Numerical studies of axially symmetric motion of an incompressible viscous fluid between two concentric rotating spheres
The transient motion of a system consisting of an incompressible, Newtonian fluid in an annulus between two concentric, rotating, rigid spheres was studied. The primary purpose was to study the use of a numerical method for analyzing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly due to the action of prescribed torques. The problems considered included cases where: (a) one or both spheres rotate with prescribed constant angular velocities, and (b) one sphere rotates due to the action of an applied constant or impulsive torque. The coupled solid and fluid equations were solved numerically by employing the finite-difference technique. With the approach adopted, only the derivatives with respect to spatial variables were approximated with the use of the finite-difference formulae. The steady-state problem was also solved as a separate problem (for verification purposes), and results were compared to those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations that resulted from the steady-state problem and the Adams fourth-order predictor corrector method was employed to solve the ordinary differential equations for the transient problem.
- Research Organization:
- Marquette Univ., Milwaukee, WI (USA)
- OSTI ID:
- 5520601
- Country of Publication:
- United States
- Language:
- English
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