Speaker
Description
The study of magnetohydrodynamic (MHD) flow is important in the application of the liquid metal blankets in thermal nuclear fusion reactors. Hunt presented an analytical solution of the conducting fluid flow in a rectangular duct under a uniform transverse magnetic field with insulating walls parallel to the magnetic field and thin walls with arbitrary conductivity perpendicular the magnetic field. The case is called Hunt’s case II, which is recommended as a benchmark to verify and validate MHD codes related to fusion applications. Hunt’s analytical solution is based on two dimensional fully developed laminar flow assumption, which means that the velocity vector has only flow direction component as a function of planar space. However, the transverse velocity component vertical to the streamwise and magnetic field direction in three dimensional numerical simulation increases with the increasing of the Reynolds number and redistributes the streamwise velocity even the flow is laminar.
Hunt’s case II with the same Hartmann number (Ha=500), wall conductance ratio (c=0.1) and wide range Reynolds number (2000≤Re≤10000) have been simulated using three dimensional MHD solver developed in OpenFOAM environment to investigate when the transverse velocity must be considered. The streamwise velocity and the pressure gradient obtained from numerical simulation are compared with Hunt’s analytical solutions, which are set as the standard results. If the relative difference of the maximum velocity or pressure gradient is more than 5%, it is defined that the two dimensional assumption breaks down. The results show that the relative difference of the velocity and the pressure gradient increases when Re≥4000. The relative difference of the velocity is 9.551% when Re=8000. The relative difference of the velocity and the pressure gradient is 14.152% and 6.229% respectively when Re=10000. Numerical simulation shows that the dimensionless transverse velocity normalized increases and rises from the order of 10^-5 to 10^-3 .
The effects of the Hartmann number on the transverse velocity has been investigated by simulating Hunt’s flow at Re=4000, C=0.1 and 50≤Ha≤1000. It shows that the relative difference of the maximum velocity is more than 20% when the Hartmann number is less than 100, which indicates that the dimensionless transverse velocity is the order of 10^-3.
Finally, the transverse velocity effect as a result of the wall conductance ratio is simulated. The difference of the pressure gradient is lower than 5% for c=0.01. When Re/Ha>12, the difference of the maximum velocity increases linearly with the Re/Ha increasing for any wall conductance ratio.
In conclusion, the comparison of the three dimensional numerical simulation and the two dimensional analytical solution of the Hunt’s case II shows that the transverse velocity is not negligible when Reynolds number is more than 4000. The transverse velocity is also influenced by the wall conductance ratio and the Hartmann numbers. As a result, if the dimensionless transverse velocity is over the order of 10^-3, the two dimensional assumption becomes invalid and the analytical solution is no longer suitable for high Reynolds number MHD duct flow validation.
Key words: Transverse velocity, Magnetohydrodynamic,Hunt’s flow, numerical simulation，three dimensional
| Eligible for student paper award? | Yes |
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