Infinite channel inlet with near-inlet feedback

A second method of defining an inlet condition which converges towards an infinite channel profile is based simply on feedback from values computed at inlet cell centers (combining the inlet boundary conditions and the effect of wall friction on the inlet walls). It assumes the mesh is very regular and orthogonal, at least on the first two inlet cell layers (using a gradient correction in the case of a less regular mesh might work, but has never been tested.

Initialization and finalization

Initialization and finalization is similar to that of the base examples

  const cs_lnum_t n_cells_ext = domain->mesh->n_cells_with_ghosts;
  const cs_lnum_t n_b_faces = domain->mesh->n_b_faces;
 
  const int n_fields = cs_field_n_fields();
  const int keysca = cs_field_key_id("scalar_id");
 
  const int nt_cur = domain->time_step->nt_cur;
 
  const cs_lnum_t *b_face_cells = domain->mesh->b_face_cells;
 
  const cs_nreal_3_t *restrict b_face_u_normal
    = domain->mesh_quantities->b_face_u_normal;
  const cs_real_t *restrict b_face_surf
    = domain->mesh_quantities->b_face_surf;
 
  const cs_real_t viscl0 = cs_glob_fluid_properties->viscl0;
 
  const auto bpro_rho = CS_F_(rho_b)->get_val_s();
  const auto cvar_vel = CS_F_(vel)->get_val_v();
 
  const cs_zone_t  *zn = nullptr;

Body

Here, we define an inlet boundary condition for a very long channel or duct with a section matching the boundary faces of zone 'INLET'.

We fix a mean inlet velocity, and use a feedback loop assuming a fixed-point type behavior will allow us to reach a state matching that of a very long inlet channel.

Warning

We assume other boundary conditions are defined before this one (ideally, using the GUI).

We also assume that the mesh is orthogonal at the inlet, and we are using a RANS (not LES) computation. to the current inlet.

For EBRSM of V2f models, to avoid laminarization at the inlet, the initial velocity (at the first time step) is divided by 10 on inlet faces adjacent to the boundary, so as to ensure a velocity gradient and turbulent production. Otherwise, the initialization may fail.

  zn = cs_boundary_zone_by_name("inlet");
 
  constexpr cs_real_t fmprsc = 1.; // mean prescribed velocity
 
  auto vel_val_ext = CS_F_(vel)->bc_coeffs->get_val_ext_v();
 
  if (nt_cur == 1) {
 
    /* For the Rij-EBRSM model (and possibly V2f), we need a non-flat profile,
     * so as to ensure turbulent production, and avoid laminarization;
     * here, we simply divide the initial velocity by 10 for inlet
     * faces adjacent to the wall.
 
     * The loop below assumes wall conditions have been defined first
     * (in the GUI, or in this file, before the current test). */
 
    cs_array<int> mrkcel;
    if ((cs_glob_turb_model->model == CS_TURB_RIJ_EPSILON_EBRSM) ||
        (cs_glob_turb_model->itytur == 5)){
 
      mrkcel.reshape(n_cells_ext);
      for (cs_lnum_t i = 0; i < n_cells_ext; i++)
        mrkcel[i] = 0;
 
      for (cs_lnum_t f_id = 0; f_id < n_b_faces; f_id++) {
        if (bc_type[f_id] == CS_SMOOTHWALL) {
          const cs_lnum_t c_id = b_face_cells[f_id];
          mrkcel[c_id] = 1;
        }
      }
    }
 
    for (cs_lnum_t e_idx = 0; e_idx < zn->n_elts; e_idx++) {
 
      const cs_lnum_t face_id = zn->elt_ids[e_idx];
      const cs_lnum_t c_id = b_face_cells[face_id];
 
      bc_type[face_id] = CS_INLET;
 
      for (int ii = 0; ii < 3; ii++)
        vel_val_ext(face_id, ii) = -fmprsc*b_face_u_normal[face_id][ii];
 
      if (mrkcel[c_id] == 1)
        vel_val_ext(face_id, 0) = fmprsc/10;
 
      cs_real_t uref2 = 0;
      for (int ii = 0; ii< CS_F_(vel)->dim; ii++)
        uref2 += cs_math_pow2(vel_val_ext(face_id, ii));
      uref2 = cs::max(uref2, 1e-12);
 
      /* Turbulence example computed using equations valid for a pipe.
 
       * We will be careful to specify a hydraulic diameter adapted
       *   to the current inlet.
 
       * We will also be careful if necessary to use a more precise
       *   formula for the dynamic viscosity use in the calculation of
       *   the Reynolds number (especially if it is variable, it may be
       *   useful to take the law from 'cs_user_physical_properties'
       *   Here, we use by default the 'viscl0" value.
       *   Regarding the density, we have access to its value at boundary
       *   faces (b_rho) so this value is the one used here (specifically,
       *   it is consistent with the processing in 'cs_user_physical_properties',
       *   in case of variable density) */
 
      /* Hydraulic diameter */
      cs_real_t xdh = 1.0;
 
      /* Calculation of turbulent inlet conditions using
         the turbulence intensity and standard laws for a circular pipe
         (their initialization is not needed here but is good practice) */
 
      cs_real_t b_rho = bpro_rho[face_id];
 
      cs_turbulence_bc_inlet_hyd_diam(face_id,
                                      uref2,
                                      xdh,
                                      b_rho,
                                      viscl0);
    }
 
    /* Initialize user scalars inlet */
 
    for (int f_id = 0; f_id < n_fields; f_id++) {
      cs_field_t *fld = cs_field(f_id);
 
      if (! (fld->type & (CS_FIELD_VARIABLE | CS_FIELD_USER)))
        continue;
      int sc_id = fld->get_key_int(keysca) - 1;
      if (sc_id < 0)
        continue;
 
      auto val_ext = fld->bc_coeffs->get_val_ext();
 
      for (cs_lnum_t e_idx = 0; e_idx < zn->n_elts; e_idx++) {
        const cs_lnum_t face_id = zn->elt_ids[e_idx];
        val_ext[face_id] = 1;
      }
 
    }
  }
 
  else {
 
    /* Subsequent time steps
     *----------------------*/
 
    cs_real_2_t acc = {0, 0};
 
    /* Accessors for BC values */
 
    cs_span<cs_real_t> k_val_ext;
    cs_span<cs_real_t> eps_val_ext;
    cs::mdspan<cs_real_t, 2, cs::layout::left> rij_val_ext;
    cs_span<cs_real_t> alp_bl_val_ext;
    cs_span<cs_real_t> phi_val_ext;
    cs_span<cs_real_t> f_bar_val_ext;
    cs_span<cs_real_t> omg_val_ext;
    cs_span<cs_real_t> nusa_val_ext;
 
    cs_span<cs_real_t> cvar_k;
    cs_span<cs_real_t> cvar_eps;
    cs_span_2d<cs_real_t> cvar_rij;
    cs_span<cs_real_t> cvar_alp_bl;
    cs_span<cs_real_t> cvar_phi;
    cs_span<cs_real_t> cvar_f_bar;
    cs_span<cs_real_t> cvar_omg;
    cs_span<cs_real_t> cvar_nusa;
 
    if (cs_glob_turb_model->itytur == 2) {
      k_val_ext = CS_F_(k)->bc_coeffs->get_val_ext();
      eps_val_ext = CS_F_(eps)->bc_coeffs->get_val_ext();
      cvar_k = CS_F_(k)->get_val_s();
      cvar_eps = CS_F_(eps)->get_val_s();
    }
    else if (cs_glob_turb_model->itytur == 3) {
      rij_val_ext = CS_F_(rij)->bc_coeffs->get_val_ext_t();
      eps_val_ext = CS_F_(eps)->bc_coeffs->get_val_ext();
      cvar_rij = CS_F_(rij)->get_val_t();
      cvar_eps = CS_F_(eps)->get_val_s();
      if (cs_glob_turb_model->model == CS_TURB_RIJ_EPSILON_EBRSM) {
        alp_bl_val_ext = CS_F_(alp_bl)->bc_coeffs->get_val_ext();
        cvar_alp_bl= CS_F_(alp_bl)->get_val_s();
      }
    }
    if (cs_glob_turb_model->itytur == 5) {
      k_val_ext = CS_F_(k)->bc_coeffs->get_val_ext();
      eps_val_ext = CS_F_(eps)->bc_coeffs->get_val_ext();
      phi_val_ext = CS_F_(phi)->bc_coeffs->get_val_ext();
      cvar_k = CS_F_(k)->get_val_s();
      cvar_eps = CS_F_(eps)->get_val_s();
      cvar_phi = CS_F_(phi)->get_val_s();
      if (cs_glob_turb_model->model == CS_TURB_V2F_PHI) {
        f_bar_val_ext = CS_F_(f_bar)->bc_coeffs->get_val_ext();
        cvar_f_bar = CS_F_(f_bar)->get_val_s();
      }
      else if (cs_glob_turb_model->model == CS_TURB_V2F_BL_V2K) {
        alp_bl_val_ext = CS_F_(alp_bl)->bc_coeffs->get_val_ext();
        cvar_alp_bl= CS_F_(alp_bl)->get_val_s();
      }
    }
    else if (cs_glob_turb_model->model == CS_TURB_K_OMEGA) {
      k_val_ext = CS_F_(k)->bc_coeffs->get_val_ext();
      omg_val_ext = CS_F_(omg)->bc_coeffs->get_val_ext();
      cvar_k = CS_F_(k)->get_val_s();
      cvar_omg = CS_F_(omg)->get_val_s();
    }
    else if (cs_glob_turb_model->model ==  CS_TURB_SPALART_ALLMARAS) {
      nusa_val_ext = CS_F_(nusa)->bc_coeffs->get_val_ext();
      cvar_nusa = CS_F_(nusa)->get_val_s();
    }
 
    /* Estimate multiplier */
 
    for (cs_lnum_t e_idx = 0; e_idx < zn->n_elts; e_idx++) {
 
      const cs_lnum_t face_id = zn->elt_ids[e_idx];
      const cs_lnum_t c_id = b_face_cells[face_id];
 
      const cs_real_t vnrm = cs_math_3_norm(cvar_vel.sub_array(c_id));
 
      acc[0] += vnrm*b_face_surf[face_id];
      acc[1] += b_face_surf[face_id];
    }
 
    cs_parall_sum(2, CS_REAL_TYPE, acc);
 
    cs_real_t fmul = 0; /* zero velocity in bulk domain */
    if (acc[0] > cs_math_epzero)
      fmul = fmprsc/(acc[0]/acc[1]); /* estimate flow multiplier */
 
    /* Apply BCs */
    for (cs_lnum_t e_idx = 0; e_idx < zn->n_elts; e_idx++) {
      const cs_lnum_t face_id = zn->elt_ids[e_idx];
      const cs_lnum_t c_id = b_face_cells[face_id];
 
      const cs_real_t vnrm = cs_math_3_norm(cvar_vel.sub_array(c_id));
 
      assert(bc_type[face_id] == CS_INLET);
 
      for (cs_lnum_t ii = 0; ii < 3; ii++)
        vel_val_ext(face_id, ii) = -fmul*vnrm*b_face_u_normal[face_id][ii];
 
      if (cs_glob_turb_model->itytur == 2) {
        k_val_ext[face_id] = cvar_k[c_id];
        eps_val_ext[face_id] = cvar_eps[c_id];
      }
 
      else if (cs_glob_turb_model->itytur == 3) {
        for (cs_lnum_t ii = 0; ii< 6; ii++)
          rij_val_ext(face_id, ii) = cvar_rij(c_id, ii);
        eps_val_ext[face_id] = cvar_eps[c_id];
        if (cs_glob_turb_model->model == CS_TURB_RIJ_EPSILON_EBRSM)
          alp_bl_val_ext[face_id] = cvar_alp_bl[c_id];
      }
 
      else if (cs_glob_turb_model->itytur == 5) {
        k_val_ext[face_id] = cvar_k[c_id];
        eps_val_ext[face_id] = cvar_eps[c_id];
        phi_val_ext[face_id] = cvar_phi[c_id];
        if (cs_glob_turb_model->model == CS_TURB_V2F_PHI)
          f_bar_val_ext[face_id] = cvar_f_bar[c_id];
        else if (cs_glob_turb_model->model == CS_TURB_V2F_BL_V2K)
          alp_bl_val_ext[face_id] = cvar_alp_bl[c_id];
      }
 
      else if (cs_glob_turb_model->model == CS_TURB_K_OMEGA) {
        k_val_ext[face_id] = cvar_k[c_id];
        omg_val_ext[face_id] = cvar_omg[c_id];
      }
      else if (cs_glob_turb_model->model ==  CS_TURB_SPALART_ALLMARAS) {
        nusa_val_ext[face_id] = cvar_nusa[c_id];
      }
    }
 
    for (int f_id = 0; f_id < n_fields; f_id++) {
      cs_field_t *fld = cs_field(f_id);
 
      if (! (fld->type & (CS_FIELD_VARIABLE | CS_FIELD_USER)))
        continue;
      int sc_id = fld->get_key_int(keysca) - 1;
      if (sc_id < 0)
        continue;
 
      auto val_ext = fld->bc_coeffs->get_val_ext();
      auto cvar = fld->get_val_s();
 
      for (cs_lnum_t e_idx = 0; e_idx < zn->n_elts; e_idx++) {
        const cs_lnum_t face_id = zn->elt_ids[e_idx];
        const cs_lnum_t c_id = b_face_cells[face_id];
        val_ext[face_id] = cvar[c_id];
      }
    }
  }