This paper investigates a specific case of one of the most popular fluid dynamic simulations, the incompressible flow around an airfoil (NACA 0012 here) at a high Reynolds number ( $$6 \times 10^6$$ ). OpenFOAM software was used to study the effect of domain size and four common choices of boundary conditions on airfoil lift, drag, surface friction, and pressure. We also examine the relation between boundary conditions and the velocity, pressure, and vorticity distributions throughout the domain. In addition to the common boundary conditions, we implement the “point vortex” boundary condition that was introduced many years ago but is now rarely used. We also applied the point vortex condition for the outlet pressure instead of using the traditional Neumann condition. With the airfoil generating significant lift at incidence angles of $$5^\circ , 10^\circ$$ , and $$14^\circ$$ , we confirm a previous finding that the boundary conditions combine with domain size to produce an induced (pressure) drag. The change in the pressure drag with domain size is significant for the commonly-used boundary conditions but is much smaller for the point vortex alternative. The point vortex boundary condition increases the execution time, but this is more than offset by the reduction in domain size needed to achieve a specified accuracy in the lift and drag. This study also estimates the error in total drag and lift due to domain size and shows it can be almost eliminated using the point vortex boundary condition. We also used the impulse form of the momentum equations to study the relation between drag and lift and spurious vorticity, which is generated as a result of using non-exact boundary conditions. These equations reveal that the spurious vorticity throughout the domain is associated with cancelling circulation around the domain boundaries.

中文翻译：

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域大小和边界条件对翼型模拟精度的一些影响

本文研究了最流行的流体动力学模拟之一的具体案例，即高雷诺数（ $$6 \times 10^6$$ ）下机翼周围的不可压缩流动（此处为 NACA 0012）。OpenFOAM 软件用于研究域大小和边界条件的四种常见选择对翼型升力、阻力、表面摩擦和压力的影响。我们还研究了边界条件与整个域中的速度、压力和涡度分布之间的关系。除了常见的边界条件外，我们还实现了多年前引入但现在很少使用的“点涡”边界条件。我们还对出口压力应用了点涡条件，而不是使用传统的诺伊曼条件。随着机翼在 $$5^\circ 、 10^\circ$$ 和 $$14^\circ$$ 入射角处产生显着升力，我们证实了先前的发现，即边界条件与域大小相结合产生感应（压力）拖动。压力阻力随域尺寸的变化对于常用的边界条件来说很重要，但对于点涡流替代方案来说要小得多。点涡流边界条件增加了执行时间，但这足以通过实现升力和阻力的指定精度所需的域大小的减小来抵消。这项研究还估计了由于域大小引起的总阻力和升力的误差，并表明使用点涡边界条件几乎可以消除该误差。我们还使用动量方程的脉冲形式来研究阻力和升力与虚假涡度之间的关系，虚假涡度是由于使用非精确边界条件而产生的。这些方程表明，整个域中的寄生涡度与域边界周围的环流抵消有关。