Laminar Flow Between Two Parallel Rotating Disks
OFFICE OF AEROSPACE RESEARCH ARLINGTON VA
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The viscous flow between two parallel disks rotating in the same direction with the same velocity is investigated. The fluid enters the space between the disks at a certain in radius in the radial direction. Because of the shear forces, it assumes a rotating motion with about the velocity of the disks. The centrifugal forces then build up a pressure increase in the radial direction. The arrangement corresponds to a centrifugal fluid pump, which may be advantageous if cavitation is a problem. The general equations of viscous flow are simplified by the assumption that the pressure difference normal to the disks is negligible boundary layer assumptions. One obtains a system of parabolic partial differential equations. For large radii the deviation from rigid body rotation with the angular velocity of the disks is small. The linearized equations which then result are solved analytically. The velocity profiles depend upon a parameter containing e kinematic viscosity, the angular velocity and the distance of the disks, but not he radius. The non-linearized parabolic differential equations are approximated by a difference scheme and solved numerically. The results are given in non-dimensional form with the entrance velocity and the distance of the disks as parameters. Furthermore, the efficiency of the pump is computed from the gain of the total pressure and the torque at the shaft of the rotating disks.
- Theoretical Mathematics
- Fluid Mechanics