Quantitative relative comparison of CFD simulation uncertainties for a transonic diffuser problem

Different sources of uncertainty in CFD simulations are illustrated by a detailed study of two-dimensional, turbulent, transonic flow in a converging–diverging channel. Runs were performed with the commercial CFD code GASP using different turbulence models, grid levels, and flux-limiters to see the effect of each on the CFD simulation uncertainties. Two flow conditions were studied by changing the exit pressure ratio: the first is a complex case with a strong shock and a separated flow region, the second is the weak shock case with no separation. The uncertainty in CFD simulations has been studied in terms of four contributions: (1) discretization error, (2) error in geometry representation, (3) turbulence model, and (4) the downstream boundary condition. In this paper, we have quantified the relative contribution and the importance of each source of uncertainty and shown the level of scatter in results that a well informed CFD user may obtain in a typical design activity. The nozzle efficiency results obtained in this study showed that the range of variation for the strong shock case was much larger than that observed in the weak shock case. The discretization errors were up to 6% and the relative uncertainty originating from the selection of different turbulence models was as large as 9% for the strong shock case. Furthermore, the results demonstrated that grid convergence is not achieved with grid levels that have moderate mesh sizes and showed that highly refined grids are required to obtain solutions with an acceptable level of accuracy in design problems that involve simulations of complex flow fields. The results illustrated the interaction of different sources of uncertainty and showed that the magnitudes of numerical errors are influenced by the physical models used.     

Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport

Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper selectively surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates.