Partie 3 :Simulation in the mantle


Critic Rayleigh Number:

The estimated viscosity in the mantle is about 10²² Poiseuilles or Kg.s¯¹.m¯¹ .
We will consider the inferior mantle to be at the temperature of 2900 K and the upper mantle around 400 K.
The thermal conductivity is about 2,7 W.(m.K)¯¹ what conduces to a thermical diffusivity k=lambda/(rho*cp) of 7,52.10¯7
The  Dilatation coefficient is  about 2,4.10¯5
The volumic weight is 33,59.10²  Kg.m¯3

These values lead to a critic Rayleigh Number of 5,88.10^7

This result is close to the estimated value between 10^6 and 10^7.

Grid size and viscosity:

As Fluent doesn`t allow so big numbers for viscosity, we decided to reduce the size of the domain and the viscosity, but still keep the Rayleigh number.
The domain is a box of 2800 m * 4000 m, the temperature repartition is given by the equation:

T= -0.8929 y +2900

The viscosity is defined by the following User Defined Fonction (UDF):

/* user define function*/
/* udf pour viscosite*/

#include "udf.h"

real nu;
real temp;


if (temp<2000)

return nu;


This  simulation leads to the stable situation of one roll in the whole domain,  effectivly, the given hypothesis of 4 rolls `superposes` is pretty unstable .


This simulation could lead us to conclude to the second hypothesis : one big convection moving the all mantle, nevertheless, we might have made many modelisation that could turn the simulation wrong.

In order to obtain the two levels convection we decided to establish several modification:

- consider a smaller domain

- use caracteric numbers for Fluent: simulate with water-liquid instead of magma

- use a gradient viscosity repartition instead of a discontinuity .


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