Influence of the flow profile to Lorentz force velocimetry for weakly conducting fluids an

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1 Home Search Collections Journals About Contact us My IOPscience Influence of the flow profile to Lorentz force velocimetry for weakly conducting fluids an experimental validation This content has been downloaded from IOPscience. Please scroll down to see the full text Meas. Sci. Technol ( View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: This content was downloaded on 11/11/2016 at 09:21 Please note that terms and conditions apply. You may also be interested in: Performance enhancement of a Lorentz force velocimeter using a buoyancy-compensated magnet system R Ebert, J Leineweber and C Resagk Towards metering tap water by Lorentz force velocimetry Suren Vasilyan, Reschad Ebert, Markus Weidner et al. Theory of the Lorentz force flowmeter André Thess, Evgeny Votyakov, Bernard Knaepen et al. Electromagnetic flow measurements in liquid metals using time-of-flight Lorentz force velocimetry Dandan Jian and Christian Karcher Numerical calibration of a Lorentz force flowmeter Xiaodong Wang, Yurii Kolesnikov and André Thess High-precision horizontally directed force measurements for high dead loads based on a differential electromagnetic force compensation system Suren Vasilyan, Michel Rivero, Jan Schleichert et al. Optimal magnet configurations for Lorentz force velocimetry in low conductivity fluids A Alferenok, A Pothérat and U Luedtke

2 (9pp) Measurement Science and Technology doi: / /27/12/ Influence of the flow profile to Lorentz force velocimetry for weakly conducting fluids an experimental validation A Wiederhold 1, R Ebert 1, M Weidner 2, B Halbedel 2, T Fröhlich 3 and C Resagk 1 1 Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Ilmenau, Germany 2 Department of Inorganic-Nonmetallic Materials, Technische Universität Ilmenau, Ilmenau, Germany 3 Institute of Process Measurement and Sensor Technology, Technische Universität Ilmenau, Ilmenau, Germany andreas.wiederhold@tu-ilmenau.de Received 11 July 2016, revised 6 October 2016 Accepted for publication 20 October 2016 Published 4 November 2016 Abstract The Lorentz force velocimetry (LFV) is a highly feasible contactless method for measuring flow rate in a pipe or in a channel. This method has been established for liquid metal flows but also for weakly conducting electrolytes where the Lorentz force amplitudes are typically six orders smaller than the ones from liquid metal flows. Due to an increased resolution of the Lorentz force measurements which was the main focus of research in the last years, now it is possible to investigate the influence of the flow profile on the amplitude of the Lorentz force. Even if there is a semi-theoretical approach an experimental validation is still outstanding. Therefore we have tested symmetric and asymmetric flow profiles to test the LFV for weakly conducting fluids for typical industrial flows. Salt water has been used as a test electrolyte with constant values of the electrical conductivity from to 20 S m 1 and of the flow velocity in a range of m s 1. We confirmed by extensive measurements that LFV is a suitable method for flow measurements even for different flow profiles within 5% measurement uncertainty. For a wide range of applications in research and industry the LFV should be not sensitive to various flow profiles. Keywords: Lorentz-force velocimetry, electrolytes, weakly conducting, flow profiles, force measurement (Some figures may appear in colour only in the online journal) 1. Introduction In industrial applications many types of flow rate sensors like mechanical, pressure-based, optical, vortex, electromagnetic, ultrasonic and Coriolis flowmeters are used. For hot, abrasive or corrosive fluids those devices cannot be applied easily due to their specific requirements. A completely non-invasive measurement method is required, where mechanical contact to the fluid is avoided. Therefore the Lorentz force velocimetry (LFV) has been developed. This technique has been explored quite fast for liquid metal flows [1, 4]. In principle an external magnetic field induces eddy currents in the moving fluid. The interaction of these eddy currents with the primary magnetic field will cause a braking force to the fluid and (as a result of Newton s 3rd law) a drag force to the magnets in the flow direction (see figure 1). This force is called Lorentz force F and is if the flow profile remains unvaried proportional to the electrical conductivity of the fluid σ and the fluid velocity v respectively the flow rate dv/ /16/ $ IOP Publishing Ltd Printed in the UK

3 Figure 1. Principle of Lorentz force velocimetry: the fluid flow gets interspersed by a static magnetic field and hence, eddy currents are generated. According to the laws of electrodynamics, the resulting force on the source of the primary magnetic field is an accelerating force in the direction of flow. This force is called Lorentz force [5]. Figure 2. Schematic illustration of the salt water test channel with (a) LFV, (b) test section/duct, (c) nozzle, (d) mechanical decoupling, (e) pump, (f) relax vessel and (g) magneto-inductive flowmeter (flow velocity reference). dt as equation (1) shows. Furthermore, the Lorentz force is proportional to the square of the magnetic flux density B that penetrates the flow and proportional to the size of the measurement volume given by the distribution of the magnetic field in the fluid which depends on the size and mass of the magnets. F ~ σvb ~ dv σ A dt B 2 2 The electromagnetic effect that is used allows various designs of sensors: The primary magnet field can be provided by a permanent magnet [2] or by current in coils [3]. In liquid metal flows it is possible to measure the flow profile [4] (spatially resolved LFV). However, there is an industrial demand for a flow rate measurement technique for weakly conducting fluids in pharma and food industries as well as in medical applications where contactless measurements are an objective coming from hygienic requirements. A further possible application can be the measurement of salt melts which are important for liquid metal batteries or heat storage devices and for weakly conducting glass melts. Thereby the volume flow is the property of interest and the flowmeter should not be sensitive to other influences like the flow profile. In the semi-theoretical approach of [1] a slight dependence of the Lorentz force signal on the mean velocity distribution in a pipe flow is predicted (1) but an experimental verification for weakly conducting fluids is still outstanding. Thess et al have investigated the sensitivity of the Lorentz force flowmeter for two cases: the longitudinal flux flowmeter and the transverse flux flowmeter. In the first case eddy currents are induced by an electrical current flowing through a coil. This case couldn t be tested experimental in this paper. In the second case the magnetic field is provided by one permanent magnet. In regard to the dependence of the Lorentz force on the velocity distribution the sensitivity S(α) can be defined as S( α) = 2 21 ( + α) ln( 1+ α) α( 2+ 3α) 8α[( 1+ α) ln( 1 + α) α] where α = κ(λ/2) 1/2 Re. Here the Reynolds number Re is calculated by Re = 2R u/ν with the radius of the pipe R, the flow velocity u and the kinematic viscosity ν. κ = 0.41 is the von-karman constant and λ is the friction factor [6]. For α 0 the profile is parabolic and for α it is piston-shaped. Furthermore in this second approach following assumptions are made: The quantity of the transverse component of the magnetic field varies only slightly (B = B y ). This is not in contrast to the large distance between the opposite permanent magnets. The second assumption is that the walls of the pipe are electrically insulated (σ = 0) which is provided in the experimental setup. 2

4 Figure 3. Left: schematic design of Halbach array at rectangular test section white arrows show the direction of single magnetization. Middle: image of used Halbach array magnet system with connecting carbon fiber bracket. Right: measured distribution of the magnetic flux density B y (x, z) in distance of 2 mm from the surface of a Halbach array. The point of origin (0, 0, 0) is exactly located in the middle of both Halbach arrays [5]. Figure 4. Schematic diagram and measurement principle of the EMFC balance (grey undeflected). Left: conventional usage of EMFC balance aligned horizontally, measuring the deflection a(β) in vertical direction. Right: usage in modified vertical alignment, measuring the deflection in horizontal direction. F C total force measured as EMFC compensation force, F G gravity force, F L horizontally acting force [12 14]. In addition, the sensitivity of the transverse flux flowmeter as investigated in [1] doesn t depend just on the shape of the velocity profile, but also on the wavenumber κ = kr of the magnetic field, where R is the radius of the pipe. If the wavenumber grows the eddy currents become more and more 3D and their contribution to the Lorentz force increases. Only small wavenumbers cause a high decrease of the sensitivity so that we neglect this dependency here. In [1] it is demonstrated that there is only a weak dependence of the sensitivity for vastly different flow profiles. Both Poiseuille-shaped and piston-shaped profiles are investigated. For a longitudinal flux flowmeter it follows from an exemplary calculation that the sensitivity differs only by 2% when the Reynolds number Re changes by one order of magnitude. For developed symmetric flow profiles in long straight tubes or ducts as well as for very asymmetric flow profiles (e.g. behind curvatures) the LFV is evaluated in this manuscript. 2. Experimental setup The investigations are made at a closed loop channel (see figure 2) where salt water is used as a working fluid. Its electrical conductivity can be set by varying the concentration of sodium chloride in the water. Thus, the electrical conductivity of the fluid can be adjusted upon necessity as it was performed and demonstrated in several other publications [7 9]. A centrifugal pump is driving the flow and enables average fluid 3

5 Figure 6. Setup with laser-doppler-velocimeter (LDV) with (a) entry nozzle of the channel, (b) transparent test section, (c) optical head of the LDV and (d) vertical and horizontal traversing system. Figure 5. Image of the differential force measurement system with two EMFC balances, (5) Halbach array magnet and (4) dummy weight. (1) Hanging common plate, (2) two separate suspension parts (in form of elbow) for fine tuning both EMFC in horizontal plane, (3) EMFC balances, (4) dummy weight, (5) Halbach array magnet, (6) channel [13, 15]. velocities up to 3 m s 1 in the test section. The nozzle and a set of mesh and honeycomb filters provide a uniform velocity profile at the nozzle s outlet. The pump and the force measurement setup are placed at a separate fundaments in order to minimize influences of the mechanical vibration. Further, a fluid temperature control system keeps the temperature of the fluid constant with a peak to peak deviation of ±25 mk. The system consist of a cooling coil which is located in the relax vessel (figure 2(f)) connected to an external chiller. The flow rate of the refrigerant fluid (water) is controlled by a PID-controlled valve. In all measurements the fluid has a temperature of 21 C while the ambient temperature is usually about 26 C which results in a further heat input by the surroundings. Hence, the electrical conductivity that varies about 2% K 1 at room temperature can be kept sufficiently constant. As a velocity reference a commercial magneto-inductive flowmeter (MID, Co. Krohne: Optiflux 2000) is used which enables the calculation of a calibration factor between Lorentz force and fluid velocity or between Lorentz force and flow rate. The measurement principle of the here applied MID is based on the separation of charges in a magnetic field and the measurement of an electrical potential which is proportional to the flow rate. Due to the quadratic dependence of the Lorentz force with the magnetic flux density B shown in equation (1) the magnetic field source has a big influence on the resolution of the LFV. Therefore a Halbach magnet system was designed and optimized regarding the dimensions of the test section and the mass limitation of 1 kg of the sensitive force measurement system [5, 10]. At this point it should be highlighted that it is possible to overcome the mass restriction by using a buoyancy-compensated magnet system which was demonstrated successfully in [11]. The build-up system used for the measurements explained in this paper consists of two opposite Halbach arrays. These are fixed by a carbon fiber lightweight yoke. Their distance amounts 56 mm so that the magnets are as close as possible to the fluid. Each array is built up by five rectangular permanent magnets with the same dimensions (15 mm 18 mm 46 mm). Like shown in figure 3(a) their magnetization direction is turned from one magnet to the other by 90 so that the second and fourth element deflects the flux of the backside of each array and the stray magnetic field is decreased. That results in three alternating flux spots in the test section which generate 2.8 times higher Lorentz forces than an optimized pair system at 1 kg [10]. In the symmetry point of the magnet system the component of the magnetic flux density B y perpendicular to the fluid flow is 160 mt. The two outer spots have a B y of 110 mt. Early measurements presented in the [8, 9] have been made with single state-of-the-art electromagnetic force compensation (EMFC) balance. In order to reduce the vibration noise in force measurements a reference system has been used. An identical EMFC balance with an equivalent mass of the dead load was used for direct referencing the Lorentz force measurements by so called differential force measurement method [7, 12, 13]. By adding the second EMFC balance with the same dynamic behaviour on-axis of the first EMFC balance allows to eliminate common measurement errors in the force signal. Thus, the complete force measurement system used for LFV application consists of two identical but independently working EMFC balances, two equal masses which are suspended from each EMFC balance (LFV magnet and dummy weight), and correspondingly identical mechanical suspension components which are fastening both EMFC balances to the common bearing plate. The mechanical diagram of the single EMFC balance is presented in figure 4. The EMFC balance is arranged in rotated 90 orientation relative to its common usage in a horizontal alignment. In figure 4 left is presented the mechanical working principle of the EMFC balance in common usage and in right adapted for LFV application. The load carrier is pointing downwards as 4

6 Figure 7. Test section with the flow obstacle positioned 150 mm behind the inlet. Figure 8. Labels of the positions where the LFV and LDV have been applied. The numbers 1 5 are devoted to measurements without an obstacle and the letters A D mark the measurement positions around the obstacle. depicted in the illustrations (see figure 4, right). The resulting special orientation of the EMFC balance assumes a naturally achievable zero stable condition, which provides an advantage of using high dead loads suspended from EMFC balances [12 15]. Both EMFC balances are aligned together to the x-axis by their natural zero stable positions. Considering that the force measurements of the reference EMFC balance with dummy weight is F 1M = F err and the force measurements with an actively used EMFC balance with LFV magnet is F 2M = F err + F L, then the difference F diff = F 2M F 1M = F L in the ideal case is equal to the Lorentz force. Under this consideration the common error is assumed to be measured by both EMFC balances. Therefore, any discrepancy between the applied F L and measured F diff forces may represent parasitic forces from other sources. Complete image of the system is presented in figure 5. For more detailed information regarding the influence of temperature effects on the measurement system and the determination of the measurement resolution see [7, 12, 13]. The test section has a length of 1.5 m. At normal operating modes the flow is in the turbulent regime (Re = (2 20) 10 4 ) and hence the profile becomes a developed turbulent shape along the test section [16]. Since the Lorentz force measurement system can be freely positioned the force signal can be measured for different flow profiles that occur in the duct at constant mean velocity. It is essential to know the underlying flow profile for the investigation of its correlation with the Lorentz force. Therefore the walls of the duct are made of transparent polycarbonate which allows the usage of a two component laser-doppler-velocimeter (LDV, Co. Dantec Dynamics). This device provides high precision velocity measurement at a local area of a few millimeters where its laser-beam gets focused. To determine the flow profile for the whole crosssection this device is mounted on a traversing system as it is shown in figure 6. By traversing the LDV rectangular to the main flow direction the full cross-section can be scanned pointwise 1.25 mm steps. During all measurements with the LDV the flow rate of the salt water in the channel has been kept constant (0.2% of mv + 1 mm s 1 ) by controlling the pump with the MID. In order to be able to investigate asymmetric flow profiles in the presented channel an obstacle (backward facing step) has been introduced. Considering the geometrical scales of the test section a cuboid (92 mm 25 mm 50 mm) obstacle, also made from polycarbonate, was placed in the test section to influence the flow profile (see figure 7). To gain asymmetric profiles it is placed at the underside wall and glued by silicone to ensure its removability. The measurements have been performed for different positions along the test section. For measurements at symmetric flow profiles they are equidistant and named by the numbers 1 5 in the flow direction. The positions for asymmetric measurements are not equidistant and named by the letters A D. The two nomenclatures are necessary because the measurement positions of the asymmetric profiles are concentrating on the area in the vicinity of the obstacle. Position A 5

7 Table 1. Distances of the measurement positions for the symmetric (1 5) and asymmetric (A D) flow profiles and the position of the obstacle. Position name 1 and A B C 2 and D Obstacle Distance x from inlet (mm) Figure 9. 2D-time-averaged velocity field v(y, z) of the flow of 1 m s 1 along the test section: Position 1 and 5 without obstacle (symmetric profile) and position C and D with obstacle (asymmetric profile). In the graphs the mean flow of v mean = 1 m s 1 from the left to the right parallel to the test section is shown. and 1 as well as position 2 and D are the same (see figure 8 and table 1 for detailed data). 3. Measurement results and discussion At the inlet of the test section (right after the nozzle) the closed loop channel provides a uniform piston-shaped flow profile. The change of the profile has been proved by LDV measurements (see figure 9). The profile of the asymmetric flows have been also extensively measured and determined. Directly behind the obstacle the highest asymmetry can be found. In contrast the profile in the region close to the outlet of the test section has turned back into a symmetric flow because of viscous effects. The corresponding force has been measured for various flow velocities v = m s 1 and electrical conductivities σ = S m 1 of the fluid. A direct comparison of the data for the different symmetrical profiles is shown in figure 10. There is only a small deviation of the slope of about 5% which is in the range of the uncertainty of the force measurements. For better visibility the fits are not shown in the figure 10. If the change of the signal gets plotted for the different positions, a slight decrease in the force amplitude (again in the range of 5%) can be seen for most of the velocity values 6

8 Figure 10. Symmetric flow profile without obstacle: Lorentz force for various flow velocities v and electrical conductivities along the flow channel (positions 1 5). Figure 11. Symmetric flow profile without obstacle: Lorentz force for different profiles along the test section. In this case the electrical conductivity of the fluid has been kept constant at 20 S m 1. A slight decrease (slope m) in the force signal between inlet (position 1: x = 65 mm) and outlet (position 5: x = 1418 mm) has been measured. (see figure 11). This decrease is mainly visible in the velocity range of m s 1 because here the measurement uncertainties do not overlie the expected slight decrease of the force signal postulated in [1]. At this point it should be mentioned that the electrical conductivity over all positions 1 5 differs about ±0.2 S m 1. This deviation is composed of the temperature dependency of the conductivity which results in ±0.02 S m 1 but mainly due to the procedure of the measurement campaign. The force measurement system was moved along the test section and as a result the electrical conductivity of e.g. 20 S m 1 has to be adjusted for every position. Because of the dimensions of the experiment it is hardly possible to adjust the electrical conductivity below an uncertainty of ±0.2 S m 1. So these deviations are a systematic error which can explain the nearly constant behaviour of the velocities 0.5 and 1.0 m s 1. Further measurements at highly asymmetric flow profiles have been performed. In figure 12 the signal gets compared to the symmetrical flow profiles. Position C (asymmetric profiles) directly behind the obstacle is compared with position 1 and 2 (symmetrical flow profiles) because it is located between them (figure 12(a)). The graphs among themselves show only a slight deviation which is mainly caused by an offset in the measurement of position 2 which could be a systematic error. This explains why the level of coincidence between 7

9 Figure 12. Comparison of Lorentz forces at strongly asymmetric and symmetrical flow profile: only a slight change in the measurement signal can be measured at different positions (a) and the same position (b) although the difference in the flow s velocity profile is enormous. an asymmetric and a symmetric profile is here higher (figure 12(b)) than between two symmetric profiles (figure 12(a)). However, the high coefficient of determination (R 2 > 0.99) which can be seen as a measure for the quality for the plotted regressions of the single graphs indicates a high linearity of the force signals. Position D and position 2 can be compared directly because they coincide with each other (figure 12(b)). The two graphs hardly diverge from each other although the flow profiles are highly different. When comparing the measurements of asymmetric flow profiles an uncertainty of about 5% is detected as well, because identical external influences are present which are listed in the conclusions. We can reason that the influence of asymmetric flow profiles is virtually negligible to LFV with regard to the force signal. This conclusion increases the versatility of LFV for industrial applications where uniform flow profiles can t be guaranteed at all configurations. 4. Summary and conclusions We tested LFV for weakly conducting fluids with electrical conductivities is in the range of tap water up to 20 S m 1 at different flow profiles. Because the product of electrical conductivity and flow velocity is six orders of magnitude smaller than in liquid metal flows, the measured forces are in the range of micronewton (µn). Symmetric flow profiles from uniform piston-shaped to pseudo-parabolic turbulent flows, because of the transition of laminar to turbulent flow they are slightly blunted, have been compared to very asymmetric flows behind an obstacle (backward facing step). Neither the comparison of the symmetric velocity profiles to each other nor the juxtaposition of symmetric and asymmetric profiles have shown a significant force influence. However, a slight decrease in the force signal can be detected when the profile becomes more parabolic. These results are in accord with the semi-analytical approach in [1]. In the measurements a deviation of about 5% is found between the force datasets with comparable configuration. This means that at same positions along the test section, symmetric profiles as well as asymmetric profiles show this uncertainty. The following sources of uncertainty are identified: instabilities in the force measurement which are mainly caused by thermal expansion of the supporting structure of the balances [12] as well as deviations in the configuration of the setup such as geometrical misalignments, small variations in the electrical conductivity, the magnetic field distribution, the temperature or the velocity v of the fluid. As a result the current experimental setup is more inaccurate than other flow measurement techniques. For instance the measurement errors for mechanical, ultrasonic or magnetic flow meters lie in the range of 0.2 1%. However, these techniques cannot fulfil the aforementioned requirements when measuring in aggressive fluids [9]. For LFV the influence of even a large variation in the flow structure to the force signal is negligible as long as the average flow velocity v mean does not change. This property of the LFV for weakly conducting fluids allows the application of this measurement technology to various industrial flows even at difficult geometries, such as behind pipe curvature. Whereas many techniques like magneto-inductive flowmeters need a minimum entrance length of up to five times the pipe diameter, this is not necessary for LFV. Acknowledgments The authors are grateful to the German Science Foundation (Deutsche Forschungsgemeinschaft) for financial support of the presented work in the framework of the Lorentz force velocimetry and Lorentz force eddy current testing Research Training Group (GRK 1567) at Technische Universität Ilmenau. We thank Suren Vasilyan for developing the force measurement setup and useful discussions. References [1] Thess A, Votyakov E, Knaepen B and Zikanov O 2007 Theory of the Lorentz force flowmeter New J. Phys [2] Wegfrass A, Diethold C, Werner M, Fröhlich T, Halbedel B, Hilbrunner F, Resagk C and Thess A 2012 A universal noncontact flowmeter for liquids Appl. Phys. Lett

10 [3] Viré A, Knaepen B and Thess A 2010 Lorentz force velocimetry based on time-of-flight measurements Phys. Fluids [4] Heinicke C 2013 Spatially resolved measurements in a liquid metal flow with Lorentz force velocimetry Exp. Fluids [5] Werner M 2013 Design, Optimierung, Realisierung und Test von passiven Magnetsystemen für die Lorentzkraftanemometrie an Elektrolyten PhD Thesis Technische Universität Ilmenau, Germany [6] Zagarola M V and Smits A J 1998 Mean-flow scaling of turbulent pipe flow J. Fluid Mech [7] Vasilyan S, Ebert R, Weidner M, Rivero M, Halbedel B, Resagk C and Fröhlich T 2015 Towards metering tap water by Lorentz force velocimetry Meas. Sci. Technol [8] Halbedel B, Resagk C, Wegfrass A, Diethold C, Werner M, Hilbrunner F and Thess A 2014 A novel contactless flow rate measurement device for weakly conducting fluids based on Lorentz force velocimetry Flow Turbul. Combust [9] Wegfrass A 2013 Experimentelle Untersuchungen zur Anwendbarkeit der Lorentzkraft-Anemometrie auf schwach leitfähige Fluide PhD Thesis Technische Universität Ilmenau, Germany [10] Werner M and Halbedel B 2012 Optimization of NdFeB magnet arrays for improvement of Lorentz force velocimetry IEEE Trans. Magn [11] Ebert R, Leineweber J and Resagk C 2015 Performance enhancement of a Lorentz force velocimeter using a buoyancy-compensated magnet system Meas. Sci. Technol [12] Vasilyan S, Rivero M, Schleichert J, Halbedel B and Fröhlich T 2016 High-precision horizontally directed force measurements for high dead loads based on differential electromagnetic force compensation system Meas. Sci. Technol [13] Vasilyan S 2016 High precision force measurements in horizontal direction in combination with high dead loads: non-contact flowmeter for low conducting electrolytes PhD Thesis Technische Universität Ilmenau, Germany [14] Diethold C and Hilbrunner F 2012 Force measurement of low forces in combination with high dead loads by the use of electromagnetic force compensation Meas. Sci. Technol [15] Sartorius Lab Instruments Model WZA16, (Accessed 2 August 2015) [16] Ebert R 2016 Kontaktlose Durchflussmessung in turbulenten Elektrolytströmungen mittels Lorentzkraft Anemometrie PhD Thesis Technische Universität Ilmenau, Germany 9