The fluids that will be studied are not real physical fluids except water (fluid1).
As the Prandtl number must be variable and the Rayleigh constant, Kappa and Nu are chosen as the only 'changing constant'.
However the Prandtl numbers were chosen to be close of real fluids.
The ProblemThe geometry used in the study is the classic Rayleigh-Benard problem: A fluid between two plates. The dimensions are 1 cm for the height and 2 cm for the width. The fluid is initially at rest.The grid
A structured orthogonal grid was used with 800 nodes (20x40).
How to 'create' a fluid ?
The principle of this study is to work with fluids that have constant Rayleigh number and wanted Prandtl numbers.
As and , Nu and Kappa are chosen as variables and Alpha, the gradient of temperature and the geometry of the problem ( it means the distance a) are kept constant.
For example, the fluid 2 was created such as: Ra= 4 796 and Pr= 0.74 ( it is the Prandtl number of air in normal conditions).
Alpha is 0.00014, DT= 0.5 Celsius degrees, a=1cm, and so: nu/kappa = 0.74 and nu*kappa=1.431e-13. Thanks to an easy 2nd degree resolution, it can be found Kappa= 4.398e-7 and Nu= 3.255e-7.
Using this method, 5 numerical fluids will be studied here. They are introduced in the following table.
The numerical fluids studied
Fluid1 Fluid2 Fluid3 Fluid4 Fluid5 Kappa 1.435e-7 4.398e-7 2.675e-6 3.26e-9 3.78e-8 Nu 1.e-6 3.255e-7 5.35e-8 4.389e-5 3.78e-6 Rho 1 000 1 000 10 000 1 000 1 000 Cp 4 182 1 000 100 1 000 1 000 Pr 7 0.74 0.02 13 460 100 Water Close to air Close to mercury Close to oil Close to nothing