Potansiyel akım-sınır tabaka yaklaşımı ile kanat profili analiz ve dizaynı
Airfoil analysis and design by using potential flow-boundary layer approximation
- Tez No: 19412
- Danışmanlar: DOÇ.DR. M. ADİL YÜKSELEN
- Tez Türü: Yüksek Lisans
- Konular: Uçak Mühendisliği, Aircraft Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1991
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 96
Özet
ÖZET POTANSİYEL AKIM-SINIR TABAKA YAKLAŞIMI İLE KANAT PROFİLİ ANALİZ VE DİZAYNI Bu çalışmada potansiyel akım sınır tabaka yaklaşımı kullanılarak kanat pro fillerinin etrafındaki akım alanmm analizi problemi ayrılmağız smır tabaka kabulü ile ele alınmıştır. Aynca potansiyel akımda verilmiş bir basınç dağılımını sağlayacak kanat profilinin dizaynı problemi incelenmiştir. Potansiyel akım smır tabaka yaklaşımında ilk adım olarak yüzey tekillik leri metoda kullanılarak kanat profilinin potansiyel akımda analizi yapılmıştır. Bu analizde profil yüzeyi panellere ayrılarak bu paneller üzerinde lineer girdap dağılımı kullanılmıştır, ikinci aşama olarak potansiyel akım basınç dağılımından faydalanılarak kanat profili etrafındaki smır tabaka analizi yapılmıştır. Laminer, geçiş ve türbülanslı smır tabaka hesabı, ayrılma olmadığı kabulü ile ek abnmıştır. Sınır tabaka içindeki detaylar yerine global büyüklükler hesaplanarak bilgisayar kullanım süresi en düşük seviyeye indirilmiştir. Potansiyel akım smır tabaka yaklaşımının en son adımı potan siyel akımla smır tabaka hesahmm birleştirilmesidir. Smır tabaka analizi sonucunda bulunan deplasman kalmbğı profil geometrisine etki ettirilmiş ve eşdeğer profil ge ometrisi hesaplanmıştır. Bu geometrinin potansiyel akıma maruz kaldığı farzedikrek yeniden potansiyel akım analizi ve bunu mütakip sınır tabaka hesabı yapılmıştır. Bu işlem basınç dağılımının değişmeyecek bir değere yakınsamasına kadar iteratif olarak devam ettirilmiştir. Ekk edilen basınç dağılımı deneylerden elde edilmiş olan gerçek basınç dağılımına çok yafan olduğu gözlenmiştir. Aynca potansiyel akımda kanat profili dizaynı problemi de ele alınarak verilmiş bir basınç dağılımını sağlayacak kanat profilinin dizaynı yapılmıştır. Dizayn probkmi için integral yöntem yaklaşımı kullanılmıştır. Amaç basınç dağılımını vere bilecek kanat profili geometrisinin elde edilebilmesi için; bir başlangıç profilinin karak- teristikkrinden faydalanılmıştır. Başlangıç profili, amaç basınç dağılımına göre ite ratif bir yöntemk tashih edilerek amaç basınç dağıbmmı sağlayacak profil geometri- sbe ulaştırılmıştır.
Özet (Çeviri)
SUMMARY AIRFOIL ANALYSIS AND DESIGN BY USING POTENTIAL FLOW-BOUNDARY LAYER APPROXIMATION Many researchers interest in the aerodynamic phenomenon occured on the aircraft wings, and other elements like as propellers, helicopter blades, wind turbines having an airfoil type cross-section. The airflow on such components are generally three-dimensional. However, the researchers prefer to solve these three-dimensional problems, by using the results obtained from two-dimensional investigation on the airfoils, since the three-dimensional researchs take excessive time and are very ex pensive. The problems related to the performances of an airfoil and the flow field around an airfoil are considered into two groups. The first one is the analysis prob lem in which the flow field around a given airfoil shape and its performances are investigated in the given free flow conditions. The second type problem is called as the design problem, in which the shape of an airfoil is searched to maintaine certain prescribed performances. In this study both of these problems are handled in limited extent. The analysis problem on an airfoil are investigated experimentally or theo- reticaly. The theoretical models depend on certain flow parameters as Mach number, Reynolds number and the geometrical characteristics of the airfoil like as thickness ratio, camber ratio, angle of attack. A simple one of these models is the potential flow-boundary layer approximation applicable when the Reynolds number is suffi ciently high and the angle of attack is low or modarate. In this approximation the flow field around an airfoil is considered in two regions : Boundary layer near theairfoil surface in which the viscous forces are effective, and the potential flow repon out of the boundary layer, in which the effects of the air viscosity can be neglected. Hie problem is solved iteratively, in this model. First the potential flow Seid is cal culated neglecting the boundary layer around the airfoil. Then the boundary layer is calculated by using the pressure distribution obtained from the potential flow solu tion. The results of the boundary layer calculations are used to modify the potential flow pressure distribution. This process b repeated until a convergence is obtained on the pressure distribution [1]. The actual methods for calculating the imcompressible potential flow field around the airfoils can be considered into two groups : methods based on the conformal-mapping, and integral methods. Many conform al mapping methods in current use are based on the well known method of Thedoreen [2] which appeared before the Second World War, The integral methods are called usually in the lit erature, as the surface singularity methods or the panel methods. The orijine of these methods is Smith and Piers [3] surface source method. There are many panel methods in the literature differing from each others with the singularity used and with the application of the surface boundary conditions. The boundary layer calculation methods for the airfoils are also considered into two groups : field methods and integral methods. The field methods solve the partial differentia! equations of the boundary layer in a mesh structure formed in the boundary layer, with the boundary condition on the surface and the outer limit of the boundary layer. This type of methods have the advantage of giving the de tailed information about the velocity distribution in the boundary layer. However, for many practical applications the details of the boundary layer are not necassary to obtain. Global boundary layer characteristics like as integral thicknesses (dis placement thickness, momentum thicknesses etc.), shape parameters, surface friction coefficient etc. are usually sufficient in order to obtain the airfoil performances. Thus, the integral methods are preffered, instead of the field methods. In this methods the integral equations of the boundary layer are solved for the above global characteristics. There are several integral method in the literature differing from each others with the integral equations used and with the closure relationships. The purpose in a design porblem is essentially to obtain the coordinates of an airfoil shape which gives certain desired performance characteristics. However, the problem can be considered in two stages. In the first stage the appropriate surface pressure distribution (or the velocity distribution) maintaining these specified viperformances is described. The second step is the determination of the coordinated of an an airfoil shape satisfying the prescribed pressure or velocity distribution. For the second problem of the design process there are two kind of methods in potential flow case : The methods based on conformal-mapping and the panel methods. Many conformal-mapping methods based on the well known method of Lighthill, in which the prescribed velocity is given on a circle, then the airfoil shape is derived from this circle by using a conformal-mapping technique. In this type of methods the prescribed pressure distribution does not quaranty to give a real airfoil shape. Therefore, this pressure distribution have to be modified iteratively until an acceptable airfoil shape is obtained. The panel methods use usually an initial airfoil geometry to derive the coor dinates of the airfoil maintaining the prescribed pressure distribution. In an iterative process the coordinates of the initial airfoil are modified to converge to a certain shape which satisfies the desired pressure distribution. In this thesis the analysis problem for the airfoils is investigated in the frame of potential flow boundary layer model. Additionally the design problem to obtain airfoil shapes for given pressure distributions is handled for the potential flow case. Potential flow calculations for the analysis problem is performed by a panel method using a linear vortex distribution on straight line panels and applying a Dirichlet type surface boundary condition. The method is based on Green's third identity as like as all the other panel methods. Green's third identity leads to an integral relation giving the value of stream function at any point in the flow filed, in terms of a singularity distribution on the surface of the airfoil. When the boundary condition is applied on the airfoil surface an integral equation is obtained. With a vortex distribution along the airfoil surface a Dirichlet type boundary condition indicating that the airfoil surface is a stream line, and stream function is constant along this fine, leads to following integral equation. vu^o = İfscos a - xsrin « ~ «- / h(^)- h f {Si S')].dJ (1) This integral equation is converted into a system of linear equations by dividing the airfoil surface into small panels, and by applying the equation (1) on the control points on each panel. An additional equation is obtained by using the Kutta condition at the trailing edge. Then this linear equation system is solved for the vortex strengths and for ^ hy using, for example, an elimination method of linear systems. The method was tested widely for single or multiply-element airfoils, by comparing with the analytical results. The numerical errors, for example, in the lift coefficent for single element airfoils with 50 panels was generally found below %l (Table 2.1). For the boundary layer calculations an integral method is preferred. And a method using the momentum integral and entrainement equations with the closure relations due to Cousteix for laminer boundary layer and Michel for turbulent bound ary layer is used. Since, this method is not capable to calculate seperated boundary layers, the work is limited with non-seperated cases. Some example applications are presented. As the last step of the analysis problem the boundary layer effects are com bined with the potential flow results, by using an equivalent airfoil approximation. In this techique, an equivalent airfoil is defined by using the displacement thicknesses obtained from the boundary layer calculations. And the potential flow solution for this new airfoil is accepted equivalent to viscous solution. This process is repeated until a convergence is obtained. Analysis method is applied for several cases. And some of these applications are presented in this thesis. The panel method used for the potential flow analysis is also appropriate for potential flow design problems. If the equation (2) is reordered for y ordinates of the airfoil the following equation is obtained. VUlThis equation can be used for creating an iteration method to obtain the ordinates of an airfoil, when the distribution of f(S) (which is equivalent to the surface velocity distribution in this method), is prescribed. For this purpose an initial airfoil geometry b chosen. By using the coordinates of this initial airfoil, and prescribed velocity distribution the y ordinates of a new airfoil b calculated from equation (2) by using, of course, the panelling technique. This new ordinates are used for the next step of this iterative process. This method converges usually rapidly if the initial airfoil shape is chosen appropriately. Several examples performed on analytically derived airfoils are presented m the text.
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