Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 31, No. 1 (January 2018) 132-138    Article in Press

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  RVMUS: RANDOM VORTEX METHOD FOR GEOMETRIES WITH UNSOLVABLE SCHWARZ-CHRISTOFFEL FORMULA
 
I. Tadayoni Navaei, B. Zafarmand and H. Ajdari
 
( Received: January 21, 2017 – Accepted: November 30, 2017 )
 
 

Abstract    As we know, Random Vortex Method is a CFD method (in both turbulent and laminar fields) which needs the Schwarz-Christoffel transformation formula to map physical geometry into the upper half plane. In some complex geometries like the flow inside cavity, Schwarz-Christoffel mapping which transfers the cavity into the upper half plane cannot be achieved easily. In this research, the mentioned mapping function for a square cavity is obtained numerally. Then the instantaneous and average velocity field are calculated inside the cavity using RVM. Reynolds numbers for the laminar and turbulent flows are 50 and 50000, respectively. In both cases, the velocity distribution of the model is compared with the fluent results that the results are very satisfactory. The advantage of this modelling is that for calculation of velocity at any point of the geometry, there is no need to use meshing in all of the flow field and the velocity in a special point can be obtained directly and with no need to the other points.

 

Keywords    Numerical simulation, Open cavity, Random vortex method, Turbulence Models

 

چکیده    همانطور که میدانیم روش گردابه های تصادفی، روشی در حوزه دینامیک سیالات محاسباتی است (در هر دو میدان درهم و آرام) که برای انتقال (نگاشت) هندسه فیزکی به نیم صفحه بالایی، احتیاج به تابع انتقال شوارز کریستوفل دارد. در برخی هندسه های پیچیده نظیر جریان داخل حفره، معادله انتقال شوارز کریستوفلی که در واقع فضای داخل حفره فیزیکی را به نیم صفحه بالایی صفحه انتقال نگاشت می کند، به راحتی به دست نمی آید. در این تحقیق ضمن یافتن تابع انتقال مربوط به حفره مربعی، با استفاده از RVM (روش گردابه های تصادفی) محاسبه توزیع سرعت لحظه ای و پس از آن توزیع سرعت متوسط زمانی انجام می شود. عدد رینولدز برای جریان آرام 50 و برای جریان درهم 50000 در نظر گرفته می شود و در هر دو حالت، توزیع سرعت به دست آمده از مدل، با نتایج حاصل از نرم افزار فلوئنت مقایسه می شوند که نتایج بسیار رضایت بخش هستند. مزیت این روش در این است که برای محاسبه سرعت در یک نقطه نیاز به شبکه بندی در کل میدان جریان نیست و سرعت در یک نقطه مشخص، مستقیما و بدون نیاز به نقاط دیگر به دست می آید.

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