Bj. Boersma et Ftm. Nieuwstadt, On the electric potential induced by a homogeneous magnetic field in a turbulent pipe flow, FLOW TURB C, 62(1), 1999, pp. 29-51
In this paper we study a turbulent pipe flow of a weakly electrical conduct
ing fluid subjected to a homogeneous magnetic field which is applied perpen
dicular to the flow. This configuration forms the basis of a so-called elec
tromagnetic induction flow meter. When the Hartmann number is small so that
modification of flow by the Lorenz force can be neglected, the influence o
f the magnetic field results only in a spatially and temporally varying ele
ctric potential. The magnitude of the potential difference across the pipe
is then proportional to the flow rate and this constitutes the principle of
the flow meter. In this study the flow and electric potential are computed
with help of a numerical flow simulation called Large-Eddy Simulation (LES
) to which we have added an equation for the electrical potential. The resu
lts of the LES have been compared with experiments in which the electric po
tential is measured as a function of time at several positions on the circu
mference of the pipe. Both the experimental and numerical results for the m
ean potential at the pipe wall agree very well with an exact solution that
can be obtained in this particular case of a homogeneous magnetic field. Fu
rthermore, it is found that fluctuations in the electric potential due to t
he turbulence, are small compared to the velocity fluctuations. Based on th
e results we conclude that electrical-magnetic effects in pipe flow can be
accurately computed with LES.