ON HYDRODYNAMIC STABILITY OF TWO-DIMENSIONAL UNSTEADY INCOMPRESSIBLE LAMINAR BOUNDARY LAYERS.
Abstract
A linearized hydrodynamic stability theory for unsteady incompressible laminar boundary layers over arbitrary cylinders is described. Criteria based on the instantaneous rate of change of the disturbance energy are introduced. In order to apply these criteria to a given unsteady laminar boundary-layer problem, it is necessary to have a complete knowledge of the instantaneous disturbance-amplitude functions. It is found that these disturbance-amplitude functions are governed by a partial differential equation, which can be solved by a numerical iteration scheme. Successive iterations are then obtained by solving an inhomogeneous ordinary differential equation repeatedly at the same time instants. Two numerical examples are calculated. One deals with unsteady flow over a flat plate when the free-stream, initially steady, undergoes a step-wise change in its velocity to one and one-half times of its original value. The second example treats an unsteady stagnation flow with its free-stream velocity, initially again steady, undergoing deceleration first and then changing to acceleration.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1964
- Accession Number
- AD0600102
Entities
People
- Kwang-tzu Yang
- Matthew D. Kelleher
Organizations
- University of Notre Dame