Flow Measurement and Instrumentation 11 (2000) 71–78 www.elsevier.com/locate/flowmeasinst
A new mechano-optical technique to measure local velocities in opaque fluids S. Eckert *, W. Witke, G. Gerbeth Forschungszentrum Rossendorf (FZR), Institute of Safety Research, P.O. Box 510119, 01314 Dresden, Germany Received 30 April 1999; received in revised form 5 January 2000; accepted 31 January 2000
Abstract A novel technique has been developed to measure the local velocities in opaque liquid flows such as liquid metals. The measuring principle is based on the separation of a direct mechanical interaction between flow and sensor tip and the optical acquisition and processing of the signal. In principle, this fact allows the extension of the range of applicability to higher temperatures. Furthermore, the insensitivity of the system to electrical noise and external magnetic fields can be considered as an important advantage. Until now, the sensor has been tested in metallic melts up to temperatures of about 350°C. We present measurements of the local velocity obtained in an eutectic InGaSn melt driven by a rotating magnetic field. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Flow measurement technique; Local sensor; Fluid velocity; Mechano-optical principle; Opaque fluids; Liquid metals; Rotating magnetic field
1. Introduction The techniques of local and instantaneous measurements in liquid metals are known to be much more difficult than in classical fluids like water and air. Whatever diagnostic method is used, two categories of problems have to be solved: those due to the nature of the fluid (opaque, hot, chemically aggressive) and, in addition, due to the presence of electromagnetic fields as in the case of magnetohydrodynamic (MHD) flows. Almost all conventional measuring techniques used for ordinary flows, for instance hot-wire anemometry or LDA, totally fail in liquid metal MHD flows, or their applicability is strongly limited. The use of local sensors inside the liquid metal requires the utilization of materials being robust against the attack of the fluid. A means to obtain the local liquid velocity in liquid metal flows is to deduce it from measurements of the dynamic and stagnation pressure by means of Pitot or Prandtl tubes. However, the presence of a magnetic field causes some serious shortcomings [1,2]. In general, the
* Corresponding author. Tel.: +49-351-260-2132; fax: +49-351260-2007. E-mail address:
[email protected] (S. Eckert).
local pressure becomes a function of the magnetic field strength requiring a special calibration of the sensor in the actual magnetic field configuration. An Ultrasound Doppler Shift method has been developed by Takeda [3]. It utilizes the pulsed echo techniques of ultrasound and can measure the velocity profile quasi-instantaneously. The applicability of this method for liquid metal flows has already been investigated. Reliable results were obtained in mercury [4] and gallium [5], while successful measurements at higher temperatures, for instance in sodium at about 200°C, have not been reported up to now. Besides the thermal limitations of the transducers, the acoustic coupling between transducer and the fluid via the channel wall and the allocation of suitable tracer particles have to be considered as relevant problems. Hot-wire and hot-film sensors were employed to perform local velocity measurements in mercury [6,7]. A special hot-wire sensor has been constructed for measurements in sodium flows [8]. However, due to the strong, chemical activity of the liquid metal its life-time is very limited. Generally, the hot-film and hot-wire sensors are less sensitive to velocity in liquid metals as compared to other fluids. This is because their large thermal conductivity is responsible for the formation of thick thermal
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boundary layers. Moreover, in the case of a sensor of low or moderate aspect ratio these thermal boundary layers become quite rounded. Hence, the sensor response might be insensitive to the flow direction [9]. A crucial problem which arises from the liquid metal properties is the non-stable thermal contact resistance due to the presence of impurities and the wetting conditions, respectively, at the sensor surface. The local velocity can also be determined from the measurements of an electric field induced by the motion of an electrically conducting fluid in the presence of a magnetic field. The magnetic field can be supplied by a miniature permanent magnet positioned inside the tip of the probe between the measuring electrodes [10–12] or by an external magnetic system [13–15] as is already present in typical MHD experiments. By means of such potential probes the components of the velocity perpendicular to the magnetic field lines can be measured. The installation of a permanent magnet inside the probe impedes a further miniaturization of the sensor and the working range is restricted to temperatures below the Curie temperature of the magnetic material. The problem of ohmic losses has to be considered as the main difficulty of the potential probe application. The velocity →
u cannot be measured precisely unless the electric cur→ →
rent is small compared to the term u ×B. This is valid only in some special cases, such as for example in twodimensional flows with a magnetic field perpendicular to the plane of the flow. Another approach to measure flow velocities is to detect the mechanical deflection of an elastic sensor affected directly by the flow. Zhilin et al. [16] proposed a two-component fiber-optic velocity sensor for the diagnostics of liquid metal flows. Inside the probe tip a pointer is placed in the gap between two pairs of light guides acting as transmitter and receiver, respectively. The interaction between sensor and flow causes a spatial shift of the pointer leading to measurable changes of the received light intensity. The quite sophisticated design of the probe tip makes it difficult to minimize the sensor dimensions and may cause problems with respect to a reproducible and robust application of the sensor. In the present paper we describe a mechano-optical sensor which aims to overcome most of the above-mentioned limitations of existing approaches. The design of this sensor is described in Section 2. Section 3 contains some theoretical considerations allowing an assessment of the main characteristics of the sensor signal. The procedure of sensor calibration is explained in Section 4 and experimental data collected with the mechano-optical sensor in a flow of eutectic InGaSn melt driven by a rotating magnetic field will be presented in Section 5.
2. Description of the measuring principle The intention to develop a new measuring technique to determine the local velocity in liquid metals arises from the following requirements: 앫 Although there is a growing interest in measuring the local velocity in opaque fluids at high temperatures (T⬎200°C), no measuring technique has been known up to now which works reproducibly and with reasonable accuracy over a sufficiently long time period. 앫 The measuring conditions at liquid metal facilities are often characterized by external magnetic fields or strong electrical noise caused for example by heating elements, pumps or power supplies. A measuring principle based on a mechanical interaction between a local sensor and the flow combined with an optical signal acquisition excludes such measuring errors. 앫 Disturbances of the flow due to the presence of the sensor should be prevented as much as possible. 앫 The measuring range should cover low (some cm/s) as well as high (some m/s) values of the velocity. The measuring apparatus described in this paper consists of a mechanical sensor, which is in direct contact with the fluid, mounted rigidly on an optical system used to acquire the measuring data. The thin tip of the probe (diameter ø⬇50 µm) acts as sensitive part. It is formed as a thin-walled glass cone by a special thermal treatment. A small glass rod, the so-called pointer, having a length of about 30–40 mm is positioned inside this glass tube and connected with the sensor tip only at the front point over a length of about 1 mm. The initial position of the free end of this pointer is approximately located in the center of the glass tube. The presence of a fluid moving around the sensor results in an elastic deformation of the tip (see Fig. 1). Consequently, at the
Fig. 1.
Measuring principle of the mechano-optical probe.
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opposite end a resulting spatial shift of the pointer can be observed by optical means in the opposite direction to the displacement of the sensor tip. This deflection is a function of the fluid velocity at the sensor position. The evaluation of amplitude and direction of the pointer displacement allows the two velocity components perpendicular to the sensor axis to be determined. An endoscope combined with a special lens system and a CCD-array is used to observe the pointer image. The pictures are digitized and analyzed by means of a frame grabber card installed in a PC. Regarding the choice of the sensor material one has to consider two aspects: First, the material has to obey Hooks law which is easily fulfilled for a large class of substances. Second, the sensor has to resist high temperatures and the chemical attacks of the liquid metal. For example, the use of borosilicate glass is favourable for applications up to temperatures of about 350°C in liquid sodium, gallium or metallic alloys such as InGaSn, SnPb, SnBi or PbBi. Borosilicate glass shows a constant elastic modulus E up to temperatures of about 400°C [17], and it is also stable against liquid sodium [18]. Moreover, the technology for manufacturing the sensor tips is rather simple regarding melting and handling of the Borosilicate glass. The utilization of higher melting materials such as quartz glass is necessary if flows in the temperature range of about 700–1000°C have to be studied.
3. Theory To calculate the pointer displacement the sensor tip is considered as a cylindrical tube with a constant cross section. It is clamped at one end and free at the other end (Fig. 2). The tube axis is directed along the z-direction. A flow around this tube causes a constant force per unit length f = F/l = Cwrrv2 leading to a deformation of the sensor. l and r denote the length and the outer radius of the cylinder. Cw, r and v stand for the drag coefficient, the fluid density and the velocity, respectively. This displacement of the tube from its equilibrium position is described by the parameter h(z). If we assume that the tube is bent by a torque Mx in x-direction the displacement is expected parallel to the y-direction. The original x-z-sections will not be deformed and remain transverse to the y-axis. Hooke’s law is assumed to be
valid. In the limit of small displacements h(z) has to satisfy the following equation [19] d 2Mx(z) d 4h(z) f⫽ ⫽EI (E,Ix⫽const.) x dz2 dz4
Schematic view of a bent cylindrical tube clamped at one end.
(1)
where E is the elastic modulus and Ix is the moment of inertia of the transverse section of the tube. The wall thickness d can be considered as small compared to r resulting in Ix ⬇ pr3d. By imposing the appropriate boundary conditions h=(dh)/(dz)=0 (z=0) and Mx=(dMx)/(dz)=0 (z=l) the solution of Eq. (1) is given by Cwrv2l4 h(z⫽l)⫽ 8Epr2d
(2)
According to the standard drag curve for a flow around a cylinder perpendicular to its axis [20] the drag coefficient Cw can be assumed as constant in a wide range of Reynolds numbers (2:103 ⱕ Re ⱕ 3:105). Thus, a parabolic dependence of the measured quantity h(z) from the velocity can be expected. A significant influence of the geometrical parameters l, r and d on the probe signal becomes obvious. By modifications of these parameters a well-defined adjustment of the sensor with respect to a desired range of velocity is possible. Let us consider a borosilicate glass sensor with the typical sizes of l =15 mm, r =0.1 mm and d =0.025 mm which is used in InGaSn-alloy at a velocity of 0.1 m/s. Applying Eq. (2) the resulting displacement h(l) of the sensor tip is about 14 µm. The pointer can be considered as the tangent at the front tip (see Fig. 1). The quantity actually measured is the deflection, hP, of the free end of the pointer given by hP = lP· sin a ⬇lP d h/dz (lP — length of the pointer). In the experiments a deflection hP of about 70 µm has been measured in InGaSn at 0.1 m/s using a probe with a pointer length of 45 mm. An enhancement of the sensitivity can be reached by attaching a small sphere to the sensor tip. The drag of the sensor is determined by that of the sphere Fs=(p)/(2)Cw,srr2s v2 (rs — radius of the sphere). We have to look for a solution of Eq. (1) for f=0 assuming the bending is only caused by the force Fs applied at the free end of the tube. This problem is characterized by the boundary conditions h=(dh)/(dz)=0 (z=0), Mx=0, (dMx)/(dz)=⫺Fs (z=l) and yields the solution Cw,srr2s v2l3 h(z⫽l)⫽ 6Er3d
Fig. 2.
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(3)
As known from the standard drag curve of a sphere [20] Cw,s is nearly constant in the range 102 ⱕ Re ⱕ 3:105. Considering a sphere with a radius of 1 mm and the same parameter as above the displacement of the sensor tip h is about 39 µm corresponding to a pointer deflec-
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Fig. 3. Photographs obtained by means of a stereo microscope showing a probe tip with and without attached spherical body.
tion hP of approximately 200 µm. Thus, by attaching the sphere we note an increase by a factor of three allowing us to measure considerably smaller velocities. Fig. 3 shows probe tips with and without installed spherical body photographed by a stereo microscope.
4. Sensor calibration To extract the actual velocity from the measurements each sensor tip has to be calibrated separately. The experimental configuration of a rotating channel used for that purpose is displayed in Fig. 4. The channel is mounted on a gear unit connected with a D.C.-motor used to create a steady motion. The resulting velocity is given by the product of the frequency w and the radial distance R of the probe from the axis of rotation. To
check the angular characteristic of the sensitivity the probe can be rotated around its axis. The diagram in Fig. 5 shows calibration data for a sensor obtained in water for different flow velocities and directions in the plane transverse to the probe axis. It becomes obvious that in this special case the sensitivity is not exactly homogeneous in the x-y-plane. Such an effect has to be taken into account for the measurements. Due to the dependence of the pointer displacement on the fluid density the calibration procedure has to be performed with the respective liquid used in the experiment. Fig. 6 shows typical calibration curves obtained in water and InGaSn, respectively, for one flow direction. The densities of water and the InGaSn alloy differ by a factor of about 6. The parabolic dependence of the pointer displacement on the velocity as predicted in Section 3 can be observed. A comparison between calibration curves obtained with and without an attached sphere at the probe tip is displayed in Fig. 7 demonstrating the significant enhancement of the measuring sensitivity in the case of the attached sphere. To allow a calibration of the sensor at higher temperatures the rotating channel containing fluids with melting points above room temperature is positioned inside an outer channel which is equipped with an electrical heater. Until now, the mechano-optical sensor has been applied to measurements at room temperature in water and InGaSn as well as at higher temperatures up to 350°C in SnPb, PbBi and SnBi, respectively.
5. Model experiments
Fig. 4.
Experimental set-up to calibrate the mechano-optical sensor.
Velocity measurements have been carried out to study a flow of eutectic InGaSn melt driven by a rotating magnetic field in order to evaluate the mechano-optical sensor under experimental conditions.
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Fig. 5. Example for the angular characteristic of the sensitivity of the sensor obtained in water at different flow velocities (the pointer displacement is given in pixel).
Fig. 6. Calibration data obtained with the same sensor in InGaSn alloy and water, respectively.
Fig. 7. Calibration data obtained with the same sensor in water with and without attached sphere at the sensor tip, respectively.
The scheme of the experimental set-up is shown in Fig. 8. The cylinder filled with a melt volume of approximately 0.3 l (radius R =4 cm, height H =5 cm) was placed in the center of the rotating magnetic field. We were able to vary the magnetic field strength up to 15 mT. The mechano-optical sensor was positioned about 1 cm below the free surface of the liquid which was covered by a thin layer of oxides. The probe was connected to a mechanical traversing system allowing an exact and reproducible position adjustment of the sensor inside
the fluid. Barz et al. [21] have already reported results of numerical simulations of the isothermal convection due to the effect of a rotating magnetic field in a cylindrical melt volume and their comparison with model experiments performed by means of micro-magnet probes. Compared to this measuring technique we deem the mechano-optical principle advantageous mainly for two reasons: 앫 The perturbation of the flow arising from the sensor
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Fig. 8. Scheme of the model experiment of a conductive melt inside a cylindrical volume driven by a rotating magnetic field.
is minimized due to the smaller size of the mechanooptical sensor. 앫 The measuring signal is not influenced by any electrical effects caused for example by the presence of external magnetic fields or the contact resistance between the measuring electrodes and the melt. Furthermore, the possibility of modifying the frequency w of the rotating field has to be considered as an important extension compared to the model experiments described in [21]. The present paper reports profiles of the azimuthal velocity measured at a horizontal line along the cylinder radius. The experimental results will be discussed in terms of the shielding pararameter K =mswR2= (R/ds)2 indicating the ratio of cylinder radius R to the skin depth ds = (msw)⫺1/2 (s — electrical conductivity of the fluid, m — magnetic permeability). A slowly oscillating magnetic field (K¿1) is able to spread out over the entire
Fig. 9.
melt volume. On the contrary, if KÀ1 the field lines are expelled from the melt volume due to the high electrical conductivity of the liquid. Consequently, the driving action of the magnetic field on the fluid is restricted to a small region at the outer surface. In our experiment the frequency has been varied between 10 and 400 Hz corresponding to a parameter region of K between 0.4 and 17. Measured profiles of the azimuthal velocity obtained at different frequencies and field amplitudes are displayed in Fig. 9. In the case of a low frequency (K ⬇1.2) the increase of the velocity starting from the center to the boundary seems to be linear. This indicates that the flow structure of the melt can be associated with a solid body rotation. The application of a magnetic field rotating with a significantly higher frequency (K ⬇16.7) results in an evident variation of the profiles. The enhancement of the velocity maxima near the boundaries corresponds to the above-mentioned skin effect of the concentration of the field action in the boundary region. The question regarding the influence of the applied frequency on the stirring process of the fluid is important for technical applications. Therefore, measurements have been performed with a variation of the frequency of the rotating field at constant field amplitude. The results for a fixed sensor position (r/R =0.75) can be seen in Fig. 10. We found a maximum of the velocity at K ⬇7, which corresponds to a frequency of about 170 Hz. However, this maximum does not have to be identical with an optimum of the stirring process. Here, the modification of the profiles with an enhancement of the frequency have to be taken into consideration. A more detailed analysis of the rotating magnetic field driven flow is beyond the scope of the present paper. Here, this flow just serves to demonstrate the applicability of the new mechanooptical probe under realistic MHD flow conditions.
Radial profiles of the azimuthal velocity for different amplitudes and frequencies of the rotating magnetic field.
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Fig. 10.
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Azimuthal velocity obtained at r/R = 0.75 as a function of the dimensionless frequency K.
6. Conclusions The measuring principle on which our new mechanooptical sensor is based consists essentially in the separation of the mechanical interaction between fluid and sensor tip and the optical acquisition and processing of the signal. Therefore, the probe can basically be employed also for high temperatures. The measuring principle is insensitive to electrical noise and external magnetic fields. This fact can be considered as an important advantage for applications in MHD experiments and measurements at facilities with a high level of electrical noise. The measuring principle has been successfully tested in water and an InGaSn eutectic melt at room temperature, as well as at higher temperatures (350°C) in PbBi and SnBi. A further extension of the application range to temperatures being relevant for Al or Mg (700– 800°C) seems to be straightforward by means of utilization of quartz glass as sensor material. Measurements in a rotating magnetic field driven flow of an InGaSn melt have been used to demonstrate the ability of the mechano-optical probe to supply reliable and reproducible data of the local liquid velocity. Further applications of the sensor are under preparation.
References [1] R. Moreau, Local and instantaneous measurements in liquid metal MHD. Proceedings of the Dynamic Flow Conference 1978. John Hopkins University, Baltimore, MD, USA.
[2] H. Branover, Magnetohydrodynamic Flow in Ducts, John Wiley and Sons, New York, 1978. [3] Y. Takeda, Development of an ultrasound velocity profile monitor, Nucl. Eng. and Design, 126 (1991) 277–284. [4] Y. Takeda, H. Kikura, G. Bauer, Flow measurement in a SINQ mockup target using mercury. Proc. of ASME FED Summer Meeting, Washington DC, 1998. [5] P. Cardin, H.C. Nataf, B. Pascal, J.C. Attiach, Velocity measurements in a vortex of liquid Gallium. 1st Int. Symposium on Ultrasound Doppler Methods for Fluid Mechanics an Fluid Engineering, Villigen PSI, 1996. [6] M. Sajben, Hot-wire anemometry in liquid mercury, Rev. Sci. Instr. 36 (1965) 945. [7] D.G. Malcolm, Some aspects of turbulence measurement in liquid mercury using cylindrical quartz-insulated hot-film sensors, J. Fluid Mech. 37 (1969) 701–713. [8] I. Platnieks, G. Uhlmann, Hot-wire sensor for liquid sodium, J. Phys. E: Sci. Instrum. 17 (1984) 862–863. [9] J.C. Hill, C.A. Sleicher, Directional sensitivity of hot film sensors in liquid metals, Rev. Sci. Instr. 42 (1971) 1461–1468. [10] R. Ricou, C. Vives, Local velocity and mass transfer measurements in molten metals using an incorporated magnet probe, Int. J. Heat Mass Transfer 25 (1982) 1579–1588. [11] T. Von Weissenfluh, Probes for local velocity and temperature measurements in liquid metal flow, Int. J. Heat Mass Transfer 28 (1985) 1563–1574. [12] J.U. Knebel, L. Krebs, Kalibrierung einer Miniatur-Permanentmagnet-Potentialsonde zur Geschwindigkeits- und Temperaturmessung in Natrium. Forschungszentrum Karlsruhe, 1993, KfK-Report 5215. [13] J.A. Shercliff, The Theory of Electromagnetic Flow Measurementy, Cambridge University Press, Cambridge, 1962. [14] I. Platnieks, Comparison of the hot-wire anemometric and conduction methods for measurements of velocity characteristics of a mercury flow under a transverse magnetic field, Magn. Gidrodin. 2 (1971) 140 in Russian. [15] A. Tsinober, Kit E. and Teitel M, On the relevance of the poten-
78
S. Eckert et al. / Flow Measurement and Instrumentation 11 (2000) 71–78
tial-difference method for turbulence measurements, J. Fluid Mech. 175 (1987) 447–461. [16] V.G. Zhilin, K.V. Zvyagin, Y.P. Ivochkin, A.A. Oksman, Diagnostics of liquid metal flows using fibre-optic velocity sensor, in: M. Lielpeteris (Ed.), Liquid Metal Magnetohydrodynamics Kluwer Academic Publishers, 1989, pp. 373–379. [17] H. Scholze, Glas–Natur, Struktur und Eigenschaft, Friedr. Vieweg and Sohn, 1965. [18] S. Eckert, Experimentelle Untersuchung turbulenter Flu¨ssigmetall- und Flu¨ssigmetall-Gas-Stro¨mungen in einem a¨ußeren Mag-
netfeld. Ph.D. Thesis, Technical University Dresden, 1997 Forschungszentrum Rossendorf, Report FZR-219, 1998. [19] L. Landau, E.M. Lifschitz, Bd. VII: Elastizita¨tstheorie, Akademie-Verlag, Berlin, 1976. [20] H. Brauer, Grundlagen der Ein- und Mehrphasenstro¨mungen, Verlag Sauerla¨nder, 1971. [21] R.U. Barz, G. Gerbeth, U. Wunderwald, E. Buhrig, Yu.M. Gelfgat, Modelling of the isothermal melt flow due to rotating magnetic fields in crystal growth, J. Crystal Growth 180 (1997) 410–421.
