Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 31, No. 1 (January 2018) 38-44   

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

Abstract    In this research we have implemented the Random Vortex Method to calculate velocity fields of fluids inside open cavities in both turbulent and laminar flows. the Random Vortex Method is a CFD method (in both turbulent and laminar fields) which needs the Schwarz-Christoffel transformation formula to map the physical geometry into the upper half plane. In some complex geometries like the flow inside cavity, the Schwarz-Christoffel mapping which transfers the cavity into the upper half plane cannot be achieved easily. In this paper, the mentioned mapping function for a square cavity is obtained numerically. Then, the instantaneous and the average velocity fields are calculated inside the cavity using the RVM. Reynolds numbers for 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. Also, for aspect ratio the cavity (α) equal 2, the same calculation was done for Re=50 and 50000. 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    در این تحقیق از روش گردابه­های تصادفی برای محاسبه میدان سرعت جریان در داخل حفره­های باز برای جریان آرام و درهم استفاده شده است. روش گردابه­های تصادفی یک روش محاسباتی است (در هر دو میدان آرام و درهم) که جهت انتقال هندسه به نیم­صفحه بالایی، از نگاشت Schwarz-Christoffel استفاده می­کند. در برخی از هندسه­های پیچیده مانند جریان داخل حفره، نگاشتی که هندسه را به نیم­صفحه بالایی منتقل می­کند به­آسانی به دست نمی­آید. در این مقاله تابع انتقال مذکور برای حفره مربعی و مستطیلی (با نسبت طول به عرض 2 ) به صورت عددی به دست می­آید. سپس، میدان­های سرعت لحظه­ای و متوسط داخل حفره توسط روش گردابه­های تصادفی محاسبه می­شوند. اعداد رینولدز برای جریان­های آرام و درهم به ترتیب 50 و 50000 است. در هر دو مورد، توزیع سرعت مدل با نتایج فلوئنت مقایسه می­شود که بسیار رضایت بخش هستند. مزیت این روش مدل سازی اینست که برای محاسبه سرعت در هر نقطه از هندسه، احتیاجی به مش بندی در کل میدان جریان نبوده و سرعت در یک نقطه خاص می­تواند مستقیم و بدون وابستگی به نقاط دیگر به دست آید.

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