Recomendation for how to add random noise at inlet of a pipe to trigger turbulence

[elinlarsson744-ux]

Hi, I am simulating a pipe flow at Re=2943, and I want to have some disturbances in the inlet which will trigger turbulence, I added a user file which I am attaching below. I want some advice on this method that how much noise should I add as I can see the pressure solver is not converging hitting its limit. Also will it be good to impose some noise which is divergence free? If so how can I do that?

Thanks in advance

user_f90 file :
module user
  use neko
  implicit none

contains

  subroutine user_setup(user)
    type(user_t), intent(inout) :: user
    user%initial_conditions => initial_conditions
    user%dirichlet_conditions => dirichlet_conditions
  end subroutine user_setup

  subroutine dirichlet_conditions(fields, bc, time)
    type(field_list_t), intent(inout) :: fields
    type(field_dirichlet_t), intent(in) :: bc
    type(time_state_t), intent(in) :: time

    type(field_t), pointer :: u, v, w
    integer :: i, n
    real(kind=rp) :: x, y, rr, uz_parab
    real(kind=rp), parameter :: R = 0.015_rp
    real(kind=rp), parameter :: U_max = 9.56_rp

    u => fields%get("u")
    v => fields%get("v")
    w => fields%get("w")

    n = u%dof%size()

    do i = 1, n
       x = u%dof%x(i,1,1,1)
       y = u%dof%y(i,1,1,1)
       rr = x*x + y*y

       uz_parab = U_max * (1.0_rp - rr / (R**2))

       u%x(i,1,1,1) = 0.0_rp
       v%x(i,1,1,1) = 0.0_rp
       w%x(i,1,1,1) = -uz_parab
    end do

  end subroutine dirichlet_conditions

  subroutine initial_conditions(scheme_name, fields)
    character(len=*), intent(in) :: scheme_name
    type(field_list_t), intent(inout) :: fields
    integer :: i
    real(kind=rp) :: uvw(3)
    type(field_t), pointer :: u, v, w

    u => fields%get("u")
    v => fields%get("v")
    w => fields%get("w")

    do i = 1, u%dof%size()
       uvw = pipe_ic(u%dof%x(i,1,1,1), u%dof%y(i,1,1,1), u%dof%z(i,1,1,1))
       u%x(i,1,1,1) = uvw(1)
       v%x(i,1,1,1) = uvw(2)
       w%x(i,1,1,1) = uvw(3)
    end do
  end subroutine initial_conditions

  function pipe_ic(x, y, z) result(uvw)
    real(kind=rp) :: x, y, z
    real(kind=rp) :: uvw(3)
    real(kind=rp) :: rand, rr
    real(kind=rp), parameter :: R = 0.015_rp
    real(kind=rp), parameter :: U_max = 9.56_rp

    rr = x*x + y*y

    ! Parabolic base profile in -z direction
    uvw(3) = -U_max * (1.0_rp - rr / (R**2))

    ! Small random perturbations to seed turbulence
    call random_number(rand)
    uvw(1) = 5e-2_rp * U_max * (rand - 0.5_rp)
    call random_number(rand)
    uvw(2) = 5e-2_rp * U_max * (rand - 0.5_rp)
    call random_number(rand)
    uvw(3) = uvw(3) - 1e-2_rp * U_max * (rand - 0.5_rp)

  end function pipe_ic
end module user

case file:

{
  "version": 1.0,
  "case": {
    "mesh_file": "pipe.nmsh",
    "output_at_end": true,
    "output_boundary": true,
    "output_checkpoints": true,
    "checkpoint_control": "simulationtime",
    "checkpoint_value": 0.01,
    "numerics": {
      "polynomial_order": 5,
      "time_order": 3,
      "dealias": true
    },
    "fluid": {
      "scheme": "pnpn",
      "Re": 2943.0,
      "boundary_conditions": [
        {"type": "outflow+dong", "zone_indices": [1]},
        {"type": "user_velocity", "zone_indices": [2]},
        {"type": "no_slip", "zone_indices": [3]}
      ],
      "initial_condition": {"type": "user"},
      "velocity_solver": {
        "type": "cg",
        "preconditioner": {"type": "jacobi"},
        "projection_space_size": 0,
        "absolute_tolerance": 1e-7,
        "max_iterations": 800
      },
      "pressure_solver": {
        "type": "gmres",
        "preconditioner": {"type": "hsmg"},
        "projection_space_size": 5,
        "absolute_tolerance": 1e-3,
        "max_iterations": 2000
      },
      "output_control": "simulationtime",
      "output_value": 0.001
    },
    "simulation_components": [
      {
        "type": "lambda2",
        "compute_control": "simulationtime",
        "compute_value": 0.001,
        "output_control": "simulationtime",
        "output_value": 0.001
      }
    ],
    "time": {
      "end_time": 20.0,
      "variable_timestep": true,
      "target_cfl": 0.4,
      "max_timestep": 1e-3
    }
  }
}

[pschlatt1]

do you have a pipe with inflow and outflow, or a periodic pipe? The answer would depend on that. For inflow/outflow, we typically would use synthetic turbulence or recycling, for a periodic pipe we have a better version for initial conditions (that are divergence free). Let us know what you want, and then we can help you.

[elinlarsson744-ux]

For this case, I used a inflow outflow type boundary conditions but my main goal is to capture the transitional type of flow, I mean to caputure the (slugs and puffs) which happens in this regime. So what do you recommend to use? Also how much long pipe should one use? I found in literature that one uses typically 50D long pipes but that would be too expensive for me to run. So do you have any suggestions.
Thanks in Advance

[timofeymukha]

So, your goal is to capture transition to turbulence in the pipe? Or do you want the inlet to already be turbulent? I am a bit confused :).

[elinlarsson744-ux]

My goal is to capture the transition in the pipe. But to trigger it I thought of puting some noise in the inlet.

[timofeymukha]

I see. There are people much more experienced with transition, but I can offer a general comment. Random uncorrelated noise at the inflow is almost never a good idea, because it typically either just dies out, or if you ramp it up, crashes your run. There is a huge body of literature devoted to turbulent inflow conditions. There is a review by Wu, if you are interested: 10.1146/annurev-fluid-010816-060322. But that applies to fully turbulent inflow, which is not what you want anyway.

One typically triggers transition with a numerical "trip", i.e. a body force applied locally along the line. There is a kind of rough, but correct, implementation of that in this PR #2229
But that really forces the flow to transition, so if you are looking to look at the structure of transitional flow, that maybe is not the right tool either. If Philipp finds time, he will be able to help you better here.

[elinlarsson744-ux]

But in this approach, the flow will transition and then the physics will decide how will it behave over time right?