论文标题
可压能的电势流围绕圆形：Janzen-Rayleigh扩展推断
Compressible potential flows around round bodies: Janzen-Rayleigh expansion inferences
论文作者
论文摘要
可以使用偶数$ \ Mathcal $ \ Mathcal {M} _ \ infty $的左右的janzen-rayleigh扩展（JRE）来得出超音速的亚音速，可压缩的电势流。 JRE在二维（2D）的高订单上使用逆半径$ r^{ - 1} $进行了术语，但仅限于$ \ MATHCAL {M} _ \ indcal {m} _ \ infty^4 $在三个维度（3D）中。我们将一般的JRE公式推向了任意秩序，绝热指数和维度。我们发现，$ \ ln（r）$的功率可以渗入扩展，并且在3D中至关重要，超出顺序$ \ MATHCAL {m} _ \ infty^4 $。在2D磁盘中显然不存在这样的术语，因为我们确认$ \ MATHCAL {M} _ \ infty^{100} $，尽管它们确实在其他维度中显示（例如，按顺序$ \ Mathcal {M} _ \ Infty^2 $ 4D中的4D）和非Circular 2D Bodies。这表明该磁盘被广泛用于研究基本流量特性，具有额外的对称性。我们的结果用于改善球体前流的基于Hodograph的近似值。轴对称流的对称轴速度曲线围绕不同的pr素球体近似相互关联。
The subsonic, compressible, potential flow around a hypersphere can be derived using the Janzen-Rayleigh expansion (JRE) of the flow potential in even powers of the incident Mach number $\mathcal{M}_\infty$. JREs were carried out with terms polynomial in the inverse radius $r^{-1}$ to high orders in two dimensions (2D), but were limited to order $\mathcal{M}_\infty^4$ in three dimensions (3D). We derive general JRE formulae to arbitrary order, adiabatic index, and dimension. We find that powers of $\ln(r)$ can creep into the expansion, and are essential in 3D beyond order $\mathcal{M}_\infty^4$. Such terms are apparently absent in the 2D disk, as we confirm up to order $\mathcal{M}_\infty^{100}$, although they do show in other dimensions (e.g. at order $\mathcal{M}_\infty^2$ in 4D) and in non-circular 2D bodies. This suggests that the disk, which was extensively used to study basic flow properties, has additional symmetry. Our results are used to improve the hodograph-based approximation for the flow in front of a sphere. The symmetry-axis velocity profiles of axisymmetric flows around different prolate spheroids are approximately related to each other by a simple, Mach-independent scaling.
