## Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions

## Abstract

The lid-driven cavity (LDC) flow is a canonic hydrodynamic problem. In this work, a 3D LDC flow of electrically conducting, incompressible fluid is studied numerically in the presence of a strong magnetic field, which is applied parallel to the lid plane and perpendicular to the direction of the lid motion. The cavity has electrically conducting walls of finite thickness and an infinitely thin moving lid. The problem is characterized by three dimensionless parameters: the Reynolds number ( *Re*), the Hartmann number ( *Ha*), and the magnetic Reynolds number ( *Re* _{m}). The primary research focus is on the effect of *Re* _{m}, which was changed in the study from *Re* _{m} $$\ll$$ 1 to the maximal *Re* _{m} = 2000 at which dynamo action may be expected, while *Ha* = 100 and *Re* = 2000. The computational approach is based on the utilization of far-field magnetic boundary conditions by solving the full magnetohydrodynamic (MHD) flow problem at finite *Re* _{m} for a multi-material domain composed of the inner conducting liquid, conducting walls, and sufficiently large insulating outer domain called “vacuum” (the induced magnetic field vanishes at the vacuum boundaries) using a fractional-step method. Lastly, the computed results show many interesting features with regard to the effect of *Re* _{m} on the MHD boundary layer and the bulk flow, generation of a magnetic field and its penetration into vacuum, energy balance, tendency of the magnetic field to become frozen in the fluid and associated magnetic flux expulsion, transition to unsteady flows, and self-excitation of the magnetic field and the associated dynamo-type action at high *Re* _{m}

- Authors:

- Univ. of California, Los Angeles, CA (United States)

- Publication Date:

- Research Org.:
- Univ. of California, Los Angeles, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- OSTI Identifier:
- 1540219

- Alternate Identifier(s):
- OSTI ID: 1457094

- Grant/Contract Number:
- FG02-86ER52123

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Fluids

- Additional Journal Information:
- Journal Volume: 30; Journal Issue: 6; Journal ID: ISSN 1070-6631

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Kawczynski, Charles, Smolentsev, Sergey, and Abdou, Mohamed. Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions. United States: N. p., 2018.
Web. doi:10.1063/1.5036775.
```

```
Kawczynski, Charles, Smolentsev, Sergey, & Abdou, Mohamed. Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions. United States. doi:10.1063/1.5036775.
```

```
Kawczynski, Charles, Smolentsev, Sergey, and Abdou, Mohamed. Mon .
"Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions". United States. doi:10.1063/1.5036775. https://www.osti.gov/servlets/purl/1540219.
```

```
@article{osti_1540219,
```

title = {Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions},

author = {Kawczynski, Charles and Smolentsev, Sergey and Abdou, Mohamed},

abstractNote = {The lid-driven cavity (LDC) flow is a canonic hydrodynamic problem. In this work, a 3D LDC flow of electrically conducting, incompressible fluid is studied numerically in the presence of a strong magnetic field, which is applied parallel to the lid plane and perpendicular to the direction of the lid motion. The cavity has electrically conducting walls of finite thickness and an infinitely thin moving lid. The problem is characterized by three dimensionless parameters: the Reynolds number (Re), the Hartmann number (Ha), and the magnetic Reynolds number (Rem). The primary research focus is on the effect of Rem, which was changed in the study from Rem $\ll$ 1 to the maximal Rem = 2000 at which dynamo action may be expected, while Ha = 100 and Re = 2000. The computational approach is based on the utilization of far-field magnetic boundary conditions by solving the full magnetohydrodynamic (MHD) flow problem at finite Rem for a multi-material domain composed of the inner conducting liquid, conducting walls, and sufficiently large insulating outer domain called “vacuum” (the induced magnetic field vanishes at the vacuum boundaries) using a fractional-step method. Lastly, the computed results show many interesting features with regard to the effect of Rem on the MHD boundary layer and the bulk flow, generation of a magnetic field and its penetration into vacuum, energy balance, tendency of the magnetic field to become frozen in the fluid and associated magnetic flux expulsion, transition to unsteady flows, and self-excitation of the magnetic field and the associated dynamo-type action at high Rem},

doi = {10.1063/1.5036775},

journal = {Physics of Fluids},

number = 6,

volume = 30,

place = {United States},

year = {2018},

month = {6}

}