Quantification of parametric uncertainty in c-Reh model for typical flat plate and airfoil transitional flows

Owing to the lack of physical knowledge of boundary layer transition,the c-Reh transi-tion model introduces closure parameters,which increase the uncertainty of transition prediction.The objective of this work is to quantify the uncertainties of closure parameters in the quantities of interests and identify the key parameters.The six closure parameters in the uncertainty intervals are used as input variables,and the uncertainties of the output results are propagated by a stochas-tic expansion based on the point-collocation nonintrusive polynomial chaos method.The relative contribution of each parameter to uncertainty is evaluated by the Sobol index.The computational cases include natural and bypass transitional flows on zero-pressure-gradient flat plates,and sub-sonic and transonic flows around airfoils.For most cases,c_(e2),c_(a2),and c_(a1)dominate the uncertainty,and the influence of r ht is also significant when the history effects of flow are evident.The contri-bution of parameters in airfoils is more complex than that in flat plates.The transonic airfoil case shows that flow separation dramatically changes the distribution of Sobol indices,which poses a challenge to the accurate prediction of transition.Generally,c_(e2)and c_(a2)are the key parameters of the c-Reh model.