تعيين ضرايب آيروديناميكي بال مافوق صوت با استفاده از روش اجزاي مرزي

PREDICTION OF AERODYNAMIC COEFFICIENTS OF A SUPERSONIC WING USING BOUNDARY ELEMENT METHOD

هدف اصلي در اين نوشتار محاسبه‌ي ضرايب آيروديناميكي بال در جريان مافوق صوت دايم برمبناي حل جريان پتانسيل با استفاده از روش اجزاي مرزي است. در اين راستا ابتدا معادلهي حاكم بر جريان پتانسيل مافوق صوت استخراج و خطي‌سازي شده، و سپس با استفاده از روش اجزاي مرزي و اعمال توابع شكل مرتبه‌ي اول، دستگاه معادلات گسسته براي محاسبات جريان تشكيل شده است. در خلال حل اين معادلات مشكلات محاسباتي مربوط به تعيين ضرايب انتگرالي تكين بروز مي‌كند كه ناشي از قطع مخروط ماخ توسط اجزاي مرزي موجود بر دامنه‌ي محاسباتي است. البته با استفاده از روش‌هاي عددي ميتوان مشكلات مربوطه را برطرف ‌كرد. در نهايت براي دو بال با هندسه‌ي مشخص، محاسبات جريان مافوق صوت دايم انجام شده است. مقايسه‌ي نتايج مزبور با جوابهاي دقيق، بيان‌گر دقت خوب روش حاضر و انعطافپذيري آن براي تحليل جريانحول بالهاي سهبعدي است

The main objective of this paper is to determine the aerodynamic coefficients of a steady supersonic wing using the Boundary Element Method (BEM) based on the solution of potential flow. In the field of computational aerodynamics and fluid dynamics, some numerical approaches, such as the boundary element method, based on finding unknown parameters only on the boundary of a body with lower computational cost than high-fidelity formulations, can be a good replacement for Computational Fluid Dynamics (CFD) methods. Hence, application of BEM based on potential flow has recently been implemented as an efficient and popular tools in many studies. An advantage of the BEM is that the method reduces problem dimensionality by one. In this study, the governing partial differential equation of a supersonic potential flow field is firstly derived and linearized. The motion of the wing is assumed to consist of small perturbations, with respect to the constant-speed motion. Using the boundary element method in conjunction with first order shape functions, one obtains the system of discrete integral equations relating the potential to its normal derivatives on the surface of the body. However, there are some numerical problems in the evaluation of integral coefficients, due to singularity, which is caused by the intersection of the mach forecone and the edge of some elements in the computational domain. Of course, this problem can be eliminated by using some numerical techniques, such as the higher point Gaussin quadrature rule of integration and/or Teles transformation based on the order of singularity. Finally, a steady supersonic flow analysis is performed for two different wings with identified geometries( biconvex and planeform wings). The perturbed potential distribution for the biconvex wing are firstly computed and compared with available results in the literature. Also, its pressure coefficient distribution, specifically in the chordwise centerline, is evaluated. In addition, in the planeform wing, variation of the lift coefficient slope, accounting for three-dimensional effects, is studied. Also, the mach cone formed at both edges of the wing is visible and corresponds to the well-known mach cone formula for estimating mach angle. Comparison between the numerical results and those obtained using the exact solution indicates the good agreement and accuracy of the present method, and its flexibility to steady supersonic flows analysis around three-dimensional wings or complex configurations.