# Documentation du code de simulation numérique SUNFLUIDH

## Web LIMSI

Not for the release SUNFLUIDH_EDU .
This data set is used to define the radiative problem. Otherwise, it can be omitted.
This module considers the Radiative Transfer Equation (RTE) for an emitting-absorbing non-scattering medium enclosed by diffuse boundaries. To take into account the gas behavior, it considers both gray-gas assumption as well as real gas behavior through the Spectral-Line-Weighted-Sum-of-Gray-Gases (SLW) model.
The final RTE-SLW problem is then discretize with the Discrete Ordinates Method (DOM).

The DOM discretize the $4\pi$ steradians integration in a set of $M$ discrete directions represented by their direct cosines and corresponding weights $\vec{q_m} = (\vec{s_m},\omega_m) = (\mu_m,\eta_m,\xi_m,\omega_m)$ for all $m \in [1,M]$.
The SLW model will change the spectral integration in a weighted sum of $N_g$ gray-gases represented by their absorption coefficient and corresponding weights $(\kappa_j,a_j)$ for all $j \in [1,N_g]$.

Thus, the resulting RTE-SLW-DOM problem for emitting-absorbing non-scattering medium stands as below :

$$\vec{s}_m \cdot \nabla I_j^m (x_i,\vec{s}_m) = \kappa_j \left[ a_j I_b({T}(x_i)) - I_j^m(x_i,\vec{s}_m) \right]; \quad \forall (m,j) \in [M,N_g]$$

where $I_j^m$ is the radiative intensity for the virtual gray-gas $j$ in direction $m$ and $I_b$ is the blackbody radiative intensity.

The dimensional radiative source term $S_r$ and boundary net radiative heat flux $q_r^{net}$ are defined as :

\begin{eqnarray} S_r(x_i,{T}) & = & - \sum_{j=0}^{N_g} \kappa_j \left[ \sum_{m=1}^{M} \omega_m I_j^m (x_i,\vec{s}_m) - 4 a_j \sigma_B ({T}(x_i))^4 \right] \\ {q}_r^{net}(x_i^{wall}) & = & \varepsilon_{wall} \left[ \sigma_B ({T}(x_i^{wall}))^4 - \sum_{j=0}^{N_g} \sum_{m:\vec{s}_m \cdot \vec{n} > 0} \omega_m |\vec{s}_m\cdot \vec{n}| I_j^m (x_i^{wall},\vec{s}_m) \right] \end{eqnarray}

where $\sigma_b$ is the Stefan-Boltzmann constant, $\varepsilon$ is the boundary emissivity and $\vec{n}$ is the normal to the wall pointing out of the domain.

This radiative solver implementation considers only cartesian problems and does not support immersed bodies.

## Full data set of the namelist

  &Radiative_Heat_Transfer_DOM  activateRadiation = .false., RadiativePeriod = 1, FirstIterations = 20,
ActivateGas = .false., NbGas = 1, ka_max = 0.0, ka_min = 0.0,
Pref = 101325.0, Tref = 300., Href = 1, speca = "H2O", xaref = 0.07, xaUniform = 0.07,
SQuad = 8, WallEmissivity = 0.0 0.0 0.0 0.0 0.0 0.0 /

## Definition of the data set for the DOM-RTE problem

• Type : Boolean value
• This option activates the radiative module.
• .false. : no radiation considered
• .true. : radiation problem is considered
• Default value = .false.

• Type : Integer value
• This option set the periodicity of resolution of the Radiative problem in time iteration.
• Default value = 1

### FirstIterations

• Type : Integer value
• In the case that no restart fields are available (start radiation from scratch), the solver will iterates “FirstIterations” times before entering the time loop.
• Default value = 20

• Type : Integer value
• Number of sub-iteration for the RTE solving at each radiative iteration.
• Default value = 1

• Type : Real value
• Convergence criteria on the wall Fluxes and radiative source term for the sub-iteration.
• Default value = 1.E-15

• Type : Real value
• Prescaler on the net radiative heat flux $q_r^{net}$ at walls.
• For debugging only.
• Default value = 1.0

• Type : Real value
• Prescaler on the radiative source term $S_r$.
• For debugging only.
• Default value = 1.0

• Type : Character string with a maximum size of 20
• Name of the interpolation scheme used in the Discrete Ordinates Method.
• Available values :
• “STEP” : first order interpolation scheme (robust)
• “DIAMOND” : second order centered interpolation scheme (could lead to negative intensity)
• “LATHROP” : second order interpolation scheme with limiter (time-consuming)
• Default value = “STEP”

• Type : Integer value.
• Order N of the level symmetric angular quadrature ($S_N$)
• This quadrature leads to $M = (N+2)\times N$ directions in volume and half at boundaries
• Available values are 2, 4, 6, 8, 10, 12, 14
• Default value = 8

### Tref

• Type : Real value.
• Reference temperature $T_{ref}$ in [$K$].
• Default value = Fluid_Properties%Reference_Temperature

### Href

• Type : Real value.
• Reference Length $H_{ref}$ in [$m$].
• Default value = Nondimensionalization%Reference_Length

### WallEmissivity

• Type : Real array of size 6.
• Boundaries emissivities $\varepsilon$ sorted as (x-,x+,y-,y+,z-,z+).
• Default values = 0.0 0.0 0.0 0.0 0.0 0.0

## Definition of the data set for the SLW model

### activateGas

• Type : Boolean value
• This option activates the SLW module.
• .false. : transparent medium under gray-gas assumption is considered (i.e. $\kappa = 0$)
• .true. : Gas absorption and emission is considered
• Default value = .false.
if activateGas == .false., the settings below are unnecessary.

### NbGas

• Type : Integer value
• This option sets the number of weighted gray-gases $N_g$ used in the SLW model.
• NbGas $=$ 1 : gray-gas assumption with $\kappa$ = ka_min
• NbGas $\ge$ 2 : SLW model is employed
• Default value = 1
Setting NbGas $=$ 1 and ka_min = 0 is equivalent to wall-to-wall radiation du to the presence of transparent medium

### ka_min , ka_max

• Type : Real values
• These options set the lower and upper bounds of dimensional absorbing coefficient [$m^{-1}$] for the SLW model.
• if NbGas $=$ 1 : $\kappa$ = ka_min, ka_max is useless
• if NbGas $\ge$ 2 : ka_min < $\kappa_j$ < ka_max for all $j \in [1,N_g]$
• Default value = [ ka_min , ka_max ] = [ 0.0 , 0.0 ]

### SPECA

• Type : Character string with a maximum size of 3
• Name of the absorbing species when NbGas $\ge$ 2 (SLW model).
• if “NbGas” $=$ 1 : useless
• Available values :
• “H2O” : $air-H_2O$ mixture
• “CO2” : $air-CO_2$ mixture
• Default value = “H2O”

### xaref

• Type : Real value
• This option set the reference molar fraction $x_{ref}$ of the absorbing species for the SLW model.
• if “NbGas” $=$ 1 : useless
• Default value = 0.07

### xaUniform

• Type : Real value
• As long as the SLW model is not coupled with species equations, this option set a uniform molar fraction $x_{a}$ of the absorbing species in the overall domain.
• if NbGas $=$ 1 : useless
• Default value = 0.07

### Pref

• Type : Real value.
• Reference pressure $P_{ref}$ in [$Pa$].
• if “NbGas” $=$ 1 : useless
• Default value = obtained from Fluid_Properties quantities