Optimal Design of Transonic Fan Blade Leading Edge Shape Using CFD and Simultaneous Perturbation Stochastic Approximation Method

Simultaneous Perturbation Stochastic Approximation method has attracted considerable application in many different areas such as statistical parameter estimation, feedback control, simulation-based optimization, signal & image processing, and experimental design. In this paper, its performance as a viable optimization tool is demonstrated by applying it first to a simple wing geometry design problem for which the objective function is described by an empirical formula from aircraft design practice and then it is used in a transonic fan blade design problem in which the objective function is not represented by any explicit function but is estimated at each design iteration by a computational fluid dynamics algorithm for solving the Navier-Stokes equationsSingapore-MIT Alliance (SMA

Aerodynamic Shape Design of Nozzles Using a Hybrid Optimization Method

A hybrid design optimization method combining the stochastic method based on simultaneous perturbation stochastic approximation (SPSA) and the deterministic method of Broydon-Fletcher-Goldfarb-Shanno (BFGS) is developed in order to take advantage of the high efficiency of the gradient based methods and the global search capabilities of SPSA for applications in the optimal aerodynamic shape design of a three dimensional elliptic nozzle. The performance of this hybrid method is compared with that of SPSA, simulated annealing (SA) and gradient based BFGS method. The objective functions which are minimized are estimated by numerically solving the 3D Euler and Navier-Stokes equations using a TVD approach and a LU implicit scheme. Computed results show that the hybrid optimization method proposed in this study shows a promise of high computational efficiency and global search capabilities.Singapore-MIT Alliance (SMA

Aerodynamic Shape Design of Transonic Airfoils Using Hybrid Optimization Techniques and CFD

This paper will analyze the effects of using hybrid optimization methods for optimizing objective functions that are determined by computational fluid dynamics solvers for compressible viscous flow for optimal design of airfoils. Previous studies on this topic by the authors had examined the application of deterministic optimization methods and stochastic optimization methods such as Simulated Annealing and Simultaneous Perturbation Stochastic Analysis (SPSA). The studies indicated that SPSA method has a greater or equal efficiency as compared with SA method in reaching optimal airfoil designs for the design problem in question. However, in some situations SPSA method has a tendency to demonstrate an oscillatory behavior in the vicinity of a local optima. To overcome this tendency, a hybrid method designed to take full advantage of SPSA’s high rate of reduction of the objective function at the inception of the design process to drive the design cycles towards the optimal zone at first, and then combining with other methods to perform the final stages of the convergence towards the optimal solutions is considered. SPSA method has been combined with the gradient-based Broydon-Fletcher-Goldfarb-Shanno (BFGS) method as well as Simulated Annealing method for the transonic inverse airfoil design problem that is concerned with the specification of a target airfoil surface pressure distribution and starting from an initial guess of an airfoil shape, the target airfoil shape is reached by way of minimization of a quantity that depends on the difference between the target and current airfoil surface pressure distribution. For a typical transonic flow test case, the effects of using hybrid optimization techniques such as SPSA+BFGS and SPSA+SA as opposed to using SPSA alone can be seen in Figure 1. After 800 design cycles using SPSA, the hybrid SPSA+SA method took 2521 function evaluations of SA while the SPSA+BFGS method took 271 function evaluations to reach similar values which are much better than that reached by using SPSA alone in the entire minimization process. Results indicate that both of the two hybrid methods have capability to find a global optimum more efficiently than the SPSA method. The paper will address issues related to hybridization and its impact on the optimal airfoil shape designs in various contexts.Singapore-MIT Alliance (SMA

Charmless Bs→PP,PV,VVB_s\to PP, PV, VV Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects II

We provide a systematic study of charmless $B_s \to PP, PV, VV$ decays ($P$ and $V$ denote pseudoscalar and vector mesons, respectively) based on an approximate six-quark operator effective Hamiltonian from QCD. The calculation of the relevant hard-scattering kernels is carried out, the resulting transition form factors are consistent with the results of QCD sum rule calculations. By taking into account important classes of power corrections involving "chirally-enhanced" terms and the vertex corrections as well as weak annihilation contributions with non-trivial strong phase, we present predictions for the branching ratios and CP asymmetries of $B_s$ decays into PP, PV and VV final states, and also for the corresponding polarization observables in VV final states. It is found that the weak annihilation contributions with non-trivial strong phase have remarkable effects on the observables in the color-suppressed and penguin-dominated decay modes. In addition, we discuss the SU(3) flavor symmetry and show that the symmetry relations are generally respected

In situ x-ray diffraction studies of a new LiMg{sub 0.125}Ni{sub 0.75}O{sub 2} cathode material

A Synchrotron x-ray source was used for In Situ x-ray diffraction studies during charge on a new LiMg{sub 0.125}Ti{sub 0.125}Ni{sub 0.75} cathode material synthesized by FMC Corp. It had been demonstrated by Gao that this new material has superior thermal stability than LiNiO{sub 2} and LiCo{sub 0.2}Ni{sub 0.8}O{sub 2} at over-charged state. In this current paper, studies on the relationship between the structural changes and thermal stability at over-charged state for these materials are presented. For the first time, the thermal stability of these materials are related to their structural changes during charge, especially to the formation and lattice constant change of a hexagonal phase (H3). The spectral evidence support the hypothesis that the improvement of thermal stability is obtained by suppressing the formation of H3 phase and reducing the shrinkage of its lattice constant c when charged above 4.3 V