Direct numerical simulation of two-dimensional and non-compressible boundary flow using compressed finite difference method

Maghrebi, M.J.; Zarghami, A.; Feyzabadi Farahani, M.

doi:10.22061/tej.2007.1285

Document Type : Original Research Paper

Authors

¹ Shahroud University of Technology,Semnan,Iran

² Department of energy conversion, Shahroud University of Technology,Semnan,Iran

https://doi.org/10.22061/tej.2007.1285

Abstract

The dimensionless Navier-Stokes equation is solved in a rotational form for the flow of a two-dimensional boundary layer of plates by a direct numerical method. Considering the speed profile at the input of the computational domain, the thickness of the boundary layer has been used as the characteristic length and the uniform velocity of the environment has been used as the characteristic velocity for dimensionlessness. The governing differential equations are broken down using the method of finite compression difference in the main directions of the flow and perpendicular to the flow. A forced mapping has been used to convert the physical domain to the computational domain. In order to develop the calculations in the time domain, the third-order compact Ranj Kota method has been used. The output boundary condition is determined using the transfer model. The simulation results of this type of flow are compared with the resolution of Blasius, which shows the accuracy of the code. In this study, the flow characteristics of the quiet boundary layer to evaluate the accuracy of the code, test and by dividing the lengths and velocities by the thickness of the boundary layer and the uniform velocity of the environment, profiles and contours of velocity and vortex in the device of dimensionless coordinates and self-similarity have seen.

Keywords

20.1001.1.20080441.1386.2.1.5.5

References

[1] F.M. White, Viscous Fluid Flow, 3rd Edition, McGraw-Hill, New York, 2000. [2] J. Mathieu, J.Scott, An Introduction to Turbulent Flow, Cambridge University Press, 2000. [3] S.A. Orszag and G.S. Patterson, Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett.,Vol 28, 1972, pp 76–79. [4] R.S. Rogallo, Numerical experiments in homogeneous turbulence. NASA TM 81315, 1981. [5] John Kim, Parviz Moin, and Robert Moser, Turbulence statistics in fully developed channel flow at low reynolds number. J. of Fluid Mech.,Vol 177, 1987, pp 133 –166. [6] H. kreplin. And H. Eckelmann , Behaviour of the three fluctuating velocity components in the wall region of a turbulent channel flow. Physics of Fluids, Vol 22, 1979, pp 1233-1239. [7] R. Spalart, Direct simulation of a turbulent boundary layer up to Re=1410 J. Fluid Mech.,Vol 187, 1988, pp 61–98. [8] Hung Le, Parviz Moin, and John Kim, Direct numerical simulation of turbulent flow over a backward-facing step. J. of Fluid Mech. Vol 330, 1997, pp 349–374. [9] Yang Na and Parviz Moin, Direct numerical simulation of turbulent boundary layers with adverse pressure gradient and separation. Rep.

TF-68, Thermosci. Div., Dept. Mech. Eng., Stanford, 1996. [10] W.J. Feiereisen, W.C. Reynolds, and J.H. Ferziger, Numerical simulation of a compresssible,homogeneous turbulent shear flow. Rep. TF-13, Thermosci. Div., Dept. Mech. Eng., Stanford, 1981. [11] W.C. Reynolds, The Potential and Limitations of Direct and Large Eddy Simulations. In J.L. Lumley, editor, Whither Turbulence? Turbulence at the Crossroads, pages, 1990, pp 313-343. Springer, New York. [12] M.J. Maghrebi, A Study of Evolution of Intense Focal Structures in Spatially-Developing Three -Dimensional Planer Wake, PhD thesis, Department of Mechanical Engineering, Monash University, Melbourne, Australia, 1999. [13] RH. Bartles, and G.W. Stewart, Solution of the Matrix Equation AX+XB=C, Communications of the ACM, Vol 15, Number 9, 1972. [14] S.K. Lele, Compact Finite Difference Scheme with Spectral-Like Resolution, Journal of Computational Physics,Vol 103, 1992, pp 1612. [15] A. Wray & M.Y. Hussaini, Numerical Experiments in Boundary Layer Stability, Proc. R. Soc. Lond. A, Vol. 392, 1984, pp 373389. [16] Howarth, L., On the solution of the Laminar Boundary – Layer Equation, Proceedings of the Royal Society of London , A164, 1983, pp. 547-479 [17] Panton, R.L., Incompressible Flow, Wiley, New York, 1984. [18] H.Schlichting, and K.Gersten, Boundary Layer Theory, Springer-Verlag, 8th Edition, 2005.

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Technology of Education Journal (TEJ)

Direct numerical simulation of two-dimensional and non-compressible boundary flow using compressed finite difference method

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Volume 2, Issue 1 - Serial Number 5
January 2008
Pages 33-42

Direct numerical simulation of two-dimensional and non-compressible boundary flow using compressed finite difference method

References

References

Send comment about this article

Volume 2, Issue 1 - Serial Number 5January 2008Pages 33-42

Volume 2, Issue 1 - Serial Number 5
January 2008
Pages 33-42