Papers »

A solution algorithm for transient compressible navier-stokes equations at all mach number​​s

A segregated algorithm is proposed to solve transient compressible Navier-Stokes equations for all Mach number. The solution algorithm is developed for collocated arbitrary polyhedral finite-volume method and is applicable for complex geometries. This approach employs strong conservation form of governing equations and uses conservative variables (momentum and total energy) as dependent variables. Pressure is used in the formulation due to its roles in all speed spectrum by acting upon density through equation of state and conservation of momentum. The proposed pressure equation is derived from conservation of mass and is perturbed by Newton’s linearisation in order to impose a hyperbolic nature. It is shown that the algorithm is effective to calculate all Mach number flows spanning the subsonic, transonic and supersonic flow regimes with shock capturing capability. Furthermore, the formulation framework of the algorithm provides a flexibility to extend to multidisciplinary fluid flows with relative ease. A sequence of validation and convergence studies is conducted to assess the transient numerical result quantitatively in a more structured and effective way. The numerical result obtained, including viscous compressible fluid flow at different Mach number and Riemann problem, is assessed by comparing with experimental data or other numerical results available in literature, illustrating the superiority of the present solution algorithm in terms of efficiency, robustness, and accuracy.

Author(s):

Kian Chuan Ong    
The University of Nottingham, Malaysia Campus
Malaysia

Andrew Chan    
The University of Nottingham, Malaysia Campus
Malaysia

Lee Peng Teo    
The University of Nottingham, Malaysia Campus
Malaysia