Chapter 3: Transonic Wind Tunnel Development (1940 -1950)
[62] More than 100 years before wind-tunnel choking became a prime problem of aeronautics, St. Venant and Wantzel derived the compressible flow relations revealing that the velocity in the throat of a channel (or empty test section of a wind tunnel) could not be increased indefinitely but rather was limited to sonic velocity, regardless of how high the driving pressure became (ref. 79). Speeds greater than Mach 1 could only be achieved by expanding the channel area downstream of the throat to accommodate the increased volume required by the supersonic flow. The first practical applications of these fundamental channel flow [63] relations to achieve supersonic velocities were in the converging-diverging nozzles of the deLaval steam turbines (ref. 80).
These inherent features and limitations of high-speed gas flow in channels did not in themselves mean that any particular regime of speeds was unattainable. Clearly, the speed in a conventional subsonic tunnel could be increased to Mach 1 in an empty throat section, and any desired supersonic speed could be obtained by converging-diverging nozzle shapes. The basic unknown factor in the twenties and thirties was the "choking" effect on the achievable speeds due to the presence of a test model.
It is interesting that Briggs and Dryden in their pioneering experimental work discussed in Chapter II avoided the choking problem by use of a free jet rather than a closed test section. This was done, however, not from any understanding or consideration of choking, but simply for reasons of expediency. It was necessary that their model and balance hardware be completely independent of the compressor equipment and easily inserted or removed. In their subsequent 1926 work in the 2-inch jet at Edgewood Arsenal they employed the first converging-diverging supersonic nozzle on record in American research, to obtain Mach 1.08 (fig. 10). But it is not clear that they understood the basic supersonic channel flow requirements; the reason given for the nozzle area expansion (ref. 13) was "to avoid pressure pulsations," and their nozzle area ratio corresponded to a theoretical Mach number of 1.25 instead of 1.08. (A listing of transonic test facilities capable of Mach 0.9 or higher is given in the Appendix.)
It remained for Jacobs and Stack in the NACA in-house tests of 1929 to demonstrate that, with a test model present, higher speeds could be reached with the open throat than with the closed throat. In fact, the natural expansion of the free boundary permitted sonic and low supersonic speeds in the open throat, although the flow was pulsating and nonuniform, and it was doubted that the near-sonic data were valid. Because of its potential speed advantage the open throat was modified and improved to the final configuration shown in fig. 11. In spite of its speed advantage, however, the open arrangement was abandoned, primarily because of flow asymmetry, pulsations, and large and indeterminate aerodynamic end effects where the test airfoils passed through....

photo of Edgewood Arsenal test area
[64] FIGURE 10.-The first American facility capable of very high subsonic and low supersonic speeds, Mach 0.95 and 1.08 Briggs' and Dryden's 2-inch jet at the Edgewood Arsenal, 1926. Jet is at the top of the pipe in the center. Test airfoil is seen rotated out of the jet; single pressure tube from airfoil attaches to manometer at right.

cross-sectional drawing of high-speed wind tunnel
[65] FIGURE 11.-The Langley 11-Inch High-Speed Tunnel with the open throat developed in 1930.

....the boundaries of the airstream. Nevertheless, these investigations of the open throat were by no means wasted effort. They demonstrated an approach in which choking due to the presence of large models did not occur, and this experience more than any other single factor encouraged Stack and his cohorts 15 years later to embark on the further developments which produced the transonic slotted tunnels. Stack often referred to this early work as the genesis of transonic facility development and said it had been set aside in 1930 because there was no need for it at that time after the decision to go ahead with the closed throat (ref. 81).

The 11-inch and 24-inch high-speed tunnels had sufficient power to reach the choked condition for all types of test models, and this condition is evident in some of the published results (ref. 18) where the drag [66] coefficient eventually rises vertically in plots against Mach number. Generally, however, such plots were arbitrarily terminated at Mach numbers .03 or so below choking because we knew that the choked data were not valid. Actually the term "choking" was seldom used then, and the phenomenon was not fully understood. Instead, we tended to think in terms of a large "constriction" or "blockage" effect by which the presence of the model increased the effective stream velocity above the values indicated by the tunnel calibration. Glauert and others had derived theoretical formulas applicable to low-speed tunnels for determining the blockage effect (ref. 82) ; however, the effect of compressibility was not known theoretically until the early forties (refs. 83, 84).
In the 8-foot high-speed tunnel an attempt was made in 1938 to determine the blockage corrections experimentally by comparing the pressure distributions on 0012 test airfoils of different chord with the low-speed distributions obtained from tests in the full-scale tunnel and from theory. The results were never published because of a number of uncertainties, but they were used to provide "corrected" data for some of the 8-foot tunnel investigations (ref. 85). These experimental blockage corrections tended to increase very rapidly at the higher speeds, and as choking was approached they became so large and doubtful that we arbitrarily terminated the data plots, omitting the points at the highest test speeds. The theoretical results that became available a few years later confirmed the rapid increase at the higher Mach numbers, and showed that there was no hope of "correcting" data taken in the choked condition.
In order to understand better the nature of the choking phenomena, a small water channel was set up at the 8-foot tunnel in 1940 (fig. 12). In this device the low-speed flow of a liquid such as water can be related to the high-speed compressible flow of a gas such as air. Developed carefully by W. J. Orlin, this little facility operating at about 3 feet per second, provided some interesting enlightenment on the process of choking, including flow visualization (ref. 86) which agreed, well with schfieren pictures taken in air.
By this time many different models had been tested in the 11-inch and 24-inch tunnels at speeds up to choking. R. W. Byrne was assigned the task of correlating the choking data. He found that the choking....

photo of water channel
[67] FIGURE 12.-Water channel used by the 8-foot tunnel group to investigate tunnel choking phenomena by means of the hydraulic analogy.

Mach number was a function primarily only of the maximum cross-sectional area of the test models; the shape of the models had only minor effects (ref. 87). Each test model in effect created a secondary throat whose area was less than that of the tunnel throat by the amount of the model's maximum cross-sectional area. Choking occurred when Mach 1 was reached in the secondary throat, and the choking Mach number in the tunnel throat could be calculated from simple one-dimensional flow relations for each size of test model. To attain a tunnel choking Mach number as high as 0.95, for example, required a test model cross-sectional area of only one-fifth of 1 percent of the tunnel throat area. This implied much smaller models than we had been using, but they were by no means out of the question for a tunnel of 8-foot throat size. For example, a typical wing of 4-inch mean chord and 36-inch span with 10-percent-thick sections, having the same Reynolds [68] number as the airfoils used in the high-speed airfoil tunnels, would have a choking speed of about Mach 0.96 in the 8-foot tunnel. The possibilities and requirements for major reductions in the "choked-out" speed region of our high-speed wind tunnels were now accurately delineated.
Unknown to us at Langley, Allen and Vincenti at Ames had undertaken a study of compressibility corrections in high-speed tunnels (ref. 84) which included more elaborate theoretical discussion of choking than that given in Byrne's paper. The end result was identical to Byrne's, but the Ames paper contained no experimental verification of the choking relationships. A useful conclusion that could be drawn for the "small-model" situation was that correctable data could be expected up to Mach numbers just below the onset of choking-but there was no hope of correcting the data for the fully-choked condition.