Tandem halde bir kanat profilinin taşıma ve yunuslama karakteristiklerinin incelenmesi

Abstract

ÖZET Bu tezde bir kanat profilinin yalnız basına ve tandem düzeninde benzeri bir diğer profilin izinde yer alması hallerindeki tasıma ve yunusî ama karakteristikleri 6.5-1Ö0 Reynolds sayısında deneysel alarak ve potansiyel akım çerçevesinde teorik olarak incelenmiştir. Tezdeki teorik incelemelere yönelik olarak iki bo yutlu potansiyel akım alanlarının hesabı için kompleks düzlemde Cauchy integral teoreminden hareketle yeni bir panel yöntemi geliştirilmiştir. Yöntem tek ve çok ele man ı kanat profilleri için analitik sonuçlarla geniş bir şekilde tahkik edilmiştir. Ayrıca rüzgar tüneli duvar etkilerinin incelenmesine yönelik olarak dairesel silin dirler üzerinde yapılan uygulamalar, bu tür hesaplamalar da seçilecek tünel boyunun ve eleman sayısının önemli ol duğunu ortaya koymuştur. Tezdeki deneyler NACA 65ı 012 profili esas alına rak imal edilen modeller üzerinde gerçekleştirilmiştir. Gerek tek profil halinde, gerekse tandem halde modele et kiyen taşıma ve yunuslama katsayıları, açıklımın ortasın daki bir kesitte yüzey boyunca ölçülen basınç dağılımla rının integrasyonu suretiyle elde edilmiştir. Katsayılar üzerindeki rüzgar tüneli duvar etkileri kompleks düzlemde geliştirilen panel yöntemi yardımıyla düzeltilmiştir. Deneysel sonuçlar panel yöntemi kullanılarak elde edilen sonuçlarla karsılastırılmıstır. Tek profil halinde taşı ma-hücum açısı ve yunuslama-hücum açısı eğril erinin eğim leri NACA profili için 3 milyon Reynolds sayısında lite ratürde verilen deneysel sonuçlara kıyasla bir miktar da ha küçük bulunmuş, modelin hücum kenarı civarında oluşan bir laminer ayrılma kabarcığının hücum açısıyla giderek uzadığı ve yumuşak bir pert dö vitese yol açtı ğı tespit edilmiştir. Tandem halde izdeki profilin taşıma ve yu nuslama eğrilerinin öndeki profilin hücum açılarına bağlı olarak ötelendiği ve bu eğrilerin eğimlerinin tek profil halindeki lere göre daha küçük olduğu görülmüştür. Ayrıca izdeki profilin pert dö vites karakteristiklerinde bazı degişi kl ikler tespit edilmiştir. İzdeki profilin tasıma, yunuslama ve pert dö vites karakteristiklerinde görülen etkilerin öncelikle öndeki profilin akımı yönlendirmesin den kaynaklandığı, ancak öndeki profilin izinin de olay lar üzerinde bir takım etkileri olduğu belirlenmiştir. (v)

SUMMARY INVEST I BAT I ON OF THE LIFT AND PITCH INS MOMENT CHARACTERISTICS OF AN AIRFOIL IN TANDEM ARRANGEMENT The chord based Reynolds numbers below lO*8* -for airfoils are generally accepted as the low Reynolds numbers. This type of -flows exist for jet engine compressor and turbine blades, gliders and sailplanes at low speeds, remotely piloted vehicles<RPVs) at high altitudes, ultra light man- carrying/man- powered recreational aircraft, wind turbines/propellers and new generation ships with wing-sails. Although many problems of the airfoils at medium and high Reynolds numbers are solved, the number of investigations at low Reynolds numbers is very limited. But the current desire to improve the performance of both military mnü civilian systems has focused attention on this flow regime, in the recent years. In this thesis the lift and pitching moment characteristics of an airfoil in isolated and tandem cases are investigated experimentally at a low Reynols number, and theoretically for the potential case. The work contains two main parts. In the first part,' a new panel method in the complex plane is developed, for the calculation of two-dimensional potential flows and wind tunnel wall interference effects. The second part is reserved for the experimental and theoretical investigations of a NACA 65» 012 based airfoil model in isolated and tandem cases. Although the flow field around an airfoil is highly complex, especially at high angles of attack, it may be accepted many times as potential flow for the first approximation. The potential flow analysis snd design problems of airfoils were investigated succesfuly by the methods based on conformal mapping, in the first half of this century. However, since this type of method needs many transformations and complex mathematical analysis for mul t i- element airfoils, they are not so practical for today's applications. Therefore the numerical methods mre preferable. Among the numerical methods, finite-differences and finite-elements type field methods &re powerful methods for calculation (vi>of full Wavier - Stokes equations. But they need usually large computer memories and speeds, since they treat the entire -flow -field. The integral methods have an advantage over the potential -flow calculations, since they investigate the -field problems on the boundary surfaces. In the recent years the most used integral methods are the well known panel methods. The panel methods are generally based on Green's third identity which yields a representation of the potential or the stream function at any point of a potential flow field in terms of a distribution of sources, doublets or vortices along the boundary surfaces. Application of the boundary condition leads to a Fredholm equation of the first or second kind. The panel methods convert this integral equation into a set of linear equations by dividing the boundary surfaces into small elements <panels>. There are many panel methods in the literature dif erring from each other in the kind of singularities used, in the application of the boundary conditions and in the numerical details. In two- dimensional cases the treatment of a potential problem in the complex plane is easier then in the real plane. Therefore, the complex variables were used by several researchers in the panel method applications, in recent years. But, there is not an essential starting point in these applications, in order to obtain the integral equations. However, in some integral methods, other than the panel methods, the development of the integral equations in the complex plane from Cauchy integral theorem is quite interesting. A new panel method in the complex plane is developed in this thesis, starting from Cauchy integral theorem. The method uses linear source distribution on straight line surface elements. Additionally, a parabolic trapesoidal vortex distribution is taken for the airfoil type surfaces. The boundary condition applied on the boundary surfaces is of the Neumann type. For the Kutta condition, the velocities on the elements adjacent to the trailing edge ar& equalised. The complex panel method is programmed for a computer to calculate multi -element airfoils. The applications on several Joukowsky and Karman- Trefftz airfoils show that the method gives generally satisfactory results for one- element airfoils by using 50 surface elements. And the c.p.u. time for an IBM 4341 computer to calculate an airfoil with 50 panels is only about 5-6 seconds. The applications on two and four- element airfoils also give good results. (vi i >The complex panel method is programmed also to calculate the wind tunnel wall interference effects. The applications on circular cylinders show that the selection of the length of the tunnel and the number of panels on the tunnel walls is important for the accuracy of this type of calculations. In the second part of the thesis the flow quality of the ITU 100*80 cm3 cross-section wind tunnel is investigated, in which the experiments are made. The investigations on the dynamic pressure of the flow in the test section show that the fluctiations have a maximum value of ±2% of the average dynamic pressure. But, if an integration for 30 seconds is made, this maximum value diminishes to ±0.5%. Therefore, if any pressure measurement in this wind tunnel is made for a period of 30 second, the uncertainty of this measurement is below 1%. A second investigation is made on the flow uniformity in the test section. For this, the total and the static pressures are measured in the horizontal mid section of the testing chamber. The total pressure is found to be uniform over entire the test section. The static pressures are uniform in a 1 meter mid-part of the test section. Only some non-uniformities in the entrance and exit parts of the test section, and a little pressure gradient along the test section is observed. Turbulence level of the flow in the test section is investigated by using both the turbulence sphere and hot- wire anemometry. The turbulence factor is found to be below 1.2, and the turbulence intensity is 0.25%. The experiments stre realized on the models based on the NACA 65a 012 airfoil section. First the two- dimensionality of the flow is observed on one of the models at several mounting conditions, by using the flow visualization method by tufts. These observations shows also that there is a laminar separation bubble near the leading edge of the model. In the isolated airfoil case, the pressures on the mid- section surface of the model are measured at several angles of attack between -12° and +12° and at a Reynolds number of about 6.5- 10s. The lift and pitching moment coefficients &.re obtained by integrating these pressure distributions. The wind tunnel wall interference effects on these coefficients Bre calculated by the complex panel method and corrected. The results are compared with the experimental results for the NACA 65* 012 airfoil given in the literature at a Reynolds number of 3 million. And the comparisons are also made with the theoretical results for both airfoils obtained by the complex panel method. While the lift- angle of attack and the pitching moment- angle of attack curves of the NACA airfoil varies linearly versus the (viii >angles of attack between -12° and +12°, the lift and pitching moment curves of the model are linear only between -4° and +4°. Above these angles of attacks the linearity disappears and the model stalls at about 12°. The slopes of the lift and pitching moment curves of the model are lower than that of the NACA airfoil. All these differences show the effects of low Reynolds number on the model. The pressure distributions measured on the model indicate that there is a laminar separation bubble near the leading edge which is aparent at about 4° angle of attack as a short bubble. This bubble lenghtens as the angle of attack increases. Bo that the model has a fairly gentle stalling characteristic. In the tandem case the pressures on the mid section surface of the model placed in the wake of a similar model are measured at a Reynolds number of about 6>.5-10°. The angles of attack of the airfoils and the distance between the airfoils are the parameters for these experiments. The lift and pitching moment coefficients of the model are obtained by integrating the pressure distributions along the surface. The wind tunnel wall interference effects are calculated by the complex panel method and corrected by a procedure developed specif i cly for the tandem airfoils case. The results are compared with the theoretical results obtained by the complex panel method, and also with the results obtained for the isolated airfoil case. Some typical conclusions are given below: i) In the tandem case the experimental lift and pitching moment-angle of attack curves of the model in the wake are displaced by some amount, depending on the angles of attack of the upstream airfoil. These displacements are such that, the lift and pitching moment coefficients of the downstream airfoil decrease, when the angles of attack of the two airfoils are in the same direction. The coefficients increase when the angles of attack are in the opposite directions. Similar displacement characteristics are seen in the theoretical lift and pitching moment curves of the downstream airfoil. This similarity between the theoretical and the experimental results points out that the displacements seen on the lift and pitching moment curves result primarly from the changes in the direction of the flow to the downstream airfoil. However, for the non- zero angles of attack of the leading airfoil, the differences in the theoretical and the experimental results of the downstream airfoil are larger than that seen in the isolated airfoil case. This discripancy shows that there is an effect other than the upstream airfoil's angle of attack, which is the effect of the leading airfoil's <ix>wake. It is very difficult to asses the degree of this effect resulting -from the turbulence or from the slipstream in the wake, by considering existing experimental and theoretical results. The displacements seen on the lift and pitching moment curves of the airfoil in the wake decrease as the distance between the airfoils increases. ii) The experimental and the theoretical results show that the slopes of the lift- angle of attack curves in the tandem case are lower than that in the isolated airfoil case. The slopes of the pitching moment- angle of attack curves are higher in absolute values than that of the isolated airfoil. These discripancies in the tandem case also decrease as the distance between the airfoils increases. iii) Another important effect in the tandem case is seen on the stalling characteristics of the downstream airfoil. There is a tendency of delay in the stall of the downstream airfoil, when the angles of attack of the two airfoils are in the same directions, and a tendency to hasten, when the angles of attack are in the opposite directions. It is possible to say that these tendencies in the stalling characteristics of the airfoil in the wake also result primarly from the changes in the direction of the flow to the downstream airfoil. However there is a similar tendency of delay in the stall of the downstream airfoil when the leading airfoil has 0° angle of attack. This result shows that there is an effect of the leading airfoil's wake on the stalling characteristics of the downstream airfoil. But it is also difficult to asses the degree of this effect resulting from the turbulence or from the slipstream in the wake, by considering existing experimental and theoretical results. (x)