The multiple-radial system of cooling large turbo-generators

The paper discusses the theoretical basis of a special turbo-generator ventilation system, in which the cooling air divides into several branches, and passes through the stator core radially in and out. An extended series of experiments on a full-size model, embodying this system, has lately been carried out by the Westinghouse Co. The tests are described in a paper by C. J. Fechheimer under the Title: “Experimental Study of Ventilation of Turbo-Alternators.” The fundamental questions in regard to the flow of air in any ventilation system are: 1. How high pressure is required to force through a certain volume of air per unit time? 2. How will the air distribute, axially and radially, in the different intake and discharge vents? 3. What will be the “balanced stale” of flow, if several branches of air meet and divide in a tube, the intake and discharge taking place normal to the walls of the tube? These questions are given a thorough analysis, under certain simplifying assumptions, and it is shown that 1. The total pressure required for a certain volume of air per unit time is expressible by means of hyperbolic and trigonometric cotangents of a certain argument, which contains the geometrical dimensions of the air-circuit. 2. The air is distributed according to a simple hyperbolic or trigonometric sine-law. 3. The “balanced state” depends on the solution of a system of simultaneous transcendental equations. A method of solution is outlined, which is applicable for such cases where the arguments are small. In such cases the transcendental equations reduce to simple algebraic equations. A numerical example is finally worked out in order to show the application of the derived formulas.