並列タイトル等Numerical Analysis of Transonic Flow around Two-Dimensional Airfoil by Solving Navier-Stokes Equations
タイトル（掲載誌）航空宇宙技術研究所特別資料 = Special Publication of National Aerospace Laboratory SP-3
一般注記An effective finite-difference scheme for solving full compressible Navier-Stokes equations was initated by Beam and Warming. The purpose of this paper is to develop that technique and apply it to the calculation of a typical subsonic or transonic, inviscid or viscous steady flow. We almost identically follow the Beam-Warming technique that may be summarized into the following threee characteristics: a) Delta-form approximate factorization algorithm, b) Implicit three-level scheme. c) The cross derivative viscous terms were explicitly replaced by the values of previous time. First, the strong conservation-law form of the Navier-Stokes equations is written in Cartesian coordinates, and then transformed into a general grid system. Following the Beam-Warming difference scheme, we generally adopt the parameter combination delta
An effective finite-difference scheme for solving full compressible Navier-Stokes equations was initated by Beam and Warming. The purpose of this paper is to develop that technique and apply it to the calculation of a typical subsonic or transonic, inviscid or viscous steady flow. We almost identically follow the Beam-Warming technique that may be summarized into the following threee characteristics: a) Delta-form approximate factorization algorithm, b) Implicit three-level scheme. c) The cross derivative viscous terms were explicitly replaced by the values of previous time. First, the strong conservation-law form of the Navier-Stokes equations is written in Cartesian coordinates, and then transformed into a general grid system. Following the Beam-Warming difference scheme, we generally adopt the parameter combination delta = l/2 and theta = 1. After introducing spatial factorization, second-order dissipative terms are added to the left-hand side, while fourth-order terms are added to the right-hand side; the fourth-order smoothing terms are changed to second-order terms at points adjacent to the boundaries. The numerical computations were carried out only for a typical NACA 0012 airfoil. The grid system used is a C-type, where 51 points are distributed uniformly over the airfoil surface with identical arc length. The lines of constant xi consist of two parts: One part of those emanating from the airfoil sulface points is the solution of the Laplace equation and the others are parabolas. The distribution of points on wake cut and in the eta-direction is exponential. The calculations start from uniform free-stream variables throughout the flow field. The boundary conditions in the far field are free-stream. The following four cases are calculated:a) M infinity =0.63 and alpha=0, causing an entirely subsonic flow. b) M infinity =0.63 and alpha=2 degrees, the highest velocity of upper surface being close to sonic c) M infinity =0.75 and alpha=0, when supersonic regions appear but there are no shock waves. The flow is supercritical. d) M infinity =0.75 and alpha=2 degrees, generating a shock wave over the upper flow field. The flow is transonic in the case of inviscid calculations. Viscous calculations, on the other hand, show no shock waves, while flow separation on the upper surface caused by the angle of attack is conspicuous.
資料番号: NALSP0003027
レポート番号: NAL SP-3
一次資料へのリンクURLhttps://jaxa.repo.nii.ac.jp/?action=repository_action_common_download&item_id=43169&item_no=1&attribute_id=31&file_no=1
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
提供元機関・データベース宇宙航空研究開発機構 : 宇宙航空研究開発機構リポジトリ