Local physical gradient-based coupling information interpolate method and application on double-wall turbine blade multidisciplinary analysis

A novel generalization interpolate modification method based on local gradient is presented. The main idea was to remove the sample points located in the gradient direction away from the unknown points compared to the sample points located in the perpendicular direction. This method first uses the Taylor expansion to construct a set of equations and solves the local physical gradient. Subsequently, a scale vector is derived to modify the interpolate space. Three classical interpolation methods were modified: Inverse Distance Weighted (IDW), Radial Basis Function (RBF), and Kriging method. The results of the test functions prove that the proposed method can effectively decrease the interpolate error regardless of low or high dimensional interpolate problem and irrespective of the sample point size. Surface and volume interpolate validations demonstrate that the local gradient generates a large interpolate error, and the modified method can essentially diminish this error with a maximum reduction of 9.94 %. Subsequently, this method is applied to implement a multidisciplinary analysis of a practical double-wall cooling blade with a large physical gradient. The results showed that the pressure and temperature interpolate errors could be decreased by 5.18 % and 14.5 %, respectively, with only an additional 115 s, at the fillet and film hole area where the local gradient was high. When the strength analysis was implemented, the maximum stress error reduction was 25.04 MPa at the stress concentration region.