Direct numerical simulations of turbulent pipe flow in a transverse magnetic field

Direct numerical simulations of turbulent pipe flow have been carried out in a constant transverse magnetic field. The Reynolds number based on bulk velocity and pipe diameter is set to Re_b = 5300 for three Hartmann numbers, Ha, 5, 10 and 20. The skin friction velocity, velocity profiles, turbulent intensities and turbulent kinetic energy budget along the circumferential direction of the pipe have been obtained and a turbulent streaky structure has been investigated via computational flow visualization. The skin friction coefficient decreases in cases of Ha = 5 and 10; however, it increases in case of Ha = 20. The velocity profile becomes more rounded in the near-wall region at φ = π/2, and the velocity acceleration appears at the top of the pipe (φ = 0), especially for Ha = 20. This clearly shows that the 'Hartmann effect' mainly occurs at φ = 0. It is also shown that all turbulent intensities and turbulent kinetic energy budget decrease at φ = 0 and remain at other positions (φ = π /4, π /2). The behaviour of drag and turbulent statistics is associated with the turbulent streaky structure which disappears at φ = 0 and still remains at φ = π /2. This means that it is necessary to consider some turbulent heat transfer and thermal mixing problems in the circumferential direction of the turbulent pipe flow in a transverse magnetic field for the design of MHD facilities.