Alexey L. Tukmakov, Andrey V. Schukin1, Vitaliy V. Kharkiv, Nadezhda A. Tukmakova, Adel A. Akhunov, Dmitry A. Tukmakov

Kazan National Research Technical University, Federal Research Center Kazan Scientific Center RAS

The paper presents a non-stationary model of the flow of a viscous compressible heat-conducting gas, which makes it possible to describe the thermal and velocity fields created by the main high-temperature flow flowing from the outside of the plate, the internal cooling flow and the jet that creates a cooling film on the protected surface. The gas dynamics is described based on the numerical solution of the Navier-Stokes system of equations by the explicit McCormack method with splitting of the original operator in spatial directions and a nonlinear correction scheme. The block finite-difference grid was constructed by the Thompson method with clustering of nodes in the near-wall region. The algebraic Smagorinsky model is used as a subgrid turbulence model. The Seidel iterative scheme for the stationary heat conduction equation in generalized curvilinear coordinates is written.

navier-Stokes equations, explicit McCormack scheme, heat equation, near-wall functions, convectivefilm cooling