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 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.

An Experimental and Theoretical Study on Cavitating Cascades and Their Application to Cavitating Propellers

1985 ◽  
Vol 29 (01) ◽  
pp. 23-38
Author(s):  
Okitsugu Furuya ◽  
Shin Maekawa
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Simple Method ◽  
Cascade Theory ◽  
Wide Range ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

In order to develop an analytical tool for predicting the off-design performance of supercavitating propellers over a wide range of operating conditions, a lifting-line theory was combined with a two-dimensional supercavitating cascade theory. The results of this simple method provided fairly accurate predictions for the performance at fully developed cavitating conditions. It was indicative that the fully developed supercavitating (s/c) propellers had strong cascade effects on their performance, and also that the three-dimensional propeller geometry corrections could properly be made by the lifting-line theory. However, the predicted performance with this propeller theory showed a significant deviation from experimental data in the range of J's larger than Jdesign, where partially cavitating conditions are expected to occur. Effort was then made on improving the prediction capability of the above propeller theory at partially cavitating (p/c) conditions. A new nonlinear partially cavitating cascade theory was then developed to provide a proper 2-D loading basis under such conditions. Two-dimensional cascade experiments were then conducted to prove the accuracy of the p/c and s/c cascade theories. The measured forces and flow observations obtained in these experiments shed a new light on the relationship between the forces and cavitation numbers at small angles of incidence. Corrected lift and drag forces were then used in the propeller program. The calculated results for KT and KQ with the new force data successfully correlated with the experimental data, now covering a large J-range where the partially cavitating conditions exist.

scholarly journals Aeroelastic behaviour of a wing with over-the-wing mounted UHBR engine

2020 ◽  
Vol 11 (4) ◽  
pp. 1045-1055 ◽  
Author(s):  
N. Neuert ◽  
D. Dinkler
Keyword(s):  
Three Dimensional ◽  
High Lift ◽  
Reduced Order ◽  
Aerodynamic Loads ◽  
Flow Simulations ◽  
Dimensional Effects ◽  
Line Theory ◽  
Lifting Line ◽  
Bypass Ratio ◽  
Lifting Line Theory

Abstract The aeroelastic behaviour of a wing with an over-the-wing pylon-mounted ultra-high bypass ratio engine and high-lift devices is studied with a reduced-order model. Wing, pylon and engine structures are reduced separately using the modal approach and described by their natural frequencies and modes. The characteristic aerodynamic loads are investigated with steady and unsteady flow simulations of a two-dimensional profile section. These results indicate possible heave instabilities at strongly negative angles of attack. Three-dimensional effects are taken into account using an adapted lifting line theory according to Prandtl. Due to high circulations resulting from the high-lift systems, the effective angles of attack are in the range of the potential instabilities. The substructures and aerodynamic loads are coupled in modal space. For the wing without three-dimensional effects, the bending instability occurs at the corresponding negative angles of attack. Even though there is potential for improvement, including the three-dimensional effects shifts the endagered area to possible operation points.

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.

An asymptotic theory of the jet flap in three dimensions

1971 ◽  
Vol 46 (4) ◽  
pp. 705-726 ◽  
Author(s):  
Naoyuki Tokuda
Keyword(s):  
Order Approximation ◽  
Three Dimensional ◽  
Outer Region ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Simple Method ◽  
Aspect Ratios ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

A uniformly valid asymptotic solution has been constructed for three-dimensional jet-flapped wings by the method of matched asymptotic expansions for high aspect ratios. The analysis assumes that the flow is inviscid and incompressible and is formulated on the thin airfoil theory in accordance with the well-established Spence (1961) theory in two dimensions.A simple method emerges in treating the bound vortices along the jet sheet which forms behind the wing with the aid of the following physical picture. Three distinct flow regions—namely inner, outer and Trefitz—exist in the problem. Close to the wing the flow approximates to that in two dimensions. Therefore, Spence's solution in two dimensions applies. In the outer region a wing shrinks to a line of singularities from which the main disturbances of flow in this region arise. In particular, we find that the shape of the jet sheet, hence the strength of vortices, is now predetermined by the strength of the singularities there. Hence a complete flow field in the outer region can now be determined first by evaluating the flow due to various degrees of singularities along this line and then adding the effect of the jet bound vortices which is now known. Far removed from the wing, the well-known Trefftz region exists in which calculations of aerodynamic forces can be most easily done.The result has been applied to various wing planforms such as cusped, elliptic and rectangular wings. The present result breaks down for rectangular wings. However, we can apply Stewartson's (1960) solution for lifting-line theory for semi-infinite rectangular wings, because, to this second-order approximation it is established that the jet sheet in the outer region makes no contribution to lift, with the direct contribution of the deflected jet at the exit being cancelled by the reduced circulation in the jet vortices. This result for the rectangular wing gives excellent agreement with the experiments made on a rectangular wing, while the result for elliptic wings underestimates them considerably.

An Alternative Approach to the High Aspect Ratio Wing With Jet Flap by Matched Asymptotic Expansions

1978 ◽  
Vol 29 (4) ◽  
pp. 227-250 ◽  
Author(s):  
T. Kida ◽  
Y. Miyai
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Matched Asymptotic Expansions ◽  
Alternative Approach ◽  
Line Theory ◽  
Physical Insight ◽  
Lifting Line ◽  
Lifting Line Theory

SummaryAn alternative method is described for solving the problem of a three-dimensional jet-flapped wing with a high aspect-ratio. This method is similar to the lifting-line theory of Kerney6 or Tokuda7, but differs in that the method of matched asymptotic expansions is applied to an integral equation, derived from the lifting surface theory, rather than a partial differential equation. The advantage of the present method over those used previously is that the necessary outer solutions are obtained directly; it is not necessary to rely upon physical insight or considerable ingenuity. The final results are different from those obtained by the previous authors; it is shown that the present result is correct, by noting some errors in the earlier theories.

Unified Lifting-Line Theory of Fully Wetted Hydrofoils

1965 ◽  
Vol 9 (03) ◽  
pp. 131-142
Author(s):  
Tetsuo Nishiyama
Keyword(s):  
Boundary Condition ◽  
Water Surface ◽  
Velocity Potential ◽  
Practical Interest ◽  
Free Water ◽  
Numerical Examples ◽  
Line Theory ◽  
Direct Problems ◽  
Lifting Line ◽  
Lifting Line Theory

Unified lifting-line theory is developed for the hydrofoil of fully-submerged and surface-piercing type. The indirect and direct problems are discussed in some detail in relation to the effect of the Froude number. The disturbing velocity potential is derived from the linearized boundary condition on the free water surface. Then from the boundary condition on the hydrofoil, a basic integral equation is obtained for the distribution of circulation over the span, from which the lift and resistance can be computed readily. Some numerical examples of practical interest are shown for the characteristics and optimum condition in a specified condition of operation for the fully-submerged and surface-piercing hydrofoils.

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