Aspects of numerical grid generation - Current science and art

Hybrid Grids and Their Applications

An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

Algebraic turbulence modeling for unstructured and adaptive meshes

This paper describes a new user-friendly hybrid surface mesh-generation method coupled with a modified hybrid volume mesh-generation method for viscous flow simulations. A suppressed marching-direction method is proposed to improve the quality of meshes at concave corners on surfaces and in volumes, such as aircraft wing–body junctions. Good-quality semistructured quadrilateral faces can be created around selected geometrical features with minimum user interventions using an advancing-layers-type method with a special treatment at concave corners. The hybrid volume mesh-generation method proposed by Ito et al. (Ito,Y., Shih, A. M., Soni, B. K., and Nakahashi, K., “Multiple Marching Direction Approach to Generate High Quality Hybrid Meshes,” AIAA Journal, Vol. 45, No. 1, 2007, pp. 162–167 and Ito, Y., Shih, A. M., and Soni, B. K., “Hybrid Mesh Generation with Embedded Surfaces Using a Multiple Marching Direction Approach,” International Journal for Numerical Methods in Fluids, Vol. 67, No. 1, 2011, pp. 1–7...

Efficient Hybrid Surface/Volume Mesh Generation Using Suppressed Marching-Direction Method

The wing tip device in this study was to mimic the wing tips of a soaring bird, featuring three smoothly blended elements. Each such multi-element winglet was integrated into a complete wing–tail–body aircraft configuration. The geometry of each of the three elements in the multi-element winglet was defined using 11 parameters, totaling 33 parameters for a complete multi-element winglet geometry. This design methodology used a three-dimensional geometry generation algorithm based on locally analytical smoothly connected surface patches, allowing for the creation of vastly diverse three-dimensional geometries with a minimal number of specified design parameters. A three-dimensional, compressible, turbulent flow, steady-state analysis was performed using a Reynolds-averaged Navier–Stokes solver on each configuration to obtain the objective function values. Each configuration was analyzed at a freestream Mach number of 0.25 and at an angle of attack of 11 deg to mimic the takeoff conditions of a passenger ai...

Multi-Element Winglets: Multi-Objective Optimization of Aerodynamic Shapes

This paper describes a study on an alternate configuration for medium size airplane. Blended-Wing-Body concept, which basically is a flying wing configuration, is applied to airplane for up to 224 passengers. An aerodynamic design tools system is proposed to realize such configuration. The design tools comprise of Takanashi’s inverse method, constrained target pressure specification method and RAPID method. The study shows that the combination of those three design methods works well.

/pdf/flying-wing-concept-for-medium-size-airplane-swrqwjhl8u.pdf

Flying wing concept for medium size airplane

Publisher Summary In this chapter, a three-dimensional supersonic wing design method that can determine both the warp and thickness at the same time is developed. The present method is extended from Takanashi's inverse design method used for the transonic wing design. Takanashi solved the inverse problem by using the integral form of the transonic small perturbation equation with ‘residual-correction’ concept. This paper will discuss the mathematical formulation of the present method, and show two design results. One is for an isolated-wing configuration and the other is for a wing‑fuselage combination that is the baseline design of the National Aerospace Laboratory's experimental scaled supersonic transport (SST). The inverse problem in the aerodynamic shape design is to find a geometry that yields a specified surface pressure distribution. The procedure of finding a corresponding geometry in the present method is described as follows. First, a target pressure distribution and an initial geometry are inputted to a design system, and then the surface pressure distribution of this initial geometry is obtained by the flow analysis. In this design system, inverse calculation stage is separated from the flow analysis stage. Thus, any type of analysis, even an experiment, can be used for the flow analysis tool. In this study, the Euler/Navier‑Stokes solver is used for the flow analysis. the pressure difference is calculate from the computed and target pressure distributions. Using this pressure difference as a boundary condition, a geometry correction is obtained by solving the linearized small perturbation (LSP) equation. By modifying the initial geometry with the geometry correction, a new geometry is produced.

/pdf/supersonic-inverse-design-method-for-wing-fuselage-design-2iqv0kujp8.pdf

Supersonic inverse design method for wing-fuselage design

Adaptive Range Multiobjective Genetic Algorithm

3차원 Euler 방정식과 adjoint 법을 이용한 공력설계코드를 개발하였으며, 이를 초음속수송기의 주날개 설계에 적용하였다. 표면형상의 변화를 위해 Hicks-Henne 함수를 사용하였으며, 내부 격자점의 수정을 위해 타원형방정식법을 이용하였다. 나셀의 수직이동과 관련되지 않은 설계변수에 대해서는 내부격자정의 이동을 무시함으로써 계산시간을 크게 단축할 수 있었다. 양력과 날개단변두께를 일정하게 유지하면서 항력을 최소화하도록 단면형상을 최적화하였으며, 성공적인 결과를 얻음으로써 본 설계시스템의 타당성 및 효율성을 확인하였다.

Supersonic wing-nacelle configuration design using an unstructured adjoint method

This paper discusses several coding methods for aerodynamic design through a reproduction of NASA supercritical airfoil and an aerodynamic shape optimization using an Evolutionary Algorithm (EA). The aerodynamic design demonstrates that the optimized designs using EAs depend on their coding methods. It also indicates the proper coding procedure leads to finding a better optimum in aerodynamic optimization problem.

Application of evolutionary algorithms to aerodynamic wing designs

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