THE METHOD OF EQUIVALENT REPLACEMENTS APPLIED TO THE INVESTIGATION OF FORCE TRANSFER AND POWER EXCHANGE IN A STAGE OF A TURBOMACHINE

Abstract

An analysis of the complicated phenomenon of power transfer in a stage of a turbomachine is presented in this paper in the simplest manner by the introduction of an original concept of "An Equivalent Stream" and the connected "Mathematical Profile". This method of investigation is very useful in connection with the development of gas turbine units, having both compressor and turbine stages.There are two acknowledged theories on arising of force on blade, worked out by the great mathematicians Euler and Joukowskl who lived in different ages and had in mind different problems. Both the theories give the same results as regards the integral force on blade, derived by the help of Euler's equation. This paper is a further development of the scientific heritage of Euler and Joukowski. Here is explained as to how both the theories are not to be opposed in favour of one against the other. One of them throws light on some aspects and the other treats the other sides of the same phenomenon. The idea advanced is "any engineering method of design is a method of evaluation by means of replacement scheme of \phenomenon".The replacement scheme has to he as simple as possible and comprehensive.On the basis of Eukr's theory, supplemented and developed with ideas on equivalent stream and mathematical profile, it is proved that the method of velocity inangles is the method of hodographs. The very important rule of "the leading and lagging vectors" is formulated and all the possible types of motion of stream are classified and considered from the point of view of theoretical mechanics of equivalent stream.A general scheme of  development of mathematical profile is presented and ths gives the scope of enveloping all forms of skeleton of conceivable substantial blade profiles. The scheme is, thus, universal in character. It further characterises the gradual transition through "the mechanically transparent system", from field to field namely turbine regime to compressor regime, the two opposite manners of force interaction. The paper presents the manner of development of turbine profiles,-compress or profiles and their attendant characteristics.To explain the direct mechnnrsm of power interaction between flow and blades,the concept of "the indicated diagram" is iotroduced, based on the idea of "meanindicated pressure"' acting on the axial projected area of the blade. This idea connects a turbomachine with a  reciprocating engine and helps to simplify the method of experimental investigation of a turbomachine stage. Only the moment on the shaft, the inlet and exit total pressures, the total mass flow and the shaft speed are all the ones that are necessary unlike the existing and the commonly used practice of using a stationary system of blades to give data. The idea suggests extraction of simpler experimental data from a dyumic sel-up, the real approach to the actualphenomena, to evaluate the characteristics of the profiles used.One of the basic ideas of the paper is that both the theories of Euler and Joukowski supplement each other covering different aspects of Lhe same question and cannot avoid each other, being only a resulting simphfied method 01 evaluating the integral force arising in the stage of a turbomachine. In the paper it is proved that Euler's theory can give very interesting rcsults by the new concept described.The idea of "indicated diagram" has to be considered as a further development of Joukowski's wing theory apphcable to turbomachines.