Using of AUSM+ Method for Improving the Results and Reducing Numerical Eror of Jameson's 2D Finite Volume Technique in Turbine Stator Blades

Authors

Abstract

Due to the importance of the role of turbines in various industries, a more precise design is needed to improve their efficiency. In this line, a more exact solution of the flow passing through turbine blades is needed. Nowadays, the advancement of numerical modeling techniques has resulted in achieving more accurate tools capable of considering the discontinuities with less oscillation and numerical errors. In this study, for modeling the flow in a supersonic 1D converging-diverging channel, the AUSM+ upwind method and a computational standard grid are used. The obtained results for a strong vertical shock agrees well with analytical results, and is considered as an initial verification of the method. In this research and for the first time, the AUSM+ numerical method has been further developed by using a simple H-grid mesh for modeling an inviscid subsonic and supersonic outlet flow in turbine stator blades. Comparing the model results with the results of Jameson’s artificial dissipation technique and experimental data showed that both numerical methods have good agreement with experimental pressure data, but the AUSM+ method has less numerical errors and improves the mass conservation by at least 25%. It is to be noted that the AUSM+ method is highly recommended for higher Mach numbers.

Keywords

Main Subjects

References

[1] Singh R, Holmes G (2012) Evaluation of an Artificial Dissipation and AUSM based Flux Formulation: AD-AUSM. AIAA paper 2012-3069.
[2] Jameson A (1995) Analysis and design of numerical schemes for gas dynamics, 1: artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int J Comput Fluid Dyn 4(2): 171-218.
[3] Jameson A (1995) Analysis and design of numerical scheme for gas dynamics, 2: artificial diffusion and discrete shock structure. Int J Comput Fluid Dyn 5(1-2): 1-38.
[4] Liu F, Jennions I, Jameson A (1998) Computational of turbomachinery flow by a convective-upwind-split-pressure (CUSP) scheme. 36th ASME. American Institue of Aeronautics and Astronautics.
[5] Pasandideh fard M,. Salari M, Mansoor M, Malek Jafarian M (2008) An investigation and comparison of ROE upwin methods with CUSP central difference schemes. 12th ACFM. Daejeon, Korea.
[6 ] مظاهری کیومرث، دربندی مسعود، وکیلی پور شیدوش (1385) اعمال یک روش ضمنی و بالادست بر روی شبکه بی‌سازمان مثلثی برای حل میدان جریان لزج. مجله علمی و پژوهشی مهندسی مکانیک مدرس، دوره6، شماره 1، صفحه 12-1.
[7] Liou MS, Steffen CJ (1993) A new flux splitting scheme. J Comput Phys 107: 23-39.
[8] Liou MS (2010) The evolution of AUSM scheme. deffence SCI J 60(6): 606-613.
[9] Liou MS (1996) A sequel to AUSM: AUSM+. J Comput Phys 129: 364-382.
[10] Jameson A (1995) Positive schemes and shock modelling for compressible flows. Int J Numer Met Fl 20(8-9): 743-776.
[11] یوسفی راد ادریس ، مه پیکر محمدرضا، تیمورتاش علیرضا (1393) بکارگیری روش کاسپ و بهینه سازی آن با استفاده از روش معکوس جهت بهبود روش حجم محدود جیمسون دوبعدی .مجله علمی و پژوهشی مهندسی مکانیک مدرس، شماره 8، صفحه 174-182.
[12] یوسفی راد ادریس، مه پیکر محمدرضا، تیمورتاش علیرضا (1391) به کارگیری روش کاسپ جهت بهبود حل عددی دو بعدی در روش حجم محدود جیمسون بین پره های ثابت توربین. دوازدهمین کنفرانس انجمن هوافضای ایران، دانشگاه صنعتی امیر کبیر.
[13] Hajzman M, Bublik O, Vimmr J (2007) On the Modelling of Compressible invisid flow problems using AUSM Schemes. ACM 1: 469-478.
[14] Liou MS, Edwards JR (1999) Numerical Speed of Sound and its Application to Schemes for All Speed. AIAA Paper 993268.
[15] Liou M S, (2006) A sequel to AUSM, Part II: AUSM+-up for all speeds. J Comput Phys 214: 137–170.
[16] Colonia S, Steiil R, Barakos GN (2014) Implicit Implementation of the AUSM+ and AUSM+up Schemes. Int J Numer Meth Eng 75: 687-712.
[17] Liou MS (2001) Ten years in the making-AUSM-family. AIAA Paper 2521.
[18] Chima RV, Liou MS (2003) Comparison of the AUSM+ and H-CUSP schemes for turbomachinery applications. AIAA Paper 4120.
[19]ابراهیم‌زاده فهیمه، پسندیده فرد محمود، مه پیکر محمدرضا (1393) بررسی طرح‌های بالادست AUSM+، تفاضل مرکزی کاسپ و اسکالر در جریان با بازه ماخ های بسیار کم تا ماوراء صوت. بیست و سومین همایش سالانه مهندسی مکانیک ایران، دانشگاه صنعتی امیر کبیر.
[20]یوسفی راد ادریس، مه پیکر محمدرضا (1391) به کارگیری روش معکوس جهت تلفیق حل عددی دوبعدی، حجم محدود و تفاضل محدود بین پره های ثابت توربین. هجدهمین همایش سالانه مهندسی مکانیک ایران.
[21] Bakhtar F, Mahpeykar MR, Abbas K (1995) An investigation of nucleating flows of steam in a cascade of turbine blading-theoretical treatment. J Fluids Eng 117(1).
Journal of Solid and Fluid Mechanics
Volume 5, Issue 4 - Serial Number 4
January and February 2016
Pages 201-212

Files

Share

How to cite

Statistics