Application Of Uncertainty Quantification Method Based On Polynomial Chaos In Hypersonic Aerodynamic Heat Transfer Prediction

The prediction of aerodynamic thermal environment is one of the key technologies for the thermal protection design of hypersonic vehicles,and the uncertainty of the incoming flow conditions and calculation model becomes an important factor restricting the robustness and reliability of the thermal protection system.At present,one common method of heat flow prediction is CFD simulation,but the current CFD software is performed under certain boundary conditions and all the results are based on deterministic assumptions.However,there are a lot of uncertain factors in real physical environment,such as the boundary conditions,geometric models,gas physical parameters,and empirical parameters in the solver.These uncertainties bring a higher risk of untrustworthiness to the results predicted by the deterministic method,which will adversely affect further development of aircrafts.To this end,based on the Non-Intrusive Polynomial Chaos(NIPC)method,the research of uncertainty quantification method of hypersonic vehicle aerothermal environment prediction is carried out.First of all,the premise of the quantitative analysis of aerothermal uncertainty is to obtain a certain scale of deterministic samples.Both numerical calculation method and engineering calculation method of aerodynamic heating used in this paper are introduced,and the multi-temperature,multi-species air model is described in detail.Numerical calculation methods and aero-thermal engineering calculation methods that consider transition and high-temperature real gas effects.Use the biconics and HB-2 as examples to verify the accuracy of numerical calculation methods in laminar and turbulent conditions.The vehicle example verifies the accuracy of the engineering aerothermal calculation method,and supports the aerothermal calculation method used in subsequent uncertainty quantitative analysis.Secondly,there are a lot of uncertain factors in the calculation of hypersonic aerodynamic heat,and the calculation efficiency of the traditional Polynomial Chaos method is relatively low.Therefore,a Sensitivity-Based Non-Intrusive Polynomial Chaos(SNIPC)method is proposed.Before the uncertainty analysis,partial derivative information is used to approximate the global sensitivity,and low-correlative random variables are eliminated,so as to reduce the dimensionality of random problems,thereby improving computational efficiency.Taking the heat flux at stagnation point of an aircraft based on the engineering method as an example,the SNIPC method and the traditional Monte Carlo method are used to quantitatively analyze the uncertainty.The results show that the aero-thermal evaluation times of the second-order SNIPC method is less than 1% of the Monte Carlo method under the premise that the error does not exceed 6%.Finally,for the HTV-2-like hypersonic vehicle,a CFD-based aerothermal calculation method is described,and the grid for subsequent calculations is determined through grid convergence analysis.Using the SNIPC and NIPC method,this paper carries out the double-loop mixed uncertainty analysis on four cognitive uncertainty variables(surface emission,specific heat at constant pressure,Prandtl number and viscosity coefficient)and three random uncertainty variables(incoming flow velocity,temperature and pressure).The analysis results of six monitoring points representing different regions show that the random uncertainty has a much higher impact on the results than the cognitive uncertainty,and the incoming flow velocity has the greatest impact on the heat flow across the entire surface.In this paper,the method of quantitative analysis on the aerodynamic heat of hypersonic vehicle can provide the confidence interval of the results of aerodynamic heat evaluation,and assist the design of the thermal protection system of hypersonic vehicle.