LiPb Flow Research Articles

Chemical and structural durability of α-Al2O3 and γ-LiAlO2 layers formed on ODS FeCrAl alloys in liquid lithium lead stirred flow

The protection performance of an α-Al2O3 layer formed on oxide dispersion-strengthened (ODS) FeCrAl alloys in liquid LiPb flow was investigated by means of the corrosion tests under stirred-flow condition at 873 K for 1000 h. The result of STEM/EELS analysis indicated the Li adsorption and diffusion into α-Al2O3 layer. The ODS FeCrAl alloys in-situ formed a durable γ-LiAlO2 layer on their bare surface in liquid LiPb. The results of micro scratch tests on the protective layers indicated that they revealed strong resistance against the exfoliation in a shearing direction after the immersion to liquid LiPb.

Direct numerical simulations of tritium extraction in PbLi-based breeding blankets in the laminar–turbulent transition region

In a lead-lithium (PbLi) based breeding blanket, the bred tritium remains dissolved in the PbLi, which flows towards the Tritium Extraction Unit (TEU). In a TEU, tritium must be extracted at a fast enough rate that guarantees the plant’s self-sufficiency and safety. Different TEU concepts exist, one of the most promising being Permeation Against Vacuum (PAV), based on the extraction of tritium from the PbLi through a highly permeable membrane.Even in the so-called low velocity blanket concepts, PbLi is expected to flow at relatively high total mass flow rates. This means that the high tritium extraction efficiencies that safe operation requires must be obtained partitioning the flow into several extraction channels, but this solution increases both cost and complexity. However, less partition channels may be required should turbulence be induced in the flow. Since turbulence increases the flow mixing, it should favor tritium extraction. Hence, in the range of velocities where turbulent phenomena start —i.e., the transition region—, extraction efficiency is expected to grow rapidly with velocity due to turbulence acting as a new transport mechanism. Thus, a turbulent flow in the TEU may achieve the high extraction efficiencies required with a more moderate partitioning scheme.In this work, a PbLi flow in a prototypical PAV channel was modeled using Direct Numerical Simulations (DNS). To trigger turbulence, two different methods were implemented, namely an instability-inducing oscillating boundary condition, and a physical turbulator consisting of a geometrical obstacle. Both methods proved successful as they resulted in greater extraction efficiencies than those seen in the analogous laminar regimes. In fact, up to a 15% increase in extraction efficiency or up to a 5-fold increase in total extraction rate were obtained.

Impact of Reverse Buoyancy on Heat and Mass Transfer in MHD Flow of PbLi Within a Poloidal Duct in a Typical DCLL Liquid Breeder Blanket

The typical dual-coolant lead-lithium (PbLi) design of a liquid breeder blanket in a magnetic confinement fusion reactor involves the utilization of PbLi as the working fluid to effectively remove neutron heat. However, the nonuniform heating of neutrons with a significant radial gradient induces a buoyancy effect, resulting in the formation of vortexes ices within the downward flow duct. These vortexes have an adverse impact on the heat and mass transfer characteristics of the magnetohydrodynamic (MHD) flow of PbLi. The simulations in this work employed a MHD buoyant mixed-convection solver to resolve the characteristics of PbLi flow and a one-way coupled Lagrangian method to analyze the qualitative characteristics of tritium transport in PbLi flow. The results indicate that buoyant reverse flow can create vortexes that contain hot spots in the PbLi fluid, which can significantly impede heat transport. Additionally, the vortex causes tritium recirculation in the flow field and retention, resulting in adverse effects on tritium transport.

Continuous deuterium extraction from falling lithium-lead droplets in a vacuum

This study experimentally verifies continuous deuterium extraction efficiency from falling liquid lithium-lead (LiPb) droplets in a vacuum, as an alternative to tritium The obtained efficiencies, from five runs, were between 0.59 and 0.69. The corresponding dispersion coefficient of deuterium in LiPb droplets is (2.6 + 0.8 – 0.6) × 10–7 m2s–1. These results closely resemble those obtained in a proof-of-principle (POP) experiment conducted at Kyoto University in 2013. Consequently, the deuterium release from falling LiPb droplets in a vacuum can be considered a stable function. The experimental campaign was carried out using a dedicated setup constructed on the liquid metal test loop (Oroshhi-2) at the National Institute for Fusion Science. Tritium breeding in a liquid LiPb blanket is substituted by the deuterium dissolution in circulating LiPb. The extraction efficiency was determined by comparing the time-series deuterium flux, released from falling droplets, with simulation. An alternative method involving a before and after concentration comparison did not yield consistent results. This inconsistency can be attributed to issues with the concentration sensor, which experienced difficulties due to surface degradation. The experimental parameters, the LiPb flow rate, nozzle diameter, falling height, temperature, and duration period, were set to 0.1 to 0.3 l-min–1, 1.0 mm, 500 mm, 350 °C, and 9 h, respectively.

Modelling the PbLi flow including tritium transport and permeation with GETTHEM

One of the main challenges to be addressed to achieve a reliable electricity production from the EU DEMO reactor is the realization of a closed fuel cycle, for which a suitable Tritium Extraction and Removal System (TERS) is required. One of the possible technologies identified for the EU DEMO TERS is the Permeator Against Vacuum (PAV): the tritium dissolved in the liquid PbLi flowing within several parallel channels will permeate towards the vacuum pumped on the other side of the channel wall (the membrane).A recently-developed model of the tritium permeation across the membrane in the PAV, involving both transport phenomena in the wall and surface processes, was already used to size the EU DEMO PAV. However, besides the component itself, it is important to properly define the interfaces of the PAV in the TERS, and of the TERS in the entire PbLi and tritium loops. The model of such a complex system is therefore implemented here in the Modelica object-oriented language used by system-level tool GETTHEM, that already includes a model of the PbLi loop. The resulting, lumped-parameter component will be able to capture the thermal-hydraulic behaviour of the PbLi, to model the tritium transport in the fluid and to estimate the tritium permeated flux supplied to the tritium processing. Such a model is tested here on a sub-scale circuit to demonstrate its capability to simulate the operation of the EU DEMO TERS using the GETTHEM code.As the physical parameters of the model are subject to a large uncertainty, an uncertainty propagation analysis is also performed, to have a preliminary quantification of the impact of such uncertainties on the model output and, therefore, on the TERS efficiency, and to drive further investigations of these physical properties. In particular, results show how the uncertainty on the solubility constant of hydrogen in PbLi represents the dominant contribution on the total variance, highlighting the need for a better accuracy of such parameter.

Hydrodynamics and electrical insulation of PbLi flow with SiC flow channel inserts in a strong magnetic field

Experimental and numerical research in a strong magnetic field is described in this article testing silicon carbide (SiC) flow channel inserts (FCI) in lead-lithium (PbLi) liquid metal flow. The study aims to further develop the High-Temperature Dual-Coolant Lead-Lithium nuclear fusion blanket concept by testing new variations of SiC inserts operating in the relevant electromagnetic conditions. These inserts act as electrical insulators in magnetohydrodynamic lead-lithium flow and can also play the role of the thermal insulator in the potentially real fusion environment. The liquid metal pressure and integral flowrate measurements were performed on up to 5T DC magnetic field created by a superconducting magnet at high temperatures up to 700 °C, which is close to the real fusion environment. Comparisons of several cases with and without inserts are provided, demonstrating their impact on hydraulic resistance. Additionally, electrical potential distribution is recorded on the lead-lithium channel walls, which can be used to evaluate the character of liquid metal velocity distribution in the lead-lithium channel.

Theoretical evaluation of the tritium extraction from liquid metal flows through a free surface and through a permeable membrane

Effective tritium extraction from PbLi flows is a requirement for the functioning of any PbLi based breeding blanket concept. For a continuous plant operation, the removal of the tritium dissolved in the PbLi has to be performed in line and sufficiently fast. Otherwise, tritium inventories in the liquid metal, start-up inventories and buffer inventories would be excessive from the safety point of view. Moreover, a slow response of the tritium extraction systems could also compromise the tritium self-sufficiency of the plant. A promising solution to this problem is to use highly permeable membranes in contact with the PbLi flow to promote the extraction via permeation. This technique is usually known as Permeation Against Vacuum (PAV). As an alternative, tritium could be extracted directly by permeation through a fluid free surface (FS) in contact with vacuum. In both configurations, the dynamics of tritium transport is ruled by a combination of convection, diffusion and surface recombination. In this paper, the tritium extraction processes in the FS and PAV configurations are studied in detail. For the first time, general analytical expressions for the extraction efficiency are derived for both techniques in a Cartesian geometry. These expressions are general in the sense that they do not impose any kind of assumption concerning the permeation regime of the membrane or the fluid boundary layer. The derived expressions have been used to analyze numerically the response of both configurations in a close loop system, such as the one of DEMO. The presented methodology allows comparing the FS and PAV configurations, assessing in which conditions one will be behave better than other.

Modeling the Transport of Activated Corrosion Products in the WCLL PbLi Loop for ITER and the EU DEMO With the GETTHEM Code

This work presents the results of the implementation in the GEneral Tokamak THErmal-hydraulic Model of available models for the generation and transport of any dispersed material in the PbLi eutectic mixture circulating in the Water-Cooled Lithium-Lead Breeding Blanket of the EU DEMO fusion reactor, with main focus on Activated Corrosion Products as solid suspension. A simple test case is used to show that the distribution of the concentration of activated corrosion products at any point of the PbLi loop, both in the water-cooled lithium-lead breeding blanket and in the related ITER Test Blanket System, can be determined by the model. The results obtained with this tool can be useful not only for radiological safety purposes, but also because activated corrosion products may affect the PbLi flow itself and the efficiency of the tritium removal system, with consequences on the achievable Tritium Breeding Ratio. A rigorous verification of the model is also performed.

Large Component Simulation of an Inboard Sector of a Dual-Coolant Lead-Lithium Blanket

Advances in high-performance computing now enable the engineering evaluation of large blanket components from a systems perspective at the beginning of a normal design cycle. As an example, we discuss the computational fluid dynamics (CFD) involved in characterizing the thermal performance of an entire 22.5 toroidal sector of a dual-coolant lead-lithium blanket with particular attention to the integrated manifolding and flow distributions. The inboard sector is roughly 7 m tall, has 321 first-wall helium-cooled channels, and five parallel PbLi breeder channels complete with insulating SiC flow channel inserts. A finite volume model was developed with various degrees of mesh refinement from 36 to 187 million cells to perform the flow calculations on disparate fluids with conjugate heat transfer in the solid. Steady-state CFD calculations were performed using a realizable k-ε turbulence model. Simplifications include a uniform applied surface heat flux and a one-dimensional radial volumetric neutron heating profile. Constant material properties were used for the F82H reduced-activation ferritic martensitic (RAFM) steel walls, SiC flow channel inserts, and the PbLi breeder. Ideal gas behavior was assumed for the helium, which includes compressibility. Helium mass flows of 54 kg/s at 8 MPa and PbLi flows of 3 kg/s at 101 kPa supply the sector, both at an inlet temperature of 350°C. This early model is not optimized; however, it reveals important features not obvious in a conglomeration of smaller independent models. For example, all the manifolding was included to evaluate flow distributions throughout the full component. Submodels were only used to obtain the convective heat transfer coefficients (HTCs) inside the helium first-wall channels equipped with enhancement vanes that allow the first wall to handle 0.8 MW/m2 of plasma heat flux with the aim of keeping bulk RAFM steel temperatures near the creep-fatigue limit of 550°C. Average HTCs obtained from these detailed submodels were then used in the large model to predict thermal performance without incurring the meshing overhead from the thousands of internal vanes. Although much progress was made, initial results indicate that more must be done to further reduce hot spots on the first wall, minimize pressure drops, and provide optimal flow distributions.

Modeling of Transport Processes in Liquid-Metal Fusion Blankets: Past, Present, and Future

The successful development of robust breeding blanket systems will strongly rely on computational tools for predicting the complex behavior of the electrically conducting liquid-metal (LM) breeder flowing in the complex-shaped blanket ducts in the presence of a strong plasma-confining magnetic field, volumetric heating, and tritium generation. Associated transport processes involve magnetohydrodynamic (MHD) flows, heat transfer, corrosion, and tritium transport. This paper is an overview of past and present efforts in the development, application, and verification and validation (V&V) of such computational tools. As a result of the ongoing campaign on V&V of computer codes for LM blankets, the international fusion community has identified several candidates that promise to become real blanket design and analysis tools in the near future. Among them are HIMAG, MHD-UCAS, COMSOL Multiphysics, ANSYS FLUENT, ANSYS CFX, and OpenFOAM. The progress, over the last decade, in the application of such codes in blanket studies is tremendous. This is illustrated with two examples for a dual-coolant lead-lithium (DCLL) blanket: (1) integrated computer modeling for the recently designed DCLL blanket in the United States and (2) application of the code MHD-UCAS to the analysis of PbLi flows and heat transfer in a generic DCLL blanket prototype at high Hartmann (Ha ~ 104) and Grashof numbers (Gr ~ 1012). This paper also presents an approach to the development of a new integrated computational tool called the virtual dual-coolant lead-lithium (VDCLL) blanket, which elaborates the existing U.S. MHD code HIMAG.

Status and initial experiments of DRAGON-V facility for lithium-lead blanket technologies of hydrogen fusion reactors

A dual-coolant integrated experimental facility named DRAGON-V has been developed at the Institute of Nuclear Energy Safety Technology, Hefei Institute of Physical Science, Chinese Academy of Sciences, for the key technology research and performance evaluation of candidate liquid lithium-lead (PbLi) blanket of hydrogen fusion reactors. The loop is composed of a material test sub-loop and thermal-hydraulic test sub-loop, the design parameters are PbLi inventory 20 tons, PbLi temperature up to 550 °C, the maximum PbLi flow rate up to 40 kg/s. A novel cold trap system is designed to remove the suspended and crystalized impurities in PbLi fluid with three cooling zones and cross row arrangement of rod bundle filter elements. The paper describes the loop itself and its major components, initial loop testing, flow and measurement diagnostics and current experiments. The obtained test results of the loop and its components have demonstrated that the new facility is fully functioning and ready for experimental studies of material corrosion with/without a magnetic field, magnetohydrodynamic (MHD) effect, purification, heat and mass transfer phenomena in PbLi flows and can also be used in mock-up testing in conditions relevant to fusion applications.

A duct-dimension-regulation approach for eliminating MHD PbLi flow reversal in buoyancy-opposed poloidal duct relevant for typical liquid breeder blanket designs

Lithium-lead (PbLi) flow plays the major roles: removing nuclear heating, breeding tritium and multiplying neutrons, in the appeared typical liquid breeder blanket designs for magnetically confined fusion reactors. Under the buoyancy effect caused by the volumetric nuclear heating with large gradient in the radial direction, flow reversals can be generated in the magnetohydrodynamic (MHD) PbLi flow in the poloidal downward-flow duct(s) of such blanket designs, which may import negative consequences to the functionality of the breeder blanket. Based on a theory regarding mixed convection in fully developed MHD duct flows developed by Smolentsev et al. (Smolentsev, Moreau & Abdou, Characterization of key magnetohydrodynamic phenomena in PbLi flows for the US DCLL blanket, Fusion Engineering and Design 83, 771-783, 2008), this study attempts to further quantitatively analyze the above-mentioned flow-reversal issues, and in the meantime to develop an approach to eliminate the reverse flow regime by regulation of the duct dimensions. Numerical simulations are performed for buoyancy-opposed MHD duct flows of PbLi in order to demonstrate the effectiveness of the proposed duct-dimension-regulation approach on eliminating the occurrence of reverse flows. It is found that, in the reverse flow regime, the reversal structures travel to the downstream from their onset locations at a speed essentially equal to the mean flow velocity in the bulk; the reverse flow regime can be effectively eliminated by regulating the duct dimensions. Comprehensive discussions about the reverse flow related issues in the DCLL type blanket are then stressed.

The Source Permeator System and Tritium Transport in the TEX PbLi Loop

Permeation is investigated for the introduction of hydrogen isotopes into lead lithium (PbLi) for the Tritium Extraction eXperiment (TEX). TEX is a forced-convection PbLi loop under construction at Idaho National Laboratory that will test the vacuum permeator (VP) method of tritium extraction from PbLi. The source permeator (SP) delivers atomic hydrogen (H, D, and T) from a gas-phase reservoir into the PbLi via a permeable dense metal membrane. A modular system and a fixed SP system are presented. In the modular design, PbLi flows through the inside of a tubular membrane, and gas-phase hydrogen is introduced on the outside of the membrane. Atomic hydrogen permeates radially inward through the membrane into the PbLi. In the fixed design, PbLi flows into an expansion chamber with closed-ended tubular membranes inserted. Gas-phase hydrogen is introduced on the inside of the closed-ended membranes, and atomic hydrogen permeates radially outward into the flowing PbLi. Hydrogen transport models based on steady-state mass transport through PbLi and permeation through the metal membrane were developed to assess the operation of the SP relative to experimental variables and to allow understanding of uncertain parameter effects, such as PbLi hydrogen transport properties and the effective hydrogen permeability of the VP. This modeling effort considers iron as the SP material and vanadium as the VP material.

Hydrodynamics and Electrical Insulation of Pbli Flow with Sic Flow Channel Inserts in a Strong Magnetic Field

Hydrodynamics and Electrical Insulation of Pbli Flow with Sic Flow Channel Inserts in a Strong Magnetic Field

Thermal Hydraulic Analysis on the Water Lead Lithium Cooled Blanket for CFETR

A new type of Water Lead Lithium Cooled (WLLC) blanket that adopts the modular design scheme, water cooling the structure components, liquid PbLi as breeder and coolant, and SiC as the thermal insulator between PbLi and structures is under development as a candidate blanket concept for the Chinese Fusion Engineering Test Reactor (CFETR). Based on a poloidal-radial slice model, thermal hydraulic analysis is performed for this blanket to validate the feasibility of design goals. Results show that the present design can achieve the outlet temperature in the range of 600–700 °C, with all the material temperatures safely below the upper limits. A series of sensitivity analyses are also carried out. It indicates that the thermal conductivity (TC) of SiC would have a significant influence on the temperature field, streamlines and pressure drop; that is, lower TC of SiC can maintain the temperature of PbLi at a high level, and induce an increased number of vortices in the liquid PbLi flow as well as a larger pressure drop. On this basis, the joint effects of the TC of SiC and inlet velocity on the performance of blanket thermal hydraulics are analyzed, then the so-called “attainable region” is proposed. Finally, optimization design studies are carried out by decreasing the width of the front channel. Comparison results show that the present design is the most reasonable.

Magneto-Convective Analyses of the PbLi Flow for the EU-WCLL Fusion Breeding Blanket

The Water Cooled Lithium Lead (WCLL) breeding blanket is one of the driver blanket concepts under development for the European Demonstration Reactor (DEMO). The majority of the blanket volume is occupied by flowing PbLi at eutectic composition. This liquid metal flow is subdued to high fluxes of particles coming from the plasma which are translated into a high non-homogeneous heat volumetric source inside the fluid. The heat is removed from the PbLi thanks to several water tubes immersed in the metal. The dynamics of the PbLi is heavily affected by the heat source and by the position of the tubes. Moreover, the conducting fluid is electrically coupled with the intense magnetic field used for the plasma confinement. As a result, the PbLi flow is strongly affected by the Magnetohydrodynamics (MHD) forces. In the WCLL, the MHD and convective interactions are expected to be comparable. Therefore, the PbLi dynamics and consequently the heat transfer between the liquid metal and the water coolant will be ruled by the magneto-convective phenomenon. This work presents 3D computational analyses of the PbLi flow in the frontal region of the WCLL design. The simulations include the combined effect of MHD forces caused by the magnetic field and the buoyancy interaction created by the temperature distribution. The latter is determined by the PbLi dynamics, the volumetric heat source and the position of the water tubes. Simulations have allowed computing the heat transfer between the PbLi and the water tubes. Nusselt and Grashof numbers have been obtained in the different regions of the system.

The influence of MHD boundary layers on tritium permeation in PbLi flows for fusion breeding blankets

In PbLi based breeding blanket concepts, tritium is produced inside the liquid metal and drag out of the reactor by the liquid metal flow. However, undesired permeation through the channels and pipes walls occurs spontaneously since tritium naturally diffuses in the opposite direction of the concentration gradient. This way tritium can reach the blanket coolant circuit or even the exterior with an impact on the tritium self-sustainability and the safety of the plant. Similarly to heat transfer processes, permeation through the walls in the interface between the flow and the steel is mostly affected by the dynamics of the boundary layers. This is ruled by the electrical coupling between the moving conductor and the conducting walls as a result of the Magnetohydrodynamics (MHD) interactions which dominate the flow dynamics. In this work, the connection between the MHD forces and tritium transport is numerically studied using the simulation platform ANSYS-Fluent. The velocity profiles of a PbLi test channel have been firstly computed in a wide range of Hartmann numbers from 102 to 104. These velocity profiles are then applied to a 3D tritium transport model developed with the customization capabilities of the same platform. A series of tritium transport simulations are carried out considering different permeation regimes: surface-limited, diffusion-limited and intermediate regimes. The development of the concentration boundary layers along the channel is studied in different permeation regimes, magnetic fields and velocity fields. This has allowed correlating the Sherwood number (Sh) with the Hartmann (Ha), Reynolds (Re) and permeation numbers (W).

Status and Progress of Liquid Metal Thermofluids Modeling for the U.S. Fusion Nuclear Science Facility

At present, the U.S. Fusion Engineering Systems Study (FESS) considers several cooling/breeding concepts that utilize flowing liquid metals (LMs), Li, or eutectic PbLi alloy as working fluids for implementation of these concepts in the Fusion Nuclear Science Facility (FNSF). In this paper, we review recent modeling activities aimed at the investigation of LM flows and heat transfer relevant to the FESS-FNSF program. In particular, considerations are given to (1) development and validation & verification of computational magnetohydrodynamic (MHD) codes, (2) characterization of critical coupled MHD/heat transfer phenomena, and (3) design and analysis for selected LM applications in the FNSF. Under these three research thrusts, the reviewed topics including the MHD code HyPerComp Incompressible MHD solver for Arbitrary Geometries (HIMAG), MHD mixed-convection flows, MHD pressure drop in the blanket inlet/outlet manifolds, PbLi flows in a thermal convection loop, MHD PbLi flows in a dual-coolant lead-lithium blanket prototype, and a design window for a flowing Li divertor with He-cooled substrate.

Numerical study of 3D MHD flow of Pb-Li liquid metal in a rectangular U-bend

The eutectic Pb-Li alloy has been chosen as a candidate material for the liquid breeder blanket, as it offers a unique combination of tritium breeding neutron absorbing and neutron multiplying capabilities. In fusion blanket, molten Pb-Li moves under plasma confining toroidal magnetic field, producing an induced electric current inside the liquid metal due to the interaction of the moving fluid with the magnetic field. The coupling of induced electric current and magnetic field generates a Lorentz force opposite to the flow direction, and this in turn, modifies the flow profile. The experimental and numerical flow studies of liquid Pb-Li under transverse magnetic field are of great importance, as it directly impacts the blanket performance. A liquid Lead Lithium MHD loop is being developed at Institute for Plasma Research (IPR), Gujarat, India for isothermal and thermo-fluid MHD studies in blanket relevant flow geometries such as sudden expansion/contraction, coupled channels and multiple bends. A test mockup with rectangular flow cross-section and having bends perpendicular to the magnetic field has been fabricated. A 3D MHD flow analysis has been performed numerically for the test mock up at a magnetic field of 1.4T (Hartmann number of order of 1500). The fabrication details of test mockup and the results of the Pb-Li flow analysis are presented and discussed. The flow field and pressure distribution in the presence and absence of the magnetic field are also compared. The existence of recirculation zones and their redistribution in the presence of magnetic field are discussed.

Pressure drop in a prototypical 3D magnetohydrodynamic flow across contraction of a fusion blanket manifold

ABSTRACT Predicting 3D magnetohydrodynamic (MHD) pressure losses associated with liquid metal flows in complex geometry ducts is required to design breeding blankets for fusion reactors. Of such components, manifolds exhibit major pressure losses. Recent correlations [T. Rhodeset al. Magnetohydrodynamic pressure drop and flow balancing of liquid metal flow in a prototypic fusion blanket manifold. Phys. Fluids. 2018; 30: 057101.] demonstrate promise for predicting pressure drops in electrically insulated inlet manifolds. In the present work, the extend to which these correlations can be applied to outlet manifolds, which feature sudden contractions, is investigated in both viscous-electromagnetic (VE) and inertial-electromagnetic (IE) regimes for Reynolds numbers 50 < Re < 1500, Hartmann numbers 2500 < Ha < 5475, and expansion/contraction ratio 10. Numerical computations have shown that the MHD pressure drops in the eutectic lead-lithium (PbLi) flows in contractions are almost identical to those in the flows featuring expansion with slightly higher magnitudes in the contraction cases. The small discrepancy in the MHD pressure drop between contractions and expansions (<8%) suggests that the earlier obtained correlations for the 3D MHD pressure drop in a duct flow with a sudden expansion can also be applied to flows with a sudden contraction.