Revisiting the combinatorics of lifting line and 2D vortex lattice theory

2019 ◽  
Vol 123 (1265) ◽  
pp. 993-1012 ◽  
Author(s):  
M. A. Yukish
Keyword(s):  
Lattice Theory ◽  
Automated Theorem Proving ◽  
Vortex Lattice ◽  
Alternative Proof ◽  
Convergence Properties ◽  
Combinatorial Properties ◽  
Line Theory ◽  
Tools And Techniques ◽  
Lifting Line ◽  
Lifting Line Theory

ABSTRACTThis work revisits analyses of lifting line theory by A.R. Collar from 1958, bringing to bear some modern tools and techniques. The 2D vortex lattice model is also considered. Interesting combinatorial properties and simplified expressions for terms are presented, a simplified proof of model convergence shown, extension of the convergence properties to elliptical and arbitrary wing planforms is demonstrated, and approximations provided. An alternative proof of the optimality of constant downwash is presented. Modern automated theorem proving techniques are employed in confirming the combinatorial results.

Comparison of Inviscid Flow Methods for Lift and Drag Calculations Over Thin-Sail Geometries

2012 ◽  
Author(s):  
Robert E. Spall ◽  
Warren F. Phillips ◽  
Brian B. Pincock
Keyword(s):  
Vortex Lattice ◽  
Lift Coefficient ◽  
Computational Cost ◽  
Inviscid Flow ◽  
Induced Drag ◽  
Line Theory ◽  
Lift And Drag ◽  
Lifting Line ◽  
Lifting Line Theory ◽  
Better Than

Solutions obtained from lifting-line, vortex-lattice, and the Euler equations are presented for a series of rigid, thin wing and sail geometries. Initial calculations were performed for an untwisted, rectangular wing. For this case, lifting line theory, vortex lattice, and Euler solutions were all in reasonable agreement. However, the lifting-line theory was the only method to predict a constant ratio of induced drag coefficient to lift coefficient squared. Similar results were found for a forward-swept, tapered wing. Additional results are presented in terms of lift and drag coefficients for an isolated mainsail, and mainsail/jib combinations with sails representative of both a standard and tall rig Catalina 27. Although experimental data is lacking, overall conclusions are that the accuracy realized from lifting-line solutions is as good as or better than that obtained from vortex-lattice solutions and inviscid CFD solutions, but at a fraction of the computational cost. The linear lifting-line results compared quite well with the nonlinear lifting-line results, with the exception of the downstream mainsail when considering jib/mainsail combinations.

An improved nonlinear lifting-line theory.

AIAA Journal ◽  
1973 ◽  
Vol 11 (5) ◽  
pp. 739-742 ◽  
Author(s):  
CHUAN-TAU LAN
Keyword(s):  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

A comprehensive comparative investigation of the Lifting Line Theory and Blade Element Momentum Theory applied to small wind turbines

2021 ◽  
pp. 1-25
Author(s):  
K.A.R. Ismail ◽  
Willian Okita
Keyword(s):  
Wind Turbines ◽  
Power Coefficient ◽  
Computational Time ◽  
Local Flow ◽  
Small Wind Turbines ◽  
Wake Effects ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory ◽  
Blade Element

Abstract Small wind turbines are adequate for electricity generation in isolated areas to promote local expansion of commercial activities and social inclusion. Blade element momentum (BEM) method is usually used for performance prediction, but generally produces overestimated predictions since the wake effects are not precisely accounted for. Lifting line theory (LLT) can represent the blade and wake effects more precisely. In the present investigation the two methods are analyzed and their predictions of the aerodynamic performance of small wind turbines are compared. Conducted simulations showed a computational time of about 149.32 s for the Gottingen GO 398 based rotor simulated by the BEM and 1007.7 s for simulation by the LLT. The analysis of the power coefficient showed a maximum difference between the predictions of the two methods of about 4.4% in the case of Gottingen GO 398 airfoil based rotor and 6.3% for simulations of the Joukowski J 0021 airfoil. In the case of the annual energy production a difference of 2.35% is found between the predictions of the two methods. The effects of the blade geometrical variants such as twist angle and chord distributions increase the numerical deviations between the two methods due to the big number of iterations in the case of LLT. The cases analyzed showed deviations between 3.4% and 4.1%. As a whole, the results showed good performance of both methods; however the lifting line theory provides more precise results and more information on the local flow over the rotor blades.

Modern Adaptation of Prandtl's Classic Lifting-Line Theory

2000 ◽  
Vol 37 (4) ◽  
pp. 662-670 ◽  
Author(s):  
W. F. Phillips ◽  
D. O. Snyder
Keyword(s):  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

Some Remarks on Vortex Drag and its Spanwise Distribution in Incompressible Flow

1968 ◽  
Vol 72 (691) ◽  
pp. 623-625 ◽  
Author(s):  
H. C. Garner
Keyword(s):  
Theoretical Data ◽  
Leading Edge ◽  
List Type ◽  
Surface Theory ◽  
Lifting Surface ◽  
Line Theory ◽  
Lifting Line ◽  
Swept Wings ◽  
Lifting Line Theory ◽  
Drag Factor

Summary Theoretical data from lifting-surface theory are presented to illustrate (i) that the vortex drag factor is closely related to the half-wing spanwise centre of pressure on simple planforms without camber or twist, (ii) that lifting-line theory is useless for predicting the spanwise distribution of vortex drag on swept wings, (iii) that recent numerical improvements in lifting-surface theory help to reconcile the concepts of wake energy and leading-edge suction in relation to vortex drag.

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