# Project Case: Parametric study

Numerical simulations

Once the mesh sensitivity has been done, the parametric study can be processed. The following figure shows the three flight conditions used. For each flight condition, the industrial partner has given the Reynolds number and the density.

We note that the following results correspond to the "lift off" flight's conditions. The next figure shows a screenshot of the temperature field in the container:

Figure: The temperature field in the container

1-  $\delta_T$ and $h_c$

The first step to estimate the evaporation rate  $W_v$ is to compute $\delta_T$ and $h_c$. For this, the simulations gave us  $\delta_T$ and $h_c$. The figure below explains how we have done to extract these values from the simulation results:

Figure:  numerical estimation of $\delta_T$ and $h_c$

2- Evaporation rate $W_v$

We remind that we have found the expression of the evaporation rate $W_v$ on account density, the boundary layer thickness  $\delta_T$ and $h_c$

 $$W_v(x)=\frac{b\lambda}{C_p} ln\left( 1+\frac{W_v(x)}{b}\frac{C_p}{h_c(x)}\right)\frac{1}{\delta_T(x)-\delta}$$

Then with this formula established previously, $W_v$ is processed.

To better understand the distribution of the evaporation model, here there is the following figure:

Figure:  distribution of the evaporation model

Otherwise, the following table gave the values of the evaporation rate in different flight cases:

It's important to note that the most accurate result is the one of the lift off flight case because all the simulations were done in this case.

Otherwise, the mass vapor rate seems to be very high. What can be interesting to validate this approach is to compare it to available experimental data but it doesn't exist yet.