High Rayleigh number flows in a cubical enclosure
The current study was undertaken with an intention to verify and extend the boundaries of the work produced by Xia & Murthy  and Vargas  on natural convective flows inside a cubical enclosure to observe the transition to turbulence. Their primary focus was to better understand the flows inside a cubical enclosure at higher Rayleigh numbers (Ra) with the help of Direct Numerical Simulation (DNS). This helps in understanding the mixing process that takes place inside the center wing tank of a commercial airplane. The motivation behind the current study was to stretch the limits of the work done by Vargas by adapting central differencing scheme (CDS) of discretization at three different grid sizes of 50^3, 75^3 and 90^3 with DNS. In order to achieve this task, we used the code developed by FLUENT for finite volume method. The cavity was created and meshed in GAMBIT with the bottom wall heated, top wall cooled and the side walls maintained adiabatic. Then, the Ra is varied between 2 x 10^4 and 10^9 maintaining the Prandtl number (Pr) to be constant at 2.5. Initially, the results were verified with those of Vargas and Xia & Murthy and similar observations were made with steady convective flows at Ra = 2 x 10^4, 10^5 and 2 x 10^5. Periodic flows were captured at the critical Ra = 4.07 x 10^5 beyond which flows exhibited the chaotic nature until Ra = 10^9. The work was then carried forward with the idea of employing the CDS of discretization at higher Ra up to 10^9 along with a finer grid density of 90^3 control volumes. The power spectrum slopes have been compared with the Kolmogorov’s -5/3 rule for turbulent flows to observe the transition to turbulence.