Response surface techniques for diffuser shape optimization

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1512-1518 ◽  
Author(s):  
Jens I. Madsen ◽  
Wei Shyy ◽  
Raphael T. Haftka
Keyword(s):  
Shape Optimization ◽  
Response Surface

Thermal Optimization of a Microchannel Heat Sink With Trapezoidal Cross Section

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Shape Optimization ◽  
Thermal Resistance ◽  
Objective Function ◽  
Response Surface ◽  
Heat Sink ◽  
Fractional Factorial ◽  
Surface Model ◽  
Microchannel Heat Sink ◽  
Reference Shape ◽  
Design Variables

A microchannel heat sink shape optimization has been performed using response surface approximation. Three design variables related to microchannel width, depth, and fin width are selected for optimization, and thermal resistance has been taken as objective function. Design points are chosen through a three-level fractional factorial design of sampling methods. Navier–Stokes and energy equations for steady, incompressible, and laminar flow and conjugate heat transfer are solved at these design points using a finite volume solver. Solutions are carefully validated with the analytical and experimental results and the values of objective function are calculated at the specified design points. Using the numerically evaluated objective-function values, a polynomial response surface model is constructed and the optimum point is searched by sequential quadratic programming. The process of shape optimization greatly improves the thermal performance of the microchannel heat sink by decreasing thermal resistance of about 12% of the reference shape. Sensitivity of objective function to design variables has been studied to utilize the substrate material efficiently.

Concurrent Blade Aerodynamic-Aeroelastic Design Optimization With Re-Scaled Response Surface

2014 ◽  
Author(s):  
O. Valero ◽  
L. He ◽  
Y. S. Li
Keyword(s):  
Shape Optimization ◽  
Response Surface ◽  
Optimization Algorithm ◽  
Multidisciplinary Optimization ◽  
Gradient Algorithm ◽  
Optimized Design ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Flow Equations ◽  
Blade Shape

Given the ever increasing demands on turbomachinery performance, various advanced blade shape optimizations have been actively developed and applied in modern blading designs. Multidisciplinary and concurrent optimizations have attracted considerable attention, offering the advantage of disciplinary interactions being included more simultaneously in a design process. This paper presents the development of a multidisciplinary optimization algorithm for the concurrent blade aerodynamic and aeromechanic shape optimization of realistic 3D turbine stages. A non-gradient algorithm is enhanced by a new re-scaled response surface (RSM) model. This meta-model is able to rescale the design space and redefine the response surface during a blade shape optimization process, leading to a much enhanced convergence compared to a standard RSM approach. The optimization algorithm is developed in conjunction with an efficient nonlinear harmonic phase solution method solving the unsteady flow equations in the frequency domain, combined with a finite element analysis (FEA) to extract the structural dynamic characteristics of the blades. The effectiveness of the concurrent method is examined for an optimized design of a realistic LP turbine stage. The optimization goals are the maximization of the isentropic stage efficiency and aeroelastic flutter stability (aero-damping). Two sets of cases are considered. In the first set, the shaping is applied only to stator blades, while for the second set, both stator and rotor blades are shaped. The concurrent cases are compared with their single-disciplinary counterparts. For both sets of the cases, the advantages of the concurrent treatment are clearly demonstrated.

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