Generation of synthetic turbulence at LES inlets

Introduction

Generation of synthetic turbulence at LES inlets can be defined using the cs_user_les_inflow_define user function, and possibly updated using cs_user_les_inflow_update, with cs_user_les_inflow_advanced allowing for finer definition of target statistics the inlet if needed.

Global caracteristics of synthetic turbulence inlets

General settings

The cs_user_les_inflow_define function is the main entry point for LES inflow definitions.

It can be used to set general options, such as the specific checkpoint/restart behavior, as in the following example:

  cs_les_inflow_set_restart(false,   /* allow_read */
                            false);  /* allow_write */

Defining inlet properties

For each LES inlet, the cs_les_inflow_add_inlet must be used.

For example, to use the Batten Method for boundary faces of a zone named INLET_1:

  {
    /* Number of turbulence structures */
    int n_entities = 50;

    /* Velocity, turbulent kinetic energy and dissipation rate */
    cs_real_t vel_r[3] = {18.0, 0, 0};
    cs_real_t k_r = 4.0;
    cs_real_t eps_r = 4.0;

    cs_les_inflow_add_inlet(CS_INFLOW_BATTEN,
                            false,
                            cs_boundary_zone_by_name("INLET_1"),
                            n_entities,
                            0,  /* verbosity */
                            vel_r,
                            k_r,
                            eps_r);
  }

And to use the Synthetic Eddy Method for boundary faces of a zone named INLET_2:

Modifying synthetic turbulence inlets

Updating base characteristics

To update reference velocity, turbulent kinetic energy, or dissipation rate for a given turbulence inlet, the cs_user_les_inflow_update function may be used. It is called automatically for each LES inlet defined previously.

The following example illustrates modifying values for the example zone named INLET_1:

  if (strcmp(zone->name, "INLET_1") == 0) {
    /* Velocity, turbulent kinetic energy and dissipation rate */
    vel_r[0] = 19.0;
    vel_r[1] = 0.0;
    vel_r[2] = 0.0;
    *k_r = 5.0;
    *eps_r = 5.0;
  }

Advanced LES inlet Example 1

Mean velocity, Reynolds stresses an dissipation are deduced from a wall law for the zone named INLET_1 (no modification of the statistics of the flow is provided for the other synthetic turbulence inlets).

  if (strcmp(zone->name, "INLET_1") == 0) {

    const cs_lnum_t n_faces = zone->n_elts;
    const cs_lnum_t *face_ids = zone->elt_ids;

    const cs_real_t d2_s3 = 2.0/3.0;

    const cs_mesh_t   *m = cs_glob_mesh;
    const cs_real_3_t *b_face_cog
      = (const cs_real_3_t *)cs_glob_mesh_quantities->b_face_cog;

    const cs_real_t *cpro_mu = CS_F_(mu)->val;

    const cs_real_t uref = cs_glob_turb_ref_values->uref;

    /* Approximation of the friction velocity */
    const cs_real_t utau = uref/20.0;

    /* Reference length scale */
    const cs_real_t h_ref = 1.0;

    const cs_real_t kappa = cs_turb_xkappa;

    for (cs_lnum_t i = 0; i < n_faces; i++) {

      const cs_lnum_t f_id = face_ids[i];
      const cs_lnum_t c_id = m->b_face_cells[f_id];

      const cs_real_t x_mu = cpro_mu[c_id];
      const cs_real_t r_fro = utau * h_ref / x_mu;

      /* Dimensionless wall distance */
      const cs_real_t yy = 1.0 - b_face_cog[f_id][1];
      const cs_real_t yplus = yy / h_ref * r_fro;

      /* Reichart laws (dimensionless) */
      const cs_real_t uplus = log(1. + 0.4*yplus)/kappa
                             + 7.8*(1. - exp(-yplus/11.0)
                                    - yplus/11.0*exp(-0.33*yplus));
      const cs_real_t kplus =   0.07*yplus*yplus*exp(-yplus/8.0)
                              + (1.0 - exp(-yplus/20.0)) *4.5
                              / (1. + 4.0*yplus/r_fro);
      const cs_real_t eplus =  (1.0/kappa)
                              / pow((  cs_math_pow4(yplus)
                                     + cs_math_pow4(15.)), 0.25);

      /* Arrays are filled with dimensionnal stats */
      vel_l[i][0] = uplus * utau;
      vel_l[i][1] = 0.0;
      vel_l[i][2] = 0.0;

      rij_l[i][0] = d2_s3 * kplus * cs_math_pow2(utau);
      rij_l[i][1] = d2_s3 * kplus * cs_math_pow2(utau);
      rij_l[i][2] = d2_s3 * kplus * cs_math_pow2(utau);
      rij_l[i][3] = 0;
      rij_l[i][4] = 0;
      rij_l[i][5] = 0;

      eps_l[i] = eplus * cs_math_pow4(utau) / x_mu;
    }
  }

Advanced LES Example 2

Reynolds stresses and dissipation at the inlet are computed using the turbulence intensity and standard laws for a circular pipe for for the zone named INLET_1 (no modification of the statistics of the flow is provided for the other synthetic turbulence inlets).

  if (strcmp(zone->name, "INLET_1") == 0) {

    const cs_lnum_t n_faces = zone->n_elts;

    const cs_real_t d2_s3 = 2.0/3.0;

    for (cs_lnum_t i = 0; i < n_faces; i++) {

      vel_l[i][0] = 1.1;
      vel_l[i][1] = 1.1;
      vel_l[i][2] = 1.1;

      cs_real_t uref2 = cs_math_3_square_norm(vel_l[i]);
      uref2 = cs_math_fmax(uref2, 1e-12);

      /* Hydraulic diameter */
      const cs_real_t x_hd = 0.075;

      /* Turbulence intensity */
      const cs_real_t x_ti = 0.02;

      cs_real_t x_k = 1e-12;
      cs_real_t x_eps = 1e-12;

      cs_turbulence_bc_ke_turb_intensity(uref2,
                                         x_ti,
                                         x_hd,
                                         &x_k,
                                         &x_eps);

      rij_l[i][0] = d2_s3 * x_k;
      rij_l[i][1] = d2_s3 * x_k;
      rij_l[i][2] = d2_s3 * x_k;
      rij_l[i][3] = 0;
      rij_l[i][4] = 0;
      rij_l[i][5] = 0;

      eps_l[i] = x_eps;
    }
  }