Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest

Early Female Maturation as a Factor Related to Early Marriage

While the number of youthful marriages in the United States is increasing, evidence continues to indicate that a significant proportion of these marriages is unstable. The marital failure rate and the extensive problems associated with early marriage have caused widespread concern and have stimulated research and theory formulation in this area

I Can\u27t Find Another Girl Like You

VERSE 1In woodland dells, where beauty dwells,And birds and flowers woo,‘Tis there I wander all alone,\And then I dream of you,Your girlish grace your childish faceAnd those big eyes of blue,No matter where,I can’t find there,Another girl like you. CHORUSThe rose is red, the violet blue, but none so sweet as you,Your golden hair, your eyes so fair, they speak of love so true,By shady nook or babbling brook, no matter where I go,In all this world, I cannot find another girl like you.The you. VERSE 2The songbirds in the trees above,They sing of love and you,‘Tis then I wonder if we’ll part,Or will you love me true,The days gone by bring back a sigh,The happy hours I knew,Will never return,My heart will yearn,For one that’s just like you. CHORU