Activation of the module

The module can be activated in the cs_user_model function in cs_user_parameters.c. The corresponding keyword is the type member of the cs_glob_rad_transfer_params structure.

This member can take the values:

CS_RAD_TRANSFER_NONE (module deactivated)
CS_RAD_TRANSFER_DOM (module activated using Discrete Ordinates Method)
CS_RAD_TRANSFER_P1 (module activated using P1 model)

Radiation module specific parameters.

When the module is activated, its specific input parameters should be set in the cs_user_radiative_transfer_parameters function of the cs_user_radiative_transfer.c file.

Calculation options for the radiative transfer module.

Radiative transfer parameters may be defined using the cs_user_radiative_transfer_parameters function.

Radiative transfer boundary conditions

Sketch of thermal flux in boundary walls

The radiative boundary condition is based on the calculation of a new wall temperature. This temperature is computed with a thermal flux balance:

${ Q_{conduction} = Q_{convection} + (Q_{rayt_{absorption}} - Q_{rayt_{emission}}})$

Therefore :

$\dfrac{xlamp}{epap} (T_{fluid} - T_{wall}) = h_{fluid} (T_{fluid} - T_{wall}) + epsp (Q_{incid} - \sigma * T_{wall})$

Note: In code_saturne the flux is positive when it is oriented from inside to outside.

Body	Emissivity
polished steel	0.06
oxidized steel	0.80
rough steel	0.94
polished aluminium	0.04
oxidized aluminium (inside)	0.09
oxidized aluminium (wet air)	0.90
brick	0.93
concrete	0.93
paper	0.8 to 0.9
water	0.96

Boundary faces identification

Boundary faces may be identified using the getfbr function, or preferrably, through boundary zones, defined using the GUI or the cs_user_zones function..

Initialization and finalization

The following declaration and initialization block needs to be added for the following examples:

  cs_real_t tkelvi = cs_physical_constants_celsius_to_kelvin;
  const cs_zone_t *zone = nullptr;
  int *izfrdp = cs_boundary_zone_face_class_id();

Remaining initialization

ivar: number of the thermal variable

cs_field_t *f_th = cs_thermal_model_field();

cs_thermal_model_field

cs_field_t * cs_thermal_model_field(void)

Definition: cs_thermal_model.cpp:216

cs_field_t

Field descriptor.

Definition: cs_field.h:131

Min and Max values for the wall temperatures (clipping otherwise)

$T_{min}$ and $T_{max}$ are given in Kelvin.

*tmin = 0.0;

*tmax = cs_math_big_r + tkelvi;

cs_math_big_r

const cs_real_t cs_math_big_r

Assign boundary conditions to boundary wall

Zone definitions

For each boundary face face_id, a specific output (logging and postprocessing) zone id may be assigned. This allows realizing balance sheets by treating them separately for each zone. By default, the output zone id is set to the general (input) zone id associated to a face.

To access output zone ids (both for reading and modifying), use the cs_boundary_zone_face_zone_id function.

Wall characteristics

Warning: The unit of the temperature is the Kelvin

Mandatory data

isothp(ifac) boundary face type
- CS_BOUNDARY_RAD_WALL_GRAY: Gray wall with temperature based on fluid BCs
- CS_BOUNDARY_RAD_WALL_GRAY_EXTERIOR_T: Gray wall with fixed exterior temperature
- CS_BOUNDARY_RAD_WALL_REFL_EXTERIOR_T: Reflecting wall with fixed outside temperature (same as Gray wall with zero emissivity)
- CS_BOUNDARY_RAD_WALL_GRAY_COND_FLUX: Gray wall with fixed conduction flux
- CS_BOUNDARY_RAD_WALL_GRAY_REFL_FLUX: Reflecting wall with fixed conduction flux

Other data (depending of the isothp)

rcodcl = conduction flux
epsp = emissivity
xlamp = conductivity ( $W.m^{-1}.K^{-1}$ )
epap = thickness ( )
textp = outside temperature ( )

Examples of boundary conditions

Here is a list of examples:

Gray or black wall with profil of fixed inside temperature

For wall boundary faces, selection criteria: color 1

  zone = cs_boundary_zone_by_name("wall_1");
 
  for (cs_lnum_t ilelt = 0; ilelt < zone->n_elts; ilelt++) {
 
    cs_lnum_t face_id = zone->elt_ids[ilelt];
 
    if (bc_type[face_id] == CS_SMOOTHWALL) {
 
      /* logging zone number */
      izfrdp[face_id] = 51;
 
      /* Type of condition: gray or black wall with fixed interior
         temperature (based on main temperature BC's) */
      isothp[face_id] = CS_BOUNDARY_RAD_WALL_GRAY;
 
      /* Emissivity */
      epsp[face_id] = 0.1;
 
    }
 
  }

Gray or black wall with fixed outside temperature \f$ T_{ext} \f$

For wall boundary faces, selection criteria: color 2

  zone = cs_boundary_zone_by_name("wall_2");
 
  for (cs_lnum_t ilelt = 0; ilelt < zone->n_elts; ilelt++) {
 
    cs_lnum_t face_id = zone->elt_ids[ilelt];
 
    if (bc_type[face_id] == CS_ROUGHWALL) {
 
      /* logging zone number */
 
      izfrdp[face_id] = 52;
 
      /* Gray or black wall with fixed exterior temperature */
      isothp[face_id] = CS_BOUNDARY_RAD_WALL_GRAY_EXTERIOR_T;
 
      /* Emissivity */
      epsp[face_id] = 0.9;
 
      /* Conductivity (W/m/K)*/
      xlamp[face_id] = 3.0;
 
      /* Thickness (m)*/
      epap[face_id] = 0.1;
 
      /* Fixed exterior temperature: 473.15 K */
      textp[face_id] = 200. + tkelvi;
 
    }
 
  }

Reflecting wall (\f$ epsp = 0 \f$) with fixed outside temperature \f$ T_{ext} \f$

For wall boundary faces, selection criteria: color 3

  zone = cs_boundary_zone_by_name("wall_3");
 
  for (cs_lnum_t ilelt = 0; ilelt < zone->n_elts; ilelt++) {
 
    cs_lnum_t face_id = zone->elt_ids[ilelt];
 
    if (bc_type[face_id] == CS_SMOOTHWALL) {
 
      /* log zone number */
      izfrdp[face_id] = 53;
 
      /* Type of condition: reflecting wall with fixed outside temperature */
      isothp[face_id] = CS_BOUNDARY_RAD_WALL_REFL_EXTERIOR_T;
 
      /* Conductivity (W/m/K) */
      xlamp[face_id] = 3.0;
 
      /* Thickness    (m)*/
      epap[face_id] = 0.10;
 
      /* Fixed outside temperature: 473.15 K */
      textp[face_id] = 200.0 + tkelvi;
 
    }
 
  }

Gray or black wall and fixed conduction flux through the wall

For wall boundary faces which have the color 4:

$\begin{array}{rcl} \frac{\texttt{xlamp}}{\texttt{epap}} \cdot (T_{wall} - T_{ext}) &=& \text{fixed conduction flux in } W.m^{-2} \\ &=& \texttt{rodcl(ifac,ivar,3)} \end{array}$

If the conduction flux is zero then the wall is adiabatic. The array $\texttt{rcodcl(ifac,ivar,3)}$ has the value of the flux.
Flux density (< 0 if gain for the fluid)

For temperature , in $W.m^{-2}$ :

$rcodcl(ifac,ivar,3)=C_p (viscls+\frac{visct}{\sigma})\cdot \grad{T}\cdot \vect{n}$

For enthalpy , in $W.m^{-2}$ :
$RCODC(IFAC,IVAR,3)=(viscls+\frac{visct}{\sigma})\cdot \grad{H} \cdot \vect{n}$

  zone = cs_boundary_zone_by_name("wall_4");
 
  for (cs_lnum_t ilelt = 0; ilelt < zone->n_elts; ilelt++) {
 
    cs_lnum_t face_id = zone->elt_ids[ilelt];
 
    if (bc_type[face_id] == CS_SMOOTHWALL) {
 
      /* log zone number */
      izfrdp[face_id] = 54;
 
      /* Type of condition: gray or black wall with fixed conduction
         flux through the wall */
      isothp[face_id] = CS_BOUNDARY_RAD_WALL_GRAY_COND_FLUX;
 
      /* Emissivity */
      epsp[face_id] = 0.9;
 
      /* Conduction flux (W/m2) */
      f_th->bc_coeffs->rcodcl3[face_id] = 0.0;
 
    }
 
  }

Reflecting wall and fixed conduction flux through the wall

For wall boundary faces which have the color 5:

$\frac{xlamp}{epap} \cdot (T_{wall} - T_{ext}) = \text{fixed conduction flux}$

and

If the conduction flux is zero then the wall is adiabatic. Flux density (< 0 if gain for the fluid)

For temperatures , in $W.m^{-2}$ :
$rcodcl(ifac,ivar,3) = C_p (viscls+\frac{visct}{\sigma}) \cdot \grad{T}\cdot \vect{n}$
For enthalpies , in $W.m^{-2}$ :
$rcodcl(ifac,ivar,3) = (viscls+\frac{visct}{\sigma}) \cdot \grad{H} \cdot \vect{n}$

  zone = cs_boundary_zone_by_name("wall_5");
 
  for (cs_lnum_t ilelt = 0; ilelt < zone->n_elts; ilelt++) {
 
    cs_lnum_t face_id = zone->elt_ids[ilelt];
 
    if (bc_type[face_id] == CS_SMOOTHWALL) {
 
      /* log zone number */
      izfrdp[face_id] = 55;
 
      /* Type of condition: reflecting wall with fixed conduction
         flux through the wall */
      isothp[face_id] = CS_BOUNDARY_RAD_WALL_REFL_COND_FLUX;
 
      /* Conduction flux (W/m2)*/
      f_th->bc_coeffs->rcodcl3[face_id] = 0.0;
 
    }
 
  }

Absorption coefficient and net radiation flux

The absorption coefficient and the net radiation flux for the radiative module can be defined in cs_user_radiative_transfer.c through the cs_user_rad_transfer_absorption and Net radiation flux subroutines.

Absorption coefficient

The absorption coefficient is defined in cs_user_rad_transfer_absorption.

Computation of the absorption coefficient

  /*
   * Absorption coefficient of the medium (m-1).
   */
 
  for (cs_lnum_t cell_id = 0; cell_id < cs_glob_mesh->n_cells; cell_id++)
    ck[cell_id] = 0.;
 

Net radiation flux

The net radiation flux is computed in Net radiation flux.

Local variables to be added

const cs_real_t stephn = cs_physical_constants_stephan;

cs_physical_constants_stephan

const double cs_physical_constants_stephan

Definition: cs_physical_constants.cpp:454

cstphy::stephn

double precision stephn

Stephan constant for the radiative module in .

Definition: cstphy.f90:53

Initialization

At the end of the subroutine, if iok is different from zero, some faces have been forgotten and the calculation stops.

  /* Initializations */
  /* get BC coeffs for radiance (explicit part of the first band) */
  cs_real_t *coefap = CS_FI_(radiance, 0)->bc_coeffs->a;
 

Computation of the net radiation flux

  /* Net flux dendity for the boundary faces
   * The provided examples are sufficient in most of cases.*/
 
  /* If the boundary conditions given above have been modified
   *   it is necessary to change the way in which density is calculated from
   *   the net radiative flux consistently.*/
 
  /* The rule is:
   *   the density of net flux is a balance between the emitting energy from a
   *   boundary face (and not the reflecting energy) and the absorbing radiative
   *   energy. Therefore if a wall heats the fluid by radiative transfer, the
   *   net flux is negative */
 
  for (cs_lnum_t ifac = 0; ifac < cs_glob_mesh->n_b_faces; ifac++) {
 
    /* Wall faces */
    if (   bc_type[ifac] == CS_SMOOTHWALL
        || bc_type[ifac] == CS_ROUGHWALL)
      net_flux[ifac] = eps[ifac] * (qincid[ifac] - stephn * pow(twall[ifac], 4));
 
    /* Symmetry   */
    else if (bc_type[ifac] == CS_SYMMETRY)
      net_flux[ifac] = 0.0;
 
    /* Inlet/Outlet    */
    else if (   bc_type[ifac] == CS_INLET
             || bc_type[ifac] == CS_CONVECTIVE_INLET
             || bc_type[ifac] == CS_OUTLET
             || bc_type[ifac] == CS_FREE_INLET) {
      if (cs_glob_rad_transfer_params->type == CS_RAD_TRANSFER_DOM)
        net_flux[ifac] = qincid[ifac] - cs_math_pi * coefap[ifac];
      else if (cs_glob_rad_transfer_params->type == CS_RAD_TRANSFER_P1)
        net_flux[ifac] = 0.0;
    }
    /* Stop if there are forgotten faces   */
    else
      bft_error
        (__FILE__, __LINE__, 0,
         "In %s:\n"
         "  non-handled boundary faces for net flux calculation\n\n"
         "  Last face: %10ld; zone = %d; nature = %d\n",
         __func__,
         (long)ifac,
         cs_boundary_zone_face_zone_id()[ifac],
         bc_type[ifac]);
 
  }