Journal of Aeronautical Engineering

Journal of Aeronautical Engineering

Numerical investigation of the AUSM-family in viscous and inviscid axisymmetric flow Field

Document Type : Original Article

Authors
1 MSc. Student, Faculty of Engineering, Ferdowsi Uneiversity of Mashhad, Mashhad, Iran
2 Ph.D. Student, Faculty of Engineering, Ferdowsi Uneiversity of Mashhad, Mashhad, Iran
3 Mech. Engg. Dept. Ferdowsi university of mashhad
Abstract
This research explores and compares the AUSM scheme family based on compressible, steady, viscous, and inviscid axisymmetric flows in a finite-volume method-based and unstructured data storage grids code. When the effects of side-velocity are taken into account, axisymmetric flows can be considered a three-dimensional problem in the longitudinal plane; as a result, there is a considerably decreased number of computations required compared to computations in three dimensions. The most important and latest modifications of the AUSM-family were developed to identify more efficient methods in the AUSM- family in terms of accurate prediction of the axisymmetric flow field in internal and external axisymmetric flows, viscous (inviscid), and high-speed flows with shock waves characteristics. The novelty of this investigation is the assessment and comparison done on the AUSM-family in resolving the compressible axisymmetric flow field, which has received less attention in prior studies. The studies determined that the AUSM+M method performs better against a strong shock wave than other methods investigated in this research. According to the modifications made in this scheme, unlike other methods, there are no wiggles in the regions mentioned earlier. Furthermore, it is discovered that the AUSM+M method had a higher rate of convergence than the AUSM+ and SLAU approaches. In addition, the AUSM+M scheme is distinctive from other techniques in viscous flows because it produces the minimum kinetic energy dissipation rate and fewer shock anomalies in the shock wave region.
Keywords

[1]        K. Peery and S. Imlay, "Blunt-body flow simulations," in 24th Joint Propulsion Conference, 1988, pp. 88-2924.
[2]      S.-s. Kim, C. Kim, O.-H. Rho and S. K. Hong, "Cures for the shock instability: development of a shock-stable Roe scheme," Journal of Computational Physics, vol. 185, no. 2, pp. 342-374, 2003.
[3]        S.-s. Chen, C. Yan, B.-x. Lin, L.-y. Liu, and J. Yu, "Affordable shock-stable item for Godunov-type schemes against carbuncle phenomenon," Journal of Computational Physics, vol. 373, pp. 662-672, 2018.
[4]        M.-S. Liou, "A sequel to AUSM, Part II: AUSM+-up for all speeds," Journal of Computational Physics, vol. 214, no. 1, pp. 137-170, 2006.
[5]        E. Shima and K. Kitamura, "Parameter-free simple low-dissipation AUSM-family scheme for all speeds," AIAA Journal, vol. 49, no. 8, pp. 1693-1709, 2011.
[6]        P. L. Roe, "Approximate Riemann solvers, parameter vectors, and difference schemes," Journal of computational Physics, vol. 43, no. 2, pp. 357-372, 1981.
[7]        E. F. Toro, M. Spruce and W. Speares, "Restoration of the contact surface in the HLL-Riemann solver," Shock Waves, vol. 4, no. 1, pp. 25-34, 1994.
[8]        S. Osher and F. Solomon, "Upwind difference schemes for hyperbolic systems of conservation laws," Mathematics of Computation, vol. 38, no. 158, pp. 339-374, 1982.
 [9]       A. Harten, P. D. Lax and B. V. Leer, "On upstream differencing and Godunov-type schemes for hyperbolic conservation laws," SIAM review, vol. 25, no. 1, pp. 35-61, 1983.
[10]      V. V. E. Rusanov, Calculation of Interaction of Non-Steady Shock Waves with Obstacles. NRC, Division of Mechanical Engineering, 1962.
[11]      B. V. Leer, "Flux-vector splitting for the Euler equation," in Upwind and High-Resolution Schemes: Springer, pp. 80-89, 1997.
[12]      J. L. Steger and R. Warming, "Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods," Journal of Computational Physics, vol. 40, no. 2, pp. 263-293, 1981.
[13]      M.-S. Liou and C. J. Steffen Jr, "A new flux splitting scheme," Journal of Computational physics, vol. 107, no. 1, pp. 23-39, 1993.
[14]      M.-S. Liou, "A sequel to ausm: Ausm+," Journal of Computational Physics, vol. 129, no. 2, pp. 364-382, 1996.
[15]      K. H. Kim, C. Kim and O.-H. Rho, "Methods for the accurate computations of hypersonic flows: I. AUSMPW+ scheme," Journal of Computational Physics, vol. 174, no. 1, pp. 38-80, 2001.
[16]      K. Chakravarthy and D. Chakraborty, "Modified SLAU2 scheme with enhanced shock stability," Computers & Fluids, vol. 100, pp. 176-184, 2014.
[17]      S.-s. Chen, F.-j. Cai, H.-c. Xue, N. Wang, and C. Yan, "An improved AUSM-family scheme with robustness and accuracy for all Mach number flows," Applied Mathematical Modelling, vol. 77, pp. 1065-1081, 2020.
[18]      K. A. Hoffmann and S. T. Chiang, Computational Fluid Dynamics Volume III (Engineering education system). 2000.
[19]      F. M. White and J. Majdalani, Viscous Fluid Flow. McGraw-Hill New York, 2006.
[20]      H. K. Versteeg and W. Malalasekera, An Introduction To Computational Fluid Dynamics: The Finite Volume Method. Pearson education, 2007.
[21]      F. R. Menter, "Two-equation eddy-viscosity turbulence models for engineering applications," AIAA Journal, vol. 32, no. 8, pp. 1598-1605, 1994.
[22]      A. Jameson, W. Schmidt and E. Turkel, "Numerical solution of the euler equations by finite volume methods using Runge-Kutta Time stepping schemes," AIAA Paper, vol. 81, 07/01 1981.
[23]      O. BELOTSERKOVSKIY, "Supersonic gas flow around blunt bodies," Computer Center of The Academy of Sciences, Moscow, 1967.
[24]      J. C. South, Calculation of Axisymmetric Supersonic Flow Past Blunt Bodies with Sonic Corners: Including a Program Description and Listing. National Aeronautics and Space Administration, 1968.
 
Volume 25, Issue 1
May 2023
Pages 1-15

  • Receive Date 30 June 2022
  • Revise Date 17 July 2022
  • Accept Date 25 July 2022