روش بدون شبکه برای حل عددی جریان‌های داخلی با تقارن محوری

نوع مقاله : مقاله پژوهشی

نویسندگان

مجتمع دانشگاهی هوافضا، دانشگاه صنعتی مالک اشتر، تهران، ایران

چکیده

در این تحقیق یک روش عددی بدون شبکه برای حل جریان‌های داخلی و متقارن محور توسعه داده شده است. در این روش از حداقل مربعات سری تیلور برای گسسته‌سازی مکانی و از روش چند مرحله‌ای صریح رانگ کوتا برای گسسته‌‌سازی زمانی استفاد‌ه ‌شده است. در الگوریتم حاکم بر این کُد از معادلات اویلر دوبعدی و متقارن محور با استفاده از ترم‌های اتلافات مصنوعی مرتبه دو و چهار برای حل جریان استفاده شده است. جهت مدل‌سازی شرایط مرزی از مرزهای ورودی و خروجی مادون‌صوت، مافوق‌صوت و مرز دیواره به تناسب مساله استفاده شده است. جهت اعتبارسنجی نتایج حاصل از کد، جریان غیر لزج درون یک نازل دوبعدی و همچنین جریان مافوق صوت داخل کانال به همراه برآمدگی مورد تحلیل قرار گرفته و نتایج با داده‌های معتبر مقایسه شده است. همچنین توانایی کد در تسخیر شوک عمودی در جریان داخل نازل دوبعدی و تقارن محور ارائه شده است. در نهایت نیز شبیه‌سازی جریان پایا درون یک نازل همگرا-واگرا متقارن‌محورِ ماوراءصوت با ماخ خروجی 5 انجام شده است تا دقت حل کدِ عددی در سرعت ماوراءصوت نیز سنجیده شود. نتایج نشان می‌دهد کد توسعه داده شده با دقت بسیار خوبی قادر به شبیه‌سازی جریان‌های داخلی پایا و متقارن محور است. روند همگرایی کُد نیز ارائه شده است که نشان از همگرایی مناسب کُد عددی دارد. زمان تحلیل برای تسخیر شوک در نازل دوبعدی تقارن محور نسبت به نرم‌افزار فلوئنت حدود 64 درصد سریع‌تر است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Meshless Method for Numerical Solution of Internal Flows with Axial Symmetry

نویسندگان [English]

  • Mostafa Hadidoolabi
  • Mahdi Hashemabadi
  • Reza Jamshidi
Faculty of Aerospace, Malek Ashtar University of Technology, Tehran, Iran
چکیده [English]

In this research, a meshless numerical method has been developed to solve internal and axisymmetric flows. In this method, the least squares of the Taylor series are used for spatial discretization and explicit multi-step Runge-Kutta method is used for temporal discretization. Governing equations are based on two-dimensional and symmetric Euler equations. The second and forth order artificial dissipation are used to solve the flows. In order to model boundary condition, subsonic and supersonic inlet and outlet boundary conditions as well as the wall boundary have been used according to the problem. To validate the results of the code, the inviscid flow inside a two-dimensional nozzle and the supersonic flow inside the channel along with bump have been simulated and the results have been compared with valid data. The simulation of the steady flow inside a axi-symmetric convergent-divergent supersonic nozzle with Mach 5 in outlet has been done to measure the accuracy of solving the numerical code at the hypersonic speed. The results show that the developed code can simulate steady internal and axi-symmetric flows with very good accuracy. The process of code convergence is also presented, which shows the appropriate convergence of the developed code. The analysis time for shock capturing in the axi-symmetric nozzle is about 64% faster than the Fluent software.

کلیدواژه‌ها [English]

  • Meshless method
  • Internal flow
  • axi-symmetric flow
  • numerical method
  • Inviscid flow
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