| The lifting theory is one of the most important branches of fluid mechanics,among which the proposal of Prandtl’s lifting line theory has greatly promoted the development of the aviation industry at that time.In recent years,with the rapid development of Wing-in-Ground craft technology,more and more researchers have been attracted by the research about the lifting theory in the vicinity of a free surface and most of them focus on exploring the physics of wing in ground effect and looking for simple efficient and precise methods to calculate lift.Under this background,lifting line theory is rejuvenated and has been highly regarded by many scholars because of its simple and distinct physics concept.They have generalized the lifting line theory to wings near a free surface and use the improved lifting line theory to calculate the lift of wing-in-ground crafts and hydrofoils and get accurate results.Based on former research,we do further research on lifting line theory near a free surface.First,according to potential flow theory,the control function and boundary conditions for steady motion above a free surface are provided and the free surface conditions are linearized based on the characteristics of the micro amplitude wave in this article.Then,we derive the velocity potential of 2D point vortex moving above the free surface.In order to simplify the calculation progress,we take the single lift line as an example,the simplest case,to further explore the lifting line theory near a free surface.By theoretical deriving and analyzing the experiment phenomena in other papers,we find that when the lifting line keeps close to a free surface or a ground surface,the free vortex lines of lifting line will tilt horizontally instead of being perpendicular to bound vortex line.Thus,the phenomenon is called lateral wash motion,the inclination angle is named lateral wash angle and the new form lifting line is called(?)vortex.Then,the formulae to calculate lateral wash velocity and lateral wash angle have been derived.Through calculating examples of WIG(wing in ground),relationships between the lateral wash angle and some factors such as relative interval,velocity and circulation of lifting line are gained.It turns out that magnitude of lateral wash angle is roughly equal to the down wash angle in the vicinity of a free surface or a ground surface.Next,based on the discovery of lateral wash,the definition and calculation method of the corresponding induced lift are given,and the Green function of the constant moving(?)vortex line above a free surface is derived.Then,we use this Green function and some specific data to calculate the total lift and induced lift of(?)vortex line near a free surface.It turns out that the induced lift accounts for 2% ~ 5% of total lift in certain situations,the lateral wash angle should be taken into account when using lifting line theory to compute the lift of WIG.On the other hand,the induced lift produced by(?)vortex line considering the effect of free surface varies with the distance between vortex line and free surface and its velocity.The aforementioned researches are based on a single lifting line.In the end,inspired by the concept of lateral wash,the improved lifting line theory has been put forward and has been employed to calculate the lift of WIG.The lifting line theory in vicinity of a free surface has also been expanded to apply to the situation of curved wings,swept wings and so on. |
