A Model of an Axisymmetrical Ducted Propeller with Zero Tip Clearance

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.

Download Full-text

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

Journal of Engineering for Power ◽

10.1115/1.3445859 ◽

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.

Download Full-text

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

Journal of Ship Research ◽

10.5957/jsr.2006.50.2.138 ◽

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.

Download Full-text

Lifting-Line Theory of a Wing with Tip Clearance

Transactions of the Japan Society of Mechanical Engineers ◽

10.1299/kikai1938.35.1003 ◽

1969 ◽

Vol 35 (273) ◽

pp. 1003-1007

Author(s):

Tetsuo NISHIYAMA ◽

Takeo TAKAGI

Keyword(s):

Tip Clearance ◽

Line Theory ◽

Lifting Line ◽

Lifting Line Theory

Download Full-text

Minimum Induced Drag of Non-Planar Ground Effect Wings with Small Tip Clearance

Aeronautical Quarterly ◽

10.1017/s0001925900006776 ◽

1974 ◽

Vol 25 (1) ◽

pp. 19-36 ◽

Cited By ~ 5

Author(s):

T Kida ◽

Y Miyai

Keyword(s):

Present Method ◽

Ground Effect ◽

Tip Clearance ◽

Approximate Theory ◽

Circular Arc ◽

Induced Drag ◽

Line Theory ◽

Lifting Line ◽

Wing Tip ◽

Lifting Line Theory

SummaryThis paper treats theoretically the problem of the minimum induced drag of non-planar ground effect wings with both tips very close to the ground, within the limitations of the linearised lifting-line theory. The gap clearance between the wing tip and the ground is assumed to be very small and, using this small parameter, an approximate theory, which yields the minimum induced drag of a non-planar ground effect wing, is formulated by the method of matched asymptotic expansions. As a check on the accuracy of the method, this theory is compared with the exact theory for a semicircular wing. This shows that the present method is accurate within the small gap clearance. Moreover, the present method is applied to other wing configurations, such as semi-elliptic wings and wings with endplates, circular arc wings in a tube and circular arc wings. These computations show the theory to be very effective and it can be easily extended to various spanwise cambers.

Download Full-text

Finite Wing Lift-Curve Slope Calculations Using Lifting-Line Theory

23rd AIAA Applied Aerodynamics Conference ◽

10.2514/6.2005-4839 ◽

2005 ◽

Cited By ~ 1

Author(s):

David Bridges

Keyword(s):

Line Theory ◽

Lift Curve ◽

Finite Wing ◽

Lifting Line ◽

Lifting Line Theory

Download Full-text

An improved nonlinear lifting-line theory.

AIAA Journal ◽

10.2514/3.6819 ◽

1973 ◽

Vol 11 (5) ◽

pp. 739-742 ◽

Cited By ~ 10

Author(s):

CHUAN-TAU LAN

Keyword(s):

Line Theory ◽

Lifting Line ◽

Lifting Line Theory

Download Full-text

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

Journal of Energy Resources Technology ◽

10.1115/1.4053066 ◽

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.

Download Full-text