MAGNETOHYDRODYNAMIC STABILITY OF CURVED VISCOUS FLOWS. Technical Report II-29
The stability of viscous flow of an electrically conducting fluid between coaxial cylinders in an external magnetic field was investigated for an arbitrary angular velocity . distribution. The cylinder walls were assumed to be nonconducting and the magnetic field had either an axial or radial orientation. Applying the method of small disturbances, the problem was reduced to an eighth order eigenvalue equation, whose solution yielded a secular relation for three dimensionless parameters (eigenvalues) representing the magnitude of the angular velocity, the wave number of the disturbance, and the magnetic field at the onset of instability. The mathematical difficulty encountered in solving the eighth order differential equation directly was avoided by applying a modified Galerkin method to an equivalent set of three simultaneous equations of lower order. Such a procedure yielded very simple polynomial expressions for the curves of neutral stability. The eigenvalue equations were solved and are discussed in detail for the velocity distributions corresponding to Couette and Poiseuille flow in an axial magnetic field and Hartmann flow in a radial field. It was found that in all cases the magnetic field hinders the onset of instability. (auth)
- Research Organization:
- Princeton Univ., N.J.
- NSA Number:
- NSA-16-008261
- OSTI ID:
- 4801530
- Report Number(s):
- NP-11269
- Country of Publication:
- United States
- Language:
- English
Similar Records
Linear and nonlinear stability of unsteady circular couette flow
A THEORETICAL INVESTIGATION OF ANNULAR MAGNETOHYDRODYNAMIC FLOW WITH A MOVING BOUNDARY