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Experimental investigation of liquid metal MHD flow entering a flow channel insert
Fusion Engineering and Design 154 (2020) 111484
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Experimental investigation of liquid metal MHD flow entering a flow channel insert
T
L. Bühler*, C. Mistrangelo, H.-J. Brinkmann Karlsruhe Institute of Technology, Postfach 3640, 76021 Karlsruhe, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Magnetohydrodynamics (MHD) Liquid metal experiments Flow channel inserts (FCI) MHD pressure drop Liquid metal blankets
Insulating flow channel inserts (FCI) in ducts of liquid metal blankets decouple electrically the fluid domain from the conducting thick-walled structure. They interrupt current paths across well-conducting walls and thereby reduce significantly magnetohydrodynamic (MHD) pressure drop. Pipe flow of an electrically conducting liquid metal entering a region where walls are covered by a FCI is investigated experimentally under the influence of a strong uniform magnetic field. The abrupt change in wall conductivity leads to 3D MHD effects that are studied by measuring pressure and electric potential distribution along the duct wall. It is shown that FCIs may reduce pressure drop by at least one order of magnitude but 3D effects at the entrance of FCIs may reduce the efficiency of the insulating inserts by some degree.
1. Introduction Liquid lead lithium (PbLi) is foreseen as breeder material, neutron multiplier and heat transfer medium in dual coolant (DCLL), heliumcooled (HCLL) and in water-cooled (WCLL) lead lithium blankets. In all these applications, the liquid metal has to be circulated under the influence of the strong plasma-confining magnetic field. The interaction with the magnetic field induces electric currents that cause strong electromagnetic Lorentz forces resulting in very high pressure drop, especially when duct walls are electrically conducting. Currents, Lorentz forces, and pressure drop may be reduced by using electrically insulating flow channel inserts (FCI) that decouple the fluid region from the electrically well-conducting blanket walls. FCIs have been proposed for DCLL blankets, which rely on convective heat transport by the liquid metal flow. However, in HCLL and in WCLL blankets, FCIs could be beneficial as well in supplying lines and in manifolds, where velocities and pressure drop are higher than in the breeding zones. However, from a technical point of view it will not be possible to cover all interfaces between liquid metal and blanket walls with insulating liners. As a consequence, in blanket ducts there will be regions in which the fluid will flow in bare ducts without insulation and other regions where walls are shielded by FCIs. At the entrance and exit of FCIs strong 3D MHD effects are expected. Insulating FCIs for pressure drop reduction in fusion blankets have been proposed in a patent by S. Malang already in 1987 [1] and promoted later by the same author in several publications (e.g. [2]) or
⁎
Corresponding author. E-mail address: [email protected] (L. Bühler).
https://doi.org/10.1016/j.fusengdes.2020.111484 Received 19 September 2019; Accepted 11 January 2020 0920-3796/ © 2020 Published by Elsevier B.V.
more recently for applications in a European DEMO reactor [3]. In order to prevent liquid metal infiltration into potentially porous insulating ceramics, sandwich-type FCIs have been proposed, where the insulating layer is protected from all sides by thin sheets of steel [4]. Experimental investigations of MHD flows in pipes with sandwichtype FCIs performed by Barleon et al. [5] showed that a pressure drop reduction by a factor of nearly 9 is possible compared to the flow in an electrically conducting circular pipe. Such FCIs are therefore considered a feasible option based on available materials and fabrication techniques [6–8] and they have been successfully tested in recent MHD experiments [9]. The present work shows results of experimental studies performed in the MEKKA laboratory at the Karlsruhe Institute of Technology (KIT). Three-dimensional liquid metal MHD flows at the entrance into a FCI are investigated. It is expected that electric currents close their paths not only in cross sectional planes. They may circulate also along a significant downstream axial distance in the thick conducting pipe wall even if the insulation provided by the FCI is perfect. The axial length of current paths is analyzed by measurements of wall potential distribution in flow direction. The variation of pressure along the upper wall is recorded at a number of pressure taps. A description of the test section is given below. 2. Test section A test section with circular cross-section is used for experimental investigation. Details of the geometry are shown in Fig. 1. The same
Fusion Engineering and Design 154 (2020) 111484
L. Bühler, et al.
Fig. 1. Geometry and principle sketch of current paths at the entrance of a FCI. The insulation inside the FCI starts at xi = 10 mm.
Fig. 2. Sketch of FCI position in pipe. The position x = 0 corresponds to the center of the pressure tap in front of the FCI. The FCI starts at x = 5 mm downstream. The insulating layer inside the FCI (not visible in the sketch) begins at a downstream position of x = 10 mm that coincides with the first pressure tap across the FCI.
rectangular cross-section and within a region of 850 × 168 × 483 mm3 the field is quite uniform with maximum strength of 2.1 T and deviations from the center value are smaller than 1%. 3D effects caused by the non-uniform entrance field decay quickly along the flow path [11] and the liquid metal approaches rapidly fully developed MHD pipe flow before it enters into the FCI. The instrumented test section in front of the magnet is shown in Fig. 3. In the experiment the distribution of electric potential is recorded on the external surface of the pipe upstream of the FCI along the periphery at different angles α (see Fig. 2). Three-dimensional effects at the entrance to the FCI lead to variations of transverse potential difference Δϕ (x ) = ϕ (x , α = −π /2) − ϕ (x , α = π /2) as a function of the axial position x. Those values are recorded with a large number of potential sensors (see Fig. 3) that are distributed with higher resolution near x = 0. For measuring pressure inside the FCI along the axial direction and for pressure equalization between the core flow and the annular gap
pipe had been used already for investigations of additional pressure drop at the junction between two FCIs [9]. The relevant information needed for the definition of the present work is briefly outlined for obtaining a complete picture, although some details have been already described in the latter reference. The thick-walled pipe has an inner radius R = L = 48.6 mm that is used as characteristic length of the problem. All dimensions, including the outer radius of the pipe Ro and the radius RFCI of the inner steel layer of the FCI, can be seen in Fig. 1. The thickness tFCI = 0.5 mm of the protection sheets has been suggested, e.g. in [10]. The coordinate x = 0 corresponds to the position of the pressure tap that is located immediately in front of the FCI. As shown in Figs. 1 and 2 the FCI starts at x = 5 mm and the insulation inside the FCI at xi = 10 mm. Sodium potassium NaK is used as a model fluid. Far upstream, two flow straighteners have been inserted into the pipe to homogenize the inflow. The liquid metal enters the normalconducting dipole magnet in the MEKKA MHD laboratory by passing first a region of an increasing magnetic field. The magnetic gap has a
2
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sensitivity in the range of a few mbar up to 7 bar. 3. Parameters and scales The strength of magnetic field and the intensity of the flow are quantified by the nondimensional Hartmann and Reynolds number
Ha = LB
σ , ρν
Re =
u0 L . ν
(1)
2
The quantity Ha stands for the ratio of electromagnetic to viscous forces and Re quantifies the ratio between inertia and viscous forces. Here, ν, ρ and σ denote the kinematic viscosity, density and electric conductivity of the fluid. The mean velocity in the bare pipe without FCI is u0 and B is the magnitude of the uniform magnetic field. The influence of wall conductivity σw on MHD pipe flow is described by using the wall conductance parameter c according to [13], which evaluates for the present problem and material properties at 50° C [14,15] for the thick-walled pipe and for the FCI to
c=
σw Ro2 − R2 = 0.0727, σ Ro2 + R2
c FCI = 0.00476,
respectively. For strong magnetic fields, the nondimensional pressure gradient in fully established pipe flow becomes
∂p*/ ∂x * ∂p c =− = −0.0678. = σu 0 B2 1+c ∂x
Fig. 3. Pressure taps and potential sensors on the surface of the pipe with connected cables before the test section is moved into the magnet.
(2)
Here “*” denotes dimensional quantities. The pressure gradient of a fully developed MHD flow inside a FCI evaluates as
between FCI and pipe, it is required to have openings (slots or holes). In order to preserve a good circular shape of the FCI, a pressure equalization slot along the entire length of the Hartmann wall has been avoided. In the present experiment a number of pressure equalization holes give access for measuring the pressure distribution along the FCI (Fig. 4). Leakage currents are minimized since the electric potential is zero along the symmetry plane of the pipe at z = 0, where the pressure taps are located [12]. Details about fabrication of the FCI are described in [7] or in [9]. The external thick-walled pipe has pressure taps primarily located on the upper Hartmann wall. Their positions for x > 0 coincide with the locations of pressure equalization holes in the FCI. Smaller axial spacing of pressure taps at the entrance of the FCI gives a higher spatial resolution at those positions, where strong 3D effects are expected. Individual pressure taps are switched by a system of computer-controlled valves to an array of pressure transducers with different
∂pFCI ∂p*FCI / ∂x * c FCI R2 =− , = 2 2 σu 0 B ∂x 1 + c FCI RFCI
(3)
2 R2 / RFCI
accounts for the fact that the mean velocity is where the factor slightly higher in the insert than in a pipe without FCI. This yields ∂pFCI/ ∂x =−0.00508. For derivation of (3) it has been assumed that the flow rate in the thin annular gap between FCI and wall is negligible in comparison with that in the core [16]. 4. Experimental results Before the liquid metal enters the FCI, i.e. at a position far enough upstream, the MHD pipe flow is fully developed. In a previous publication [9] the pressure gradient of fully developed MHD pipe flow without FCI had been measured and good agreement with Miyazaki's predictions had been confirmed. The distribution of electric potential on the external surface of the pipe ϕ (Ro , α ) in fully established pipe
Fig. 4. Pressure equalization holes in the FCI. 3
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L. Bühler, et al.
Fig. 5. Electric wall potential ϕ/mV in fully established pipe flow upstream of the FCI as a function of the circumferential angle α.
Fig. 8. Variation of nondimensional transverse Δϕ (x / L)/(u 0 BL) near the entrance of the FCI.
potential
difference
established conditions with uniform values along x. Those values are proportional to the strength of the applied magnetic field. Approaching the FCI, the potential starts monotonically decreasing. At downstream positions x > xi, where current paths into the wall are interrupted by the insulation of the FCI, values of Δϕ (x ) decay to zero over a length of about 200 mm. By comparison of data in Fig. 7 and in Fig. 5 one may notice some difference in dimensional values of Δϕ/mV. This difference is caused by the fact that both series of experiments have been performed at different temperature (i.e. with different fluid viscosity) leading to different velocities u0 for same values of Re. In addition, also values of Re differ by some amount between both figures. However, when results for Δϕ are scaled with relevant characteristic values as shown below, this seemingly discrepancy does not occur anymore. When potential results are scaled by characteristic values u0BL, all curves collapse onto a single line as shown in Fig. 8. This confirms the validity of the universal scaling law for potential over a wide range of Hartmann numbers investigated in the present experiments. Results Δϕ (x / L < − 2) agree well with theoretical predictions for fully developed MHD pipe flow [17]. We observe that 3D effects near the entrance of the FCI extend upstream over more than 2L. Fig. 8 further shows that Δϕ (x / L) is affected along a downstream fraction of the pipe, 0 < x/ L ≲ 5, caused by recirculating currents inside the wall. The currents flowing in this part of the wall are separated from those inside the fluid by the insulation in the FCI. These currents enter or leave the wall upstream where no insulation is present, i.e. for x < xi. This leads to locally increased current density in the fluid near xi which may create some additional pressure drop Δp3D. The fact that Δϕ vanishes as x/ L ≳ 5 confirms full functionality of the ceramic insulation inside the sandwich FCI. The variation of pressure along the axis of the test section is shown in Fig. 9 for the flow at Ha = 2000 and different Reynolds numbers. In order to compare results for different Ha and Re in the region of major interest near the position where the insulation in the FCI starts, the reference value of pressure has been placed at this location, i.e. p (x i ) = 0 . We observe a fast decay of pressure in the bare pipe and a slower decrease of pressure in the insulated region. As expected, the pressure drop increases with velocity (Re). When scaled with characteristic quantities σu0B2L, all results come close to a single line as shown in Fig. 10. The pressure gradients in the bare pipe and in the part with FCI agree well with theoretical predictions for fully developed MHD flow in a pipe (2) or in a FCI (3), which yields an experimentally confirmed possible pressure drop reduction factor of 0.0678/0.00508 = 13.3. Nevertheless, recirculating additional currents near the entrance of the FCI give rise to extra Lorentz forces that create some additional pressure drop Δp3D caused by 3D effects. Even if the absolute value of Δp3D appears acceptable one should keep in mind that it corresponds to a pressure drop in the FCI over more than 4 characteristic lengths L. Since similar pressure losses
Fig. 6. Nondimensional electric wall potential ϕ/u0BL in fully established pipe flow upstream of the FCI as a function of the circumferential angle α.
flow upstream of the FCI has been measured as a function of the circumferential angle α for various Hartmann numbers in the range 1000 ≲ Ha ≲ 5000. Results are shown in Fig. 5. As expected from theoretical considerations [17], the potential varies sinusoidally with α and increases in magnitude proportional to the strength of the magnetic field. The latter observation is confirmed by plotting the results in nondimensional form as ϕ/u0BL in Fig. 6, where all results collapse onto a single curve that coincides well with theoretical predictions. From Fig. 5 it is possible to observe a potential difference between both sides of the pipe Δϕ = ϕ (−π /2) − ϕ (π /2) . This quantity is used in the following to investigate the influence of 3D MHD effects at the entrance of the FCI on the distribution of electric potential. Results are displayed in Fig. 7. Far upstream, Δϕ (x ≲ −100 mm) shows fully
Fig. 7. Variation of transverse potential difference Δϕ (x ) near the entrance of the FCI for different Hartmann numbers. 4
Fusion Engineering and Design 154 (2020) 111484
L. Bühler, et al.
Fig. 12. 3D MHD flow at the entrance into a FCI. Nondimensional pressure along the axis for Ha = 5000 and different Re.
Fig. 9. Pressure along the axis for Ha = 2000 and different Re for 3D MHD flow at the entrance into a FCI. Positions of pressure taps are illustrated in the sketch 2.
steeper decay when approaching xi and apparently some sudden pressure recovery at x = xi. One should notice here that experiments at very high Ha are more difficult to perform and they require long time after switching of pressure valves until the reading at the transducers reaches final values. Those results should be reconsidered in future. 5. Conclusions The present investigations of MHD flows entering a flow channel insert (FCI) show that sandwich-type FCIs can efficiently reduce MHD pressure drop. It has been shown that the correlations (2) and (3) for pressure gradient based on the theory presented in [13] describe the fully developed flow in the circular pipe and in the sandwich FCI in very good agreement with experimental observations at some distance from the FCI entrance. Recirculating 3D currents at the entrance to the FCI cause some additional Lorentz forces and associated pressure drop that corresponds roughly to that in fully developed MHD flow in a FCI over a distance of about 4 characteristic lengths.
Fig. 10. 3D MHD flow at the entrance into a FCI. Nondimensional pressure along the axis for Ha = 2000 and different Re.
Acknowledgment This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratomresearch and training programme 2014–2018 and 2019–2020 under grant agreement no. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. We further acknowledge industrial in-kind support by Fischer Group, Achern, Germany and HGGS LaserCUT GmbH & Co. KG, Hatzenbühl, Germany for valuable discussions and technical support during fabrication of FCIs. References Fig. 11. 3D MHD flow at the entrance into a FCI. Nondimensional pressure along the axis for Ha = 3000 and different Re.
[1] S. Malang, Einrichtung zur Verringerung des MHD-Druckverlustes in dickwandigen Kanälen, Patent DE 36 00 645 C2 (1987). [2] S. Malang, M. Tillack, C.P.C. Wong, N. Morley, S. Smolentsev, Development of the lead lithium DCLL blanket concept, Fusion Sci. Technol. 60 (2011) 249–256. [3] D. Rapisarda, I. Fernandez, I. Palermo, F. Urgorri, L. Maqueda, D. Alonso, T. Melichar, O. Frýbort, L. Vála, M. Gonzalez, P. Norajitra, H. Neuberger, A. Ibarra, Status of the engineering activities carried out on the European DCLL, Fusion Eng. Des. 124 (2017) 876–881. [4] S. Malang, K. Arheidt, L. Barleon, H.U. Borgstedt, V. Casal, U. Fischer, W. Link, J. Reimann, K. Rust, G. Schmidt, Self-cooled liquid-metal blanket concept, Fusion Technol. 14 (1988) 1343–1356. [5] L. Barleon, V. Casal, K. Mack, H. Kreuzinger, A. Sterl, K. Thomauske, Experimental and theoretical work on MHD at the Forschungszentrum Karlsruhe, the MEKKAProgram, in: J. Lielpetris, R. Moreau (Eds.), Liquid Metal Magnetohydrodynamics, Kluwer, 1989, pp. 55–61. [6] P. Norajitra, W.W. Basuki, M. Gonzalez, D. Rapisarda, M. Rohde, L. Spatafora, Development of sandwich flow channel inserts for an EU DEMO dual coolant blanket concept, Fusion Sci. Technol. 68 (3) (2015) 501–506. [7] C. Koehly, L. Bühler, Fabrication issues of sandwich-like flow channel inserts for
occur also at the exit of the FCI or at gaps between two FCIs [9], these 3D effects may reduce the efficiency of FCIs by an amount that is not negligible. For stronger magnetic fields, i.e. higher Hartmann numbers, the behavior is quite the same as shown in Fig. 11 for Ha = 3000. Further experiments have been performed for Ha = 5000 and results are shown in Fig. 12. For such high values of Ha and for Re = 10219 the distribution of pressure drop corresponds to that discussed previously for Ha = 2000 and Ha = 3000. However, for the smaller Re = 4984 the pressure distribution at the entrance to the FCI is different. Although the total nondimensional pressure drops do not really differ for both Reynolds numbers, we observe for the smaller Re a 5
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[12] S. Smolentsev, M. Abdou, N. Morley, M. Sawan, S. Malang, C. Wong, Numerical analysis of MHD flow and heat transfer in a poloidal channel of the DCLL blanket with a SiCf/SiC flow channel insert, Fusion Eng. Des. 81 (1–7) (2006) 549–553. [13] K. Miyazaki, K. Konishi, S. Inoue, MHD pressure drop of liquid metal flow in circular duct under variable transverse magnetic field, J. Nucl. Sci. Technol. 28 (2) (1991) 159–161. [14] O.J. Foust, Sodium – NaK Engineering Handbook, Gordon and Breach Science Publishers, New York, London, Paris, 1972. [15] Stahl-Eisen-Werkstoffblätter (SEW 310), Physikalische Eigenschaften von Stählen, Verlag Stahleisen Düsseldorf, 1992. [16] S. Smolentsev, N. Morley, M. Abdou, Code development for analysis of MHD pressure drop reduction in a liquid metal blanket using insulation technique based on a fully developed flow model, Fusion Eng. Des. 73 (1) (2005) 83–93. [17] K. Miyazaki, S. Kotake, N. Yamaoka, S. Inoue, Y. Fujii-E, MHD pressure drop of NaK flow in stainless steel pipe, Nucl. Technol./Fusion 4 (1983) 447–452.
circular pipes, Fusion Sci. Technol. 72 (2017) 660–666. [8] D. Rapisarda, I. Fernandez, I. Palermo, M. Gonzalez, C. Moreno, A. Ibarra, E. Mas de les Valls, Conceptual design of the EU-DEMO dual coolant lithium lead equatorial module, IEEE Trans. Plasma Sci. 44 (99) (2016) 1–10. [9] L. Bühler, H.-J. Brinkmann, C. Koehly, Experimental study of liquid metal magnetohydrodynamic flows near gaps between flow channel inserts, Fusion Eng. Des. 146 (2019) 1399–1402. [10] F. Urgorri, S. Smolentsev, I. Fernández-Berceruelo, D. Rapisarda, I. Palermo, A. Ibarra, Magnetohydrodynamic and thermal analysis of PbLi flows in poloidal channels with flow channel insert for the EU-DCLL blanket, Nucl. Fusion 58 (10) (2018) 106001. [11] L. Bühler, H.-J. Brinkmann, C. Mistrangelo, Experimental investigation of liquid metal pipe flow in a strong non-uniform magnetic field, Proceedings of the 11th International PAMIR Conference – Fundamental and Applied MHD, July 01–05, 2019, Reims, France, 2019.
6
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Experimental investigation of liquid metal MHD flow entering a flow channel insert
T
L. Bühler*, C. Mistrangelo, H.-J. Brinkmann Karlsruhe Institute of Technology, Postfach 3640, 76021 Karlsruhe, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Magnetohydrodynamics (MHD) Liquid metal experiments Flow channel inserts (FCI) MHD pressure drop Liquid metal blankets
Insulating flow channel inserts (FCI) in ducts of liquid metal blankets decouple electrically the fluid domain from the conducting thick-walled structure. They interrupt current paths across well-conducting walls and thereby reduce significantly magnetohydrodynamic (MHD) pressure drop. Pipe flow of an electrically conducting liquid metal entering a region where walls are covered by a FCI is investigated experimentally under the influence of a strong uniform magnetic field. The abrupt change in wall conductivity leads to 3D MHD effects that are studied by measuring pressure and electric potential distribution along the duct wall. It is shown that FCIs may reduce pressure drop by at least one order of magnitude but 3D effects at the entrance of FCIs may reduce the efficiency of the insulating inserts by some degree.
1. Introduction Liquid lead lithium (PbLi) is foreseen as breeder material, neutron multiplier and heat transfer medium in dual coolant (DCLL), heliumcooled (HCLL) and in water-cooled (WCLL) lead lithium blankets. In all these applications, the liquid metal has to be circulated under the influence of the strong plasma-confining magnetic field. The interaction with the magnetic field induces electric currents that cause strong electromagnetic Lorentz forces resulting in very high pressure drop, especially when duct walls are electrically conducting. Currents, Lorentz forces, and pressure drop may be reduced by using electrically insulating flow channel inserts (FCI) that decouple the fluid region from the electrically well-conducting blanket walls. FCIs have been proposed for DCLL blankets, which rely on convective heat transport by the liquid metal flow. However, in HCLL and in WCLL blankets, FCIs could be beneficial as well in supplying lines and in manifolds, where velocities and pressure drop are higher than in the breeding zones. However, from a technical point of view it will not be possible to cover all interfaces between liquid metal and blanket walls with insulating liners. As a consequence, in blanket ducts there will be regions in which the fluid will flow in bare ducts without insulation and other regions where walls are shielded by FCIs. At the entrance and exit of FCIs strong 3D MHD effects are expected. Insulating FCIs for pressure drop reduction in fusion blankets have been proposed in a patent by S. Malang already in 1987 [1] and promoted later by the same author in several publications (e.g. [2]) or
⁎
Corresponding author. E-mail address: [email protected] (L. Bühler).
https://doi.org/10.1016/j.fusengdes.2020.111484 Received 19 September 2019; Accepted 11 January 2020 0920-3796/ © 2020 Published by Elsevier B.V.
more recently for applications in a European DEMO reactor [3]. In order to prevent liquid metal infiltration into potentially porous insulating ceramics, sandwich-type FCIs have been proposed, where the insulating layer is protected from all sides by thin sheets of steel [4]. Experimental investigations of MHD flows in pipes with sandwichtype FCIs performed by Barleon et al. [5] showed that a pressure drop reduction by a factor of nearly 9 is possible compared to the flow in an electrically conducting circular pipe. Such FCIs are therefore considered a feasible option based on available materials and fabrication techniques [6–8] and they have been successfully tested in recent MHD experiments [9]. The present work shows results of experimental studies performed in the MEKKA laboratory at the Karlsruhe Institute of Technology (KIT). Three-dimensional liquid metal MHD flows at the entrance into a FCI are investigated. It is expected that electric currents close their paths not only in cross sectional planes. They may circulate also along a significant downstream axial distance in the thick conducting pipe wall even if the insulation provided by the FCI is perfect. The axial length of current paths is analyzed by measurements of wall potential distribution in flow direction. The variation of pressure along the upper wall is recorded at a number of pressure taps. A description of the test section is given below. 2. Test section A test section with circular cross-section is used for experimental investigation. Details of the geometry are shown in Fig. 1. The same
Fusion Engineering and Design 154 (2020) 111484
L. Bühler, et al.
Fig. 1. Geometry and principle sketch of current paths at the entrance of a FCI. The insulation inside the FCI starts at xi = 10 mm.
Fig. 2. Sketch of FCI position in pipe. The position x = 0 corresponds to the center of the pressure tap in front of the FCI. The FCI starts at x = 5 mm downstream. The insulating layer inside the FCI (not visible in the sketch) begins at a downstream position of x = 10 mm that coincides with the first pressure tap across the FCI.
rectangular cross-section and within a region of 850 × 168 × 483 mm3 the field is quite uniform with maximum strength of 2.1 T and deviations from the center value are smaller than 1%. 3D effects caused by the non-uniform entrance field decay quickly along the flow path [11] and the liquid metal approaches rapidly fully developed MHD pipe flow before it enters into the FCI. The instrumented test section in front of the magnet is shown in Fig. 3. In the experiment the distribution of electric potential is recorded on the external surface of the pipe upstream of the FCI along the periphery at different angles α (see Fig. 2). Three-dimensional effects at the entrance to the FCI lead to variations of transverse potential difference Δϕ (x ) = ϕ (x , α = −π /2) − ϕ (x , α = π /2) as a function of the axial position x. Those values are recorded with a large number of potential sensors (see Fig. 3) that are distributed with higher resolution near x = 0. For measuring pressure inside the FCI along the axial direction and for pressure equalization between the core flow and the annular gap
pipe had been used already for investigations of additional pressure drop at the junction between two FCIs [9]. The relevant information needed for the definition of the present work is briefly outlined for obtaining a complete picture, although some details have been already described in the latter reference. The thick-walled pipe has an inner radius R = L = 48.6 mm that is used as characteristic length of the problem. All dimensions, including the outer radius of the pipe Ro and the radius RFCI of the inner steel layer of the FCI, can be seen in Fig. 1. The thickness tFCI = 0.5 mm of the protection sheets has been suggested, e.g. in [10]. The coordinate x = 0 corresponds to the position of the pressure tap that is located immediately in front of the FCI. As shown in Figs. 1 and 2 the FCI starts at x = 5 mm and the insulation inside the FCI at xi = 10 mm. Sodium potassium NaK is used as a model fluid. Far upstream, two flow straighteners have been inserted into the pipe to homogenize the inflow. The liquid metal enters the normalconducting dipole magnet in the MEKKA MHD laboratory by passing first a region of an increasing magnetic field. The magnetic gap has a
2
Fusion Engineering and Design 154 (2020) 111484
L. Bühler, et al.
sensitivity in the range of a few mbar up to 7 bar. 3. Parameters and scales The strength of magnetic field and the intensity of the flow are quantified by the nondimensional Hartmann and Reynolds number
Ha = LB
σ , ρν
Re =
u0 L . ν
(1)
2
The quantity Ha stands for the ratio of electromagnetic to viscous forces and Re quantifies the ratio between inertia and viscous forces. Here, ν, ρ and σ denote the kinematic viscosity, density and electric conductivity of the fluid. The mean velocity in the bare pipe without FCI is u0 and B is the magnitude of the uniform magnetic field. The influence of wall conductivity σw on MHD pipe flow is described by using the wall conductance parameter c according to [13], which evaluates for the present problem and material properties at 50° C [14,15] for the thick-walled pipe and for the FCI to
c=
σw Ro2 − R2 = 0.0727, σ Ro2 + R2
c FCI = 0.00476,
respectively. For strong magnetic fields, the nondimensional pressure gradient in fully established pipe flow becomes
∂p*/ ∂x * ∂p c =− = −0.0678. = σu 0 B2 1+c ∂x
Fig. 3. Pressure taps and potential sensors on the surface of the pipe with connected cables before the test section is moved into the magnet.
(2)
Here “*” denotes dimensional quantities. The pressure gradient of a fully developed MHD flow inside a FCI evaluates as
between FCI and pipe, it is required to have openings (slots or holes). In order to preserve a good circular shape of the FCI, a pressure equalization slot along the entire length of the Hartmann wall has been avoided. In the present experiment a number of pressure equalization holes give access for measuring the pressure distribution along the FCI (Fig. 4). Leakage currents are minimized since the electric potential is zero along the symmetry plane of the pipe at z = 0, where the pressure taps are located [12]. Details about fabrication of the FCI are described in [7] or in [9]. The external thick-walled pipe has pressure taps primarily located on the upper Hartmann wall. Their positions for x > 0 coincide with the locations of pressure equalization holes in the FCI. Smaller axial spacing of pressure taps at the entrance of the FCI gives a higher spatial resolution at those positions, where strong 3D effects are expected. Individual pressure taps are switched by a system of computer-controlled valves to an array of pressure transducers with different
∂pFCI ∂p*FCI / ∂x * c FCI R2 =− , = 2 2 σu 0 B ∂x 1 + c FCI RFCI
(3)
2 R2 / RFCI
accounts for the fact that the mean velocity is where the factor slightly higher in the insert than in a pipe without FCI. This yields ∂pFCI/ ∂x =−0.00508. For derivation of (3) it has been assumed that the flow rate in the thin annular gap between FCI and wall is negligible in comparison with that in the core [16]. 4. Experimental results Before the liquid metal enters the FCI, i.e. at a position far enough upstream, the MHD pipe flow is fully developed. In a previous publication [9] the pressure gradient of fully developed MHD pipe flow without FCI had been measured and good agreement with Miyazaki's predictions had been confirmed. The distribution of electric potential on the external surface of the pipe ϕ (Ro , α ) in fully established pipe
Fig. 4. Pressure equalization holes in the FCI. 3
Fusion Engineering and Design 154 (2020) 111484
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Fig. 5. Electric wall potential ϕ/mV in fully established pipe flow upstream of the FCI as a function of the circumferential angle α.
Fig. 8. Variation of nondimensional transverse Δϕ (x / L)/(u 0 BL) near the entrance of the FCI.
potential
difference
established conditions with uniform values along x. Those values are proportional to the strength of the applied magnetic field. Approaching the FCI, the potential starts monotonically decreasing. At downstream positions x > xi, where current paths into the wall are interrupted by the insulation of the FCI, values of Δϕ (x ) decay to zero over a length of about 200 mm. By comparison of data in Fig. 7 and in Fig. 5 one may notice some difference in dimensional values of Δϕ/mV. This difference is caused by the fact that both series of experiments have been performed at different temperature (i.e. with different fluid viscosity) leading to different velocities u0 for same values of Re. In addition, also values of Re differ by some amount between both figures. However, when results for Δϕ are scaled with relevant characteristic values as shown below, this seemingly discrepancy does not occur anymore. When potential results are scaled by characteristic values u0BL, all curves collapse onto a single line as shown in Fig. 8. This confirms the validity of the universal scaling law for potential over a wide range of Hartmann numbers investigated in the present experiments. Results Δϕ (x / L < − 2) agree well with theoretical predictions for fully developed MHD pipe flow [17]. We observe that 3D effects near the entrance of the FCI extend upstream over more than 2L. Fig. 8 further shows that Δϕ (x / L) is affected along a downstream fraction of the pipe, 0 < x/ L ≲ 5, caused by recirculating currents inside the wall. The currents flowing in this part of the wall are separated from those inside the fluid by the insulation in the FCI. These currents enter or leave the wall upstream where no insulation is present, i.e. for x < xi. This leads to locally increased current density in the fluid near xi which may create some additional pressure drop Δp3D. The fact that Δϕ vanishes as x/ L ≳ 5 confirms full functionality of the ceramic insulation inside the sandwich FCI. The variation of pressure along the axis of the test section is shown in Fig. 9 for the flow at Ha = 2000 and different Reynolds numbers. In order to compare results for different Ha and Re in the region of major interest near the position where the insulation in the FCI starts, the reference value of pressure has been placed at this location, i.e. p (x i ) = 0 . We observe a fast decay of pressure in the bare pipe and a slower decrease of pressure in the insulated region. As expected, the pressure drop increases with velocity (Re). When scaled with characteristic quantities σu0B2L, all results come close to a single line as shown in Fig. 10. The pressure gradients in the bare pipe and in the part with FCI agree well with theoretical predictions for fully developed MHD flow in a pipe (2) or in a FCI (3), which yields an experimentally confirmed possible pressure drop reduction factor of 0.0678/0.00508 = 13.3. Nevertheless, recirculating additional currents near the entrance of the FCI give rise to extra Lorentz forces that create some additional pressure drop Δp3D caused by 3D effects. Even if the absolute value of Δp3D appears acceptable one should keep in mind that it corresponds to a pressure drop in the FCI over more than 4 characteristic lengths L. Since similar pressure losses
Fig. 6. Nondimensional electric wall potential ϕ/u0BL in fully established pipe flow upstream of the FCI as a function of the circumferential angle α.
flow upstream of the FCI has been measured as a function of the circumferential angle α for various Hartmann numbers in the range 1000 ≲ Ha ≲ 5000. Results are shown in Fig. 5. As expected from theoretical considerations [17], the potential varies sinusoidally with α and increases in magnitude proportional to the strength of the magnetic field. The latter observation is confirmed by plotting the results in nondimensional form as ϕ/u0BL in Fig. 6, where all results collapse onto a single curve that coincides well with theoretical predictions. From Fig. 5 it is possible to observe a potential difference between both sides of the pipe Δϕ = ϕ (−π /2) − ϕ (π /2) . This quantity is used in the following to investigate the influence of 3D MHD effects at the entrance of the FCI on the distribution of electric potential. Results are displayed in Fig. 7. Far upstream, Δϕ (x ≲ −100 mm) shows fully
Fig. 7. Variation of transverse potential difference Δϕ (x ) near the entrance of the FCI for different Hartmann numbers. 4
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Fig. 12. 3D MHD flow at the entrance into a FCI. Nondimensional pressure along the axis for Ha = 5000 and different Re.
Fig. 9. Pressure along the axis for Ha = 2000 and different Re for 3D MHD flow at the entrance into a FCI. Positions of pressure taps are illustrated in the sketch 2.
steeper decay when approaching xi and apparently some sudden pressure recovery at x = xi. One should notice here that experiments at very high Ha are more difficult to perform and they require long time after switching of pressure valves until the reading at the transducers reaches final values. Those results should be reconsidered in future. 5. Conclusions The present investigations of MHD flows entering a flow channel insert (FCI) show that sandwich-type FCIs can efficiently reduce MHD pressure drop. It has been shown that the correlations (2) and (3) for pressure gradient based on the theory presented in [13] describe the fully developed flow in the circular pipe and in the sandwich FCI in very good agreement with experimental observations at some distance from the FCI entrance. Recirculating 3D currents at the entrance to the FCI cause some additional Lorentz forces and associated pressure drop that corresponds roughly to that in fully developed MHD flow in a FCI over a distance of about 4 characteristic lengths.
Fig. 10. 3D MHD flow at the entrance into a FCI. Nondimensional pressure along the axis for Ha = 2000 and different Re.
Acknowledgment This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratomresearch and training programme 2014–2018 and 2019–2020 under grant agreement no. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. We further acknowledge industrial in-kind support by Fischer Group, Achern, Germany and HGGS LaserCUT GmbH & Co. KG, Hatzenbühl, Germany for valuable discussions and technical support during fabrication of FCIs. References Fig. 11. 3D MHD flow at the entrance into a FCI. Nondimensional pressure along the axis for Ha = 3000 and different Re.
[1] S. Malang, Einrichtung zur Verringerung des MHD-Druckverlustes in dickwandigen Kanälen, Patent DE 36 00 645 C2 (1987). [2] S. Malang, M. Tillack, C.P.C. Wong, N. Morley, S. Smolentsev, Development of the lead lithium DCLL blanket concept, Fusion Sci. Technol. 60 (2011) 249–256. [3] D. Rapisarda, I. Fernandez, I. Palermo, F. Urgorri, L. Maqueda, D. Alonso, T. Melichar, O. Frýbort, L. Vála, M. Gonzalez, P. Norajitra, H. Neuberger, A. Ibarra, Status of the engineering activities carried out on the European DCLL, Fusion Eng. Des. 124 (2017) 876–881. [4] S. Malang, K. Arheidt, L. Barleon, H.U. Borgstedt, V. Casal, U. Fischer, W. Link, J. Reimann, K. Rust, G. Schmidt, Self-cooled liquid-metal blanket concept, Fusion Technol. 14 (1988) 1343–1356. [5] L. Barleon, V. Casal, K. Mack, H. Kreuzinger, A. Sterl, K. Thomauske, Experimental and theoretical work on MHD at the Forschungszentrum Karlsruhe, the MEKKAProgram, in: J. Lielpetris, R. Moreau (Eds.), Liquid Metal Magnetohydrodynamics, Kluwer, 1989, pp. 55–61. [6] P. Norajitra, W.W. Basuki, M. Gonzalez, D. Rapisarda, M. Rohde, L. Spatafora, Development of sandwich flow channel inserts for an EU DEMO dual coolant blanket concept, Fusion Sci. Technol. 68 (3) (2015) 501–506. [7] C. Koehly, L. Bühler, Fabrication issues of sandwich-like flow channel inserts for
occur also at the exit of the FCI or at gaps between two FCIs [9], these 3D effects may reduce the efficiency of FCIs by an amount that is not negligible. For stronger magnetic fields, i.e. higher Hartmann numbers, the behavior is quite the same as shown in Fig. 11 for Ha = 3000. Further experiments have been performed for Ha = 5000 and results are shown in Fig. 12. For such high values of Ha and for Re = 10219 the distribution of pressure drop corresponds to that discussed previously for Ha = 2000 and Ha = 3000. However, for the smaller Re = 4984 the pressure distribution at the entrance to the FCI is different. Although the total nondimensional pressure drops do not really differ for both Reynolds numbers, we observe for the smaller Re a 5
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circular pipes, Fusion Sci. Technol. 72 (2017) 660–666. [8] D. Rapisarda, I. Fernandez, I. Palermo, M. Gonzalez, C. Moreno, A. Ibarra, E. Mas de les Valls, Conceptual design of the EU-DEMO dual coolant lithium lead equatorial module, IEEE Trans. Plasma Sci. 44 (99) (2016) 1–10. [9] L. Bühler, H.-J. Brinkmann, C. Koehly, Experimental study of liquid metal magnetohydrodynamic flows near gaps between flow channel inserts, Fusion Eng. Des. 146 (2019) 1399–1402. [10] F. Urgorri, S. Smolentsev, I. Fernández-Berceruelo, D. Rapisarda, I. Palermo, A. Ibarra, Magnetohydrodynamic and thermal analysis of PbLi flows in poloidal channels with flow channel insert for the EU-DCLL blanket, Nucl. Fusion 58 (10) (2018) 106001. [11] L. Bühler, H.-J. Brinkmann, C. Mistrangelo, Experimental investigation of liquid metal pipe flow in a strong non-uniform magnetic field, Proceedings of the 11th International PAMIR Conference – Fundamental and Applied MHD, July 01–05, 2019, Reims, France, 2019.
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