Numerical Study of Transient Behavior of a NACA 0008 Airfoil Equipped with a Gurney Flap Using a Control-Volume Based Finite-Element Collocated Scheme

摘要

Gurney flap is a tab of small length located at the trailing edge of the airfoil normal to the chord line. Addition of gurney flap changes the unsteady nature of flow around airfoil by producing asymmetric Von-Karman vortex street in its wake. Gurney flap has been the subject of many experimental and numerical studies. Most of the investigations have modeled flow over a gurney flapped airfoil using a quasi-steady approach, resulting in time-averaged values with no information on the unsteady features of the flow. Having studied numerical results of this approach, some investigations have showed that to some extent the quasi-steady approach has the capability of predicting the physics of flow. It is shown that the calculated flow quantities such as lift or drag coefficient from quasi-steady approach are in good agreement with the time averaged values of these quantities in time accurate computations. These investigations however are conducted in medium to high Reynolds numbers regimes where the flow is turbulent. Whether this is true for all flow regimes especially the regime of very low Reynolds numbers, is open to question. So it is deemed necessary to examine the previous investigations in other flow regimes, especially in very low Reynolds numbers. The numerical algorithm adopted for this purpose is the MCIM algorithm of Alisadeghi and Karimian. This algorithm has been previously verified for the solution of incompressible steady and unsteady internal and external flows. MCIM algorithm is employed to solve unsteady incompressible laminar flow over a Gurney flapped airfoil using three approaches; namely unsteady accurate, unsteady inaccurate, and quasi-steady. Grid refinement and time-step dependent studies are conducted to ensure generation of accurate solution. Results obtained from these approaches are studied in detail and compared with each other. Since fully implicit procedure is used here, the following measures are taken into account to reduce the CPU time and the required memory; 1) employment of a band solver with node renumbering, and 2) employment of a direct sparse solver. Overall, all the simulations show that at low Reynolds numbers quasi-steady solution doesn't necessarily have the same correlation with the results time averaged 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.