Pervane aerodinamiği için girdap kafes uygulamaları
Vortex lattice applications for propeller aerodynamics
Yazar: EMRE ŞAHİN
Danışman: PROF. DR. MAHMUT ADİL YÜKSELEN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Uçak ve Uzay Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2013
Konu: Uçak Mühendisliği = Aircraft Engineering
Dizin: Aerodinamik = Aerodynamics ; Girdap =  ; Pervaneler = Fans

Özet:
Bir hava aracı tasarımı yapılırken ortaya çıkan geometriden doğabilecek aerodinamik yüklerin bilinmesi gerekir. Bu yükler deneysel çalışmalar ve teorik çalışmalar olmak üzere iki yolla elde edilir. Deneysel çalışmalar hem maliyet hem de zaman açısından dezavantajlı olduğu için sayısal çözüm tekniklerinin geliştirilmesi oldukça faydalıdır.
Bu çalışmada pervane analizi üzerine bir inceleme yapılmıştır. Kullanılan yöntemin analojisi girdap kafes yöntemlerine dayanan non-lineer nümerik taşıyıcı çizgi yöntemidir.
Literatürde taşıyıcı çizgi yöntemlerinin dihedral açılı ve ok açılı taşıyıcı elemanlar için hatalı sonuçlar vermesine rağmen girdap kafes yöntemleriyle ok açılı ve dihedral açılı her türlü taşıyıcı elemanın ve eleman kombinasyonlarının analiz edilebileceği belirtilmektedir. Ancak girdap kafes yöntemleri taşıyıcı elemanı kamburluk eğrisinden ibaretmiş gibi varsaydığından viskoz etkileri hesaba katamamaktadır. Bu nedenle kesit profil bilgisini kullanarak kamburluk ve viskoz etkileri hesaba katabilen non-lineer nümerik taşıyıcı çizgi teorisi taşıyıcı çizgi teorilerinin ve girdap kafes yöntemlerinin ara kesiti durumundadır.
Çalışmada non-lineer nümerik taşıyıcı çizgi yöntemini kullanarak pervane analizi yapabilen bir bilgisayar programı geliştirilmiştir. Programın doğrulama çalışmaları kanat üzerinde yapılarak tatminkâr sonuçlar elde edilmiştir. Pervane üzerindeki uygulamalar için literatürden geometrisi ve performans değerleri bilinen test pervaneleri seçilmiştir. Bu pervane geometrileri Adkins (1994), Larrabee (1979) ve Bauer (1997)?nin çalışmalarından alınmıştır.
Programın tasarım dışı noktalardaki başarısını hesaplamak için Yaggy (1960) tarafından çeşitli oturma açılarında geometrisi verilmiş bir pervane modeli kullanılmıştır. Bu pervane NACA 0009 kesitinden imal edilmiştir. Klasik teoride ihtiyaç duyulan kesit karakteristikleri çeşitli Reynolds sayısı ve hücum açısı aralıklarında Abbott (1945) ve Sheldahl (1981)?den alınmıştır.

Abstract:
In the history of aviation, the propeller played an important role in the development of powered aircraft. When it comes to moving a piston engine airplane through the air, there is no alternative to the propeller. Most commercial airliners are now driven by propeller in the form of turbofan engines and turboprop engines.
Propellers are the most efficient means of aircraft propulsion. By imparting a small pressure change over a large area, propellers achieve much higher efficiency than jet engines. In the past, propellers were highly efficient at cruise speeds up to approximately Mach 0.6. However, above this speed, large compressibility losses on the blading caused the efficiency to fall rapidly. The increase emphasis on fuel conservation has stimulated developments on propeller powered aircraft. Nowadays, advanced design concepts make possible the design of high efficiency Propeller capable of Mach 0.8 crusing. Currently, popular numerical methods in used include the vortex lattice methods, the lifting line surface methods, are expected to provide extremely reliable predictions.
The literature of propeller aerodynamics is scattered and in some respects is inconsistent and incomplete. Of basic importance for the theory and design of propellers is the treatment of propellers with load distribution for best efficiency developed by Theodorsen in a series of NACA reports and finally presented in his book published in 1948, but now long out of print. This work is a milestone in the development of the theory of propellers, but parts of it are obscure, it is not without errors, and the application to the design of an efficient propeller needs clarification. The consequence of these difficulties has been a general neglect, both in theoretical studies and in practical propeller design, of the underlying theory developed by Theodorsen.
It has been shown that the ideal distribution of circulation first computed by Goldstein need not be limited to the condition of light loading as assumed by Goldstein. Nonetheless propeller design methods in current use are limited by the light loading assumption and fail to take advantage of the more general possibilities.
Quite remarkable is the lack in the aeronautical literature of a complete and accurate tabulation of the Goldstein circulation function, which is essential for the design of a propeller with minimum energy loss. In general, it is a very difficult problem to compute rigorously the velocity induced by the vortex system. Theodorsen, employing an electrical analog, expanded Goldstein?s very limited tables, but his results are also limited and not very accurate.
The theory of aircraft propellers, following the original development of finite wing theory, has nearly always proceeded as a lifting line analysis. That is, blade elements may be considered to act as two-dimensional foils upon which the forces are the same as would be found in a uniform two-dimensional flow with the same velocity and direction as occurs locally at the blade element. This approach to the design of blade elements is continued in the present study. The lifting line treatment does not restrict the generality of the underlying analysis of the trailing vortex system.
The lifting line theory is the best known and most readily applied theory for obtaining the spanwise lift distribution of a wing and the subsequent determination of the aerodynamic characteristics of the wing from two dimensional airfoil data. The characteristics so determined are in fairly close agreement with experimental results for wings with small amounts of sweep and with moderate to high values of aspect ratio. For this reason, this theory has served as the basis for a large part of precent aeronautical knowledge.
The hypothesis upon which tho theory is based is that a lifting wing can be replaced by a lifting line and that the incremental vortices ahed along the span trail behind the wing in straight lines in the direction of the free-stream velocity. The strength of these trailing vortices is proportional to the rate of change of the lift along the span. The trailing vertices induce a velocity normal to the direction of the free stream velocity and to the lifting line. The effective angle of attack of each section of the wing is therefore different frcm the geometric angle of attack by the amount of the engle (called the induced angle of attack) whose tangent is the ratio of the value of the induced velocity at the lifting line to the value of the free stream velocity. The effective angle of attack is thus related to the lift distribution through the induced angle of attack. In addition, the effective angle of attack is related to the section lift coefficient according to two dimensional data for the airfoil sections incorporated in the wing. Both relationships must be simultaneously satisfied in the calculation of the lift distribution of the wing.
If the section lift curves are linear, these relationships may be expressed by a single equation which can be solved analytically. In general, however, the section lift curves axe not linear, particularly at high angles of attack, and analytical solutions are not feasible. The method of calculating the sponwise lift distribution using nonlinear section lift data thus becomes one of making successive approximations of the lift distribution until one is found that simultaneously satisfied the aforementioned relationships.
Since the theory of propellers with minimum induced loss is founded on considerations of the trailing vortex sheet, it was thought to be necessary to present a more detailed discussion of the dynamics of vortex sheets and the consequences of their instability and roll up than is usually found in treatments of propeller aerodynamics.
In this thesis, non-lineer lifting line method is used to predict the performance of a number of propellers. The objective of this thesis is to develop computer codes of vortex lattice method of lifting line analysis.
The vortex lattice method approximates a lifting surface and its wake by a discrete vortex lattice system. The propeller is considered to be blades of arbitrary planeform, rotating with a constant angular velocity about a common axis in an unbounded fluid. Interaction between blades is considered. The presence of the hub is ignored. The vortex wake of the propeller is assumed to be a helix of constant pitch and diameter. This assumption is coincident with Goldstein?s helical vortex model. In both cases, the propeller is considered to be lightly loaded, and to have no slipstream contraction.
As it is applied in this study, it is common for the helical vortices in the wakes of propellers, rotors to be represented computationally by a sequence of straight vortex segments.
In lifting line analysis, the propeller blade is assumed sufficiently thin to be represented by distribution of horseshoe vortices lying in the mean camber surface of each blade. Steady flow conditions are assumed; the circulation is only a function of location along the radius. The induced flow at any radial location due to the horseshoe vortex is given by the Biot-Savart equation.
Non-lineer numerical lifting line method takes into viscous effects and chambering account. Also it can be used for the lifting element that has dihedral angle, sweep angles and both of them. So it can be thought of as a cross-section of vortex lattice method and classical lifting line methods.
A Computer program is developed that uses non-lineer numerical lifting line methods in Matlab computer language. To verify program, some applications was made on wing. Some test propeller has been choosen from literatüre to verify program on the design point. These propellers are selected from the studies of the Adkins (1994), Larrabee (1979) and Bauer (1997).
In order to test the computer program around the off-design point of propellers experimental data is required. In this respect, the study of Yaggy (1960) which presents the performance data of a few propellers tested in wind tunnel is considered. One of these propellers has NACA 0009 airfoil sections. The classical theory needs section characteristics in several Reynolds number and angle of attack ranges and this data is taken from Abbott (1945) and Sheldahl (1981).