Calculation method of radiation heat flux for quartz lamp array for variable curvature cabins of missile

Aiming at the problem of analytical calculation of heat flux density field for variable curvature cabin such as conical cabin in thermal strength tests of missiles, we propose an analytical method for calculating radiation heat flux of the conical quartz lamp array with filament semi-cylindrical surfaces divided into multiple elements. By solving the coordinates of the intersection points between the tangent through the conical generatrix and the central axis of the filament element surfaces, as well as the intersections between the filament element surfaces and the conical generatrix, explicit expressions for the irradiation ranges of single quartz lamp under external and internal heating conditions are derived. We analyze the influence of element number on the heat flux density distribution in typical regions and examines the discrepancies in heat flux density results under single-intersection and double-intersection criteria. Comparisons with finite element models results of linearly variable diameter surface and non-linearly variable diameter surface show that the relative errors between the two methods are small, validating the accuracy of the proposed calculation method. This method provides important reference value for response prediction and scheme evaluation of the thermal test for missile cabins with variable curvature.