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1 Bulletin of the JSME Mechanical Engineering Journal Vol.2, No.5, D MHD simulation of pressure drop and fluctuation in electromagnetic pump flow Takatoshi ASADA*, Rie AIZAWA**, Tetsu SUZUKI**, Yasushi FUJISHIMA** and Eiji HOASHI*** *Toshiba Corporation 2-4, Suehiro-cho, Tsurumi-ku, Yokohama, , Japan **Toshiba Corporation 8, Shinsugita-Cho, Isogo-ku, Yokohama, , Japan ***Department of Mechanical Engineering, Osaka University 2-1 Yamadaoka, Suita, Osaka, , Japan Received 7 April 2015 Abstract Electromagnetic (EM) pumps, which drive liquid metals by electromagnetic force for Fast Reactor, had been developed. Annular Linear Induction Pumps (ALIPs) are one of EM pumps. There are some reports in which a drop and a fluctuation of the developed pressure occurred near the top of the developed pressure and flow rate relation curve (P-Q curve). This phenomenon was reported by Gailitis, Kirillov and Araseki. They simulated it using two-dimensional (2D) code and reported that it was characterized by vortices, which were initiated by azimuthal non-uniformity of sodium flow velocity and/or magnetic field, in the liquid sodium flow. We have calculated the developed pressure of EM pump by 2D magnetohydrodynamics (MHD) code and designed an EM pump. It was found that the code simulated the developed pressure with high accuracy in normal operations. When the flow rate was lower than one in the top of P-Q curve, the developed pressure s drop and fluctuation occurred. The fluctuation would disturb the stable operation of the pump. For avoiding this phenomenon, the EM pump s design becomes sometimes too conservative. To evaluate the quantitative effect of this phenomenon and occurred conditions, we have developed a new three-dimensional(3d) MHD code. Clarification of these conditions and its phenomena will enable us to design a new structure or determine operation conditions. This paper presents the simulation results in terms of the generation of a developed pressure s drop and fluctuation occurrence. We used initial conditions which had azimuthal non-uniformity of sodium velocity to simulate vortices in the liquid sodium. Our 3D MHD code simulated the developed pressure s drop and fluctuation by vortices in radial and circumferential direction. It was confirmed that the vortices developed in the radial direction and then the vortices in circumferential direction developed. Key words : Electromagnetic pump, ALIP, MHD simulation, Instability, Pump head 1. Introduction Electromagnetic (EM) pumps, which drive liquid metals by electromagnetic force for Fast Reactor (FR), have been developed in many countries (Kittaka, et al., 2011; Ota, et al., 2004) EM pumps are static equipment which have no mechanical moving parts and circulate liquid sodium by electromagnetic force, and are advantageous in its reliability and maintainability compared with mechanical pumps. Annular Linear Induction Pumps (ALIPs) are one of the EM pumps and are relatively easy to size up pump capacity. ALIP mainly consists of multiple coils, iron cores and an annular flow channel mainly. Multiple coils are supplied with three-phase currents and then the magnetic field is introduced into annular flow by iron cores. Generally, the performance of EM pump is indicated by the developed pressure and flow rate relation curve (P-Q curve). When a lower flow rate than the peak of the P-Q curve is selected as the operation point, we sometimes encounter the developed pressure s drop and fluctuation during the operation of EM pump (Ota, et al., 2004). The fluctuation then has lower than frequency than 10Hz. Such a fluctuation was reported by Araseki, Gailitis and Kirillov Paper No J-STAGE Advance Publication date: 29 September,

2 (Araseki, et al., 2004; Gailitis and Lielausis, 1975; Kirillov, et al., 1980). The developed pressure s drop and fluctuation are characterized by vortices, which are initiated by azimuthal non-uniformity of liquid sodium velocity and/or magnetic field, in the liquid sodium flow. According to Gailitis, the stable/unstable boundary is defined as the condition that the overall magnetic Reynolds number, Rm, times the slip, s, is higher than unity. We developed a new three-dimensional magnetohydrodynamics (3D MHD) code and tried to simulate the developed pressure s drop and fluctuation in ALIP using this code (Asada, et al., 2014). In this paper, we focus on the initiation of this developed pressure s drop and fluctuation in ALIP by our 3D MHD code. 2. Simulation method and model A new 3D MHD code is mainly separated as two parts. One is magnetic field simulation part, and another is fluid dynamics simulation part. The former is then coupled with the later. The magnetic field simulation part has been uniquely developed by Toshiba, and commercial computational fluid dynamics (CFD) software, Star-CD is used as the fluid dynamics simulation part. The flow velocity in the annular channel is calculated by Star-CD and transferred to the magnetic field simulation part to calculate the Lorentz force. Calculated Lorentz force is transferred back to the fluid dynamics simulation part. In the magnetic field simulation, simulation model includes a pump casing, nitrogen region, iron cores, coils, inner and outer ducts, in addition to liquid sodium. On the other hand, the fluid dynamics simulation is carried out only for liquid sodium. Therefore, both simulations can use same mesh of liquid sodium region. We use the magnetic field equations in the A-φ formulation as governing equation, which are given followings: 1 A A = I 0 + σ φ + u ( A), (1) μ t ( A) σ φ + = t [ u ( A) ] 0, (2) B = A. (3) These equations are discretized by the edge-based finite element method. The edge-based finite element method has some advantages over usual node-based FEM. Firstly, discretization automatically satisfies the boundary conditions of magnetic fields between permeability materials. Next, the number of unknown variables generally becomes smaller. Then element coefficient matrices obtained for various materials are added to construct the global coefficient matrix. In solving the discretized simultaneous global coefficient matrix, BiCGSTab with the Jacobi pre-conditioner was selected. A sparse matrix solver package, Library of Iterative Solvers (LIS) (Nishida, 2010), which was developed by Japanese National Project, was used as matrix solver in our 3D MHD code. The magnetic flux density, B, and the eddy current density, I, in liquid sodium are solved using vector and scalar potentials, A and φ, and then the Lorentz force at every fluid cell is given by F mag I B = (4) The Lorentz force is transferred to the fluid dynamics simulation part and substituted into external forces term in momentum equation. Dirichlet conditions are applied to the boundary in magnetic field. The EM pump had iron cores that was higher magnetic permeability than other material s one. Thus no magnetic field leaks outside. Inlet velocity, non-slip on the wall, and free outlet conditions are applied to each boundary in fluid dynamics simulation. The turbulence model is K-epsilon model. The higher-order MARS differencing scheme is used. 3. Simulation Condition We considered EMP pump with the rated flow rate of 160m3/min as this simulation target (Ota, et al., 2004). Design specifications of this EMP pump are shown in Table 1, and simulation conditions are shown in Table 2. Simulation parameters are operation frequencies, coil currents and flow rate of sodium. The conditions of sodium velocity, operation frequency and coil currents match the operation values used in the experiment using above EM 2

3 pump. The time step in this simulation is decided as a 1/200 of sine-wave period of operation frequencies. Table 1 Design specifications of 160m 3 /min EM pump Items Specification Flow rate 160 m 3 /min Developed pressure (pump head) 0.25 MPa Sodium temperature 335 C Design specification Input power 1680 kw Terminal voltage 884 A Frequency 20 Hz Rm 6.42 Slip 0.16 Rm Slip 1.06 Number of poles 14 Flow gap 77 mm Flow velocity 10.4 m/s Number of coils 84 2 Outer dia. of casing 1900 mm Table 2 Simulation parameters No Flow rate [m 3 /min] Inlet velocity [m/s] Frequency [Hz] Ave. coil currents [A] Velocity distribution [%] Overview of EM pump and the mesh for magnetic field simulation and CFD are shown in Fig. 1. The mesh for CFD agrees with the sodium simulation area for magnetic field. The yellow, green and gray grids in mesh of EM pump present the liquid sodium, air and pump casing respectively. These meshes are constructed by structured mesh. 23

4 Fig. 1 Overview of EM pump and mesh Here, the case No.7 in Table 2 has the azimuthally non-uniform velocity distribution which is shown in Fig.2. The mass flow rate in inlet boundary is equal to that in the simulation No.1. Since the actual pump would have non-uniform velocity distribution for an elbow near the pump inlet, the simulation with this velocity distribution is conducted as sensitivity simulation for the developed pressure s drop and fluctuation. The peak range agrees with the condition of Araseki s simulation (Araseki, et al., 2004). Fig.2 Flow velocity distribution in inlet boundary 4. Simulation Results and Discussions Figures 3 and 4 show comparison of developed pressures calculated using our 3D MHD code with experimental data and time histories of developed pressures in the experiment and the simulation No.4, respectively. Vertical axes are developed pressure in both figures, and horizontal axes in Figs.3 and 4 are inlet flow rate and time, respectively. Developed pressures in cases from No.1 to No.6 are averaged values because they have periodic fluctuation temporally as shown in Fig.4. Figure 5 shows the time histories of developed pressure in case of simulations No.1 and No.7. The vertical and horizontal axes in Fig.5 are equal to them in Fig.4. The developed pressure of No.7 is largely fluctuated 24

5 unlike No.1 as shown in Fig.5 and thus it in Fig.3 is the averaged value from 2.0 to 3.0 sec. The condition of simulation No.4 indicates the rated flow condition, 159 m 3 /min, in our targeted EM pump, and the developed pressure in this case is in good agreement with experimental data. The error between our simulation and the experiment in this case is then smaller than 6%. The frequency in the rated flow rate condition, No.4, is about 40Hz from Fig.4 and agrees with the experimental data. The fluctuation of developed pressure in case of No.4 is a double-supply-frequency (DSF) (Araseki, et al., 2000). However, the developed pressure of simulation No.1 with uniform flow velocity distribution is higher than that of experimental data in P-Q curve as shown in Fig.3. On the other hand, the developed pressure of simulation No.7 with non-uniform flow velocity distribution agrees with the experimental data. Fig. 3 P-Q curve Fig. 4 Developed pressure (159m3/min, No.4) In simulation No.7, the inlet boundary condition has non-uniform flow velocity distribution as shown in Fig.2. In Fig.5, the developed pressure in simulation No.7 has both periodic and random fluctuations. The frequency of this periodic fluctuation has root of operation frequency and such periodic fluctuation is also observed in other cases in 25

6 Fig.4. However, the random fluctuation is only generated in simulation No.7, only. Figure 6 shows the linear spectrum obtained using Fast Fourier Transform in simulation No.1 and 7. The frequency in simulations No.1 and No.7 have a peak at 40Hz which is DSF. In simulation No.7, the linear spectrum also has a peak only under 10Hz and this peak indicates random fluctuations of the developed pressure. Fig.5 Developed pressure (140m3/min, No.1 and No.7) Fig.6 Linear spectrum (No.1 and No.7) These random fluctuations would be caused by vortices in liquid sodium flow. Figure 7 shows contours of the axial flow velocity and vectors at center of the annular channel in the circumferential direction. The dotted frame on contours in 0.4, 1.7 and 2.0sec indicates the extended region for vectors. Firstly, the axial flow velocity distribution in pump outlet maintains one in pump inlet at 0.2sec. Next, the reverse flow of the axial flow velocity is generated in pump outlet at 0.4sec and the reverse flow region changes to the shape with narrow region in the middle at 1.0sec. After 1.0sec, this reversed flow region, that is vortices, swings in the circumferential direction from 1.5sec to 3.0sec. The vortices have several sizes and swings would cause random pressure fluctuation. Figure 8 shows the magnetic force and magnetic flux at the center of annular flow channel. Vertical axes are the magnetic force of axial direction averaged 26

7 from 1.72 to 1.77 seconds and the magnetic flux in the upper and the lower figure of Fig.8, respectively. The averaged time indicates 1 cycle times. Horizontal axes are the position in the flow direction (axial length) and magnetic flux in the lower figure of Fig.8 is the instantaneous distribution at 1.72 and 1.77 seconds. The magnetic forces are extracted at three points of 0, 90 and 180 degrees in circumferential direction as shown in the upper figure of Fig.8. At the position of 0 degree, the magnetic force has periodic fluctuation and negative value in EM pump outlet. At the position of 90 degree, the magnetic force has similar tendency to that at the position of 0 degree and a peak can be observed near EM pump outlet. At the position of 180 degree, the magnetic force has no fluctuation and negative value in EM pump outlet. The peak is observed near EM pump outlet is lower than that at the position of 90 degree. The disappearance of the force fluctuation and negative value is caused by vortices which has several frequencies. The magnetic flux at position of 180 degree shows the influence of vertexes. Magnetic flux distributions at position of 0 and 90 degree at 1.72 seconds agree with one at 1.77 seconds. However, magnetic flux distribution in 180 degree point at 1.72 seconds disagrees with one at 1.77 seconds when the axial length is over 3m. The agreement at position of 0 and 90 degree indicates that the magnetic flux has periodic change and the disagreement at position of 180 degree indicates that the magnetic flux has random change. This disagreement region in Fig.7 has a reversed flow generated by vertexes. The vortices are also observed in the radial direction. The axial flow velocity in cross section of annular channel is shown in Fig.9. Contour diagram indicates the axial flow velocity distribution in cross-sections of the radial direction at positions of the 0 and 180 degree in Fig. 7 and the blue region then means the flow reverses to the flow direction. It is found that the liquid sodium flow is reversed near EM pump outlet and the area of the reverse flow region changes. The flow vector near EM pump outlet is shown in Fig.10. The contour level indicates the axial flow velocity but vectors have the direction of the flow. The flow velocity in Fig.10 is partially reversed near outer duct at 0.38 sec. After that, the reversed flow region expands to inner duct at 0.4 sec. At 0.5 sec, the flow in this region reversed on the whole. The reversed flow velocity region changes continuously according to elapsed time. They would be caused vortices swings in Fig.7. The reversed flow would be caused by the change of magnetic flux near outer duct. Figure 11 shows the magnetic force in annular channel at 0 degree. The horizontal axis denotes the radial distance and the vertical axis denotes the magnetic force of axial direction averaged from 1.72 to 1.77 seconds. The magnetic force in liquid sodium flow decreased and becomes lowest at the center of annular channel and the magnetic force near outer duct was stronger than the one near inner duct. The radius of inner duct was smaller than the outer duct and the friction force by inner duct was strong. Therefore, the liquid sodium flow would be reversed by this strong magnetic force and weak friction force near outer duct firstly. 27

8 Fig. 7 Contour figures of axial flow velocity at annular channel (140m3/min, No.7) 28

9 Fig. 8 Magnetic force and magnetic flux (140m3/min, No.7) 29

10 Fig. 9 Axial flow velocity in cross section Fig. 10 Flow vector near pump outlet at 180 degree 210

11 Fig. 11 Magnetic force in sodium flow at 0 degree 5. Conclusion This paper indicated the simulation of developed pressure s drop and fluctuation in extraordinary operating range by our newly developed 3D MHD code. Numerical results focusing on vortices triggered by distributed inlet flow were presented. 3D simulations provided more clear illustration of vortices. Conclusions obtained are as follows: 1. The code could simulate the developed pressure within 6% in rated flow rate condition. 2. The code simulated the vortices in circumferential and radial directions that cause the pressure s drop and fluctuation. 3. The vortices starts near outer duct and transferred to inner duct. 4. The magnetic force and flux distorted in reversed flow region. NOMENCLATURE B magnetic flux density vector F mag magnetic force A magnetic vector potential vector Φ electric scholar potential μ magnetic permeability σ electric conductivity I 0 coil current I induced current vector u liquid sodium velocity vector Rm magnetic Reynolds number References Araseki, H., Kirillov, I. R., Preslitsky, G. V. and Ogorodnikov, A. P., Double-supply-frequency pressure pulsation in annular linear induction pump Part I: Measurement and numerical analysis, Journal of Nuclear Engineering and Design, No.195 (2000), pp Araseki, Hideo, Kirillov, I R., Preslitsky, G. V., and Ogorodnikov, A. P., Magnetohydrodynamic instability in annular linear induction pump Part I. Experiment and numerical analysis, Journal of Nuclear Engineering and Design, No.227 (2004), pp Asada, T., Hirata, Y., Aizawa, R., Fujishima, Y., Suzuki, T. and Hoashi, E., Development of Three-Dimensional 211

12 Magnetohydrodynamics Code for Electromagnetic Pump, Journal of Nuclear Science and Technology, vol.52, No. 5 (2014), pp Gailitis, A. and Lielausis, O., Instability of homogeneous velocity distribution in an induction-type MHD machine, English translation from Magnitnaya Gidrodinamika, No.1, (1975), pp Kirillov, I. R., Ogorodnikov, A. P. and Ostapenko, V. P., Experimental investigation of flow nonuniformity in a cylindrical linear induction pump, Translated from Magnitnaya Gidrodinamika, No.2 (1980), pp Kittaka, D., Asada, T., Aizawa, R., Komai, M. and Oota, H., Development of Electromagnetic Pump and Electromagnetic Flow Meter for 4S, Transactions of American Nuclear Society, Vol.105, (2011), pp Nihida, A., Experience in Developing an Open Source Scalable Software Infrastructure in Japan, Computational Science and Its Applications - ICCSA 2010, vol.6017 (2010), pp Ota, H., Katsuki, K., Funato, M., Taguchi, J., Fanning, A. W., Doi, Y., Nibe, M., Ueta, N. and Inagaki, T., Development of 160m3/min Large Capacity Sodium-Immersed Self-Cooled Electromagnetic Pump, Journal of Nuclear Science and Technology, Vol.41, No.4 (2004), pp Product names mentioned herein may be trademarks of their respective companies. 212