Prediction of Lift Coefficient for Tandem Wing Configuration or Multiple-Lifting-Surface System Using Prandtl’s Lifting-Line Theory

Abstract

In tandem airfoil configuration or multiple-lifting-surface layouts, due to the flow interaction among their lifting surfaces, the aerodynamic characteristics can be affected by each other. In accordance with Prandtl's classical lifting-line theory, a method to calculate the section lift coefficient for the tandem wing configuration or multiple-lifting-surface system is presented. In that method, the form of Fourier sine series is used to express the variation of the section circulation which changes continuously along the wingspan. The accuracy of the numerical solutions obtained by the method has been validated by the data obtained from computational fluid dynamics and tunnel experiment. By varying the design parameters, such as the gap, the stagger, the incidence angle, the wingspan, the taper ratio as well as the aspect ratio, a series of tandem wing configurations are tested to analyze the lift coefficient and the induced drag of each lifting surface. From the results, it can be seen that the bigger negative gap and stagger can produce better lift characteristic for tandem wing configuration. Besides, it will also be beneficial for the lift characteristic when the incidence angle and the wingspan of fore wing are appropriately declined or if the incidence angle and the wingspan of hind wing are appropriately increased.

An Adaptive Sequential Sampling Strategy-Based Multi-Objective Optimization of Aerodynamic Configuration for a Tandem-Wing UAV via a Surrogate Model

“…This research confirmed that the vortex-lattice method can accurately predict the unsteady aerodynamic performance [12]. Besides, the same team also proposed a method of predicting the lift coefficient of tandem-wing aircraft systems based on Prandtl's lifting-line theory [13]. The conclusions revealed the influence of some configuration variables acting alone on the performance of the aircraft systems.…”

“…The differences in aerodynamic characteristics for tandem-wing aircraft are primarily influenced by the aerodynamic interaction between the two pairs of wings, with little relationship of the fuselage and especially at a low angle-of-attack. This was verified with computational fluid dynamics (CFD) and use of the lifting line method by Cheng et al [13]. Five design variables are considered from the aspect of the three-dimensional position distribution between fore and rear wings and the wingspans of the two pairs of wings, as shown in Fig.…”

“…Nevertheless, the RMSE values appeared to be on the decline gradually to the target after adding more refinement samples. If RMSE= [0.011, 0.0061] is taken as the benchmark, the LHS method needed to increase [40,40] samples and LMD sampling method needed to add [30,25] samples, and the ESP adaptive sequential sampling method required only [13,24] samples. From the aspect of RMSE convergence trends, the ESP sampling strategy shows that there was a faster decline in prediction errors and smaller fluctuations than that of the LMD method.…”

Unsteady aerodynamics investigation of deploying tandem-wing with different methods

“…So, the lifting-line method has been widely used in aerodynamic characteristics calculation during the early aircraft conceptual design stage. 31–35…”

“…So, the lifting-line method has been widely used in aerodynamic characteristics calculation during the early aircraft conceptual design stage. [31][32][33][34][35] As the lifting-line theory stated, a wing is synthesized by composing a series of horseshoe-shaped vortices. Without approximation, the distributions of the bound vortices over the wing surface and that of the trailing vortices in the wing wake are continuous.…”