Mathematical model for takeoff simulation of a wing in proximity to the ground

Abstract

Aircraft flying close to the ground benefit from enhanced efficiency owing to decreased induced drag and increased lift. In this study, a mathematical model is developed to simulate the takeoff of a wing near the ground using an Iterative Boundary Element Method (IBEM) and the finite difference scheme. Two stand-alone sub-codes and a mother code, which enables communication between the sub-codes, are developed to solve for the self-excitation of the Wing-In-Ground (WIG) effect. The aerodynamic force exerted on the wing is calculated by the first sub-code using the IBEM, and the vertical displacement of the wing is calculated by the second sub-code using the finite difference scheme. The mother code commands the two sub-codes and can solve for the aerodynamics of the wing and operating height within seconds. The developed code system is used to solve for the force, velocity, and displacement of an NACA6409 wing at a 4° Angle of Attack (AoA) which has various numerical and experimental studies in the literature. The effects of thickness and AoA are then investigated and conclusions were drawn with respect to generated results. The proposed model provides a practical method for understanding the flight dynamics and it is specifically beneficial at the pre-design stages of a WIG effect craft.

Keywords

wing-in-ground effect / ground proximity / flight dynamics / iterative boundary element method

References

[1] Ahmed MR, Sharma SD. An investigation on the aerodynamics of a symmetrical airfoil in ground effect. Experimental Fluid and Thermal Sciences, 2005, 29(6): 633-647

[2] Bal S. Prediction of wave pattern and wave resistance of surface piercing bodies by a boundary element method. International Journal for Numerical Methods in Fluids, 2008, 56(3): 305-329

[3] Bal S, Kinnas SA. A BEM for the prediction of free surface effects on cavitating hydrofoils. Computational Mechanics, 2002, 28(3-4): 260-274

[4] Barber TJ. A study of water surface deformation due to tip vortices of a wing-in-ground effect. Journal of Ship Research, 2007, 51(2): 182-186

[5] Boschetti PJ, Cardenas EM, Amerio A. Increasing the lift-drag ratio of an unmanned aerial vehicle using local twist. Journal of Aircraft, 2008, 45(1): 10-15

[6] Chun HH, Chang CH. Longitudinal stability and dynamic motions of a small passenger WIG craft. Ocean Engineering, 2002, 29(10): 1145-1162

[7] Halloran M, O’Meara S. Wing in ground effect craft review, 1999, Melbourne: DSTO Aeronautical and Maritime Research Laboratory, 14

[8] Katz J, Plotkin A. Low speed aerodynamics-from wing theory to panel methods, 1991, 52-87

[9] Kinaci OK. Effect of wing twist in ground proximity, 2013

[10] Kinaci OK. An iterative boundary element method for a wing-in-ground effect. International Journal of Naval Architecture and Ocean Engineering, 2014, 6(2): 282-296

[11] Kinaci OK. A numerical parametric study on hydrofoil interaction in tandem. International Journal of Naval Architecture and Ocean Engineering, 2015, 7(1): 25-40

[12] Kinnas SA, Fine NE. A numerical nonlinear-analysis of the flow around 2-dimensional and 3-dimensional partially cavitating hydrofoils. Journal of Fluid Mechanics, 1993, 254: 151-181

[13] Liang H, Wang X, Zou L, Zong Z. Numerical study of two-dimensional heaving airfoils in ground effect. Journal of Fluids and Structures, 2014, 48: 188-202

[14] Liang H, Zong Z. A subsonic lifting surface theory for wing-in-ground effect. Acta Mechanica, 2011, 219(3-4): 203-217

[15] Luo SC, Chen YS. Ground effect on flow past a wing with a NACA0015 cross-section. Experimental Thermal and Fluid Sciences, 2012, 40: 18-28

[16] Matveev KI. Heave-pitch motions of a platform flying in extreme ground effect. Journal of Aerospace Engineering, 2012, 25(2): 238-245

[17] Nebylov AV. Controlled WIG flight–Stability and efficiency problems, 2003

[18] Qu Q, Lu Z, Liu P. Numerical study of aerodynamics of a wing-in-ground effect craft. Journal of Aircraft, 2014, 51(3): 913-924

[19] Rostami AB, Ghadimi P, Ghassemi H. Adaptive viscous-inviscid interaction method for analysis of airfoils in ground effect. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2016

[20] Rozhdestvensky KV. Wing-in-ground effect vehicles. Progress in Aerospace Sciences, 2006, 42(3): 211-283

[21] Tavakoli M, Seif MS. A practical method for investigation of aerodynamic and longitudinal static stability of wing-in-ground effect. International Journal of Maritime Technology, 2015, 3(4): 11-19

[22] Uslu Y, Bal S. Numerical prediction of wave drag of 2-D and 3-D bodies under or on a free surface. Turkish Journal of Engineering and Environmental Sciences, 2008, 32(3): 177-188

[23] Yang W, Lin F, Yang Z. Investigation on application of high-lift configuration to wing-in-ground effect. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2012, 226(G3): 260-271

[24] Yang W, Yang Z. Schemed power-augmented flow for wing-in-ground effect craft in cruise. Chinese Journal of Aeronautics, 2011, 24(2): 119-126

[25] Yang W, Yang Z, Collu M. Longitudinal static stability requirements for wing in ground effect vehicle. International Journal of Naval Architecture and Ocean Engineering, 2015, 7(2): 259-269

[26] Yang Z, Yang W. Complex flow for wing-in-ground effect craft with power augmented ram engine in cruise. Chinese Journal of Aeronautics, 2010, 23(1): 1-8

[27] Yang Z, Yang W, Jia Q. Ground viscous effect on 2D flow of wing in ground proximity. Engineering Applications of Computational Fluid Mechanics, 2010, 4(4): 521-531