Fusion Engineering and Design 85 (2010) 138–145 Contents lists available at ScienceDirect Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes Development of a potential based code for MHD analysis of LLCB TBM P.J. Bhuyan a,b,∗ , K.S. Goswami a a Centre of Plasma Physics, Tepesia, Sonapur, Assam, PIN – 782402, India b Nowgong College, Nagaon, Assam, PIN – 782001, India article info Article history: Received 1 April 2009 Received in revised form 19 August 2009 Accepted 28 August 2009 Available online 25 September 2009 Keywords: ITER LLCB TBM MHD simulation Liquid breeder blanket Hartmann number abstract A two dimensional solver is developed for MHD flows with low magnetic Reynolds’ number based on the electrostatic potential formulation for the Lorentz forces and current densities which will be used to calculate the MHD pressure drop inside the channels of liquid breeder based Test Blanket Modules (TBMs). The flow geometry is assumed to be rectangular and perpendicular to the flow direction, with flow and electrostatic potential variations along the flow direction neglected. A structured, non-uniform, collocated grid is used in the calculation, where the velocity (u), pressure (p) and electrostatic potential () are calculated at the cell centers, whereas the current densities are calculated at the cell faces. Special relaxation techniques are employed in calculating the electrostatic potential for ensuring the divergence- free condition for current density. The code is benchmarked over a square channel for various Hartmann numbers up to 25,000 with and without insulation coatings by (i) comparing the pressure drop with the approximate analytical results found in literature and (ii) comparing the pressure drop with the ones obtained in our previous calculations based on the induction formulation for the electromagnetic part. Finally the code is used to determine the MHD pressure drop in case of LLCB TBM. The code gives similar results as obtained by us in our previous calculations based on the induction formulation. However, the convergence is much faster in case of potential based code. © 2009 Elsevier B.V. All rights reserved. 1. Introduction Tritium breeding blanket is one of the major technolog- ical breakthroughs that need to be accomplished before the deuterium–tritium (D–T) based fusion reactors become commer- cially feasible. A principal mission of the ITER is to develop, deploy and operate DEMO-relevant Test Blanket Module (TBM) that can provide integrated experimental and operational experience in a true fusion environment [1–5]. Two basic tritium breeder choices have been investigated by the ITER parties are the solid ceramic breeder (CB) [4] and the liquid breeder (LB) [1–4,6–13]. This paper focuses on liquid metal based TBM, in which a liquid metal flowing within channels in the breeding blanket will do the tritium breed- ing along with cooling and high-grade heat extraction. Pb–17Li has been identified as a potential liquid metal (LM) for use in ITER–TBMs [1–4,6–13,23–25], as well as in reactor first wall [26] and in divertors [27]. All the ITER partners, except Japan, are devel- oping their own concept of LB based TBM [4]. This includes the HCLL TBM (EU [20,21,30]), DFLL TBM (China [29]), DCLL TBM (US [13]), HCML TBM (Korea [22]) and LLCB TBM (India [2–5]). The LLCB TBM is a new concept that aims at optimizing the tritium production by taking the advantages of both LB and CB. In this TBM, lithium ∗ Corresponding author at: Nowgong College, Nagaon, Assam, PIN – 782001, India. E-mail address: pranjal.bhuyan@rediffmail.com (P.J. Bhuyan). titanate in form of packed pebble beds is used as the solid breeder and the PbLi eutectic flowing in rectangular channels around these solid-breeder zones acts as tritium breeder, neutron multiplier and coolant [2,3]. Within the TBM, the LM will flow in rectangular channels crossed by strong magnetic field of the confinement magnets. Motion of the LM in the magnetic field generates currents, and interaction of this current with the imposed magnetic field results in motion opposing Lorentz forces, so that a much higher pressure drop needs to be maintained across the channel to keep the LM moving at the desired flow rate. This MHD force is thus undesirable as it warrants a lot of pumping power and reduction of MHD pres- sure drop is one of the prime concerns for the design of TBMs. One way for lowering this MHD pressure drop is to decrease the wall conductivity through an insulation coating in the inner walls of the channel or using flow channel inserts (FCI) [31]. The insulation layer decouples the currents in the bulk region from the walls, so that the eddy currents cannot penetrate the insulation and they closes their circuit through the thin liquid layers close to the duct wall per- pendicular to the applied field (called the Hartmann layers). As the resistance offered by these layers far exceeds the resistance offered by the conducting walls, the eddy current reduces significantly, and so also the MHD pressure drop. To numerically model the flow within the TBM, one need to incorporate the Lorentz force as a volumetric source term in the Navier Stokes equations and then solve these equations along 0920-3796/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2009.08.008