Detailed Numerical Study on the Aerodynamic Behavior of a Gurney Flapped Airfoil in the Ultra-low Reynolds Regime

ABSTRACT: The addition of Gurney flap changes the nature of flow around airfoil by producing asymmetric Von-Karman vortex in its wake. Most of the investigations on Gurney flapped airfoils have modeled the flow using a quasi-steady approach, resulting in time-averaged values with no information on the unsteady features of the flow. Among these, some investigations have shown that quasi-steady approach does a good job on predicting the aerodynamic coefficients and physics of flow. Previous studies on Gurney flap have shown that the calculated aerodynamic coefficients such as lift and drag coefficients from quasi-steady approach are in good agreement with the time averaged values of these quantities in time accurate computations. However, these investigations were conducted in regimes of medium to high Reynolds numbers where the flow is turbulent. Whether this is true for the regime of ultra-low Reynolds number is open to question. Therefore, it is deemed necessary to examine the previous investigations in the regime of ultra-low Reynolds numbers. The unsteady incompressible laminar flow over a Gurney flapped airfoil is investigated using three approaches; namely unsteady accurate, unsteady inaccurate, and quasi-steady. Overall, all the simulations showed that at ultra-low Reynolds numbers quasi-steady solution does not necessarily have the same correlation with the time averaged results over the unsteady accurate solution. In addition, it was observed that results of unsteady inaccurate approach with very small time steps can be used to predict time-averaged quantities fairly accurate with less computational cost.

摘要：格尼襟翼(Gurney flap)的加装会通过在翼型(airfoil)尾流中生成不对称冯·卡门涡(Von-Karman vortex)，改变翼型周围的流动特性。当前绝大多数针对加装格尼襟翼的翼型的研究均采用准稳态方法(quasi-steady approach)对流动进行建模，仅能得到流动的时间平均值，无法反映其非定常特性。其中部分研究表明，准稳态方法可较好地预测气动系数与流动物理规律。过往针对格尼襟翼的研究显示，通过准稳态方法计算得到的升力系数、阻力系数等气动参数，与时间精确计算(time accurate computations)得到的对应物理量的时间平均值吻合度较高。但此类研究均开展于流动为湍流的中高雷诺数(Reynolds numbers)流场场景中，该结论是否适用于超低雷诺数流场仍有待考证。因此，有必要针对超低雷诺数流场场景下的相关研究开展验证工作。本研究采用三种方法对加装格尼襟翼的翼型的非定常不可压缩层流(unsteady incompressible laminar flow)展开研究，分别为：时间精确法、非精确非定常法与准稳态法。整体而言，所有仿真结果均表明，在超低雷诺数条件下，准稳态解与基于时间精确解得到的时间平均值未必具有一致的相关性。此外，研究还发现，采用极小时间步长的非精确非定常方法，可在较低计算开销下较为精准地预测时间平均物理量。