Chapter 5: High-speed Cowlings, Air Inlets and Outlets, and Internal-Flow Systems
[159] During the course of my cowling and inlet work in the late thirties and early forties and in my first contacts with the Power Plant Installation group virtually all engineering calculations relating to internal flow and cooling were based on incompressible (low-speed) formulas. I first became involved in applying compressible flow relations in extending internal drag calculations to high speeds during my inlet-outlet opening project. It seemed obvious that before long there would be a widespread need for such refinement, and Baals and I therefore set out to develop engineering formulas likely to prove generally useful. It was obvious from the outset that the addition of heat in fins and radiators was a prime factor to be accounted for. The chief value of our engineering analysis probably was its illustration of the importance of density changes due to heat and compressibility in advanced systems then under development (ref. 187). For example, our calculations showed that the pressure drop for cooling an R-2800 engine in Mach 0.6 flight at 35 000 feet was almost 50 percent higher than predicted by simple methods then in use, which neglected the density change across the cylinders. A blower would be needed for cooling at higher altitudes, and at about 42 000 feet sonic velocity (choking) would occur at the baffle exits. These results implied a very difficult future for the piston engine, from which we were all spared by the advent of the jet engine. We felt somewhat uneasy over these predictions, because the actual flow in a baffled cylinder undoubtedly violated our basic flow assumption of one-dimensionality. Confirmation was provided about a year later in a completely independent....

photo of 8foot wind tunnel with electric heating coil attached
[160] FIGURE 41-Electrically heated finned-cylinder model used by 8-foot tunnel group to investigate cooling-airflow relationships at high speeds. by Brevoort (ref. 188), but so many simplifying assumptions had been made in both studies that we decided to undertake measurements of high-speed flows within the fins of a baffled electrically heated test cylinder (fig. 41). A few test runs were made in the spring of 1943 producing data which would require much study and analysis to interpret correctly. Under the press of more urgent business (the high-speed propeller problems previously discussed and my impending departure for the 16-foot tunnel) we set aside the heat-cylinder data, fully intending to take it up later, and not realizing that interest in piston-engine development would shortly disappear and with it our plans for future work with these data.
Closely related to the complex flow problem of the baffled cylinder was the more tractable case of high-speed heated flow in constant-area straight radiator tubes. Baals and I had applied our one-dimensional engineering procedure to this case and issued a paper outlining a simple approximate method for dealing with it (ref. 189). A few months after my arrival at 16-foot, I interested engineers Habel and Gallagher in [161] investigating the flow in an electrically heated tube up to choking conditions. Their tests provided general confirmation of our prediction method and some added insights into the nature of these flows from the point of view of the designer of radiator installations (ref. 190). The boundary condition in this problem is the fixed assumed flow rate and trance Mach number, and the problem is to relate the conditions at the it of the tubes to the specified entrance conditions, the tube geometry id heat input being principal variables. Actually, we were dealing with relatively simple special case of the much more complex general problem of heat addition in a constant-area duct, which assumed great importance in the later forties because of its relevance to ramjet combustor design. In the general case, heat addition in subsonic flow affects the upstream conditions and the resulting changes are, of course, different and .lore complex than those of the simple radiator. No less than 20 significant papers dealing with the general problem, several of them with conflicting and controversial conclusions, had appeared by 1950 (ref. 191).