Mathematical simulation of the hypersonic aircraft pressurized compartment thermal state

A method for determining the hypersonic airplane pressurized compartment thermal state is developed based on the use of a mathematical model of the compartment with metal honeycomb constructions thermal state. The mathematical model of the system of the pressurized thermal-insulated compartment with a surface cooling system is represented by a system of differential and algebraic equations describing the convective and radiation heat transfer of the skin outer surface, convective heat transfer in the cooling system channel, and heat exchange by direct conduction of the honeycomb structure. The development of a stochastic method for solving the direct heat exchange problem of a metal honeycomb construction using stochastic differential equations by the Euler method and random walk by spheres method is carried out. The random process trajectories simulation was carried out using the parallel sensor of Gaussian random variables from the Intel MKL library. To solve the stiff set of ordinary differential equations the implicit Rosenbrock method of second-order is used. The inverse problem for the metal honeycomb construction is solved by a stochastic quasigradient algorithm with a variable metric. In addition, parametric identification of the compartments thermal state model is proposed to be carried out by the composition of the steepest descent method, Newton’s method and the quasi-Newton method of Broyden-Fletcher-Goldfarb-Shanno. The product vector of estimated coefficients errors of a nonlinear mathematical model is determined by the expression that is a quantile function χ2 - distributions and the Gram matrix. At the same time, the method of joint confidence evaluation region projection on the coordinate axes of the coefficients space is used. Investigations of the hypersonic aircraft were conducted in accordance with the Airworthiness standards. The required thickness of the metal honeycomb construction of the pressurized compartment, the temperature and the refrigerant consumption of the hypersonic airplane surface cooling system are obtained. Optimization of the metal honeycomb structure of the hypersonic aircraft pressurized compartment and the surface cooling system was carried out to ensure the reliability of the aircraft and its on-board equipment operation, comfortable conditions in the cockpit and passenger cabin.