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 Problem

The 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