A three-dimensional unstructured Incompressible flow solver has been developed to solve the Navier-Stokes equations based on the Pseudo-compressibility method. The code is applicable to steady Incompressible flow problems. A cell-centered finite volume method has been used in which all flow variables are defined at the centroid of the tetrahedrons (control volume) in an unstructured grid. The inviscid fluxes are computed using the Roe's Flux Difference Splitting scheme, and higher-order spatial accuracy is attained by data reconstruction based on Taylor's series expansion. The first derivatives of the viscous flux are evaluated by a linear reconstruction method. For time integration, an Implicit Jacobi/Gauss-Seidel method has been used to solve the resulting set of Governing equations. The one-equation turbulence model of Spalart and Allmaras has been used in the present code for calculating high Reynolds number flows. Wall function has been used to resolve the near solid-wall effects for turbulent flow problems to reduce the computational memory requirements.
The inviscid flow solver has been validated using the NACA-0012 wing configuration and compared with the results of the well known Panel method results for $C_p$ distribution. The invisicd flow solver was then applied to the Sphere geometry and the $C_p$ distribution around the sphere was compared with available analytical data.
The laminar flow solver was validated using the flat plate configuration and the results were compared with the blasius solution. The laminar flow solver was then applied to the sphere geometry and the comparisons were made for $C_D$ with experimental data.
The turbulent flow solver was validated using the flat plate configuration. The flow solver was then applied to NACA-0012 configuration with different angle of attacks and the results were compared with the validated inhouse compressible flow solver for Ma=0.3 and with compressible experimental data for Ma=0.3. The results in all cases are comparable. Finally the code was applied to a 6:1 Spheroid geometry and the results were compared with experimental data and results of DES simulation for angle of attack 10° and 20° for a Reynolds number $4.2\times10^6$ based on the spheroid length.
삼차원 비압축성유동의 정상상태 점성유동장을 해석하기 위해 비정렬 격자계에서 Pseudo-compressibility 방법을 이용한 유동해석코드를 개발하였다. 지배방정식은 유동변수가 사면체 격자중심에 위치하는 격자중심기법을 사용하여 차분화되었으며, 비점성 플럭스는 Roe의 FDS(flux difference splitting) 방법을 이용하여 계산하였다. 공간상의 고차정확도를 얻기 위해 Taylor's series expansion 에 기초한 재구성방법을 이용하였으며, 점성 플럭스의 일차 미분항은 격자중심의 유동변수를 선형적으로 재구성하여 계산되었다. 시간전진을 위해 내재적 Jacobi/Gauss-Seidel 방법을 사용하였으며, 높은 Reynolds 수를 가지는 난류유동에 대해서는 one-equation Spalart-Allmaras 난류모형을 적용하였다. 난류유동장의 물체벽면에서는 메모리의 절감과 계산시간의 단축을 위해 wall-function 을 사용하였다.
첫 번째로 유동해석코드의 비점성 유동 검증을 위해 NACA0012 날개형상에 대한 해석을 수행하고, 해석에서 얻어진 표면압력분포를 panel method 를 이용한 결과와 비교하였다. 또한 구형상에 대한 해석을 수행하여 analytic 결과와 비교하였다.
두 번째로 층류유동장의 검증을 위해서 평판에 대한 층류유동을 계산하고 이를 Blasius solution 과 비교하였으며, 구형상에 대해 계산을 통해 얻어진 항력계수와 실험에 대한 결과를 비교하였다.
마지막으로 난류유동장에 대해 평판을 지나가는 난류유동을 해석하고, NACA0012 날개에 대해 자유류 마하수 0.3에서 여러가지 받음각에 대한 유동을 해석하여 이를 압축성 유동해석 결과 및 실험치와 비교하였다. 또한 6:1의 비를 가지는 spheroid 형상에 대해 받음각 10˚, 20, Reynolds 수 $4.2\times10^6$ 에서의 유동을 해석하여 이를 DES 결과와 비교하였다.