A New Approach to Lifting Line Theory: Hub and Duct Effects

2006 ◽  
Vol 50 (02) ◽  
pp. 138-146
Author(s):  
Victor G. Mishkevich
Keyword(s):  
Mathematical Model ◽  
Singular Integrals ◽  
Jacobi Polynomials ◽  
New Approach ◽  
Improve Design ◽  
Propeller Design ◽  
Line Theory ◽  
Circulation Distribution ◽  
Lifting Line ◽  
Lifting Line Theory

This paper deals with a new approach to lifting line theory in which the presence of a hub and/or duct is taken into account by introducing the generalized induction factors. The proposed mathematical model is built on the assumption that the hub and/or duct are simulated with infinite cylinders. The circulation distribution function is represented in the form of a series of orthogonal Jacobi polynomials that covers all cases that can occur in practical propeller design, including both zero and nonzero gap conditions. The integral equation of the lifting line theory is solved numerically by applying the highest accuracy quadrature formula for singular integrals. Propellers with optimum and arbitrary circulation distribution are considered. The proposed theory is intended to improve design of the near hub and duct blade sections, cavitation control, and integral propeller characteristics. Numerical results are presented for the purpose of comparison with different methods and to illustrate the developed approach.

Unified Rotor Lifting Line Theory

2013 ◽  
Vol 57 (04) ◽  
pp. 181-201
Author(s):  
Brenden P. Epps ◽  
Richard W. Kimball
Keyword(s):  
Axial Flow ◽  
Preliminary Design ◽  
Propeller Design ◽  
Performance Curves ◽  
Line Theory ◽  
Parametric Studies ◽  
Lifting Line ◽  
Lifting Line Method ◽  
Lifting Line Theory ◽  
Line Analysis

A unified lifting line method for the design and analysis of axial flow propellers and turbines is presented. The method incorporates significant improvements to the classical lifting line methods for propeller design to extend the method to the design of turbines. In addition, lifting line analysis methods are developed to extend the usefulness of the lifting line model to allow generation of performance curves for off-design analysis. The result is a fast computational methodology for the design and analysis of propellers or turbines that can be used in preliminary design and parametric studies. Design and analysis validation cases are presented and compared with experimental data.

Development of a Lifting-Line-Based Method for Preliminary Propeller Design

2018 ◽  
Author(s):  
Jose Rodolfo Chreim ◽  
Marcos de Mattos Pimenta ◽  
Joao Lucas Dozzi Dantas ◽  
Gustavo R. S. Assi ◽  
Eduardo Tadashi Katsuno
Keyword(s):  
Convergence Rates ◽  
Control Points ◽  
Numerical Implementation ◽  
Marine Propellers ◽  
Propeller Design ◽  
Line Theory ◽  
Thrust And Torque ◽  
Lifting Line ◽  
Lifting Line Theory

A novel formulation for marine propellers based on adaptations from wing lifting-line theory is presented; the method is capable of simulating propellers with skewed and raked blades. It also incorporates the influence of viscosity on thrust and torque from hydrofoil data through a nonlinear scheme that changes the location of the control points iteratively. Several convergence studies are conducted to verify the different aspects of the numerical implementation and the results indicate satisfactory convergence rates for Kaplan, KCA, and B-Troost propellers. It is expected that the method accurately describes thrust, torque, and efficiency under the moderately loaded propeller assumption.

A Model of an Axisymmetrical Ducted Propeller with Zero Tip Clearance

1979 ◽  
Vol 23 (04) ◽  
pp. 253-259
Author(s):  
Monir F. George
Keyword(s):  
Double Fourier Series ◽  
Tip Clearance ◽  
Longitudinal Vortex ◽  
Ducted Propeller ◽  
Line Theory ◽  
Blade Tip ◽  
Circulation Distribution ◽  
Free Running ◽  
Lifting Line ◽  
Lifting Line Theory

This paper is concerned with the case of a propeller working inside a symmetrical duct of finite length, zero thickness, zero camber and zero tip clearance. The propeller is modeled by the well-known Lerbs lifting-line theory while its radial circulation distribution is represented by a double Fourier series which allows for a nonzero circulation to occur at the blade tip. At the same time the duct circulation is considered to vary axially and circumferentially, which results in a system of longitudinal vortex filaments shed from each point on the duct surface. A comparison is made between the present method and the more sophisticated Tachmindji potential theory and the agreement is very good. Comparison is also made between the ducted and free-running (open) propeller.

A Three-Dimensional Theory for Calculating Circulation in Axial Turbomachines (Direct Problems)

1974 ◽  
Vol 96 (4) ◽  
pp. 365-371
Author(s):  
E. Lumsdaine ◽  
A. Fathy
Keyword(s):  
Finite Length ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Two Dimensional ◽  
Line Theory ◽  
Large Length ◽  
Circulation Distribution ◽  
Direct Problems ◽  
Lifting Line ◽  
Lifting Line Theory

In this work the steady-state spanwise circulation distribution of thin, slightly cambered radial blades of finite length is calculated using the method of singularities. The analysis extends the method of Scholz [1] for two-dimensional cascades to the three-dimensional case of radial blades of finite length. The effect of the casing enclosing the cascade is introduced by the method of images. The present analysis uses the generalized cylindrical coordinates without the restriction of the Prandtl lifting line theory. Comparisons show that for large hub-tip ratios, the use of the lifting line approximation will result in large errors. For small tip clearance or large length-chord ratio the present results reduce to the two-dimensional cascade solution.

A New Approach To High-Aspect-Ratio Supercavitating Hydrofoils

1979 ◽  
Vol 23 (03) ◽  
pp. 218-227
Author(s):  
Teruhiko Kida ◽  
Yoshihiro Miyai
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Present Theory ◽  
Cavitation Number ◽  
New Approach ◽  
Surface Theory ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

A three-dimensional cavity hydrofoil with a high aspect ratio is analyzed by a new lifting-line theory. Unlike Leehey's (1971) approach, which formulates the lifting-line theory from differential equations, the present theory has extracted the similar lifting-line theory from integral equations derived from the lifting-surface theory. The chief advantage of this method is that it is not necessary to match the inner and outer solutions. This lifting-line theory seems to be close to experimental results for the elliptic planform with aspect ratio 3 and 5, and for the rectangular planform with aspect ratio 6, in the case of δ/α ≥ 1, where σ is the cavitation number and α the incidence of the foil.

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.

Sign in / Sign up

Export Citation Format

Share Document