Heating Simulations

At the beginning of the X-15 program, researchers used the methods developed by Edward Van Driest and Ernst Eckert to determine the heat-transfer coefficients for temperature calculations. However, the measured heat-transfer coefficients during the early flight program were considerably lower than the predicted values. Based on these preliminary results, derived primarily from the initial low-angle-of-attack flights, engineers modified Eckert’s turbulent-flow method to produce the adiabatic-wall reference-temperature method.[48]

fuselage. The boundary-layer transition was completely unpredictable, but since researchers expected turbulent flow during the major portion of most flights, they normally used turbulent – flow calculations for the entire flight. Next came determining the heat-transfer coefficients, and finally calculating the skin temperature. Due to the tedious work involved in this process, which was done mostly by hand since general-purpose computers were not yet in widespread use, the researchers made many assumptions that simplified the procedure. For instance, it was assumed that temperature did not vary through the thickness of the skin, no heat was transferred along the skin, the specific heat of the skin was constant, solar radiation to the skin was negligible, the emissivity of the skin was constant, and no net heat transfer occurred between surfaces by radiation.[49]

Temperatures calculated using the adiabatic-wall reference-temperature method tended to agree closely with measured data from the flight program. In several instances the calculated temperature was somewhat higher because the analytical method assumed turbulent flow all of the time. This was considered reasonable and sufficient for flight-safety purposes since it erred on the side of caution.-50

In 1957, Lockheed Aircraft Company developed a thermal analyzer program that ran on an IBM 704 digital computer, the largest of its type then available. This program was capable of running the heating prediction equations, including the effects of transient conduction, convection, radiation, and heat storage, that researchers had previously omitted for the sake of expediency. With Lockheed’s assistance, researchers modified the program to reflect the X-15 configuration. The program estimated the heat input to the skin elements using the attached-shock Prandtl- Meyer expansion method for flow conditions, and the adiabatic-wall reference-temperature method for heat transfer. Researchers used the laminar-flow theory of Fay and Riddell to compute the heat input to the stagnation points, with curves developed by Lester Lees used to weight the periphery.-50

One of the primary goals of the X-15 program was to validate the various heat-transfer methods with actual flight results. Many of the early X-15 flights were dedicated to gathering data that the researchers would spend years comparing against wind tunnel and theoretical results. The results were vastly improved heat-transfer models that were used during the Apollo and space shuttle programs. (NASA)

To accompany the Lockheed-developed software, North American developed two other programs to predict structural heating values and their distribution along the airframe. The first program computed local-flow conditions on the aircraft, and the second program used the local-flow conditions to calculate the aerodynamic heat transfer to the skin. The program developed by Lockheed calculated the transient heating of internal structure based on the results of the other two programs.-1521

To evaluate the acceptability of the thermal analyzer program, researchers compared calculated results with actual flight results on several occasions. The values always compared favorably, and were usually slightly better than the hand-calculated values for the same conditions. North American and NASA quickly adopted the automated process based largely on the tremendous labor savings it offered.

After the flight planners established a flight profile on the fixed-base simulator, they digitized the results of a clean flight and input them into the IBM 704 to predict the skin and structural temperatures and thermal gradients for the flight. This was a time-consuming process. Researchers then compared the resulting data with the design conditions to ensure that the X-15 did not violate any structural margins. If any exceptions were uncovered during the comparison, researchers modified the flight profile and the entire process was repeated. Emergency and contingency flight profiles went through the same rigorous process. After the flight, researchers compared the heating predictions with actual flight data and then refined the simulations.-1531