Evaluation of Modeling Accuracy of Aircraft Wing Aerodynamic Parameters on the Basis of Measurement Results ; Orlaivio sparno aerodinaminių parametrų modeliavimo tikslumo įvertinimas remiantis matavimų rezultatais
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2006
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Egidijus PAKALNIS EVALUATION OF MODELING ACCURACY OF AIRCRAFT WING AERODYNAMIC PARAMETERS ON THE BASIS OF MEASUREMENT RESULTS Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T) 1183 Vilnius 2005 VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Egidijus PAKALNIS EVALUATION OF MODELING ACCURACY OF AIRCRAFT WING AERODYNAMIC PARAMETERS ON THE BASIS OF MEASUREMENT RESULTS Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T) Vilnius 2005 Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001 – 2005 Scientific Supervisor Prof Dr Habil Jonas STANK ŪNAS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) The Dissertation is being defended at the Council of Scientific Field of Measurement Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Vytautas GINIOTIS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Members: Prof Dr Habil Vladas VEKTERIS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering – 10T) Prof Dr Habil Ramutis Petras BANSEVI ČIUS (Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T) Prof Dr Habil Jonas SKEIVALAS (Vilnius Gediminas Technical University, Technological
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Publié par
Publié le
01 janvier 2006
Egidijus PAKALNIS EVALUATION OF MODELING ACCURACY OF AIRCRAFT WING AERODYNAMIC PARAMETERS ON THE BASIS OF MEASUREMENT RESULTS Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T) 1183
Vilnius
2005
VILNIUS GEDIMINAS TECHNICAL UNIVERSITY Egidijus PAKALNIS EVALUATION OF MODELING ACCURACY OF AIRCRAFT WING AERODYNAMIC PARAMETERS ON THE BASIS OF MEASUREMENT RESULTS Summary of Doctoral Dissertation Technological Sciences, Measurement Engineering (10T)
Vilnius
2005
Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2001 2005 Scientific Supervisor Prof Dr Habil Jonas STANKNAS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering 10T) The Dissertation is being defended at the Council of Scientific Field of Measurement Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Vytautas GINIOTIS (Vilnius Gediminas Technical University, Technological Sciences, Measurement Engineering 10T)Members: Prof Dr Habil Vladas VEKTERIS Gediminas Technical (Vilnius University, Technological Sciences, Measurement Engineering 10T)Prof Dr Habil Ramutis Petras BANSEVIČIUS University of (Kaunas Technology, Technological Sciences, Mechanical Engineering 09T) Prof Dr Habil Jonas SKEIVALAS Gediminas Technical (Vilnius University, Technological Sciences, Measurement Engineering 10T)Prof Dr Habil Stanislavas SAKALAUSKAS University, (Vilnius Technological Sciences, Measurement Engineering 10T) Opponents: Prof Dr Habil Andrejus Henrikas MARCINKEVIČIUS (Vilnius Gediminas Technical University, Technological Sciences, Mechanical Engineering 09T) Prof Dr Habil Danielius EIDUKAS(Kaunas University of Technology, Technological Sciences, Measurement Engineering 10T) The dissertation will be defended at the public meeting of the Council of Scientific Field of Measurement Engineering in the Senate Hall of Vilnius Gediminas Technical University at 11 a. m. on 25 November 2005. Address: Saultekio al. 11, LT10223 Vilnius40, Lithuania Tel.: +370 5 274 49 52, +370 5 274 49 56; fax +370 5 270 01 12, email doktor@adm.vtu.lt The summary of the doctoral dissertation wasdistributed on 25 October 2005. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saultekio al. 14, Vilnius, Lithuania) © Egidijus Pakalnis, 2005
VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS Egidijus PAKALNIS ORLAIVIO SPARNO AERODINAMINIPARAMETRMODELIAVIMO TIKSLUMO VERTINIMAS REMIANTIS MATAVIMREZULTATAIS Daktaro disertacijos santrauka Technologijos mokslai, matavimininerija (10T)
Vilnius
2005
Disertacijarengta20012005metaisVilniausGediminotechnikos universitete. Mokslinis vadovas prof. habil. dr. Jonas STANKNAS Gedimino technikos (Vilniaus universitetas, technologijos mokslai, matavimininerija 10T) Disertacija ginama Vilniaus Gedimino technikos universiteto Matavimininerijos mokslo krypties taryboje: Pirmininkas prof. habil. dr. Vytautas GINIOTIS Gedimino technikos (Vilniaus universitetas, technologijos mokslai, matavimininerija 10T)Nariai: prof. habil. dr. Vladas VEKTERIS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, matavimininerija 10T)prof. habil. dr. Ramutis Petras BANSEVIČIUS technologijos (Kauno universitetas, technologijos mokslai, mechanikos ininerija 09T) prof. habil. dr. Jonas SKEIVALAS Gedimino technikos (Vilniaus universitetas, technologijos mokslai, matavimininerija 10T)prof. habil. dr. Stanislavas SAKALAUSKAS (Vilniaus universitetas, technologijos mokslai, matavimininerija 10T) Oponentai: prof. habil. dr. Andrejus Henrikas MARCINKEVIČIUS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, mechanikos ininerija 09T) prof. habil. dr. Danielius EIDUKAS(Kauno technologijos universitetas, technologijos mokslai, matavimininerija 10T) Disertacija bus ginama vieame Matavim ininerijos mokslo krypties tarybos posdyje 2005 m. lapkričio 25 d. 11 val. Vilniaus Gedimino technikos universiteto senato posdisalje. Adresas: Saultekio al. 11, LT10223 Vilnius40, Lietuva. Tel.: +370 5 274 49 52, +370 5 274 49 56; faksas +370 5 270 01 12, el. patas doktor@adm.vtu.lt Disertacijos santrauka isiuntinta 2005 m. spalio 25 d. Disertaciją galima perirti Vilniaus Gedimino technikos universiteto bibliotekoje (Saultekio al. 14, Vilnius, Lietuva) VGTU leidyklos Technika 1183 mokslo literatros knyga © Egidijus Pakalnis, 2005
1. General Characteristic of the Dissertation Topicality of the problem. Equal flight safety requirements are applied to the piloted aircraft despite their size and flight speed. In the growing industry of low-speed aviation it is a matter of great relevance to decrease design, production and test costs of low-speed aircraft keeping the same level of the flight safety. Due to the fact that aircraft flight characteristics are mainly determined by aerodynamic properties of a wing it is relevant to design wings for low-speed aircraft fast and with a low cost. This demands of reliable, relatively simple method of the wing design which accuracy has to be based on airfoil measurement results in wind tunnel. Application of direct measurement of the wing aerodynamic characteristics theirself is limited in the design stage of low-speed aircraft because these measurements should be unique and complex due to wide variety of wing configurations. Circumstances stated above made conditions to start the research on adaptation of methods of measurement engineering in the mathematical simulation of aerodynamic forces of the wing. Aim and tasks of the work. The aim of this research is to develop and examine a method for analysis of aerodynamic parameters of the aircraft wing based on the airfoil measurement results and mathematical simulation using non-linear characteristics of airfoils constituting the wing. In order to attain this aim, the following tasks are raised: 1. to develop a numerical model of the finite-span wing tested on measurements on the basis of one of the currently used calculation methods; 2. to complement the wing model with an algorithm which takes into consideration non-linear characteristics of wing airfoils and provides for a possibility of using the results of both numerical and measurement methods; 3. to carry out calculations for various geometry wings under different passing airflow characteristics and to determine the particularities of the iterative process on the basis of obtained results as well as the errors and reliability of those results; 4. to determine the limits of the methods application by comparing the obtained results with the measurement data of the aerodynamic forces of the wing.
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Scientific novelty.Development of the finite-span wing model, complemented with the algorithm assessing non-linear characteristics of the airfoils which has not been applied before. The analysis method includes original technique to evaluate convergence of the iteration process and to establish conditions of reliability of the results. Methodology of research. An algorithm for analysis of the finite-span wing aerodynamic parameters, assessing the non-linear characteristics of the wing airfoils in one of the few possible ways, is applied to the analysis of the method. The analysis algorithm is based on the vortex grid or so called vortex step method. Methods of numerical analysis and experimental measurement are applied in the research. Practical value. analysis method proposed in this research may be The applied to the designing of various wings. The method can be particularly useful in those aircraft design stages where it is necessary to expeditiously analyse many varying wing geometry options. The method can also be applied for determination of theoretical aerodynamic parameters of manufactured wings. Defended propositions • The algorithm what takes into consideration non-linear characteristics of wing airfoils and provides for a possibility of using the results of both numerical and measurement methods in calculation of aerodynamic forces of a wing. • The methodology to evaluate convergence of the calculation process and to establish conditions of reliability of the results. The scope of the scientific work. scientific work consists of the The general characteristic of the dissertation, 4 chapters (Methods of Analysis of Wing Aerodynamic Parameters; Evaluation of Measurement Results of Airfoil Non-Linear Aerodynamic Parameters in the Model of Finite-Span Wing; Analysis of Calculation and Measurement Results of Aerodynamic Parameters of Rectangular, Swept-Back and Tapered Wings; Analysis of Errors of Wing Aerodynamic Parameters and Reliability of Calculation Results) conclusions, list of literature, list of publications and addendum. The total scope of the dissertation 90 pages, 96 pictures, 1 table and 1 addendum.
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2. Mathematical Model of Wing The selected wing modelling with flat elements (panels) and horseshoe-shaped vortices is relatively simple yet covers all elements used in more complex panel methods and is suitable to modelling of the wing shape effect and calculating airflow generated forces affecting the wing. The wing is modelled with panels, which are set at the angle corresponding to the zero wing airfoil lift force angle. Taking into account that the angle of attack of the non-symmetric airfoil's zero lift force is normally negative, the angles of attack of the panel and the wing are related by an equation
pl=sp−, (1) 0herepl of attack of a model panel, angle wing angle of attack,0 spairfoil zero lift angle of attack. The wing is divided into a certain number of uniform width panels along the span (Fig 1). The number of panels selected for the purpose of this research was 14 (seven for each side of the wing), which allowed describing the distribution of symmetric lift force along the wing with a trigonometric series, using 7 coefficients:A1, A3, A5, A7, A9, A11andA13.
1
2
4
3
5
Γ1
6
7
8
z
Γ8
Fig 1. Wing modelling with horseshoe-shaped vortices
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The lift and the drag forces are modelled with horseshoe-shaped vortices, which are set in such way as to permit each bound vortex to coincide with the ¼ wing chord line (Fig 1 displays eight vortices composing the wing), i.e. in such way that there are two free vortices running from the centre of pressure of a symmetric airfoil (panel) and from its end points in the direction of thexaxis towards infinity. Control points are set on the ¾ chord line under the condition that the directions of airflow streamlining the vortex and the panel coincide at these points (Fig 2) Vwj=sinαpl, (2) ∞ hereV∞is velocity of undisturbed airflow. ¾c
¼c
V∞
Γ
pl
V∞+wj
wj
Fig 2. Control point condition According to Bio-Savarts law, induced velocity at the control pointj of the vortexΓset in elementiis equal to wj=4ΓiAij, (3) π whereAijis a wing geometry coefficient, which takes into account the position of the control pointj with regard to the horseshoe-shaped vortex in theithelement. By setting Eq. 3 against Eq. 4, we obtain
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ΓA i⋅ij=sinαpl i(4) . V∞4π, The lift force of a wing section, whose length in the direction of wingspan isΔz, equals to ΔLi= ρV2∞2⋅Cli⋅Δzi⋅ci, (5) hereciis a chord of wing model element,ρ air density. According to Kuta-Zhukovsky law, the lift force of the same wing section is
Li= ⋅V∞⋅i⋅zi. (6) From Eq. 4, 5 and 6 c⋅A i4ij⋅Cli=2πsinαpl ,i. (7) Having assessed the impact of all wing-modelling vortices at the control points, a system of linear equations is obtained on the basis of Eq. 7 [b]⋅ {Cl} =2sinpl, (8) here[b] is a matrix of wing geometrical coefficients,{Cl} vector of lift coefficients of wing model elements. Element of the matrix is defined as ci⋅Aij bij=4(9). The solution to this system of linear equations (Eq. 8) is the lift force coefficients in different sections of the wing. Due to viscosity of the real airflow, the effective curvature of the wing airfoils is smaller, which leads to a lower lift force than in the case of the non-viscous airflow. This reduction in the lift force is modelled through reduction of
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the panel setting angles (Fig 3) αl(pi+1)= αpli()Δα−(0i ), where superscriptihere and further defines number of iteration. α
α0(i)
(i) α0
Cl
Cl(i) Cl*(i)
α(i+1) 0
1
α(i)
α(i+1) α(i)
ps
2
4
3
(10)
1 infinite panel(i)
2 nite panel(i+1) infi
3 model(i) 4 airfoil
α
Fig 3. Assessment of the real airfoil characteristics in the wing model A change in the angle of attackΔα(0i )is determined through iterative process under the condition that Dskam)i(≤Dlim=0.03%, (11) hereDrepresents a difference between the estimated wing section lift force coefficient and the airfoil lift force coefficient ( i ) *( i ) D( i )=⎧Cl−( i )Cl⋅ (12)100 , ⎨⎪⎩⎪Cl⎫⎬⎪⎭⎪
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