Three-Dimensional Building-Cube Method for Inviscid Compressible Flow Computations

김래성,Kazuhiro Nakahashi,Zhe-Zhu Xu,Hong Xiao,류성기 한국정밀공학회 2015 International Journal of Precision Engineering and Vol.16 No.13

In this study, the Building-Cube method (BCM) devised for calculating large-scale flows and getting rid of the grid dependencies of computational results is extended to perform 3D inviscid compressible fluid flow simulations. The proposed scheme divides a computational domain into a large number of cubes with different sizes, and each individual cube is a sub-flow field simulated with a Cartesian grid of uniform spacing and an equal number of cells and nodes. Through the proposed scheme, we determine the geometric size of individual cube by Adapting the flow characteristics and geometrical shapes using an adaptively refining Cartesian grid approaches. The uniform spacing and equal number of cells and nodes in the Cartesian grid of individual cubes ensure a good performance for parallel computations; large result data can be handled efficiently. Further, an algorithm to solve the inviscid flow equations on the Building-Cube mesh for three-dimensional (3D) geometries is presented. The validation and performance of the proposed 3D BCM are demonstrated through comparisons of the computed results with the experimental data for the ONERA M6 wing and ONERA M5 wing-fuselage configurations.

Adaptive Mesh Refinement Using Viscous Adjoint Method for Single- and Multi-Element Airfoil Analysis

Yamahara, Toru,Nakahashi, Kazuhiro,Kim, Hyoungjin The Korean Society for Aeronautical and Space Scie 2017 International Journal of Aeronautical and Space Sc Vol.18 No.4

An adjoint-based error estimation and mesh adaptation study is conducted for two-dimensional viscous flows on unstructured hybrid meshes. The error in an integral output functional of interest is estimated by a dot product of the residual vector and adjoint variable vector. Regions for the mesh to be adapted are selected based on the amount of local error at each nodal point. Triangular cells in the adaptive regions are refined by regular refinement, and quadrangular cells near viscous walls are bisected accordingly. The present procedure is applied to single-element airfoils such as the RAE2822 at a transonic regime and a diamond-shaped airfoil at a supersonic regime. Then the 30P30N multi-element airfoil at a low subsonic regime with a high incidence angle (${\alpha}=21deg.$) is analyzed. The same level of prediction accuracy for lift and drag is achieved with much less mesh points than the uniform mesh refinement approach. The detailed procedure of the adjoint-based mesh refinement for the multi-element airfoil case show that the basic flow features around the airfoil should be resolved so that the adjoint method can accurately estimate an output error.

Adaptive Mesh Refinement Using Viscous Adjoint Method for Single- and Multi-Element Airfoil Analysis

Toru Yamahara,Kazuhiro Nakahashi,김형진 한국항공우주학회 2017 International Journal of Aeronautical and Space Sc Vol.18 No.4

An adjoint-based error estimation and mesh adaptation study is conducted for two-dimensional viscous flows on unstructured hybrid meshes. The error in an integral output functional of interest is estimated by a dot product of the residual vector and adjoint variable vector. Regions for the mesh to be adapted are selected based on the amount of local error at each nodal point. Triangular cells in the adaptive regions are refined by regular refinement, and quadrangular cells near viscous walls are bisected accordingly. The present procedure is applied to single-element airfoils such as the RAE2822 at a transonic regime and a diamond-shaped airfoil at a supersonic regime. Then the 30P30N multi-element airfoil at a low subsonic regime with a high incidence angle (α=21deg.) is analyzed. The same level of prediction accuracy for lift and drag is achieved with much less mesh points than the uniform mesh refinement approach. The detailed procedure of the adjoint-based mesh refinement for the multi-element airfoil case show that the basic flow features around the airfoil should be resolved so that the adjoint method can accurately estimate an output error.

Study of Mild-Stall Wings with a Fixed Slat

Atsushi Ito,Daisuke Sasaki,Kazuhiro Nakahashi 한국항공우주학회 2008 한국항공우주학회 학술발표회 논문집 Vol.- No.-

Much attention has been paid to PAY (Personal Air Vehicle) as a new-generation small aircraft, It is expected that PAY will be widely used as a short-range transport aircraft in the future for countermeasure against traffic jam, One of the key technologies to make PAY much popular is to enhance the safety, which is crucial to small planes, In order to enhance the safety of PAY, mild-stall high-lift characteristics of the wing are especially needed. This study aims to propose a mild-stall wing with a fixed slat for PAY use, Two mild-stall airfoils are combined to form a new rectangular wing: NACA4415 and SLAT4415, NACA4415 is known as a conventional mild-stall airfoil, and SLAT4415 is a fixed slat airfoil based on NACA4415 for further improvement in stall characteristic, The higher lift characteristic ofSLAT4415 was obtained via the optimization by Genetic Algorithm. Designed wings composed ofNAC4415 and SLAT4415 airfoils are numerically analyzed by solving the Navier-Stokes equations on the unstructured mesh to examine the performance at high-angle of attack for low-speed region, The computational results indicate that designed wings are able to achieve mild-stall characteristics, Lift coefficients of the designed wings tend to drop at 22 degrees of A.o.A, however, increase again as A.o.A becomes higher, For further analysis, numerical simulations for the wing that has a taper or that has only SLAT4415 airfoil were also conducted, As a result, it was proved that the designed rectangular wing that has SLAT4415 airfoil of fixed slat only in outboard wing had very mild stall characteristic.

Numerical Simulation to Detect the Change of Airfoil Stalling Characteristics Dependent on Reynolds number

Shinsuke NISHIMURA,Kisa MATSUSHIMA,Kazuhiro NAKAHASHI 한국항공우주학회 2008 한국항공우주학회 학술발표회 논문집 Vol.- No.-

The compact scheme with a new method to detect the transition point is applied to low-Reynolds number (Re = 3.43 x 10?, 2.51 x 10?) over the NACA9324 airfoil. RANS simulations have difficultly to predict the stalling characteristics because the large separation and transition occur in flow at low-Reynolds number region, NACA9324 shows peculiar aerodynamic characteristics. Its stall type change from leading-edge stall to trailing-edge stall when the Reynolds number increase over 3.43 x 10?. In preliminary study, fully laminar computations using conventional 3<SUP>rd</SUP>-order TVD and 2<SUP>nd</SUP>-order central differencing could not predict stalling characteristics of the NACA9324. Because that computations couldn’t resolve a laminar bubble and a transition from laminar to turbulent flow. Thus, compact high-order scheme with the new transition method is applied to the flow around the NACA9324 airfoil. As a current result, the compact scheme succeeds in predicting the trailing-edge stalling aerodynamic characteristics. The new transition method is being examined.

Supersonic Wing Design Method Using an Inverse Problem for Practical Application

Kisa Matsushima,Shoji Sakashita,Kazuhiro Nakahashi 한국항공우주학회 2008 한국항공우주학회 학술발표회 논문집 Vol.- No.-

A wing design system using an inverse problem has many advantages, The system can design with much smaller number of now simulations than generic design system. Moreover it can use many geometrical control points, So it was used in “NEXST-I” project and successfully designed the NLF wing. However it needs to be improved to apply this method to critical or severe design problems, One of the required improvements is in accuracy in determining geometric correction values, In this research. we aim to improve the design system by introducing high order term of the geometric perturbation, The redesign or a known wing was conducted to validate the modified design system, It is preliminary confirmed that the modified one has more accuracy and robustness than the original one.

FLAP DEFLECTION OPTIMZATION FOR TRANSONIC CRUISE PERFORMANCE IMPROVEMENT OF SUPERSONIC TRANSPORT WING

Hyoung-Jin Kim,Shigeru Obayashi,Kazuhiro Nakahashi 한국전산유체공학회 2000 한국전산유체공학회 학술대회논문집 Vol.2000 No.10

Wing flap deflection angles of a supersonic transport are optimized to improve transonic cruise performance. For this end, a numerical optimization method is adopted using a three-dimensional unstructured Euler code and a discrete adjoint code. Deflection angles often flaps; five for leading edge and five for trailing edge, are employed as design variables. The elliptic equation method is adopted for the interior grid modification during the design process. Interior grid sensitivities are neglected for efficiency. Also tested is the validity of the approximate gradient evaluation method for the present design problem and found that it is applicable for leading edge flap design in cases of no shock waves on the wing surface. The BFGS method is used to minimize the drag with constraints on the lift and upper surface Mach numbers. Two design examples are conducted; one is leading edge flap design, and the other is simultaneous design of leading edge and trailing edge flaps. The latter gave a smaller drag than the former by about two counts.

SUPERSONIC WING-NACELLE CONFIGURATION DESIGN USING AN UNSTRUCTURED ADJOINT METHOD

김형진(Hyoung-Jin Kim),Shigeru Obayashi,Kazuhiro Nakahashi 한국전산유체공학회 2000 한국전산유체공학회지 Vol.5 No.3

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.

FLAP DEFLECTION OPTIMZATION FOR TRANSONIC CRUISE PERFORMANCE IMPROVEMENT OF SUPERSONIC TRANSPORT WING

Kim Hyoung-Jin,Obayashi Shigeru,Nakahashi Kazuhiro 한국전산유체공학회 2001 한국전산유체공학회지 Vol.6 No.2

초음속 여객기의 천음속 순항 성능을 개선하기 위하여 날개의 플랩 꺽임각을 최적화하였다. 이를 위하여 3차원 Euler 코드와 adjoint 코드를 이용한 최적설계기법을 적용하였다. 설계변수로서, 앞전플랩 5개, 뒷전 플랩 5개 등 총 10개의 플랩의 꺽임각이 사용되었다. 설계과정중에 격자계 내부격자점의 수정을 위해 타원형방정식법을 이용하였다. 계산 시간의 단축을 위해 내부격자의 민감도는 무시하였다. 또한 본 설계문제에 근사구배기법의 적용가능성 여부를 조사하였다. 충격파가 없는 경우 앞전 플렙에 한하여 근사구배기법을 적용할 수 있음을 알았다. 최적설계기법으로 BFGS기법을 적용하여 항력을 최소화하였으며, 양력 및 날개 표면 마하수에 대한 제약조건을 적용하였다. 앞전 플랩의 최적화 및 앞전과 뒷전 플랩의 최적화 등 두 개의 설계 문제를 고려하였다. 성공적인 결과를 얻음으로써 본 설계방법의 타당성 및 효율성을 확인하였다.

AERODYNAMIC OPTIMIZATION OF SUPERSONIC WING-NACELLE CONFIGURATION USING AN UNSTRUCTURED ADJOINT METHOD

Hyoung-Jin Kim,Shigeru Obayashi,Kazuhiro Nakahashi 한국전산유체공학회 2000 한국전산유체공학회 학술대회논문집 Vol.2000 No.5

An aerodynamic design method has been developed by using a three-dimensional unstructured Euler code and an adjoint code with a discrete approach. The resulting adjoint code is applied to a wing design problem of supersonic transport with a wing-body-nacelle configuration. Hicks-Henne shape functions are adopted for the surface geometry perturbation, and the elliptic equation method is employed for the interior grid modification during the design process. Interior grid sensitivities are neglected except those for design parameters associated with nacelle translation. The Sequential Quadratic Programming method is used to minimize the drag with constraints on the lift and airfoil thickness. Successful design results confirm validity and efficiency of the present design method.