Two-dimensional ultrasound Doppler velocimeter for flow mapping of unsteady liquid metal flows

Ultrasonics 53 (2013) 691–700

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Two-dimensional ultrasound Doppler velocimeter for flow mapping of unsteady liquid metal flows S. Franke a,⇑, H. Lieske a, A. Fischer a, L. Büttner a, J. Czarske a, D. Räbiger b, S. Eckert b a b

Technische Universität Dresden, Faculty of Electrical Engineering and Information Technology, Laboratory for Measurements and Testing Technologies, 01062 Dresden, Germany Helmholtz-Zentrum Dresden-Rossendorf, Institute of Fluid Dynamics, Department Magnetohydrodynamics, P.O. Box 510119, 01314 Dresden, Germany

a r t i c l e

i n f o

Article history: Received 12 April 2011 Received in revised form 20 July 2012 Accepted 19 October 2012 Available online 31 October 2012 Keywords: Ultrasound Doppler velocimetry Flow field measurements Ultrasound flow mapping Liquid metal flows Rotating magnetic field

a b s t r a c t We present a novel pulsed-wave ultrasound Doppler system for fluid flow investigations being able to determine two-dimensional vector fields of flow velocities. Electromagnetically-driven liquid metal flows appear as an attractive application field for such a measurement system. Two linear ultrasound transducer arrays each equipped with 25 transducer elements are used to measure the flow field in a square plane of 67  67 mm2. The application of advanced processing methods as a multi-beam operation, an interlaced echo signal acquisition and a segmental array technique enable high data acquisition rates and concurrently a high spatial resolution, which have not been obtained so far for flow measurements in liquid metals. The extended pulsing strategy and essential operation principles such as the multiplexing electronic concept will be presented within this paper. The capabilities of the measuring system make it suitable for investigations of non-transparent, turbulent flows. Here, we present measurements of liquid metal flows driven by a rotating magnetic field for demonstration purposes. The measuring setup realized here reveals details of the swirling fluid motion in a horizontal section of a cube. Frame acquisition rates up to 30 fps were achieved for a complete two-dimensional flow mapping. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction The development of innovative liquid metal technologies, in particular the optimized flow control by tailored electromagnetic fields, requires a detailed knowledge of the flow structure and, hence, the availability of efficient and reliable measurement techniques for liquid metal flows. Well-proven laser-based methods [1] as usually used for flow measurements in transparent fluids will obviously fail for this specific case owing to the fluid’s opacity. Since the first pioneering work of Takeda in the late eighties [2,3] the pulsed-wave ultrasound Doppler velocimetry (UDV) has been continuously developed to become a powerful tool for flow investigations in non-transparent liquid metal flows. Numerous studies have already been published reporting successful measurements in single and two-phase metallic flows for different applications and temperature ranges (see [4] for a review). The existing UDV technique provides instantaneous profiles of the velocity component aligned with the direction of ultrasound propagation. The enhancement of the capabilities towards a multidimensional flow mapping with high frame acquisition rates and high spatial resolution would be exceedingly desirable for the examination of complex turbulent flows as occurring e.g. during electromagnetic stirring of metals. For instance, the use of modulated AC magnetic fields as recently ⇑ Corresponding author. Tel.: +49 351 2603113; fax: +49 351 2602007. E-mail address: [email protected] (S. Franke). 0041-624X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultras.2012.10.009

proposed by [5] generates three-dimensional flows with transient vortical structures. Detailed investigations of such flows and a validation of respective numerical simulations require a multidimensional acquisition of the flow field with a reasonable temporal and spatial resolution. Imaging techniques become more and more important for detailed explorations of three-dimensional turbulent flows, in particular with respect to the generation of a suitable experimental data base for an efficient validation of respective numerical simulations. The development of ultrasound imaging methods was started by several research groups coming mainly from the biomedical field (see for instance [6–8]). The need for considering complex flow patterns motivated several researchers to use multi-transducer Doppler systems. For instance, Fox [9] proposed a concept of a multiple crossed beam technique for obtaining three-dimensional velocity vectors of the flow field. The operational principle of a so-called vector Doppler system based on continuous-wave Doppler was introduced by Fox and Gardiner [6] in order to reconstruct real vector velocities irrespective of the particular angle between the ultrasound beam direction and the flow. Overbeck et al. [7] used a single transmitter and two receivers in a pulsed-wave Doppler system to resolve orthogonal velocity components. A similar measuring system composed of a constant-beam-width emitting transducer and up to four receiving transducers was developed by Hurther and Lemmin [10] to conduct 3D flow measurements across the cross section of an open water channel. Scabia et al. [8,11]

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presented a real-time 2D vector Doppler system based on a 128element linear transducer array with electronic focusing. First attempts have already been made to realize a flow mapping of liquid metal flows by the pulsed ultrasound Doppler technique. Takeda and Kikura [12] investigated the mercury flow in a mockup liquid metal target of a spallation neutron source. A semi-circular arrangement of 20 single transducers allowed them to reconstruct two-component (2C) flow vectors at discrete nodes inside the hemispherical two-dimensional (2D) window region. The measurement rate of the flow mapping amounted to 2 fps. A mapping of a steady liquid metal channel flow impacted by an inhomogeneous DC magnetic field has been carried out by Andreev et al. [13]. The authors generated a sophisticated mesh of superposed beam lines by consecutive measurements using one transducer at different positions and under various inclinations with respect to the channel axis. Time-averaged 2C velocity vectors were calculated at the crossing points of the measurement lines. More recently, measurements of a submerged liquid metal jet have been reported by Timmel et al. [14]. A horizontal adjustment of 10 transducers provided a two-dimensional visualization of the horizontal velocity component. These references outline the demand for spatially as well as temporally highly resolved, multi-dimensional UDV measurements which are not covered by the current state-of-the-art. Our paper presents an ultrasound Doppler measurement system using two linear ultrasound transducer arrays each equipped with 25 transducer elements. The orthogonal arrangement of the transducer arrays allows to measure two-dimensional flow fields composed of the in-plane velocity components. Realized acquisition rates of several ten vector maps per second meet the requirements for measurements of highly turbulent flows. For demonstration purposes velocity measurements have been performed in a liquid metal cube exposed to a rotating magnetic field (RMF) driving a swirling flow. 2. Vector field UDV system 2.1. Ultrasonic sensor design A time-dependent flow mapping requires the application of transducer arrays allowing a fast electronic traversing of the ultrasonic measuring beam. The sensor system used here consists of two identical linear transducer arrays in an orthogonal arrangement spanning a square measuring plane of 67 mm by 67 mm (see Fig. 1). The transducer elements allow for the measurement of the velocity component aligned with the direction of the ultrasonic beam, particularly, the array aligned with the direction of the x-axis measures the y-component of the flow velocity and vice versa. The arrays span a mesh of profile lines in the square measuring plane. The flow field is reconstructed by determining the velocity vectors from the measured components at each crossing point. Each array consists of 25 elements (size 2.4 mm  5 mm) with an element pitch of 2.7 mm [15]. The dimensions are depicted in Fig. 2a. The ultrasound arrays are designed to operate as segmental arrays. Segmental arrays can be actuated in groups of elements to

Segmental array x-component of flow

Segmental array y-component of flow

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Fig. 1. Sensor setup for vector field measurements.

achieve a lower beam divergence (resulting in a sufficient high spatial resolution along the entire measuring depth) on the one hand and a small beam line pitch (resulting in a higher measuring line density) on the other hand [16,17]. For the present sensor design the vertical extent of an array element is twice the horizontal extent. The elements are operated in pairs of two transducers resulting in an active square transducer area with an almost identical lateral resolution in the vertical and the horizontal direction. This square transducer can be traversed by half of its edge length that corresponds to one element pitch. The procedure is shown in Fig. 2b in general. The succession of excitation of the transducer elements as used here will be described in the next section. As a consequence of the element binning, the segmental operation principle provides 24 measuring lines per array [15]. The resulting acoustic field was estimated by sound field simulations and is shown in Fig. 3. The area where the slope of the intensity is less than 6 dB can be defined as measuring volume. This gives us a lateral resolution of approximately 3 mm at the near field distance of 25.4 mm, which is in the same order of magnitude as the element pitch. More details regarding the characteristics of the sound field can be found in [15]. The emitting frequency of f0 = 8 MHz was chosen for the demonstration measurements presented within this paper. The ultrasound pulses are composed of NC = 8 harmonic wave cycles yielding an axial resolution of approx. 1.4 mm inside the liquid metal alloy GaInSn. For a more detailed description of the sensor design the authors refer to [15]. 2.2. Operation principle Previous applications of multiline Doppler systems for velocity measurements in liquid metals (for instance [12]) used sequential multiplexers to actuate several transducers and to record various measuring lines in succession. Depending on the signal-to-noise ratio and the desired measurement uncertainty a number of 20 to 100 bursts, designated as emissions per profile, are necessary for each transducer to determine the respective velocity profile. The subsequent recording of the profiles from each measuring line by conventional multiline systems results in a distinct time lag between scanning the first and the last measuring line which complicates the simultaneous acquisition of the complete flow field. This problem aggravates with increasing number of measuring lines making such multiline systems apparently not applicable for measurements of turbulent flows which require a high temporal resolution. Two novel approaches are implemented in the pulsing strategy to overcome this problem. The first method concerns a multi-beam operation. The basic idea is to scan as many ultrasonic beams (respectively transducer pairs) in parallel as possible. However, this concept is restricted by the beam divergence since the ultrasound beams may overlap and induce a crosstalk between the different measuring lines. This problem can be solved by selecting a sufficient distance between the transducer elements being active at the same time. Experimental investigations revealed a tolerable crosstalk of less than 40 dB for the current array design if a distance of 4 inactive array elements is chosen between the active element pairs [15]. For our array comprising 25 transducer elements such a spacing permits the parallel operation of four transducer pairs (see also Fig. 4). The second improvement of the temporal resolution results from an efficient segmentation of the overall acquisition time. As already mentioned above, the reconstruction of the velocity profiles relies on the analysis of many consecutive echo signals excited by a sequence of equidistant ultrasound pulses. The related parameter NEP denotes the number of pulse emissions per velocity profile. The time between consecutive ultrasound pulses, the pulse repetition time (TPR), defines the effective velocity range to be measured.

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The proper choice of this parameter is important: It should be small enough to avoid aliasing in case of high flow velocities; however, the adjustment of too small values of TPR decreases the respective velocity resolution of the measurements. The acquisition time of a single echo TE is determined by the measuring depth and the sound velocity of the liquid to be measured. This acquisition time can be distinctly shorter as TPR if moderate flow velocities are considered in sufficiently small vessels. Conventional multiline Doppler systems leave the time gap between the reception of the echo signal and the transmission of the next ultrasound pulse unused. Our system uses this idle time for the excitation of other transducer pairs and the acquisition of the respective ultrasonic echoes. For the application presented here this kind of interlaced echo acquisition enables a complete sampling of all remaining measuring lines within this time gap. This feature implies a distinct increase of the temporal resolution as compared to conventional multiline Doppler systems which obtain only one profile while the complete two-dimensional flow field is measured by our system. Moreover, the interlaced data acquisition guarantees a quasi-simultaneous measurement of all velocity profiles. In this specific case the resulting temporal resolution of the flow mapping is only defined by the velocity range and the size of the fluid vessel. Obviously, an increasing number of channels decrease the overall frame rate. The applied beam excitation pattern for both sensor arrays are shown in Fig. 4. The parallel excitation of always four transducer pairs requires 6 time steps to record the complete velocity field for each component. The excitation pattern does not consider a linear progression of the ultrasonic beam along the sensor array. This procedure avoids a multiple excitation of the same sensor element in successive time steps which reduces the risk of temporary crosstalk. Both arrays cannot be operated simultaneously because the tracer particles inside the fluid scatter the ultrasound pulse in all directions causing undesired crosstalk in the profile lines perpendicular to the propagation direction of the ultrasound beam. However, the mutual operation mode is not a disadvantage for the actual technical implementation since during the excitation of one array the electronic unit of the other array can be reprogrammed according to next step of the pattern which may take several micro seconds. The resulting temporal resolution, respective the frame rate, will be exemplarily calculated hereafter for the sensor setup

presented in Fig. 1. The acquisition time of a single echo TE consists of the duration of ultrasonic pulse TP = NC/f0 and the transit time of the ultrasonic wave in the liquid to be measured. Taking into account a measurement depth of d = 75 mm and a sound velocity in GaInSn of cGaInSn = 2740 m/s we obtain:

TE ¼

2d NC 2  0:075 m 8 þ ¼ 55:7 ls þ ¼ cGaInSn f0 2740 m=s 8 MHz

ð1Þ

which is the shortest possible time before jumping to the next step of the excitation pattern. The maximum selectable pulse repetition frequency (fPR = 1/TPR) is determined by the reciprocal of the product of TE and the number of time steps being necessary to scan the measuring cross section completely [15,18]:

fPR ¼

1 1 ¼ ¼ 1:5 kHz n  T E 12  55:7 ls

ð2Þ

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ð3Þ

can be achieved which corresponds to an overall acquisition time of 33 ms for measuring a complete instantaneous vector map of the two-dimensional flow field. 2.3. Measuring electronics The schematic diagram of the measuring system is shown in Figs. 5 and 6. The core unit of the system is the multiplex circuit (an in-house development) which manages the implementation of the excitation pattern and the pulse triggering. It comprises two switching matrices, one for each array, and a control unit, which generates the trigger signals, configures the switching matrices and communicates with the signal processing computer (Fig. 5). In equally-spaced time intervals corresponding to the fPR, the trigger control initiates the arbitrary function generators (AFG) from models Tektronix AFG3011B/AFG3102 to generate burst signals for the ultrasonic pulses. These signals are amplified by the high voltage RF amplifiers and transmitted to the corresponding switching matrices. Each switching matrix consists of two units of electronic multiplexers, the transmitting multiplexer and the receiving multiplexer (Fig. 6). The transmitting multiplexer, a set

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Fig. 4. Excitation pattern of segmental arrays. The transducer elements being active at the same time are marked in blue. The blue lines illustrate the active measuring profile lines, the grey ones the already measured profile lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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of fast electronic high-voltage switches, distributes the high-voltage burst signal to the active transducer elements according to the respective step of the excitation pattern. Transmitting/receiving (T/R) switches separate the received pulse echoes from the exciting burst signals. The received echo signals are amplified, directed to the 4-channel matrix output by the receiving multiplexer and filtered by a bandpass. The switching matrices are managed by the multiplex control and synchronized with the burst triggers [18,19]. The multiplexed echo signals of both switching matrices are digitized by two 4-channel data acquisition (DAQ) cards (model

Octopus CompuScope CS 8347 from the Company GaGe) installed in a personal computer. The sampling rates are set to 25 MHz being the lowest available sampling rate of the DAQ cards above the Nyquist frequency. Every time a burst signal is triggered, the segment of the echo signal, which corresponds to the measurement depth, is recorded. After the acquisition of the echo signals, the velocity vectors of the flow maps are calculated by an offline digital signal processing. A software interface configures the multiplex and trigger control of the multiplex circuit. The built-up multiplex system offers a high flexibility since it allows the programming of customized excitation patterns for various pulsing strategies at

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different sensor setups and is not exclusively limited to the setup described in this article. Due to the limited data storage of the DAQ cards the measurement duration is restricted to separate acquisition periods lasting from some seconds to a few minutes (depending on the applied pulse repetition frequency). The interruption of the measurements is caused by the necessity to read out the memory of the DAQ card before the next data acquisition cycle can be started.

estimator [23] and can also be applied at signals with a poor signal-to-noise ratio [24]. For flow visualization the velocity components, which are determined separately, are composed to the vector field. The arrangement of the two transducer arrays each comprising 25 elements allows for the reconstruction of the two-dimensional velocity field of 24  24 vectors. The offline signal processing and the visualization are realized in MATLAB.

2.4. Signal processing

3. Experimental setup

In pulsed-wave Doppler systems the echo signals contain all information to reconstruct the profile of the velocity component in the direction of the ultrasound beam. The depth information is deduced from the time offset between the transmission and the reception of an ultrasound pulse assuming a constant and known sound velocity throughout the measuring volume. To obtain the velocity profile the echo signal is divided into uniform sections, the designated gates, each representing one particular measuring position along the ultrasonic beam. Usually, the gate spacing is chosen to be in the same order of magnitude as the axial spatial resolution. The velocity related to each gate can be derived from the Doppler frequency. However, an accurate determination of the Doppler frequency becomes difficult since the period of the Doppler frequency is significantly longer than the ultrasound pulse duration. This problem is usually solved by evaluating the phase shift of the pulse echoes on the basis of several subsequent echo signals. The phase shift corresponds to the displacement of the scattering particles with respect to the sensor position between two successive echo acquisitions. The sequence of phase shifts derived from consecutive echo signals reveals the time-discrete velocity signal [3,20,21]. The digital signal processing is shown schematically in Fig. 7. At first the sampled echo signal is filtered by a Butterworth-bandpass of 8th order to cut spectral components without any flow information. The velocity estimation requires a complex signal since the quadrature component is required for the directional discrimination [20]. For this purpose the sampled echo signal is split into the in-phase signal (I-component) and the quadrature signal (Qcomponent) shifted by 90°. The 90° phase shift is generated by a Hilbert transform. Afterwards the phase information of the separate measuring positions are acquired and accumulated in a memory matrix until all velocity signals are fully recorded. The velocity estimator is adopted from the autocorrelation algorithm suggested by Kasai et al. [22]. This phase-based mean frequency estimator is considered to be the most robust frequency

Our model experiments have been carried out using the ternary eutectic alloy Ga68In20Sn12, which has a melting point of about 10 °C and shows the following material properties at room temperature: electrical conductivity r = 3.2  106 S/m, density q = 6.36  103 kg/m3 and kinematic viscosity v = 3.4  107 m2/s. Under our experimental conditions the alloy GaInSn contains a multitude of natural scattering particles, which obviates the need for adding artificial particles. It is assumed that these natural particles are metal oxides or microscopic segregations of the eutectic alloy. The liquid metal was situated inside a cube made of Plexiglas with an interior edge length of l = 75 mm. A schematic view of the experimental setup is depicted in Fig. 8. The experiments were performed in the magnetic induction system PERM at HelmholtzZentrum Dresden-Rossendorf (HZDR). Six coils are arranged in a pole-pair connection to create the rotating magnetic field (RMF) with an effective magnetic induction up to 25 mT. The bore diameter of the magnetic system is 200 mm, wherein the fluid vessel was placed concentrically. In order to preclude flow artifacts arising from symmetry deviations of the experimental setup, special care was necessary to ensure a precise positioning of the cylinder inside the magnetic system. The homogeneity of the magnetic field was checked using a 3-axis Gauss meter (Lakeshore model 560, sensor type MMZ2560-UH). Within a radius of 75 mm the variance of the magnetic field strength was found to be less than 5%. The magnetic field is characterized by the field strength B0 and the angular frequency xRMF = 2p fRMF. A frequency fRMF = 50 Hz was selected being small enough to avoid the skin effect, in other words the low field frequency ensures the complete penetration of the time-varying magnetic field through the fluid volume. The magnetic field 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 [25] (compare to Fig. 8). The angular velocity of the fluid is always smaller than the rotating field, since the induction of the electrical currents relies on a relative motion between field

Gate sampling

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S/H Sampled echo signals

Memory matrix

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S/H Q Channel

Hilbert transform Gate sampling Fig. 7. Digital signal processing for Doppler-shift velocity estimator.

Velocity profiles

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697

Fig. 8. Experimental setup: plexiglas cube filled with GaInSn and located in a RMF stirrer.

demonstrate the capabilities of our measuring system. The vector field of the horizontal velocity components were measured for an RMF with a field strength B0 = 4.8 mT. This field strength corresponds to a magnetic Taylor number of:

Ta ¼

Fig. 9. Arrangement of the ultrasound sensor arrays for a two-dimensional flow mapping of two velocity components in the mid-plane of the cube. The velocity vectors can be determined at the crossing points of the measuring lines.

and fluid. Similar to the principle of the asynchronous motor a slip occurs. The angular velocity of the swirling flow depends on both the magnitude and the angular frequency of the rotating magnetic field. RMF-driven flows are already well investigated for axisymmetric configurations like a circular cylindrical vessel. The steady RMFdriven flow in a cylindrical container consists of an almost rigidly rotating core. In case of the square cross section as considered here non-axisymmetric flows have to be expected. For a more detailed review about RMF-driven flows the reader is referred to Davidson and Hunt [25] or Priede and Gelfgat [26]. The ultrasound arrays are mounted horizontally at half height of the container to measure the swirling flow in the horizontal mid-section (front view in Fig. 8). The sensor surfaces are brought in direct contact to the fluid since measurements through container walls may cause non-measurable regions up to 25 mm behind the walls due to multiple reflections in the wall material disturbing the echo signals rising from the flow. The arrangement of the sensor arrays at the mid-section of the fluid container is shown in Fig. 9. The resultant two-component measuring field arises from the overlap of the particular acquisition fields of each array and has an extent of 67 mm  67 mm. Due to the dimensions of the sensor housing and constructive limitations of the container design the flow field cannot be acquired in the vicinity of the vessel walls, especially not at the vicinity of the arrays. 4. Results of the flow measurements 4.1. Measurements of an RMF-driven flow The configuration of an RMF-driven flow inside a cube has been chosen as an example for a real liquid metal flow in order to

rxB20 l4 ¼ 3:12  107 32qm2

ð4Þ

where r, q and v denote the electrical conductivity, the density and the kinematic viscosity of the fluid. The related parameter l denotes the interior edge length of the cube (Fig. 8). The calculated Ta number from Eq. (4) is two orders of magnitude higher than the critical Taylor number of Tacr = 1  105 for a container of aspect ratio one [27], which indicates a fully developed turbulent flow in the experiment. The measurements were carried out selecting a pulse repetition frequency of fPR = 1.5 kHz and a emissions per profile value of NEP = 50. An overall frame rate of fFrame = 30 fps was achieved coinciding with the value calculated in Section 2.2. Since the following measurements are intended to demonstrate the reliability of the measuring system for a two-dimensional mapping of the two-component velocity vectors the measuring data are not post processed, that means no algorithms for error correction, interpolation (except the color coding of the contour plots) or noise reduction are applied. Fig. 10 shows a snapshots of the swirling flow. Fig. 10a and b contains the contour plots of the particular velocity components, whereas Fig. 10c presents the resulting instantaneous vector field. As expected the flow is dominated by a single vortex which occupies almost the complete cross sectional area. Deviations from an ideal axisymmetric pattern become obvious especially in the near-wall regions. Fig. 10c shows that the center of the vortex does not coincide exactly with the cube axis. Our observations revealed that the center of the main vortex fluctuates with an amplitude of about 5 mm around the cube axis. This finding is not really surprising because a pronounced turbulent melt flow is supposed to occur at the Taylor number applied in this experiment. Furthermore, the formation of counter-rotating vortices is expected in the corners of the cross section. The vector plots show some indication for the existence of such vortices, however, the current measuring setup does not allow for a sufficient resolution of the corner regions. The contour plots of the particular velocity components in Fig. 10a and b reveal also some artifacts (marked with an ‘‘a’’) occurring at various positions within the flow fields. The misorientation of several vector arrows in Fig. 10c can be related to these inaccurate measurements. The artifacts may arise from a temporary and local deficit of scattering particles. Another reason for the artifacts may be an insufficient transducer-fluid coupling leading to a low signal-to-noise ratio. These artifacts might be reduced

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Fig. 10. Instantaneous vector field of the fluid velocity in the mid-plane of the cubic vessel. The flow is driven by an RMF (temporal resolution DT = 33 ms).

by increasing the emissions per profile NEP; however, such a step deteriorates the temporal resolution. These effects are common for ultrasound Doppler techniques and cannot be considered as specific issues of our measurement system (refer to [28]). Furthermore, the occurrence of stationary echoes (marked with ‘‘b’’ in Fig. 10b) has to be taken into account. The echoes arise from multiple pulse reflections between the vessel walls. Stationary echoes become particularly significant at high pulse repetition frequencies, since the wall reflections do not decay noticeably until the next ultrasonic burst is transmitted. The application of specific filters in the signal processing (clutter or wall filter) may eliminate the stationary echoes [24,20]. These problems will be taken into account in more detail at upcoming measurements which will focus on quantitative investigations of the flow structure. 4.2. Flow mapping of transient flows A continuous stirring of metal melts by rotating magnetic fields is often inadequate for metallurgical applications because small magnetic field strengths provide only an insufficient mixing, whereas higher field intensities cause deflections of free liquid metal surfaces. Strong turbulent flows may lead to material defects due to the risk to entrain solid impurities or gas into the bulk liquid. The use of RMF pulse sequences of alternating direction turned out to be an efficient technique to overcome this problem [5]. The capability to reveal transient flow structures occurring during an inversion of the rotational direction of the RMF makes our measuring system particularly suited for investigations of such kind of flows. We present exemplary measurements performed at a magnetic field strength of B0 = 3.1 mT. The temporal progress of the applied RMF is shown in Fig. 11. An external wave form generator synchronizes the start of the measurement with the reversal of the RMF. The data acquisition was initiated just 200 ms before the electromagnetic driving force was inverted. The measuring data presented below were recorded at a pulse repetition frequency of fPR = 500 Hz using NEP = 100 emissions per

Fig. 11. Sketch showing the measured time interval during a reversal of the RMF direction.

profile corresponding to a temporal resolution of 200 ms. Velocity data of the two-dimensional flow field were acquired within an overall measuring time of 22 s. A sequence of selected snapshots of the flow pattern is displayed in Fig. 12. Fig. 12a shows the initial state of a steady flow before the rotational direction of the RMF was reversed. The first significant perturbations of the swirling flow pattern occur in the outer regions of the cross section where the electromagnetic force achieves its maximum (see Fig. 12b). As shown in Fig. 12c a residual core rotating in the primary direction can be observed until about 4 s after the reversal, whereas an erratic flow structure without any prevailing direction is found near the wall. Fig. 12d presents a time period without dominating swirl. In this situation the cross section is occupied by a transient ensemble of several vortices. The reappearance of the swirl begins about 9 s after the reversal. The first regions where the opposite vortex can be detected are located near by the walls (see Fig. 12e). Fig. 12f and h document the ongoing strengthening of the central vortex. In Fig. 12h the new final state is almost achieved. 5. Summary and outlook This article presents an imaging technique for flow measurements based on the ultrasound Doppler velocimetry. It allows for the investigation of time-varying liquid metal flows. The measuring

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system employs two linear ultrasound arrays in an orthogonal arrangement to capture the two-dimensional velocity field in the plane spanned by the two arrays. The measuring field covers a cross section of 67  67 mm2 which is divided into a grid of 24  24 vectors. Taking account of these 576 grid points an overall frame rate of 30 fps, respective a temporal resolution of 33 ms, was achieved. To accomplish simultaneously the requirement for a high spatial resolution and a high temporal resolution advanced processing methods were applied: A multi-beam operation in conjunction with an interlacing pulsing strategy utilizing the idle time between succeeding ultrasonic bursts facilitate high measurement rates whereas the application of the segmental array technique with a high number of measuring lines provides an adequate spatial resolution. As a result, our system records the complete twodimensional vector field of two velocity components in the same time as required by conventional UDV processing techniques for determining a single velocity profile. This feature makes the system suitable for multi-dimensional measurements of turbulent electromagnetically-driven liquid metal flows, especially for the investigation of mixing processes induced by electromagnetic stirring. In the present paper the capabilities of the measuring system have been demonstrated in two experiments. At first the swirling fluid motion excited by a rotating magnetic field inside a cube was measured in the horizontal mid-plane. In a second experiment the liquid metal in the cube was exposed to a rotating field reversing its rotational direction. The measurements showed the collapse of the original vortex structure and the development of the swirling flow in the opposite direction. It becomes obvious that the new US-array technique equipped with adequate data processing techniques enables the experimenter to obtain a flow mapping in nontransparent liquids with a high temporal and spatial resolution. The next activities of our research program consider a further test phase of our measuring system using various liquid metal experiments with different challenges regarding the type of the flow pattern or the velocity range to be measured (see [5,14,29]). Continuing development work concerns further improvements and extensions of the features of the measuring system, for instance, the application of the synthetic aperture focusing techniques will be considered. The current problem of the limited measurement duration is caused by the data acquisition via a subsequent offline signal processing. In future it will be solved by implementing an online signal processing using FPGA techniques. Another goal of our work is the extension to a three-dimensional UDV system, which can provide visualizations of the three-dimensional velocity field in turbulent liquid metal flows. Acknowledgments The research is supported by the Deutsche Forschungsgemeinschaft (DFG) in form of the SFB 609 ‘‘Electromagnetic Flow Control in Metallurgy, Crystal Growth and Electrochemistry’’. This financial support is gratefully acknowledged by the authors. Additionally we thank Dr. K.-P. Richter from company Richter STT for manufacturing the ultrasound arrays. References [1] J. Czarske, Laser Doppler velocimetry using powerful solid-state light sources, Meas. Sci. Technol. 17 (2006) R71–R91.

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