Documentation du code de simulation numérique SUNFLUIDH

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 difuse 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 angular 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 and $(\kappa_j,a_j)$.

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

$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] $

${q}_r^{net}(x_i^{wall}) = \varepsilon_{wall} \left[ \sigma_B ({T}(x_i^{wall}))^4 - \sum_{j=0}^{N_g} \sum_{m:\vec{s}_m \cdot \vec{n} > 0} \omega_m |\vec{s}_m\cdot \vec{n}| I_j^m (x_i^{wall},\vec{s}_m) \right]$

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.

  &Radiative_Heat_Transfer_DOM  activateRadiation = .false., RadiativePeriod = 1, FirstIterations = 20, 
			RadiativeLocalIterations = 1, RadiativeConvergenceTolerance = 1.E-15,
			WallRadcoeff = 1.0 , VolRadCoeff = 1.0, RadiativeScheme = "STEP",
			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 /

• 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

• 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 at walls.
• For debugging only.
• Default value = 1.0

• Type : Real value
• Prescaler on the radiative source term.
• 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

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

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

• 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

—–

• 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.

• 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

• 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 ]

• 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”

• 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

• 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

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