The time needed to achieve fully developed convection cells and thermal boundary layers in CFD simulations depends on various factors, including the properties of the fluid and the simulation setup, as well as the mesh statistics and the complexity of the geometry.
In the case of low Prandtl number fluids, such as air with Pr < 1, the longer simulation time required to reach fully developed flow patterns and thermal boundary layers is primarily due to the fluid's properties. The low Prandtl number indicates that the thermal diffusivity is relatively high compared to the momentum diffusivity, resulting in a slower establishment of convective heat transfer. This means that heat is conducted more rapidly than momentum is transferred through the fluid, leading to a longer time for the flow to reach a fully developed state.
However, it is also important to consider the influence of the simulation setup. The mesh plays a crucial role in accurately resolving the flow features and capturing the boundary layer dynamics. The mesh density and quality affect the accuracy and convergence of the simulation. Complex geometries with intricate details may require a finer mesh to accurately capture the flow behavior, which can increase the computational cost and simulation time.
Moreover, solving the governing equations in CFD simulations is computationally expensive. The number of equations that need to be solved increases with the mesh size, and the time required for the simulation scales accordingly. The computational capabilities of the hardware used for the simulation also play a role in determining the simulation time.
In summary, the longer simulation time required for fully developed convection cells and thermal boundary layers in low Prandtl number fluids is primarily due to the fluid's properties, but it is also influenced by the mesh statistics and the complexity of the geometry. The mesh needs to be appropriately refined to accurately capture the flow behavior, and the computational capabilities of the hardware can also impact the simulation time.
Hope this helps
Prandtl number for air is O(1), that is the therma BL develops as similar ad the dynamic BL.
The simulation of thermal boundary layers in low Pr fluids within CFD frameworks is inherently time-intensive due to the exigencies posed by singular perturbation phenomena and the requisite deployment of numerical stabilizers. The low Pr scenario, characterized by a Pr < 1, necessitates refined spatial discretization to resolve the rapidly developing and physically thinner thermal boundary layers, a direct consequence of the disproportionate rates of thermal and momentum diffusivity.
This requirement precipitates a singular perturbation challenge, compelling the application of numerical stabilizers to maintain simulation stability and accuracy. Such stabilizers mitigate the stiffness resultant from the sharp thermal gradients, enabling the simulation to progress without succumbing to numerical instability or convergence difficulties.
Employing techniques such as artificial diffusion, flux correction, and adaptive mesh refinement (not general), numerical stabilizers facilitate the resolution of the critical scales of thermal transport while circumventing the computational burdens imposed by an excessively fine mesh or overly restrictive time steps.
Hence, the temporal demands in simulating low Pr fluids are principally attributed to the complexities introduced by the singular perturbation issue and the operational imperative for numerical stabilizers to ensure fidelity and computational efficiency in capturing the nuanced dynamics of thermal boundary layer development.
I wish you good luck with your research
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