Jens Ingemann Madsen

Response Surface Techniques for Diffuser Shape Optimization

The design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of eow devices. Two examples involving two and eve design variables are treated, with the diffuser wall shapes described by polynomials and B-splines. In both cases monotonicity conditions drastically reduce the design space. In this irregularly shaped space, a pool of designs is selected by a D-optimality criterion and analyzed by a e nite volume computational euid dynamics (CFD) code. Quadratic polynomial response surfaces are then e tted to the pressure recovery coefe cients. To improve the prediction accuracy, uncertain regressor terms and possible outlier design points are excluded based on statistical tests. A standard optimization algorithm is used to e nd the optimal diffuser design from the response surface approximations. The optimum diffusers exhibit minimal e ow separation and yield similar wall shapes for the two parameterizations. A main asset of the response surface optimization approach lies in the smoothing of noisy response functions.Therefore, theissueofnumericalnoiseinCFD results basedon theuseof two different analysis codes is addressed.

Multifidelity Response Surface Approximations for the Optimum Design of Diffuser Flows

Response surface methods use least-squares regression analysis to fit low-order polynomials to a set of experimental data. It is becoming increasingly more popular to apply response surface approximations for the purpose of engineering design optimization based on computer simulations. However, the substantial expense involved in obtaining enough data to build quadratic response approximations seriously limits the practical size of problems. Multifidelity techniques, which combine cheap low-fidelity analyses with more accurate but expensive high-fidelity solutions, offer means by which the prohibitive computational cost can be reduced. Two optimum design problems are considered, both pertaining to the fluid flow in diffusers. In both cases, the high-fidelity analyses consist of solutions to the full Navier-Stokes equations, whereas the low-fidelity analyses are either simple empirical formulas or flow solutions to the Navier-Stokes equations achieved using coarse computational meshes. The multifidelity strategy includes the construction of two separate response surfaces: a quadratic approximation based on the low-fidelity data, and a linear correction response surface that approximates the ratio of high-and low-fidelity function evaluations. The paper demonstrates that this approach may yield major computational savings.

Optimization of flow geometries applying quasianalytical sensitivity analysis

An efficient approach for the optimization of three-dimensional viscous flow geometries is presented. A general purpose optimization tool has been developed and implemented into the finite volume-based computational fluid dynamics (CFD) environment of CFDS-FLOW3D. Of principal interest is the calculation of sensitivity coefficients, which follow by a quasianalytical method rather than the time-intensive approximation by finite differences. It is verified that major time savings can be obtained in the sensitivity analysis, especially when using a large number of design variables. The sensitivity analysis involves the solution of a large system of linear equations, which would require an excessive amount of memory with a full matrix solver. Different types of equation solvers have been investigated to overcome this problem, and a banded out of core solver has been found to be the most acceptable. The optimization tool is applied on a two-dimensional laminar diffuser in order to obtain maximum pressure recovery by contouring the divergent wall section. This investigation yields a diffuser performance improved by about 5% when compared with a straight-walled geometry.