Patterned Turbulence in Liquid Metal Flow: Computational Reconstruction of the Hartmann Experiment

We present results of a numerical analysis of Hartmann’s historical experiments on flows of mercury in pipes and ducts under the influence of magnetic fields. The computed critical parameters for the laminar-turbulent transition as well as the friction coefficients are in excellent agreement with Hartmann’s data. The simulations provide a first detailed view of the flow structures that are experimentally inaccessible. Novel flow regimes with localized turbulent spots near the sidewalls parallel to the magnetic field and otherwise laminar flow are discovered. We finally suggest how these predictions can be tested in a transparent fluid using optical flow measurement.

Figure 1

Friction factor $C_f$ as obtained in our simulations and compared to Hartmann’s data recalculated from Ref. 2.

Figure 2

TKE visualized in the flow domains for (a) pipe at $L_x=80R$, $\mathrm{Ha}=22$; (b) duct at $L_x=32\pi$, $\mathrm{Ha}=22$; (c) duct at $L_x=32\pi$, $\mathrm{Ha}=25$. Isosurfaces corresponding to 2% of the maximum are shown. Insets present TKE distributions in selected cross sections. The isolevels are the same in all insets.

Figure 3

Two regimes with different puff patterns in duct at $L_x=64\pi$, $\mathrm{Ha}=25$. Integrated TKE for east ($E_E$, lower curves) and west ($E_W$, upper curves) sides is shown.

Figure 4

Evolution of turbulent spots in ducts shown as spatiotemporal distribution of integrated TKE $E(t,x)$: (a) $E_W$ at $L_x=64\pi$, $\mathrm{Ha}=25$ [see Fig. 3a]; (b) $E_E$ at $L_x=32\pi$, $\mathrm{Ha}=25$ [see Fig. 2c]; (c) $E_E$ at $L_x=32\pi$, $\mathrm{Ha}=22$ [see Fig. 2b]; (d) $E_E$ in another run at $L_x=32\pi$, $\mathrm{Ha}=22$. Labels M and S mark the events of puff merging and splitting.