Document Type: Research Paper

Author

department of Mechanical Engineering, University of Bonab

Abstract

In this paper the characteristics of unsteady three-dimensional incompressible flows with heat transfer are obtained along with artificial compressibility of Chorin. At first, compatibility equations and pseudo characteristics for three-dimensional flows are derived from five governing equations (continuity equation, Momentum equations in three directions, and energy equation) and then results are simplified to two dimensional flows. Pseudo Mach hyper-cone (four dimensional cone) are found and its cross-section with physical axis is calculated numerically. Unlike compressible flow, this is not a sphere. It is found that the pseudo acoustic speed within the incompressible flow is function of artificial compressibility parameter and the directions. In two dimensional, Pseudo Mach cone is obtained by numerical solution of characteristic equations. Unlike compressible flow, the cross section of Mach cone with x-y plane is not circle. This shape is not oval, too. The influence of artificial compressibility parameter on convergence history and accuracy was surveyed by simulation of cavity flow as a benchmark

Graphical Abstract

Keywords

Main Subjects

[1]     D, Drikakis, P. A. Govatsos, and D. E. Papantonis, A characteristic-based method for incompressible flows. International journal for numerical methods in fluids. 19: p. 667-685(1994).

 

[2]     S. E. Razavi, and T. Adibi, A novel multidimensional characteristic modeling of incompressible convective heat transfer. Journal of Applied Fluid Mechanics, 9 (4). (2016)

 

[3]     T. Adibi, and S. E. Razavi, A new-characteristic approach for incompressible thermo-flow in Cartesian and noncartesian grids. International journal for numerical methods in fluids, 79: p. 371-393(2015).

 

[4]     S. E. Razavi, and M. Hanifi, A multi-dimensional virtual characteristic scheme for laminar and turbulent incompressible flows. Journal of Applied Fluid Mechanics, 2016.

 

[5]     K. Zamzamian, and S.E. Razavi, Multidimensional upwinding for incompressible flows based on characteristics. Journal of Computational Physics,. 227 (19): p. 8699-8713(2008).

 

[6]     R. Fathollahi, and K. Zamzamian, An improvement for multidimensional characteristic-based scheme by using different selected waves. International Journal for Numerical Methods in Fluids, 76(10): p. 722-736(2014).

 

[7]     I., Abdollahi, K. Zamzamian, and R. Fathollahi, High-accuracy upwind method using improved characteristics speeds for incompressible flows. International Journal for Numerical Methods in Fluids, 80(8): p. 476-489(2016).

 

[8]     J. B. Franklin, and J. M. Harris, A high-order fast marching scheme for the linearized eikonal equation. Journal of Computational Acoustics, 09(03): p. 1095-1109 (2001).

 

[9]     van der Velden, W. C. P., J. T. Akhnoukh, and A.H. van Zuijlen, Low-Order Finite-Volume Based Riemann Solver for Application to Aeroacoustic Problems. Journal of Computational Acoustics, 25(03): p. 175-185 (2017).

 

[10]   R. Kaviani, and M. Nikkhah-Bahrami, Improved Navier–Stokes Boundary Conditions Based on Generalized Characteristics. Journal of Computational Acoustics, 23(02): p. 155-161 (2014).

 

[11]   A Munir, M Rizwan, and A. Shah, Simulation of incompressible flow in two sided lid driven cavity using upwind compact scheme, CFD LETTERS, 5(3): p. 57-66(2013).

 

[12]   T, Adibi, R. A. Kangarluei, and V. Farhangmehr, Numerical Study of Natural Convection Flow I nside Squared and Trapezoidal Cavities in Various Conditions. International Journal of Science, Engineering and Technology Research, 06: p. 882-886 (2017).

 

[13]   C. Moyne, and H. P. A. Souto, Multi-Scale approach for conduction heat transfer: one and two-equation models. Computational and Applied Mathematics, 33(2): p. 433-449(2014).

 

[14]   T. S. Cheng, and W.H. Liu, Effect of temperature gradient orientation on the characteristics of mixed convection flow in a lid-driven square cavity. Computers & Fluids, 39(6): p. 965-978, (2010).

 

[15]   R. Iwatsu,  J. M. Hyun, and K. Kuwahara, Mixed convection in a driven cavity with a stable vertical temperature gradient. International Journal of Heat and Mass Transfer, 36(6): p. 1601-1608(1993).

CAPTCHA Image