Evaluate the Performance of the Scalar and Cusp Central Difference Schemes, AUSM+ Upwind Method in Very Low Mach Number up to Supersonic Flow

Authors

ferdowsi university of mashhad

Abstract

In recent years, achievement more accurate numerical method in different flow regimes for the discontinuities with less oscillation and numerical errors is the interest of many researchers. What distinguishes this paper is, comparison of the performance of artificial dissipation and upwind methods, in solving the Euler equations for internal compressible flows in a wide range of inlet Mach numbers. In this study we examined the ability of three AUSM+ upwind method, Scalar and Cusp artificial dissipation methodes from very low Mach up to ultrasound and non-viscous flow in a convergent-divergent nozzle. The ability of AUSM+ method and Scalar methods in two-dimensional inviscid sonic flow between turbine stator blades at both supersonic and subsonic outlet is also investigated. In this study an excellent performance for AUSM+ method with more convergence speed and low numerical error in all flow regimes at a converging-diverging nozzle is observed. In the second example, in both flow AUSM+ method presents the results based on experimental, with low numerical errors and satisfy the mass conservation better than Scalar. It should be mentioned that the AUSM+ method is highly recommended for higher Mach numbers.

Keywords

Main Subjects

References

[1] 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.
[2] 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.
[3] Liou MS, Steffen CJ (1993) A new Flux Splitting Scheme. J Comput Phys 107: 23-39.
[4] Liou MS (2010) The evolution of AUSM scheme. Deffence SCI J  60( 6): 606-613.
[5] Liou MS (1996) A Sequel to AUSM: AUSM+. J Comput Phys 129: 364-382.
[6] Hajzman M, Bublik O, Vimmr J (2007) On the modelling of compressible invisid flow problems using AUSM schemes. ACM 1: 469-478.
[7] Chima RV, Liou MS (2003) Comparison of the AUSM+ and H-CUSP schemes for turbomachinery applications. AIAA Paper 4120.
[8] Zha GC, Hu Z (2004) Calculation of transonic internal flows using an efficient high resolution upwind scheme. AIAA paper 2004-1097.
[9] Liou  MS (2006) A sequel to AUSM, Part II: AUSM+-up for all speeds. J Comput Phys 214: 137-170.
[10] 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.
[11] Younis MY, Sohail MA, Rahman T, Muhammad Z, Bakaul SR (2011) Application of AUSM+ scheme on subsonic, supersonic and hypersonic flows fields.  J Eng Tech 49: 242-248.
[12] Singh R, Holmes G (2012) Evaluation of an artificial dissipation and AUSM based flux formulation: AD-AUSM. AIAA paper 2012-3069.
[13] 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 دو بعدی. مجله علمی و پژوهشی مهندسی مکانیک مدرس،  شماره  8، صفحه 174-182.
[14] Robbins DJ, Cant RS, Gladden LF (2013) Development of accurate liquid equations of state for multi-phase CFD simulations with a modified AUSM+up scheme. J Comput Fluids 77: 166-180.
[15] Qu F, Yan C, Yu J, Sun D (2014) A new Flux Splitting Scheme for the Euler Equations. J Comput Fluids 102: 203-214.
[16] Jamson A,  Schmidt  W ( 1985) Some recent developments in numerical methods for transonic flows. Comput Method Appl M 51: 467-493.
[17] Shah A, Yuan L, Khan A (2010) Upwind compact finite difference scheme for time-accurate solution of the incompressible navier-stockes equation. Appl Math Comput 215(9): 3201-3213.
[18] Liou MS, Edwards JR (1999) Numerical speed of sound and its application to schemes for all speed. AIAA Paper 993268.
[19] Liou MS (2001) Ten years in the making-AUSM-family. AIAA Paper 2521.
[20] Colonia S, Steiil R, Barakos GN (2014) Implicit implementation of the AUSM+ and AUSM+up schemes. Int J Numer Meth Eng 75: 687-712.
[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 6, Issue 1
March and April 2016
Pages 225-237

Files

Share

How to cite

Statistics