Choking Flow

Figure 1.2:

The schematic of deLavel's turbine after Stodola, Steam and Gas Turbine

The choking problem is almost unique to gas dynamics and has many different forms. Choking wasn't clearly to be observed, even when researcher stumbled over it. No one was looking for or expecting the choking to occur, and when it was found the significance of the choking phenomenon was not clear. The first experimental choking phenomenon was discovered by Fliegner's experiments which were conducted some time in the middle of 186x^1.29on air flow through a converging nozzle. As a result deLavel's nozzle was invented by Carl Gustaf Patrik de Laval in 1882 and first successful operation by another inventor (Curtis) 1896 used in steam turbine. Yet, there was no realization that the flow is choked just that the flow moves faster than speed of sound.

The introduction of the steam engine and other thermodynamics cycles led to the choking problem. The problem was introduced because people wanted to increase the output of the Engine by increasing the flames (larger heat transfer or larger energy) which failed, leading to the study and development of Rayleigh flow. According the thermodynamics theory (various cycles) the larger heat supply for a given temperature difference (larger higher temperature) the larger the output, but after a certain point it did matter (because the steam was choked). The first to discover (try to explain) the choking phenomenon was Rayleigh^1.30.

After the introduction of the deLavel's converging-diverging nozzle theoretical work was started by Zeuner^1.31. Later continue by Prandtl's group^1.32 starting 1904. In 1908 Meyer has extend this work to make two dimensional calculations^1.33. Experimental work by Parenty^1.34 and others measured the pressure along the converging-diverging nozzle.

It was commonly believed^1.35 that the choking occurs only at M=1 . The first one to analyzed that choking occurs at $1/\sqrt{k}$ for isothermal flow was Shapiro (195x). It is so strange that a giant like Shapiro did not realize his model on isothermal contradict his conclusion from his own famous paper. Later Romer at el extended it to isothermal variable area flow (1955). In this book, this author adapts E.R.G. Ecert's idea of dimensionless parameters control which determines where the reality lay between the two extremes. Recently this concept was proposed (not explicitly) by Dutton and Converdill (1997)^1.36. Namely, in many cases the reality is somewhere between the adiabatic and the isothermal flow. The actual results will be determined by the modified Eckert number to which model they are closer.

Figure: The measured pressure in a nozzle taken from Stodola 1927 Steam and Gas Turbines