The global exploring feature of the surrogate model makes it a useful intermedia for design optimization. The accuracy of the surrogate model is closely related with the efficiency of optima-search. The cokriging approach described in present studies can significantly improve the surrogate model accuracy and cut down the turnaround time spent on the modeling process. Compared to the universal Kriging method, the cokriging method interpolates not only the sampling data, but also on their associated derivatives. However, the derivatives, especially high order ones, are too computationally costly to be easily affordable, forming a bottleneck for the application of derivative enhanced methods. Based on the sensitivity analysis of Navier–Stokes equations, current study introduces a low-cost method to compute the high-order derivatives, making high order derivatives enhanced cokriging modeling practically achievable. For a methodological illustration, second-order derivatives of regression model and correlation models are proposed. A second-order derivative enhanced cokriging model-based optimization tool was developed and tested on the optimal design of an automotive engine cooling fan. This approach improves the modern optimal design efficiency and proposes a novel direction for the large scale optimization problems.

In centrifugal compressors, Mild Surge (MS) leads to unstable operation. Previous experimental work on a centrifugal compressor designed and built by Safran Helicopter Engines (SafranHE) showed that MS corresponds to the pulsation of an alternate stall pattern at the Helmholtz frequency of the test rig on two channels in the radial diffuser. The present contribution experimentally investigates the impact of the Inlet Guide Vane (IGV) stagger angle on this alternate flow and numerically studies the topology of this pulsating alternate flow. The experimental investigation is performed with unsteady pressure sensors, and shows that the IGV stagger angle only impacts the pulsation frequency of the alternate flow pattern. This change is explained by the dependence of the Helmholtz frequency on the compressor inlet section. The topological analysis of the average flow field, computed from wall-resolved Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations, demonstrates that the saddle point (major critical point) in the corner hub/suction side of the stalled blade migrates upstream while staying in the corner if the mass flow rate decreases. One main blade over two is stalled on both sides because the flow originating from this corner separation circumvents the trailing edge and migrates upstream along the pressure side. In the simulation, the pulsation of the alternate stall is coupled with the reflection of acoustic waves on the inlet and outlet planes, regarded as an environmental effect.