# Calculation of Heat Transfer and Drag Coefficients for Aircraft Geometric Models
###### Abstract
This is because the size of the body (about ten meters) is much larger than the characteristic size of the boundary layer (about 1 mm), and the need to resolve the boundary layer near the surface of the streamlined body leads to the fact that the computational grid will require large sizes of random access memory (RAM). Therefore, one of the objectives of the research is to develop a simplified (operational) method for assessing convective heat fluxes and drag coefficients for bodies of complex spatial shapes. The estimation (based on the simplified method) of heat fluxes and drag coefficients should be preceded by the calculation, using the Euler equations. Focusing on the related achievements that are used as reference data [10; 11] for the proposed work, [10] provides an overview of hypersonic computational fluid dynamics research conducted at the NASA Langley Research Center to support the Phase II development of the X-33 vehicle. The X-33, which is being developed by Lockheed Martin in partnership with NASA, is an experimental single-stage-to-orbit demonstrator that is intended to validate critical technologies for a full-scale reusable launch vehicle. Laminar and turbulent predictions were generated for the X-33 vehicle using two finite-volume Navier-Stokes solvers. Inviscid solutions were also generated with an Euler code. Computations were performed for Mach numbers from 4.0 to 10.0, at angles of attack from 10 deg to 48 deg, with body flap deflections of 0, 10, and 20 deg. Comparisons between predictions and wind tunnel aerodynamic and aero-heating data are presented in this paper. In paper [11], computer modeling of the aerodynamic coefficients of a model of a high-speed aircraft similar to the X-43, moving with a Mach number M = 7, was performed. Devices with arbitrary geometry in three-dimensional unstructured tetrahedral meshes. A cross-verification of these computer codes was carried out based on a comparison of the distributions of aerodynamic parameters, and values of aerodynamic characteristics. It is shown that these computer codes give a fairly reliable picture of the distribution of the fields of the sought values, and also calculate the aerodynamic characteristics with high accuracy relative to each other. Mathematical Model for Assessing Convective Heat Fluxes near the Surface of Bodies of a Simple Geometric Shape  
This section provides a brief 2D description of an approximate method for estimating heat fluxes in key elements (hull and wing edges, nose fairing, etc.,) of an aircraft that have the simplest spatial forms, for example, in the form of a sphere or a wedge associated with a cylinder, etc. Note that in the situation under consideration, compressed and heated (in a shock wave) to a high temperature (>1000 K), air convectively transfers energy into the wall material of the HSA head. This energy is further redistributed along the walls of the working compartment of the HSA. At the same time, it is in the key elements and the head part that the wall material experiences the maximum thermal load. In the general case, to solve such a problem it is necessary to carry out a computational-theoretical study of the features of the structure and the spatial distributions of the gas-dynamic parameters of the flow near the HSA surface, and, based on this study, evaluate the convective heat fluxes. It follows from the formulas below that the heat transfer coefficient at the critical point is inversely proportional to the square root (proportional in the turbulent case) of the blunt radius. Therefore, at high flight speeds and, accordingly, high stagnation temperatures, with a decrease in the bluntness radius at the critical point, the values of convective and radiative fluxes, as well as the magnitudes of thermal deformations, sharply increase (i.e., the geometric shape of the streamlined body changes). The mathematical relationships of the 2D model follow from the relationships of the 3D model.