Study of coupling effects on the three-dimensional magnetohydrodynamic flows around single and tandem cylinders in duct

Abstract

This work focuses on magnetohydrodynamic (MHD) flow around either single or two identical tandem circular cylinders confined in a duct under external transverse magnetic field. The influences of transverse magnetic field, inlet velocity of conducting fluid, and the distance between two cylinders arranged along the flow direction on the flow modes, vortex shedding frequency, separation angle, and drag coefficient are investigated. The simulations are conducted with the Hartmann number Ha and Reynolds number Re and are varied from 0 to 1.35 and from 100 to 200, respectively. For the MHD flow around single cylinder, the map of flow instability is set up and the relation between critical Hartmann number Ha_cr and Re is concluded as ${\text{Ha}}_{\text{cr}}\sim {(\text{Re}-100)}^{2/3}.$ The coupling effect of geometry confinement and external transverse magnetic field can increase the separation angles and drag coefficients and decrease vortex shedding frequencies and lengths of reverse flow. For the tandem double cylinder cases, the spacing ratio between two cylinders L/d changes from 2 to 8. The boundary between steady regime and unsteady regime is described as, ${(\text{Re}/{\text{Ha}}^{0.5})}_{\text{cr}}\sim (L/d).$ The three wake patterns are found under various magnetic fields. The nonlinear and nonmonotonous characteristics of coupling effects of Ha, Re, and L/d are summarized. The physical mechanisms of influences of MHD flow field in gap region between tandem cylinders and the existence of upstream cylinder on flow instability and wake pattern are revealed. Finally, the critical conditions corresponding to the transition from steady flow to unsteady flow are achieved with formulas.

Keywords:

• Flow instabilities
• fluid flows
• magnetohydrodynamic (MHD)
• two tandem circular cylinders
• vortex dynamics

Disclosure statement

The authors have no conflicts to disclose.

Additional information

Funding

The authors gratefully acknowledge the support from NSFC (No. 52176089, No. 51776194), National Key Research and Development Program of China (No. 2017YFE0301300), and Fundamental Research Funds for Central University.