STUDY ON MECHANICAL AND THERMAL CHARACTERISTICS OF FLAT PLATE WITH SELF-SIMILAR BOUNDARY LAYER OF EQUILIBRIUM FLOW

It is of great significance for engineering design to accurately know the mechanical and thermal characteristics of hypersonic laminar flow plate wall. In this paper, the hypersonic self-similar flat laminar boundary layer equations under the assumption of equilibrium air are solved using the finite difference method. The obtained wall heat flux and shear stress distributions are consistent with the results obtained from direct numerical simulation (DNS) and the experimental results of flat heat flux measurements in shock tunnel tests. Based on this, the deviation analysis of engineering formulas for calculating force, heat and boundary layer thickness of plate by Eckert reference temperature method and Eckert reference enthalpy method is carried out for 993 working conditions with height of 10 ~ 65 km, velocity 1 ~ 8 km/s and different wall temperatures. The results show that Eckert reference enthalpy method is relatively effective, the absolute value of shear stress deviation calculated by Eckert reference enthalpy method is less than 6.1%, but the maximum deviation of boundary layer thickness reaches 45%; when the wall temperature is less than 0.5 times the adiabatic wall temperature, the absolute deviation of heat flux is less than 7% and the absolute deviation of Reynolds analogy factor is less than 8%. However, when the wall temperature is close to the adiabatic wall temperature, the deviation of heat flux and Reynolds analogy factor increases rapidly, and it is difficult to improve effectively under the reference enthalpy method frame. The combined parameters of enthalpy and velocity of boundary layer are added to the calculation formula of boundary layer thickness. After fitting and optimizing the parameters for 223 typical working conditions, the calculation effect is significantly improved. In the deviation analysis of boundary layer thickness calculation for 993 working conditions, the maximum absolute deviation of the new calculation formula of boundary layer thickness is reduced from 45% to 12%.