In-flight boundary-layer measurements on a hollow cylinder at a Mach number of 3.0

Skin temperatures, shear forces, surface static pressures, boundary layer pitot pressures, and boundary layer total temperatures were measured on the external surface of a hollow cylinder that was 3.04 meters long and 0.437 meter in diameter and was mounted beneath the fuselage of the YF-12A airplane. The data were obtained at a nominal free stream Mach number of 3.0 (a local Mach number of 2.9) and at wall to recovery temperature ratios of 0.66 to 0.91. The local Reynolds number had a nominal value of 4,300,000 per meter. Heat transfer coefficients and skin friction coefficients were derived from skin temperature time histories and shear force measurements, respectively. In addition, boundary layer velocity profiles were derived from pitot pressure measurements, and a Reynolds analogy factor was obtained from the heat transfer and skin friction measurements. The measured data are compared with several boundary layer prediction methods

In-flight Compressible Turbulent Boundary Layer Measurements on a Hollow Cylinder at a Mach Number of 3.0

Skin temperatures, shearing forces, surface static pressures, and boundary layer pitot pressures and total temperatures were measured on a hollow cylinder 3.04 meters long and 0.437 meter in diameter mounted beneath the fuselage of the YF-12A airplane. The data were obtained at a nominal free stream Mach number of 3.0 and at wall-to-recovery temperature ratios of 0.66 to 0.91. The free stream Reynolds number had a minimal value of 4.2 million per meter. Heat transfer coefficients and skin friction coefficients were derived from skin temperature time histories and shear force measurements, respectively. Boundary layer velocity profiles were derived from pitot pressure measurements, and a Reynolds analogy factor of 1.11 was obtained from the measured heat transfer and skin friction data. The skin friction coefficients predicted by the theory of van Driest were in excellent agreement with the measurements. Theoretical heat transfer coefficients, in the form of Stanton numbers calculated by using a modified Reynolds analogy between skin friction and heat transfer, were compared with measured values. The measured velocity profiles were compared to Coles' incompressible law-of-the-wall profile

Thermal response of Space Shuttle wing during reentry heating

A structural performance and resizing (SPAR) finite element thermal analysis computer program was used in the heat transfer analysis of the space shuttle orbiter that was subjected to reentry aerodynamic heatings. One wing segment of the right wing (WS 240) and the whole left wing were selected for the thermal analysis. Results showed that the predicted thermal protection system (TPS) temperatures were in good agreement with the space transportation system, trajectory 5 (STS-5) flight-measured temperatures. In addition, calculated aluminum structural temperatures were in fairly good agreement with the flight data up to the point of touchdown. Results also showed that the internal free convection had a considerable effect on the change of structural temperatures after touchdown

Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.Comment: 24 pages, 12 figure

Reentry heat transfer analysis of the space shuttle orbiter

A structural performance and resizing finite element thermal analysis computer program was used in the reentry heat transfer analysis of the space shuttle. Two typical wing cross sections and a midfuselage cross section were selected for the analysis. The surface heat inputs to the thermal models were obtained from aerodynamic heating analyses, which assumed a purely turbulent boundary layer, a purely laminar boundary layer, separated flow, and transition from laminar to turbulent flow. The effect of internal radiation was found to be quite significant. With the effect of the internal radiation considered, the wing lower skin temperature became about 39 C (70 F) lower. The results were compared with fight data for space transportation system, trajectory 1. The calculated and measured temperatures compared well for the wing if laminar flow was assumed for the lower surface and bay one upper surface and if separated flow was assumed for the upper surfaces of bays other than bay one. For the fuselage, good agreement between the calculated and measured data was obtained if laminar flow was assumed for the bottom surface. The structural temperatures were found to reach their peak values shortly before touchdown. In addition, the finite element solutions were compared with those obtained from the conventional finite difference solutions

Reentry heating analysis of space shuttle with comparison of flight data

Surface heating rates and surface temperatures for a space shuttle reentry profile were calculated for two wing cross sections and one fuselage cross section. Heating rates and temperatures at 12 locations on the wing and 6 locations on the fuselage are presented. The heating on the lower wing was most severe, with peak temperatures reaching values of 1240 C for turbulent flow and 900 C for laminar flow. For the fuselage, the most severe heating occured on the lower glove surface where peak temperatures of 910 C and 700 C were calculated for turbulent flow and laminar flow, respectively. Aluminum structural temperatures were calculated using a finite difference thermal analyzer computer program, and the predicted temperatures are compared to measured flight data. Skin temperatures measured on the lower surface of the wing and bay 1 of the upper surface of the wing agreed best with temperatures calculated assuming laminar flow. The measured temperatures at bays two and four on the upper surface of the wing were in quite good agreement with the temperatures calculated assuming separated flow. The measured temperatures on the lower forward spar cap of bay four were in good agreement with values predicted assuming laminar flow