Success by this cycle of operations requires (1) A rotary or turbine compressor of high relative efficiency (2) An expanding nozzle which shall insure that free expansion is quantitatively equivalent to adiabatic expansion behind a piston. (3) A rotating turbine of such construction as to secure a very high efficiency of kinetic energy of the moving gas into effective work available at the turbine shaft.
Assuming air to be the working fluid, and the specific heat to be constant through the temperature range, it is easy to calculate the efficiency of the Joule or Brayton cycle, that these operations in effect represent. It would be useless to attempt to work a turbine at a pressure so low as to be relatively inefficient compared with the gas-engine, so I have chosen a Joule cycle of (say) 48 per cent ideal efficiency, which in a cylinder gas-engine would probably give in practice about 30 percent, indicated efficiency. For the ideal efficiency the pressure of compression would require to be 141 lbs. per square inch absolute. To give power with a reasonably small pump, I shall assume a maximum temperature of 1700° C. - that is, assuming a perfect compressor and a perfect nozzle expander, the temper-ture would only fall from 1700° C. to 750 C. Plainly, this temperature would be too high for a Laval disc with blades. In order to get a reasonable temperature in the combustion chamber, no higher than 1000° C; and this would bring down the temperature after complete expansion to about 500° C, which, no doubt, steel turbiue blades can be expected to stand for some considerable time.
With these assumptions, however, the gas-turbine would not be very economical as compared with cylinder engines, even assuming all difficulties overcome. The theoretical and practical difficulties, however, are very serious indeed. To begin with the question of an efficient air-compressor, I am not aware of any turbine compressor capable of compressing up to 140 pounds, absolute from atmosphere from anything like 60 per cent, efficiency. Before success could be attained, this efficiency of compression, so far as the diagram is concerned, should be at least 90 per cent in order to allow for unavoidable mechanical and other losses in the subsequent processes. It has, it is true, been proposed to substitute cylinder compressors operated from the turbine, instead of turbine compressors; but this, it appears to me, would be equivalent to abandoning at once all the advantages of the turbine principle. If reciprocating cylinders are to be used for compressing, there is no objection to using them also for expanding. No gas turbine with cylinder compressors could, in my view, succeed.
Assuming, however, even 90 per cent efficiency from a turbine compressor, and assuming that, we have a compressed gaseous mixture burning freely in the •combustion chamber at the desired pressure and temperature, we have yet to face the problem of the expanding nozzle. It is always assumed that, with the use of an expanding nozzle, temperature drop can be as certainly attained as with an expanding piston in a cylinder. This, it seems to me, has by no means been proved.
You will all recollect Dr. Soule's famous experiment with two vessels immersed in water and connected together by a pipe having a stop-cock upon it. Air was compressed into one of the vessels, the water round ' the vessels stirred and equilibrium obtained, while the other vessel was rendered as vacuous as possible, and it was then found that, when the water was stirred again no disturbance of the equilibrium ensued. This, of course, meant that though heat was lost in the one vessel - giving velocity to the gases - it was gained in the other by the impact of the gases against the walls.
Joule modified this experiment by placing the two air-vessels in separate water containers. He then found that the temperature of the one dropped, due to expansion, but temperature of the other rose as much as the first dropped. Apply this experiment to reasoning on the behavior of the flame in an expanding nozzle. Assume the two vessels to be connected by a Laval nozzle, and assume that while in the nozzle the gases experienced the full temperature fall due to ad-iabatic expansion. Immediately, however, on contact with the walls of the second vessel, the velocity of the particles would be stopped, and the temperature would be restored to a point somewhat above the original temperature - that is, the mass of expanding flame in the pressure vessel would gain heat by the amount the first vessel lost. This is the result of the final process. It will be easily recognized that to obtain sufficient temperature drop in an expanding nozzle, necessitates the practical absence of turbulent motion of every kind - that is, to expand adiabetically, the jet must be so constructed that there is an absolutely smooth flow from high pressure to low, and no impact or loss of velocity from any cause whatever. So far as I understand expanding jets, no adiabatic expansion so perfect as this has ever been obtained.
Assume, however-, that the efficiency of expansion in such a jet is (say) 90° per cent. We now come to the question of the efficiency of conversion by the turbine blades. In many calculations from diagrams, it is assumed that the efficiency of conversion of motion into work is practicaly perfect. This, however, is by no means the case in present turbines. Even the steamturbine, high as its efficiency is, compared with the reciprocating engine, has no very high efficiency of conversion in any of the forms of turbines that are at present on the market. That is, if we assume a mass of gas to exist in a compressed state in a reservoir, and we choose to expand this mass of gas in two ways - for the sake of comparison, (1) behind a piston, and (2) by means of a Laval jet and turbine - we shall find that the efficiency of conversion of the turbine, when once high velocity is attained, does not exceed 80 per cent. In this respect the efficiency of conversion of rotating turbine blades is inferior to that of a moving piston in a cylinder. The reason of this is obvious. It is impossible to so arrange the impact of a rapidly moving gas with a turbine blade or blades in such a manner as to entirely avoid any turbulent motion.