Similarity Solution In Hypersonic Flat Plate Boundary Layer Under Convective Heat Transfer Boundary

Aerodynamic heating and thermal protection are the key problems in thehypersonic boundary layer and affect the aircraft’s aerodynamic shape design. Directnumerical simulation based on the similarity solution of the compressible boundary isthe main research mean of aerodynamic heating. Although compressible similaritysolution has obtained numerous mature results for the adiabatic wall and isothermalwall, there was still lacking related research on compressible similarity solution underconvective heat transfer boundary.According to the feature of similarity solution exist at convective heat transferboundary, the mathematical expressions suitable for convective heat transferboundary conditions in hypersonic flat laminar boundary layer has been explored andstudied, and the results provide a basic for further direct numerical simulation ofaerodynamic heating, obtaining accurate wall heat flux, and the design of pneumaticthermal protection.Through the research we got the conclusions as follows:1The coefficient formula of convective heat transfer in compressiblehypersonic flat laminar flow is different from the incompressible. It is needed toconsider the effects of the compressibility. That means the coefficient of convectiveheat transfer in the incompressible needs correction.2According to the research method of normalized, similarity etc, a methodhas been proposed to determine the correction factor of convective heat transfercoefficient in the flat hypersonic laminar, which means while Mach number was fixed,different wall temperature in isothermal wall got a different correction factor. Thecorrect results will be got on the zero point of the second derivative.3The Mach number is the characterization parameters for the effect of gascompressibility, and the criteria relationship in hypersonic flat laminar convectiveheat transfer between correction coefficient and Mach number was established byanalogy method with the experimental data. Meanwhile, the relational expressionbetween the normalization correction coefficient of the convection heat transfer andwall temperature has been established which will be convenient for engineeringapplications in the future. 4By comparing the convective heat transfer boundary use the correctioncoefficient with adiabatic boundary conditions for the cases Mach number are5,6,9,the results show that there exist different in velocity and temperature profile and thetemperature in boundary layer has decreased significantly when take the convectiveheat transfer boundary conditions.