# Calculation of Heat Transfer and Drag Coefficients for Aircraft Geometric Models
###### Abstract  
A numerical model to calculate the heat transfer and resistance coefficients near the bodies of complex geometric shapes moving at high velocity is formulated. The processes of heat and mass transfer and flow around aircraft elements are considered. An algorithm for calculating heat fluxes and the heat transfer coefficient is proposed. The developed numerical technique can give an idea of the essential features of the flow, heat transfer at the end keels of the wings, and integral layouts of high-speed aircraft. An approximate mathematical model for calculating the heat transfer processes and resistance coefficients near the bodies of complex geometric shapes moving at high speed in the Earth's atmosphere is formulated. The calculated results for convective heat transfer and friction coefficients for the X-33 and X-43 vehicles are obtained. a +
Footnote †: journal: Applied Sciences  
1
Footnote 1: Thermal Physics Department, Bauman Moscow State Technical University, 105005 Moscow, Russia 1  
Footnote 2: footnotetext: Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia 2
aerodynamic coefficients in a wide range of Mach numbers and angles of attack makes it possible to calculate the trajectory of a high-speed aircraft in the Earth's atmosphere, as well as to validate the developed computational codes. Many physical problems arise when designing HSA integrated circuits. For example, the flow of gas (plasma) in the shock layer is complicated due to the development of several phenomena specific to HSA. First, the flows behind intense shock waves are very inhomogeneous and contain sharp gradients of vorticity, pressure, temperature, entropy, etc. The interaction of these subregions (entropy and vortex layers) with a viscous boundary layer significantly affects the heat transfer and frictional resistance to HSA motion. Secondly, at high speeds and flight altitudes, the air in the shock layer can no longer be considered a perfect gas, and its real properties must be taken into account. At the same time, at the Mach number, the shock layer is strongly compressed due to intense plasma-chemical reactions (mainly due to nonequilibrium reactions of dissociation, recombination, and ionization of molecules in a compressed and chemically active boundary layer), leading to a decrease in the effective adiabatic exponent. Thirdly, it is necessary to evaluate the effect of the possibility of cooling the surface of the wings, keel, and body of the HSA on the flow characteristics in a laminar boundary layer flown by a high-speed viscous gas (plasma) flow in the regime of strong viscous-inviscid interaction. Fourthly, at high angles of attack, the central keel (such an arrangement of the keel facilitates the solution of the problem of its thermal protection), streamlined by a detached stream of rarefied air, is ineffective and is used for stabilization and control purposes only at the end of the descent trajectory, when the flight passes at a low angle of attack. In this case, the use of end keels is often envisaged (the numerical technique proposed in this paper allows one to study heat transfer on the surface of the end keel and in the zone of its interface with the wing), which are effective both at low and at high angles of attack. A lot of physical problems arise when developing HSA [1; 2; 3; 4; 5; 6; 7; 8; 9], of which we single out the following two (this paper is devoted to these problems): the calculation of viscous shear stresses (and coefficient of friction \(C_{f}\)) on an aircraft surface and heat flow \(q_{w,L}\). The direct way to quickly estimate the friction coefficient and heat fluxes by numerically integrating the complete system of Navier-Stokes equations is problematic.