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首页> 外文期刊>International Journal of Aeroacoustics >A primitive-variable boundary integral formulation unifying aeroacoustics and aerodynamics, and a natural velocity decomposition for vortical fields
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A primitive-variable boundary integral formulation unifying aeroacoustics and aerodynamics, and a natural velocity decomposition for vortical fields

机译：结合空气声学和空气动力学以及涡旋场自然速度分解的原始变量边界积分公式

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The paper presents an integrated approach to the study of aeroacoustics and unsteady aerodynamics, which is based upon the use of the boundary integral equation approach. Accordingly, the boundary integral formulation in primitive variables is thoroughly developed, for Euler as well as Navier-Stokes equations. As a result, one obtains explicit time-domain expressions for velocity and pressure in terms of the Cauchy data of the problem (boundary integral), plus the contribution of the nonlinear terms (field integral). It is shown that the representation for the pressure is very closely related to the classical boundary integral formulations in aeroacoustics (such as the Ffowcs Williams and Hawkings equation and the Kirchhoff method). Similarly, the representation for the velocity is closely related to a formulation introduced by the author for unsteady viscous compressible aerodynamics. In the process, however, a new velocity decomposition of the type v = grad φ + w is uncovered. The novelty is that the vortical velocity w is not defined in terms of the vorticity ω; on the contrary, w is defined through its own governing equation. Such a decomposition (and the governing equation for w, which does not involve the pressure) arises in a very natural way from the mathematical approach used, and hence is here named the natural velocity decomposition. In addition, two innovative results are obtained. First, for all the cases addressed (incompressible and compressible, inviscid and viscous fields) there exist generalizations of the Bernoulli theorem (formally very similar to the classical Bernoulli theorems, with the potential φ of the irrotational portion of the velocity replacing the velocity potential φ). Second, it is shown that the velocity field may be obtained independently of the pressure, which may be evaluated a-posteriori in terms of the potential φ (akin to the evaluation of the pressure in a Venturi tube), through the appropriate generalized Bernoulli theorem. The paper is of theoretical nature - no numerical results are included; however, the schemes for computational implementations are presented and the advantages discussed.
机译：本文提出了一种基于边界积分方程法的航空声学和非定常空气动力学研究的综合方法。因此，对于欧拉以及Navier-Stokes方程，对原始变量中的边界积分公式进行了全面开发。结果，根据问题的柯西数据（边界积分）加上非线性项的贡献（场积分），获得了速度和压力的显式时域表达式。结果表明，压力的表示与航空声学中的经典边界积分公式（例如Ffowcs Williams和Hawkings方程以及Kirchhoff方法）密切相关。同样，速度的表示与作者为不稳定的可压缩空气动力学引入的公式密切相关。但是，在此过程中，发现了类型v = gradφ+ w的新速度分解。新颖之处在于，没有根据涡度ω定义涡旋速度w;相反，w是通过其自己的控制方程式定义的。这种分解（以及不涉及压力的w的控制方程）是从所使用的数学方法中非常自然地产生的，因此在此称为自然速度分解。另外，获得了两个创新的结果。首先，对于所有涉及的情况（不可压缩和可压缩，不粘和粘滞场），存在伯努利定理的一般化（形式上与经典伯努利定理非常相似，用速度的非旋转部分的势φ代替速度势φ ）。其次，表明可以通过适当的广义伯努利定理独立于压力而获得速度场，可以根据势φ进行后验评估（类似于对文丘里管中压力的评估）。 。本文具有理论性质-不包括数值结果;然而，提出了用于计算实现的方案并讨论了优点。

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