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Boundary Layer Analysis of Two-Phase (Liquid-Gas) Flow Over a Circular Cylinder and Oscillating Flat Plate

Report Number: ARL 66-0010 Part IV
Author: Goldstein, M. E.
Author: Yang, Wen-Jei
Author: Clark, J. A.
Corporate Author: University of Michigan
Laboratory: Aerospace Research Laboratories
Date of Publication: 1966-01
Pages: 335
Contract: AF 33(657)-8368
Project: 7063
AD Number: AD0639217

An analysis is carried out of a two phase (gas/liquid) flow over a circular cylinder and over an oscillating flat plate. The flow is assumed two dimensional and gravity, vaporization of the liquid phase, and compressibility are ignored. The liquid is assumed to be in the form of small drops far upstream from the body. The liquid film which forms on the surface of the body due to drop impingement is analyzed extensively. In the case of the cylinder the analysis is started from the full incompressible Navier-Stokes and energy equations in the film which are simplified by using dimensional arguments. The order of magnitude of the physical properties of the fluids is taken to be those of air/water mixtures. The analysis is careried out for two ranges of a parameter appearing in the problem. For low values of the parameter the liquid drop trajectories deviate appreciably from straight lines and are obtained numerically. For the flat plate the boundary layer approximations are assumed to hold a priori in the film. The plate is taken to be oscillating sinusoidally in its plane with small amplitude and small frequency; and the drops are assumed to move in straight lines. After appropriate changes of variable the solutions to the governing equations and boundary conditions are carried out by a series expansion technique which results in a series of ordinary differential equations which have been solved numerically on a 7090 computer. The solutions are used to calculate velocity and temperature profiles in the film and also such physical quantities as local film thickness, local Nusselt Number, and local skin friction. The analysis shows that in general there is a significant increase in heat transfer as well as skin friction over what would be obtained from a single component gas flow. In the case of the flat plate only a very small permanent change in the heat transfer was found due to the oscillations. In the case of the cylinder a peaking in the heat transfer, film thickness and skin friction was found with respect to the parameter E squared (the product of the volume fraction of the liquid in the free stream, squared, and the diameter Reynolds number based on liquid properties). The peaking occurs at a value of this parameter of about unity. The theoretical prediction compares favorably with the experimental results of Acrivos et al. (ARL-64-116).

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