UNSTEADY, VISCOUS, CIRCULAR FLOW. PART I. THE LINE IMPULSE OF ANGULAR MOMENTUM.
CONVAIR SCIENTIFIC RESEARCH LAB SAN DIEGO CALIF
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The report discusses the transfer of energy between fluid elements due to viscous work and to heat conduction within but not across the fluid boundaries. The particular class of problems studied are unsteady, two-dimensional flows with circular streamlines. The work was originally motivated by a desire to understand the temperature separation phenomenon exhibited by the Ranque-Hilsch vortex tube. The investigation is divided into three parts. In Part I the energy field is an infinite fluid associated with the decay of what will be defined as a line impulse of angular momentum is considered. The flows of both a liquid and of a gas in the limit of Mach number equal to zero are studied, and solutions, in closed form, are obtained and compared. In Part II the corresponding flows in a cylinder of finite radius are considered. In these cases it is necessary to resort to numerical integration to obtain the desired solutions of the energy equation. In Part III a new model for the flow in a vortex tube is proposed. Using the methods developed in Part II, velocity and energy profiles are calculated and compared with previously published measurements. Some new experimental work based upon the proposed flow model is also presented. Author
- Fluid Mechanics