Theoretical and experimental investigation of the photographic reconnaissance plane instrument bay thermal state

The mathematical model of the venting heat-insulated instrument bay of the photographic reconnaissance plane thermal state is developed. The direct and inverse problems of heat exchange are solved, the confidence intervals of estimated parameters are determined. Mathematical modeling of the instrument compartment thermal state is needed for the conducting of flight and bench tests of airborne equipment located in the venting heat-insulated compartment of the aircraft. Mathematical model of the venting heat-insulated instrument compartment with the thermal conditions supporting system is represented by the system of one-dimensional equations of heat-insulated skin and ordinary differential heat transfer equations of the inner surface of thermal insulation of skin, onboard equipment, air and enthalpy transport from the thermal conditions supporting system. In order to solve the direct problem of the compartment thermal state, one-dimensional equations for heat-insulated skin are discretized with respect to the space variable by the Galerkin method that uses a piecewise-linear basis. Solving of the inverse problem, i.e. estimation of the coefficients of the model equation is reduced to the minimization of the weighted sum of quadratic residuals between the values specified by the adopted criteria and the corresponding values obtained during the calculations by the equations of the model. A combination of steepest descent method, quasi-Newton method of Broyden - Fletcher -Goldfarb - Shenno and the Newtons method was used to minimize a function. It is reasonable to define confidence intervals of estimated coefficients of the nonlinear mathematical model of the compartment thermal state by the covariance matrix of estimation errors of the desired coefficients of the model equation. Parametrical identification was carried out by the measured in the compartment surface temperatures of one of the blocks and the inner surface of the heat insulation sheathing around the block. In this case, the measurement results for a cold climate in a typical flight mode of a photoreconnaissance plane were used. For the purpose of experimental verification of the proposed model in different flight modes and air overboard, as well as on elements of the instrument compartment, temperatures of the compartment elements calculated by the model were compared with measured values. The verification showed that the constructed mathematical model of the instrument compartment thermal state is adequate to the real thermal state of unpressurized venting heat-insulated compartment of the photoreconnaissance plane.