of ultrasound transducers which can be controlled simultaneously. Moreover, there the measurement rate is decreased since a high number of scanning lines and a high measurement rate are contrary demands and are not achieved simultaneously. In summary an efficient flow mapping is strongly restricted with commercial ultrasound Doppler devices. However, multidimensional flow mapping with a high spatial and temporal resolution is desired for investigations of turbulent flows occurring, for example, during the electromagnetic stirring of metal melts. Therefore, novel techniques for pulsed wave ultrasound Doppler measurement systems have to be found to facilitate multidimensional flow field measurements at high measurement rates and high spatial resolution. This paper will present and investigate methods to increase the temporal resolution of flow mapping distinctly and to allow a close scanning of flow fields contemporary with a good lateral resolution of lower than 5 mm. The concept of a 2d–2c UDV measurement system will be introduced in the outlook which will apply these novel methods to facilitate frame rates up to several 10 Hz for an instantaneous flow mapping while using a high number of scanning lines and maintaining high spatial resolutions. 2. 2d–1c measurement system involving novel techniques in UDV The concept of the pulsed wave ultrasound Doppler measurement system includes the use of monolithic linear arrays of ultrasound transducers allowing an electronic traversing and therewith a fast scanning of flow fields compared to the mechanical traversing of a single ultrasound transducer. Thereby, each array element operates as transmitter of the ultrasound pulse and receiver of the echo signal, therewith providing a two-dimensional measurement of one velocity component. For measuring flow fields in plane of 70 × 70 mm2 an array was manufactured (customized development from Richter STT ) spanning 25 piezo elements over a length of 70 mm according to the design in Fig. 1. A high measurement rate shall be achieved by parallelizing the measurement of velocity profiles. This means that multiple transducer pairs operate simultaneously. The parameters of the linear array design and the operation mode are defined by some specific marginal conditions and considerations. For determining these parameters calculations and experimental investigations as simulations and experiments were performed and will be presented in this section.

1z =

Ncycles · c

(1)

2 · fe

where c is the sound velocity, fe the emission frequency and NCycle the number of wave cycles of the ultrasound pulse. Eq. (1) is a rough estimation for the axial resolution since it assumes an unlimited transducer bandwidth. However, it implies that a high axial resolution requires a high emission frequency and a low number of wave cycles. The lateral resolution in ultrasound systems is determined by the −6 dB-width of sound pressure of the ultrasound beam [16]. The best lateral resolution is given in the focal point of the beam or rather in the near field depth separating the near field and the far field. According to the Fraunhofer diffraction beam divergence δ of the far field is expressed by [15]: sin δ =

1.22 · λ D

=

1.22 · c D · fe

(2)

where λ is the ultrasound wavelength and D the transducer diameter. Eq. (2) results in a lower beam divergence or rather a better lateral resolution over the beam length for an increased emission frequency. As a consequence a high emission frequency is desired for a high axial as well as a high lateral resolution. However, the emission frequency cannot be increased arbitrarily since the acoustic attenuation rises at decreasing wavelengths which restricts the penetration depth. As a compromise between a high spatial resolution and a high penetration depth an emission frequency of fe = 8 MHz for the ultrasound transducer design was chosen. The resulting spatial resolution is considered and investigated in detail at Section 2.3. 2.2. Design considerations of the linear ultrasound transducer arrays For the design of the dimension of the piezo transducer elements, contrary demands have to be considered. A dense scanning (i.e. a large number of scanning lines with small lateral traversing step width) of flow fields necessitates a high number of array elements resulting in a small size of these elements over the given length. In contrast a low divergence of the ultrasound beam requires an edge length of a piezo element much bigger than the ultrasound wavelength [15]. To comply with both requirements, a small traversing step width for scanning and a low divergence of the ultrasound beam, a segmental array design and operation mode is introduced. Instead of using square piezo elements for the linear array, rectangular elements with a width half of the height are implemented bisecting the traversing step width. For the present design the size of 2.5 × 5 mm2 per piezo element was applied. To maintain the low beam divergence in operation two adjacent rectangular piezo elements are combined in pairs resulting in an active square transducer (size 5 × 5 mm2 ) which can be shifted by half of its edge length. By using this method the 25 piezo elements of the linear arrays result in 24 applicable transducer pairs or rather 24 measuring lines. This technique is usually established in medical ultrasound imaging applications [15,17,18]. The linear array structure is shown in Fig. 1. The sensitive array length is 70 mm due to gaps of around 0.3 mm between adjacent piezo elements caused by the production process.

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Diagonal cross-section 100

Parallel cross-section 100

-20 0 dB z = 50 mm z = 100 mm

-30 90

90

80

80

70

70

-40

60

z [mm]

z [mm]

50

-5 dB

60

Crosstalk [dB]

-50 dB -50 -60 -70 -80 -90

50

-100 40

-10dB

40

1

3

5

7

9

11

13

15

17

19

21

23

Distance (in array elements) from of transmitting transducer 30

30 Fig. 3. Crosstalk measurement: the diagram pictures the crosstalk in dependence from distance (in array elements) to the transmitting transducer.

20

20

10

10

-5

0 x [mm]

5

-15dB -5

0 x [mm]

5

Fig. 2. Simulated sound field of a square ultrasound transducer (5 × 5 mm2 ) in diagonal and parallel cross-section in normalized sound pressure.

2.3. Characterization of sound field and spatial resolution The lateral resolution of an ultrasound transducer is defined by its sound field which can be determined by numerical simulations. Concerning this, the transducer surface is segmented into small elements of area, each transmitting a spheric wave, and solving the resulting Rayleigh integral [19]. This is implemented by a small inhouse script in MATLAB. From the simulation both the position of the focus (identical to the near field) depth and the −6 dB-focus width (identical to the lateral resolution) is obtained. For a 5 × 5 mm2 square transducer representing one pair of piezo elements from the linear array as specified above the results of the sound field simulation of the diagonal and parallel crosssection are shown in Fig. 2. Thereby, the gap of 0.3 mm between the piezo elements is insignificant small and was neglected. The simulation was performed for GaInSn (c = 2730 m s−1 at room temperature [20]) assuming an ultrasound burst frequency of fe = 8 MHz corresponding to a wavelength of λ = 0.342 mm. The near field depth was computed with z = 25.4 mm There, the lateral resolution for both cross sections can be evaluated with 1x ≈ 3 mm. This complies with the small traversing step width of about 2.8 mm (transducer element width plus gap). A number of NCycle = 8 wave cycles at a burst frequency of fe = 8 MHz was chosen as a compromise between high axial resolution and high acoustic energy corresponding to a high SNR. It yields an axial resolution of 1z ≈ 1.4 mm in GaInSn according to Eq. (1). 2.4. Parallel operation mode Generally, ultrasound arrays in medical as well as in industrial applications work in sequential time-division multiplexing. This means that the array elements are operated one after the other. There, the demand for a high measurement rate contrasts with the demand for a high number of transducer elements (corresponding to the number of scanning lines) since a rising number of array elements increases the measurement duration and worsens the

temporal resolution. Hence, a merely sequential time-division multiplexing for operating the transducer elements of the arrays is not sufficient. To achieve a high measurement rate notwithstanding the measurement of velocity profiles is parallelized. That means several transducer pairs transmit and receive in parallel, thereby reducing the measurement duration by the number of simultaneously active transducer pairs. However, at this operation principle spatial crosstalk between active channels may appear since the sound fields overlap and distort the measurement of adjacent velocity profiles. To minimize this crosstalk a sufficient distance between the active transducer pairs must be chosen. To that, crosstalk investigations were performed to determine this minimum distance. In the experimental setup a pinhead (diameter 1 mm) in water was applied as scattering particle in a pulse-echo operation mode. At these investigations one transducer pair was transmitting and all other transducer elements were receiving. The excitation burst signal (8 sinusoidal wave cycles at 8 MHz) for the transmitting transducer pair was generated by an arbitrary function generator (AFG 3022b from Tektronix) and amplified by a RF amplifier (AN779L from Communication Concepts). The echo signals of the receiving transducers were amplified by an inhouse 4-channel amplifier and digitized by a 4-channel data acquisition card (Octopus CompuScope CS 8347 from GaGe) in a personal computer. The 23 receiving channels were measured one after another in groups of 4 with the 4 acquisition channels. This is possible since the echo signals are stationary for the fixed scattering test particle. For different measurement depths the received signal energy of the transmitting transducer pair was measured and normalized. The result for two measurement depths is pictured in Fig. 3. A threshold value of −50 dB is defined as sufficient resulting from signal processing where signals below this level are treated as noise. This threshold value amounts a crosstalk of less than 0.3% resulting in a minimum required distance of two transducer elements. Since this investigation was performed in water and the ultrasound beam divergence in GaInSn is approximately twice the beam divergence in water (due to double the sound velocity of GaInSn; see Section 2.1) it is assumed that for the considered linear arrays a spacing of at least four inactive transducer elements between the active ones results in a negligible acoustic crosstalk (Fig. 4). With this spacing four transducer pairs may be addressed simultaneously at the present array configuration. Implementing

S. Franke et al. / Flow Measurement and Instrumentation 21 (2010) 402–409

405

is obtained. Its intensity-weighted mean frequency is expressed by [22]:

R fd = Fig. 4. Parallelized operation: 4 inactive transducer elements between two operating pairs.

burst generator

T/R switch RF signal

preamplifier

ultrasound transducer

4-channel data aquisition card for PC

T/R switch preamplifier

ultrasound transducer

P (f )df

(3)

where f are the frequencies of the power spectral density. The velocity is calculated by:

v=

preamplifier

f · P (f )df

R f

T/R switch ultrasound transducer

f

c ·fd 2 · fe

(4)

where fe is the ultrasound burst emission frequency and c the sound velocity. A rough estimation for the relative uncertainty of Eq. (3) is expressed with [22]:

√ σ ≈ 1/ 3M

(5)

where M is the number of bins occupied by the power spectrum. M depends on the acquisition length of the Doppler signal which complies with the number of echoes per profile EPP (see [13,21] for a more detailed description). M is expressed as M = EPP /2. Typical values for EPP are located between 100 and 500.

T/R switch ultrasound transducer

preamplifier

Fig. 5. Parallelized measuring system with 4-channel T/R switching and amplifying unit.

this in a multiplexing scheme reduces the measurement duration by a factor of 4. That means the present array configuration allows scanning the entire flow field in 6 steps compared to 24 steps in a merely sequential multiplexing. The application of this principle is explained in detail in the outlook (Section 4). 3. Flow measurements Experiments with one linear array were performed to prove the functionality of the parallel operation of multiple transducer pairs at flow field measurements. For this purpose, liquid metal flow in a cubic vessel driven by a magnetic field has been investigated within this study. 3.1. Measuring system To validate the control of transducer elements by pairs and the parallelized operation mode a simplified measurement system was built according to Fig. 5. There, the burst generator (AFG 3022b arbitrary function generator plus AN779L RF amplifier) providing the sinusoidal pulses drives four transmitting/receiving switches (T/R switches) simultaneously each actuating one transducer pair of the linear array. The transmitting/receiving switch of every transducer element automatically toggles between transmitting stage and receiving stage. The 4-channel T/R switching unit including the preamplifiers is an in-house development. After amplification and filtering the received echo signals are digitized and recorded by the 4-channel CompuScope data acquisition card (resolution 14 bits, sample rate 100 MS/s). The PC performs the offline digital signal processing of these recorded signals in MATLAB to determine the velocity components of flow field. This is implemented by a digital quadrature demodulation obtaining the Doppler signal [13,21]. From a complex FFT of the quadrature components the power spectral density P (f )

3.2. Flow test setup A magnetic stirrer is deployed to drive the liquid metal flow. The stirrer (manufactured by the Perm State University, Russia) consists of a systems of induction coils (Figs. 6 and 7) generating a rotating magnetic field (RMF). The inner diameter is around 200 mm. A cubic vessel made of acrylic glass with an edge length of 70 mm is filled with the liquid metal alloy GaInSn. There, no additional seeding of tracer particles for UDV was required. It is assumed that the tracer particles in GaInSn are metal oxides and microscopic segregations of the eutectic alloy. This vessel is placed in the center of the magnetic field stirrer. Let us consider the application of a rotating magnetic field on a liquid metal. The RMF rotates around the vertical vessel axis and induces electrical currents inside the liquid metal. These currents interact with the imposed magnetic field and generate a dominating angular component of the electromagnetic force which drives a swirling flow with a rotating direction equal to the magnetic field [23]. The angular velocity of the fluid is always smaller than the rotating field, because the induction of the electrical currents relies on a relative motion between field and fluid. Similar to the principle of the asynchronous motor a slip occurs. The angular frequency of the swirling flow depends on both the magnitude and the angular frequency of the rotating magnetic field. Within the presented investigations such a vortex structure flow field is measured. Thereto, one linear array is mounted at one of the side walls of the vessel as shown in Fig. 8. With it, the measurement plane conforms to the horizontal mid-plane of the cubic vessel. The measurement results are discussed in the following. 3.3. Parallel measurement of velocity profiles In a first experiment the reliability of the parallel operation mode was investigated. For this purpose, in a first measurement a transducer pair was driven exclusively this means without other transducers being active. In a subsequent measurement this transducer pair (with the same location according to the flow) was operated in combination with other transducer pairs being active simultaneously. Thereby a spacing of four inactive elements between the active ones was applied according to the introduced parallel operation mode (Section 2.4). At both configurations the mean flow of the RMF driven liquid metal was obtained by averaging the

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Fig. 7. Measurement setup with magnetic field stirrer.

Fig. 8. Measurement configuration (2d–1c) for visualization of the vortex flow structure in the marked measurement plane. Fig. 6. Measurement setup: acrylic glass cube filled with GaInSn in a magnetic field stirrer.

0 Exclusive operation mode Parallel operation mode -5

Velocity [mm/s]

profile measurements. The angular frequency of the RMF amounts to ωRMF = 2π · 50 Hz = 314 s−1 , the applied magnetic flux density to B = 1.2 mT. Every averaged profile is determined from 100 velocity profiles each obtained from EPP = 100 echo signals. The velocity profiles comprise of 52 values along the measurement direction which complies with the best axial resolution of 1z ≈ 1.4 mm in GaInSn over the measurement depth of 70 mm. A pulse repetition frequency of PRF = 500 Hz was deployed. In Fig. 9 the result of this measurement is pictured. There, a very good congruence of the velocity profiles of exclusive and parallel operation mode is shown. A maximum relative deviation of approximately 2% was calculated, however, please note that these differences can also occur since the compared profiles were not measured simultaneously and the measurement duration for capturing the mean flow was limited. The result implies that in parallel operation the influence of adjacent active transducer pairs (related to the spacing of four transducer elements) is insignificant small. Therewith, the parallel measurement of several velocity profiles is proved.

-10

-15

-20

-25 10

20

30 40 Depth [mm]

50

60

70

Fig. 9. Comparison of the velocity profiles of a transducer pair (transducer elements 3 and 4) operating exclusively and in parallel with other transducer pairs.

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70

0

25

DOP2000

20 60

15

-5

10

Y (Width) [mm]

Velocity [mm/s]

50 -10

5 0

40

-5 30

-10

-15

Velocity [mm/s]

TUD -UDV

-15 20 -20

-20 -25

10 0

10

20

30

40

50

60

70

X (Length) [mm] -25 10

20

30 40 Depth [mm]

50

60

70

Fig. 10. Comparison of our ultrasound Doppler system (TUD-UDV ) to a commercial ultrasound Doppler device (DOP2000). Transducers 1+2

Fig. 12. Vortex flow in counter-clockwise direction in GaInSn; the vertical velocity component (y-direction) of the vortex is measured.

follows that the flow cannot be detected in the approximately first 5 mm in GaInSn (Figs. 9–11). 3.4. Vortex flow structure in a square plane

Transducers 7+8

30

Transducers 13+14 Transducers 19+20

20

Velocity [mm/s]

10

0

-10

-20

-30 10

20

30

40

50

60

70

Depth (y) [mm] Fig. 11. Parallel measurement of four velocity profiles in a vortex flow field.

Additionally, the velocity profiles of our UDV system were compared to profile measurements of the commercial ultrasound Doppler device DOP2000, model 2125 (from Signal Processing, Lausanne, Switzerland [24]) in Fig. 10. Thereby, the measurements of our UDV system conforms well to the DOP2000 measurements (with a maximum relative deviation of approximately 5%). Reasons for slight variations can be varying signal processing parameters and the finite averaging time for capturing the mean flow since the comparative measurements were not performed simultaneously. In Fig. 11 the result of a parallel measurement of velocity profiles is shown. Thereby, the outermost velocity profile and further profiles in a spacing of four transducer elements were measured. The curves indicate different profile lines of the vortex structure driven by the rotating magnetic field. Due to the saturation of the preamplifier by the high voltage ultrasound pulse the echo signal is overdriven the first few microseconds. This means that no reflections from micro particles in this section of the echo signal can be observed. From this it

To demonstrate the mapping of entire flow fields the parallelized velocity profile measurement was performed for all 24 scanning lines in 6 steps consecutively. Due to averaging the velocity profiles over an extended time, profile lines of the mean flow are obtained. Merging them all creates the 2d–1c map of the entire flow field. This is shown in the contour plot in Fig. 12 for the investigated flow field (compare Fig. 8). There, the x-axis complies with the position of the linear array; the y-axis corresponds to the measurement depth. That implies that the velocity component of flow in y-direction is measured. The nomenclature is such, that for positive velocities the flow moves away from the transducer. Thus, the flow field in the plot characterizes a counter-clockwise rotating flow (vortex) in GaInSn with a ωflow = 0.86 s−1 . Due to the square cross-section of the vessel in the edges counter-rotating vortices arise which were well resolved at these measurements. 4. Outlook The presented UDV system provides the two-dimensional measurement of one velocity component (2d–1c). However, the objective is to measure both velocity components (2d–2c). Thereto, the concept of the measurement system involving the novel driving techniques will be extended by arranging two linear arrays orthogonally to each other. This allows a square measurement plane of 70 × 70 mm2 e.g. of a block-shaped vessel. A further future aspect of the concept for the UDV system is to achieve high measurement rates despite the high number of scanning elements and two measurement directions. For this reason, the principle of the parallelized measurement of velocity profiles is introduced proved by the preceding investigations shown in Section 3.3. There, a minimum distance of four inactive elements between the active ones was determined resulting in the simultaneous operation of four transducer pairs. From this, a modified time-division scheme according to Fig. 13 is implemented to address the array transducer elements. This addressing scheme also reduces temporal crosstalk from multiple echoes by preventing that a transducer element is actuated on two sequent time steps. In the orthogonal array configuration the linear arrays in x- and ydirection are addressed alternately.

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piezo transducer element 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 time step 1 time step 2 time step 3 time step 4 time step 5 time step 6

active piezo elements

inactive piezo elements

Fig. 13. Addressing scheme of transducer channels for the simultaneous measurement of 4 channels (parallel time-division).

The introduced time-division scheme in Fig. 13 allows to scan the entire flow field in n = 6 steps. The earliest point of time the measurement system can switch to the next time step is determined by the transmit time of the echo signal of the maximum measurement depth. Assuming the flow field measurement in GaInSn (c = 2730 m s−1 ) in the area of 70 × 70 mm2 the measurement depth of d = 70 mm yields a time interval of Tscan = 2d/c = 2 · 0.07 m/2730 m s−1 = 51 µs and a respective scanning frequency of fscan = 1/Tscan = 19.5 kHz. Based on the alternating operation of both arrays the maximum pulse repetition frequency for each transducer element is estimated by PRF = fscan /2n = 19.5 kHz/(2 · 6) = 1.6 kHz. The applied signal processing requires the minimum number of around 30 echo signals to determine one velocity profile. Therefore, the specified pulse repetition rate allow measurement rates approximately up to 50 frames/s contemporary with a substantially increased number of measuring lines compared to commercial Doppler devices with rates approximately up to 25 frames/s.

mapping with frame rates up to 50 fps. The system will be supplemented by an additional linear array to extend the flow mapping by the second velocity component. Finally, this 2d–2c ultrasound Doppler system will utilize a five times higher number of scanning lines with at least twice the measurement rate compared to commercial systems. Acknowledgements The project workers thank the Deutsche Forschungsgemeinschaft (DFG) for the financial support of the project in context of the collaborative research center SFB 609 ‘‘Electromagnetic Flow Control in Metallurgy, Crystal Growth and Electrochemistry’’. Furthermore we thank Michael Lenz and Andreas Fischer, as well as the group members in the Forschungszentrum Dresden-Rossendorf for their support. In particular we thank Dr. Richter from the company Richter Sensor and Transducer Technologie who produced the linear ultrasound transducer arrays. References

5. Summary and conclusions A 2d–1c ultrasound Doppler system for measuring flow fields in liquid metals has been presented involving the application of a linear ultrasound transducer array. Thereby, two novel operation methods has been implemented and investigated: The first method facilitate an electronic traversing with a small scanning step width by applying a segmental array design. Its objective is to achieve a scanning step width in the same extend as the lateral spatial resolution which is not obtained for two-dimensional flow mapping up to the present. With the implemented scanning step width of 2.8 mm a high lateral resolution of 1x ≈ 3 over a long beam length was achieved. The second method allows handling a high number of scanning elements of the transducer array by parallelizing the profile measurement. Namely, four transducer pairs operate simultaneously decreasing the number of steps by this factor to measure the entire flow field. Respective experimental investigations validated the parallel operation mode showing an negligible crosstalk. Velocity profiles of a liquid metal flow driven by a rotating magnetic field were measured and compared to a commercial Doppler device. A mapping of the mean flow structure was measured showing the main vortex and counter-rotating vortices in the edges. Prospectively, both methods will be implemented in a measurement system with a fast multiplexing electronics facilitating a flow

[1] Eckert S, Gerbeth G, Räbiger D, Willers B, Zhang C. Experimental modelling using low melting point metallic melts: relevance for metallurgical engineering. Steel Res Int 2007;78(5):419–25. [2] Eckert S, Nikrityuk PA, Räbiger D, Eckert K, Gerbeth G. Efficient melt stirring using pulse sequences of a rotating magnetic field: part I. Flow field in a liquid metal column. Metall Mater Trans B 2008;39B:375–86. [3] Willers B, Eckert S, Nikrityuk PA, Räbiger D, Dong J, Eckert K, et al. Efficient melt stirring using pulse sequences of a rotating magnetic field: part II. Application to solidification of Al–Si alloys. Metall Mater Trans B 2008;39B:304–16. [4] Langlois WE. Buoyancy-driven flows in crystal-growth melts. Annu Rev Fluid Mech 1985;17:191–215. [5] Hainke M, Friedrich J, Vizman D, Müller G. MHD effects in semiconductor crystal growth and alloy solidification. In: International scientific colloquium modelling for electromagnetic processing. 2003. p. 73–8. [6] Watanabe M, Eguchi M, Hibiya T. Silicon crystal growth by the electromagnetic Czochralski (EMCZ) method. Japan J Appl Phys 1999;38(1A–B):L10–3. [7] Watanabe M, Vizman D, Friedrich J, Müller G. Large modification of crystal–melt interface shape during Si crystal growth by using electromagnetic Czochralski method (EMCZ). J Cryst Growth 2006;292:252–6. [8] Gardin P, Galpin J-M, Regnier M-C. Liquid steel flow control inside continuous casting mold using a static magnetic field. IEEE Trans Magn 1995;31(3): 2088–91. [9] Chang F-C, Hull JR, Beitelman L. Simulation of flow control in the meniscus of a continuous casting mold with opposing alternating current magnetic fields. Metall Mater Trans B 2004;35B:1129–37. [10] Toh T, Takeuchi E. Electromagnetic phenomena in steel continuous casting. In: Aref H, Philips JW, editors. Mechanics for a new millennium. Chicago: Kluwer; 2001. p. 99–112. [11] Nikrityuk PA, Eckert K, Grundmann R. Numerical study of a laminar melt flow driven by a rotating magnetic field in enclosed cylinders with different aspect ratios. Acta Mech 2006;186:17–35. [12] Czarske J. Laser Doppler velocimetry using powerful solid-state light sources. Meas Sci Technol 2006;17:R71–91.

S. Franke et al. / Flow Measurement and Instrumentation 21 (2010) 402–409 [13] Takeda Y. Development of ultrasound velocity profile monitor. Nucl Eng Des 1991;126:277–84. [14] Eckert S, Cramer A, Gerbeth G. Velocity measurement techniques for liquid metal flows. In: Molokov S, Moreau R, Moffatt HK, editors. Magnetohydrodynamics—historical evolution and trends. Dordrecht: Springer; 2007. p. 275–94. [15] Hedrick WR, Hykes DL, Starchman DE. Ultrasound physics and instrumentation. 4th ed. St. Louis: Elsevier Mosby; 2005. [16] Raum K, O’Brien WD. Pulse-echo field distribution measurement technique for high-frequency ultrasound sources. IEEE Trans Ultrason Ferroelectr Freq Control 1997;44(4):810–5. [17] Szabo TL. Diagnostic ultrasound imaging: inside out. London: Elsevier Academic Press; 2004.

409

[18] Fischetti AJ, Scott RC. Basic ultrasound beam formation and instrumentation. Clin Tech Small Anim Pract 2007;22(3):90–2. [19] Blauert J, Xiang N. Acoustics for engineers. Berlin (Heidelberg): Springer; 2008. [20] Morley NB, Burris J, Cadwallader LC, Nornberg MD. GaInSn usage in the research laboratory. Rev Sci Instrum 2008;79:056107. [21] Takeda Y. Velocity profile measurement by ultrasonic Doppler method. Exp Therm Fluid Sci 1995;10(4):444–53. [22] Evans DH. Doppler ultrasound: physics, instrumentation and signal processing. 2nd ed. New York: John Wiley & Sons; 2000. [23] Davidson PA, Hunt JCR. Swirling recirculating flow in a liquid–metal column generated by a rotating magnetic field. J Fluid Mech 1987;185:67–106. [24] www.signal-processing.com [Internet]. Switzerland: Signal Processing SA. Available from: http://www.signal-processing.com.