Şakir BAL, Mesut GÜNER

Sayısal bir yöntem ile podlu pervane analizi

Bu çalışmada, podlu pervane birimlerinin (pervane + eksenel simetrik “pod” + “taşıyıcı eleman”) etrafındaki akımın sayısal analizi yapılmış ve podlu pervane performans karakteristikleri incelenmiştir. Temel amaç, podlu pervanelerin performans analizini yapan sayısal bir yöntem geliştirmektir. Ayrıca, pod ve taşıyıcı elemanların, hem beraber hem de ayrı ayrı pervane üzerindeki etkilerinin ve podlu pervane birimi üzerine gelen kuvvetlerin ve torkların sayısal olarak hesaplanması amaçlanmıştır. Bunun için, podlu pervane birimi etrafındaki akım üç bölgeye ayrılmıştır: 1) Eksenel simetrik pod bölgesi, 2) Taşıyıcı Eleman bölgesi ve 3) Pervane kanatları bölgesi. Pod ve taşıyıcı eleman bir panel yöntemiyle (BEM, Boundary Element Method) modellenirken pervane kanatları etrafındaki akım alanı ve kanatlara gelen kuvvetler bir girdap-ağ yöntemiyle (Vortex-Lattice Method) hesaplanmıştır. Panel yöntemi uygulanırken pod ve taşıyıcı eleman dörtgen (ve/veya üçgen) panellere bölünerek herbir panel üzerinde sabit şiddetli kaynak ve duble (dipol) dağılımı olduğu düşünülmüştür. Pervane kanatları girdap-ağ tekniği ile modellenirken de kanatlar üzerinde hem kaynak hem de girdap dağılımı yapılmıştır. Pod ve taşıyıcı elemanların pervane kanatları üzerindeki ya da pervane kanatlarının pod ve taşıyıcı eleman üzerindeki etkileri iteratif bir şekilde, bu iki yöntem kullanılarak gerçekleştirilmiştir. Bu önerilen iteratif sayısal yöntemin doğruluk ve duyarlılığını test edebilmek için, literatürde verilen diğer sayısal ve deneysel çalışmalarla yöntem karşılaştırılmalıdır. Elde edilen sonuçlar, literatürde verilen diğer sayısal ve deneysel sonuçlarla karşılaştırılmıştır. Yine, pod açısının sonuçlar üzerindeki etkileri de tartışılmıştır.

Analysis of podded propulsors by a numerical methods

In this study, the flow around the pod unit (propeller+ axisymmetric pod+taşıyıcı eleman) are analysed and the performance characteristics of the propeller on the pod are investigated. The main objective of the present work is to establish a numerical method for the prediction of performance of podded propeller. The flow domain around the podded propeller is mainly divided into three parts; i) the axisymmetric pod part, ii) the strut part and iii) the propeller part. While the pod and strut parts are modelled by a low-order boundary element method (BEM), the propeller is represented by a vortex lattice method (VLM). A vortex lattice (lifting surface) method is developed and used to calculate the propulsive performance and induced velocities due to propeller blades. This model is based on appropriate vortex and sourcesink distribution. The singularities are distributed on the mean lines of the propeller blade sections. Those vortices are divided into two parts; bound and trailing vortices. The bound vortices, located in a radial direction, are to simulate the load distribution on the propeller blade. The trailing vortices are placed in the direction of the flow, obtained from the different intensities of adjacent bound vortex elements. A number of source elements are taken at adjacent bound vortex to simulate the thickness of the blade. The vortex strengths are calculated by solving a set of simultaneous equations which satisfy the flow tangency condition at the blade control points. Induced velocities due to vortex elements of the lifting surface are calculated using Biot-Savart Law. Once the bound vortex elements intensity is solved, then the velocity induced by the propeller in any point in space can be computed using five angular position of the propeller blade. Finally, the arithmetic average of these five values becomes induced velocity at the corresponding point. During the calculation of induced velocities, nine (9) span-wise and twelve (12) chord-wise elements are taken into account while high number of elementary vortex lines (450) are located on the blade surface to discrete the blade. The BEM, which is based on Green’s Third Identity, allows the separation of axisymmetric pod and the strut problems. Those two (axisymmetric pod and strut) sub-problems are solved separately, with the effects of one on the other being accounted for in an iterative manner. The integral equations (both for axisymmetric pod and strut) which are obtained from Green’s Third Identity are discretized using quadrilateral panels. In order to achieve this, the axisymmetric pod surface and the strut surface are modelled with constant strength dipole and constant strength source panels. The discretized integral equations that form the linear algebraic equation systems can be solved for unknown potential values. Coupling of the BEM and the VLM is, on the other hand, carried out in an iterative manner to incorporate the effect of the pod unit on the propeller, and vice versa. Initially, the VLM is applied for the propeller in the absence of pod and strut and calculates the perturbation velocities on the control points of pod unit (including strut). Then, the BEM is applied to the axisymmetric pod problem, including the effect of propeller and later, the BEM is used for the strut problem with the effects of propeller and axisymmetric pod. The induced velocities due to pod unit (pod + strut) at the propeller disk plane are calculated by corresponding BEMs and the VLM is re-applied to the propeller problem with the modifed right hand side. All those sub-problems (axisymmetric pod + strut + propeller) interact with eachother in terms of induced velocities and induced potential values and the rigth hand sides of BEMs and VLM are modified according to those induced velocities and induced potential values. The iterative steps between BEMs and VLM are repeated until the results are converged. This iterative numerical method is applied to two different podded propellers to compare the results with those of experimental measurements and other numerical methods. It was found that the results by the present numerical method were in good agreement with those of experimental measurements and other numerical methods. The effect of pod unit on the propeller and vice versa are discussed for different type of podded propulsor with zero yaw angle and with a yaw angle. Some preliminary results on the effect of yaw angle on pressure distribution on pod and strut are shown in the paper as well.

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