{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# DARPA SUBOFF Actuator Disk\n", "\n", "This notebook demonstrates the setup of an actuator disk in Flow360 using the DARPA SUBOFF geometry, configured for liquid operating conditions. The actuator disk is positioned at the aft end of the hull.\n", "\n", "![DARPA SUBOFF geometry](figures/darpa_geo.png)\n", "\n", "**Note:** The settings in this example are by no means a validation setup; they are crafted to showcase the capabilities of Flow360 and we have intentionally reduced node count and example FC cost. For rigorous validation, modify the settings as needed." ], "id": "33751567" }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Create Project from geometry\n", "Load Python libraries that are used throughout the notebook and Flow360 client.\n", "For this project we are starting from the geometry of the DARPA SUBOOF model. The geometry file is in the class `DARPA_SUBOFF` as a download link which gets the STEP file \"DARPA.STEP\". To use your own geometry, replace the file path in `from_geometry` with the path to your CAD file." ], "id": "0608628e" }, { "cell_type": "code", "metadata": {}, "source": [ "import flow360 as fl\n", "from flow360.examples import DARPA_SUBOFF\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.integrate import trapezoid\n", "\n", "DARPA_SUBOFF.get_files()\n", "project = fl.Project.from_geometry(\n", " DARPA_SUBOFF.geometry,\n", " name=\"Tutorial DARPA Actuator Disk from Python\",\n", ")\n", "geo = project.geometry\n", "geo.group_faces_by_tag(\"faceId\") # group faces by faceId" ], "execution_count": 1, "outputs": [ { "output_type": "display_data", "data": { "text/html": [ "
[20:16:16] INFO: The file (DARPA.STEP) is being downloaded, please wait.                                           \n",
       "
\n" ], "text/plain": [ "\u001b[2;36m[20:16:16]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: The file \u001b[1m(\u001b[0mDARPA.STEP\u001b[1m)\u001b[0m is being downloaded, please wait. \n" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f37c2987b5494b17934d742cbf0e22b7", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/html": [ "
\n"
      ],
      "text/plain": []
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[20:16:33] INFO: Geometry successfully submitted:                                                                  \n",
       "                   type        = Geometry                                                                          \n",
       "                   name        = Tutorial DARPA Actuator Disk from Python                                          \n",
       "                   id          = geo-feb73017-72fb-40e7-a974-c0509ab8f39a                                          \n",
       "                   status      = uploaded                                                                          \n",
       "                   project id  = prj-fa790634-10b7-40ca-a6a9-fdb62f9556fc                                          \n",
       "                                                                                                                   \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[20:16:33]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Geometry successfully submitted:                                                                  \n",
       "\u001b[2;36m           \u001b[0m        type        = Geometry                                                                          \n",
       "\u001b[2;36m           \u001b[0m        name        = Tutorial DARPA Actuator Disk from Python                                          \n",
       "\u001b[2;36m           \u001b[0m        id          = geo-\u001b[93mfeb73017-72fb-40e7-a974-c0509ab8f39a\u001b[0m                                          \n",
       "\u001b[2;36m           \u001b[0m        status      = uploaded                                                                          \n",
       "\u001b[2;36m           \u001b[0m        project id  = prj-\u001b[93mfa790634-10b7-40ca-a6a9-fdb62f9556fc\u001b[0m                                          \n",
       "\u001b[2;36m           \u001b[0m                                                                                                        \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: Waiting for geometry to be processed.                                                             \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Waiting for geometry to be processed.                                                             \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f73f6f36648e456ba0a1ca178d0ef835",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[20:17:03] INFO: Regrouping face entities under `faceId` tag (previous `groupByBodyId`).                           \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[20:17:03]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Regrouping face entities under `faceId` tag \u001b[1m(\u001b[0mprevious `groupByBodyId`\u001b[1m)\u001b[0m.                           \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "881341eb"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Define Actuator Disk\n",
    "To define the actuator disk these steps are required:\n",
    "- Find force distribution along the radius of the actuator disk.\n",
    "- Define a volume zone where the actuator disk where the volumetric forces are applied inside the solver iterations. This zone can intersect any surface and only the nodes in the fluid zone will be affected. If an inner surface is present (like in this case), it is recommended to place the inner radius of the actuator disk volume to intersect with the surface. This is to prevent a hub vortex to appear close to the surface due to jump in pressure forces at the hub, creating circulating regions not realistic.\n",
    "- Define an axisymmetric refinement inside the actuator disk region to properly capture the volumetric forces discontinuities. This refinement cannot intersect any surface.\n",
    "\n",
    "Optionally:\n",
    "- Add volumetric refinements around the actuator disk for proper wake capturing.\n",
    "- Add surface refinements close to the actuator disk inner radius."
   ],
   "id": "a0934750"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Find force distributions\n",
    "The axial and circumferential force distributions are the external pressure forces that are applied to each control volume over the actuator disk radius. The input for the actuator disk is a pressure distribution. Axial distribution will act on the axial momentum creating a downwash and circumferential distribution will act perpendicular to the axial direction by adding a swirl velocity on the wake. These distributions can be found from two sources:\n",
    "- Radial thrust and torque distributions provided from manufacturer or measured experimentally. For this cases, we need to convert the thrust and torque distributions to pressure distributions.\n",
    "- Approximated distributions based from total thrust and torque. These approximations range from simple uniform distributions to more advanced analytical formulations based on vortex theory.\n",
    "\n",
    "First, we define the geometry of the rotor and operating conditions:"
   ],
   "id": "f8f9e33b"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Define geometry\n",
    "R_out = 0.3  # Outer radius of the actuator disk\n",
    "R_hub = 0.0597 / 2  # Blade root radius\n",
    "R_in = (\n",
    "    R_hub * 0.98\n",
    ")  # Inner radius of the actuator disk, smaller than the blade root radius to prevent hub vortex affecting the surface flow\n",
    "NBlades = 5  # Number of blades\n",
    "\n",
    "# Define operating conditions\n",
    "thrust = 2000  # Thrust force\n",
    "torque = 100  # Torque force\n",
    "omega = 100 * 2 * np.pi / 60  # Rotation rate\n",
    "rho = 1000  # Density\n",
    "Uinf = 5  # Freestream velocity"
   ],
   "execution_count": 2,
   "outputs": [],
   "id": "df82e275"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**If thrust and torque radial distributions are given:**\n",
    "\n",
    "We would read the data from a dataset and convert the force distribution to pressure distribution. However, for this example, we assume a triangular distribution with a maximum value at 70% radial location for both of them. We follow this method:"
   ],
   "id": "e4872ec2"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Read or input the thrust and torque radial distributions\n",
    "r_from_data = [R_in, R_out * 0.7, R_out]\n",
    "thrust_max = (2 * thrust) / (R_out - R_in)\n",
    "torque_max = (2 * torque) / (R_out - R_in)\n",
    "thrust_radial = [0, thrust_max, 0]  # Triangular distribution\n",
    "torque_radial = [0, torque_max, 0]  # Triangular distribution\n",
    "\n",
    "# Convert to pressure force distributions\n",
    "r_from_data = np.array(r_from_data)\n",
    "thrust_radial_from_data = np.array(thrust_radial)\n",
    "torque_radial_from_data = np.array(torque_radial)\n",
    "f_ax_from_data = thrust_radial_from_data / (2 * np.pi * r_from_data)\n",
    "f_cir_from_data = torque_radial_from_data / (2 * np.pi * r_from_data**2)"
   ],
   "execution_count": 3,
   "outputs": [],
   "id": "559fd770"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**If thrust and torque radial distributions are not given:**\n",
    "\n",
    "We can approximate with a realistic distribution from the Betz-Prandtl vortex theory described [here](https://simcloud-public-1.s3.amazonaws.com/publications/Electra_Joint_Paper/Electra_FC_Impact_of_Propulsion_Modeling_Approach_on_High_Lift_Force_Prediction_of_Propeller_Blown_Wings.pdf)."
   ],
   "id": "7a3c6632"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Radial discretization\n",
    "n_points = 200\n",
    "r_theory = np.linspace(R_in, R_out, n_points)\n",
    "xi = r_theory / R_out\n",
    "\n",
    "# Step 1: Compute axial velocity through disk\n",
    "v_ax = 0.5 * (np.sqrt((2 * thrust) / (rho * np.pi * R_out**2) + Uinf**2) + Uinf)\n",
    "\n",
    "# Step 2: Wake advance ratio\n",
    "lambda_w = v_ax / (omega * R_out)\n",
    "\n",
    "# Step 3: Compute Prandtl tip-loss and hub-loss functions\n",
    "f_tip = (NBlades / 2) * (1 - xi) * np.sqrt(1 + 1 / lambda_w**2)\n",
    "f_hub = (NBlades / 2) * (xi - R_in / R_out) * np.sqrt(1 + 1 / lambda_w**2)\n",
    "F_tip = (2 / np.pi) * np.arccos(np.exp(-f_tip))\n",
    "F_hub = (2 / np.pi) * np.arccos(np.exp(-f_hub))\n",
    "F = F_tip * F_hub\n",
    "\n",
    "# Step 4: Non-dimensional circulation (Gamma_1)\n",
    "gamma_tmp = (F * xi**2) / (lambda_w**2 + xi**2)\n",
    "\n",
    "# Step 5: Compute local body forces per unit area\n",
    "f_ax = NBlades * (rho * omega * gamma_tmp) / (2 * np.pi)\n",
    "f_cir = NBlades * (rho * v_ax * gamma_tmp) / (2 * np.pi * r_theory)\n",
    "\n",
    "# Step 6: Scale thrust and torque\n",
    "integrand_thrust = f_ax * 2 * np.pi * r_theory\n",
    "integrand_torque = f_cir * r_theory * 2 * np.pi * r_theory\n",
    "thrust_tmp = trapezoid(integrand_thrust, r_theory)\n",
    "torque_tmp = trapezoid(integrand_torque, r_theory)\n",
    "K_thrust = thrust / thrust_tmp\n",
    "K_torque = torque / torque_tmp\n",
    "f_ax_from_theory = K_thrust * f_ax\n",
    "f_cir_from_theory = K_torque * f_cir"
   ],
   "execution_count": 4,
   "outputs": [],
   "id": "b5f8f7ee"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a final step we define the pressure distributions that will be used for the actuator disk model. Furthermore, we can check that our distributions give the desired total thrust and torque by integrating them over the radius."
   ],
   "id": "b0c9ffde"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "data_is_given = False\n",
    "if data_is_given:\n",
    "    r = r_from_data\n",
    "    f_ax = f_ax_from_data\n",
    "    f_cir = f_cir_from_data\n",
    "else:\n",
    "    r = r_theory\n",
    "    f_ax = f_ax_from_theory\n",
    "    f_cir = f_cir_from_theory\n",
    "\n",
    "thrust_check = trapezoid(f_ax * 2 * np.pi * r, r)  # Pressure force integrated over the radius\n",
    "torque_check = trapezoid(f_cir * r * 2 * np.pi * r, r)  # Pressure force integrated over the radius\n",
    "\n",
    "print(f\"Desired thrust: {thrust}, computed thrust: {thrust_check}\")\n",
    "print(f\"Desired torque: {torque}, computed torque: {torque_check}\")"
   ],
   "execution_count": 5,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "Desired thrust: 2000, computed thrust: 2000.0000000000002\n",
      "Desired torque: 100, computed torque: 100.00000000000003\n"
     ],
     "name": "stdout"
    }
   ],
   "id": "382eb5eb"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Define volumetric zone for the actuator disk\n",
    "In this zone the volumetric source termns will be applied. The actuator disk is aligned with axis (-1, 0, 0) (negative x-direction) and is centered around x = 4.2609 m. The height of the actuator disk is recommended to be 10% of the outer radius. The inner radius is smaller than the blade root radius to prevent the artificial hub vortex to affect the surface flow.\n",
    "\n",
    "**The pressure distributions found previously are used here.**"
   ],
   "id": "7687b7e7"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    x_AD = 4.2609  # x-location of the actuator disk center\n",
    "    AD_zone = fl.Cylinder(\n",
    "        name=\"AD\",\n",
    "        axis=(-1, 0, 0),\n",
    "        center=(x_AD, 0, 0),\n",
    "        inner_radius=R_in,\n",
    "        outer_radius=R_out,\n",
    "        height=R_out * 0.1,\n",
    "    )\n",
    "\n",
    "    AD_model = fl.ActuatorDisk(\n",
    "        name=\"AD_model\",\n",
    "        volumes=AD_zone,\n",
    "        force_per_area=fl.ForcePerArea(\n",
    "            radius=r,\n",
    "            thrust=f_ax,\n",
    "            circumferential=f_cir,\n",
    "        ),\n",
    "    )"
   ],
   "execution_count": 6,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "7410ce8d"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Define the axisymmetric refinement\n",
    "The zone where the actuator disk model is applied will be discretised with a structured cylindrical mesh. This results in a more accurate discretisation since the nodes are aligned with the strong gradients. It is recommended to place >= 30 nodes in the axial direction and x2 spatial distance in the radial and circumferential directions. For higher disk loading cases this values will change with more nodes required the higher the disk loading."
   ],
   "id": "95d39dc8"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "d_axial = R_out * 0.1 / 30  # 30 nodes in the axial direction\n",
    "d_radial = d_axial * 2  # x2 spatial distance in the radial direction\n",
    "d_circumferential = d_axial * 2  # x2 spatial distance in the circumferential direction"
   ],
   "execution_count": 7,
   "outputs": [],
   "id": "9bc115fc"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The surface close to the inner radius of this region will grow layers until the growth is stopped due to the presence of the refinement. Depending on the surface elements length and the axisymmetric refinement spacings, this can lead to bad quality meshes close to the surface. Therefore, the inner radius for this region must be chosen with care since we want to accurately predict the boundary layer but also have the axisymmetric refinement.\n",
    "\n",
    "One solution is to force a number of layers that we want to have between the surface and the refinement region by changing the inner radius of the axisymmetric refinement. The amount of layers needed until isotropy is influenced by the first layer thickness, surface element length and the growth rate so playing with these values will give the desired mesh."
   ],
   "id": "1ee7fe00"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "first_layer_thickness = 1e-5\n",
    "growth_rate = 1.2\n",
    "surface_elements_length = 0.001\n",
    "n_layers = 20\n",
    "\n",
    "total_height = first_layer_thickness * growth_rate**n_layers\n",
    "\n",
    "inner_radius = R_hub + total_height"
   ],
   "execution_count": 8,
   "outputs": [],
   "id": "95808c07"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now define the axisymmetric refinement region which has a modified inner radius to fit the specified layers."
   ],
   "id": "14889087"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    refinements = [\n",
    "        fl.AxisymmetricRefinement(\n",
    "            name=\"AD_axisym\",\n",
    "            spacing_axial=d_axial,\n",
    "            spacing_radial=d_radial,\n",
    "            spacing_circumferential=d_circumferential,\n",
    "            entities=[\n",
    "                fl.Cylinder(\n",
    "                    name=\"AD_axisym\",\n",
    "                    axis=(1, 0, 0),\n",
    "                    center=(x_AD, 0, 0),\n",
    "                    inner_radius=inner_radius,\n",
    "                    outer_radius=R_out,\n",
    "                    height=R_out * 0.1,\n",
    "                ),\n",
    "            ],\n",
    "        )\n",
    "    ]"
   ],
   "execution_count": 9,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "0b8e94cb"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Surface and Volume Refinements\n",
    "It is possible to use surface refinements to force the maximum surface element length between the surface and the axisymmetric refinement and control the number of layers to fit. Additionally, the influence of the actuator disk wake on the surface will be captured more accurately.\n",
    "\n",
    "Besides, volumetric refinements around the actuator disk volume region will capture the wake with more accuracy."
   ],
   "id": "f9a900f6"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    faces_close_to_AD = [\n",
    "        geo[f\"body00001_face000{n:02d}\"] for n in [2, 4, 19, 21]\n",
    "    ]  # Surface faces close to axisymmetric refinement\n",
    "    surface_refinement = fl.SurfaceRefinement(\n",
    "        name=\"surface_refinement\",\n",
    "        max_edge_length=1 * fl.u.mm,\n",
    "        faces=faces_close_to_AD,\n",
    "    )\n",
    "\n",
    "    height = R_out * 3  # Height of the volume refinement\n",
    "    front_space = R_out * 0.5  # Space in front of the actuator disk to the volume refinement\n",
    "    center_volume = x_AD + (height / 2 - front_space)\n",
    "    volume_refinement = fl.UniformRefinement(\n",
    "        name=\"volume_refinement\",\n",
    "        spacing=10 * fl.u.mm,\n",
    "        entities=[\n",
    "            fl.Cylinder(\n",
    "                name=\"volume_refinement\",\n",
    "                axis=(1, 0, 0),\n",
    "                center=(center_volume, 0, 0),\n",
    "                outer_radius=R_out * 1.5,\n",
    "                height=height,\n",
    "            )\n",
    "        ],\n",
    "    )\n",
    "\n",
    "    L = 4.3562\n",
    "    height_general = L * 2\n",
    "    front_space_general = 0.5\n",
    "    center_general = height_general / 2 - front_space_general\n",
    "    general_refinement = fl.UniformRefinement(\n",
    "        name=\"general_refinement\",\n",
    "        spacing=20 * fl.u.mm,\n",
    "        entities=[\n",
    "            fl.Cylinder(\n",
    "                name=\"general_refinement\",\n",
    "                axis=(1, 0, 0),\n",
    "                center=(center_general, 0, 0),\n",
    "                outer_radius=R_out * 2,\n",
    "                height=height_general,\n",
    "            )\n",
    "        ],\n",
    "    )\n",
    "    refinements += [\n",
    "        surface_refinement,\n",
    "        volume_refinement,\n",
    "        general_refinement,\n",
    "    ]"
   ],
   "execution_count": 10,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "9009c27a"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mesh looks like:\n",
    "\n",
    "![DARPA MESH](figures/DARPA_mesh.png)\n",
    "\n",
    "Taking a zoom view around the axisymmetric refinement close to the hull we can visually check that the specified number of layers to fit inside the gap between the outer radius of the hull and the inner radius of the refinement is correct.\n",
    "\n",
    "![DARPA MESH ZOOM](figures/DARPA_zoom_mesh.png)"
   ],
   "id": "05b3d9f4"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Use Liquid Condition\n",
    "\n",
    "For this example we want to simulate the veihcle in free water conditions. To do this, the class fl.LiquidOperatingCondition() is used:"
   ],
   "id": "e22bd4c0"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    operating_condition = fl.LiquidOperatingCondition(velocity_magnitude=5, alpha=0 * fl.u.deg)"
   ],
   "execution_count": 11,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "c52871fd"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Define SimulationParams\n",
    "- The simulation parameters are defined in the python class fl.SimulationParams()\n",
    "- Reference geometry for the non-dimensionalisation of the coefficients are specified\n",
    "- Operating conditions are specified using LiquidOperating condition.\n",
    "- Time settings are defined to run a steady simulation.\n",
    "- Actuator Disk model is included in the model definitions."
   ],
   "id": "ed62a488"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    farfield = fl.AutomatedFarfield()\n",
    "    params = fl.SimulationParams(\n",
    "        meshing=fl.MeshingParams(\n",
    "            defaults=fl.MeshingDefaults(\n",
    "                boundary_layer_first_layer_thickness=first_layer_thickness,\n",
    "                surface_max_edge_length=20 * fl.u.mm,\n",
    "            ),\n",
    "            refinements=refinements,  # All refinements previously defined\n",
    "            volume_zones=[farfield],  # Farfield volume zone\n",
    "        ),\n",
    "        operating_condition=operating_condition,  # Liquid operating condition\n",
    "        time_stepping=fl.Steady(max_steps=5000),\n",
    "        models=[\n",
    "            fl.Fluid(\n",
    "                navier_stokes_solver=fl.NavierStokesSolver(),\n",
    "                turbulence_model_solver=fl.SpalartAllmaras(),\n",
    "            ),\n",
    "            fl.Freestream(surfaces=farfield.farfield),\n",
    "            fl.Wall(surfaces=geo[\"*\"]),\n",
    "            AD_model,  # Actuator disk model\n",
    "        ],\n",
    "        reference_geometry=fl.ReferenceGeometry(\n",
    "            moment_center=(0, 0, 0),\n",
    "            moment_length=(3.81, 3.81, 3.81),\n",
    "            area=45.604,\n",
    "        ),\n",
    "        outputs=[\n",
    "            fl.VolumeOutput(\n",
    "                output_fields=[\n",
    "                    \"primitiveVars\",\n",
    "                    \"Cp\",\n",
    "                    \"qcriterion\",\n",
    "                ],\n",
    "            ),\n",
    "            fl.SurfaceOutput(\n",
    "                surfaces=geo[\"*\"],\n",
    "                output_fields=[\n",
    "                    \"primitiveVars\",\n",
    "                    \"Cp\",\n",
    "                    \"Cf\",\n",
    "                    \"CfVec\",\n",
    "                    \"yPlus\",\n",
    "                ],\n",
    "            ),\n",
    "        ],\n",
    "    )"
   ],
   "execution_count": 12,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "919ae459"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Run Case\n",
    "Run the case specifying parameters and the case name."
   ],
   "id": "c09f0d6a"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "case = project.run_case(\n",
    "    params=params,\n",
    "    name=\"Tutorial DARPA Actuator Disk from Python\",\n",
    ")"
   ],
   "execution_count": 13,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[20:17:06] INFO: Successfully submitted:                                                                           \n",
       "                   type        = Case                                                                              \n",
       "                   name        = Tutorial DARPA Actuator Disk from Python                                          \n",
       "                   id          = case-01625cd5-4a98-453d-bf97-b94a81babda7                                         \n",
       "                   status      = pending                                                                           \n",
       "                   project id  = prj-fa790634-10b7-40ca-a6a9-fdb62f9556fc                                          \n",
       "                                                                                                                   \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[20:17:06]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Successfully submitted:                                                                           \n",
       "\u001b[2;36m           \u001b[0m        type        = Case                                                                              \n",
       "\u001b[2;36m           \u001b[0m        name        = Tutorial DARPA Actuator Disk from Python                                          \n",
       "\u001b[2;36m           \u001b[0m        id          = case-\u001b[93m01625cd5-4a98-453d-bf97-b94a81babda7\u001b[0m                                         \n",
       "\u001b[2;36m           \u001b[0m        status      = pending                                                                           \n",
       "\u001b[2;36m           \u001b[0m        project id  = prj-\u001b[93mfa790634-10b7-40ca-a6a9-fdb62f9556fc\u001b[0m                                          \n",
       "\u001b[2;36m           \u001b[0m                                                                                                        \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "fa37b01c"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Post Processing\n",
    "Once the simulation is finished, we will monitor the convergence of residuals over the pseudo steps:\n"
   ],
   "id": "cfe4fc89"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "case.wait()\n",
    "results = case.results\n",
    "non_linear = results.nonlinear_residuals\n",
    "non_linear = non_linear.as_dataframe()\n",
    "non_linear.plot(\"pseudo_step\", [\"0_cont\", \"1_momx\", \"2_momy\", \"3_momz\", \"4_nuHat\"], logy=True)\n",
    "plt.show()"
   ],
   "execution_count": 14,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "927ec65b71624441932dd15764e8d2e9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a6dec97e9433420aabaebd0d90f67d9c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[20:29:01] INFO: Saved to /tmp/tmp1fkdwydy/197e50bd-f6d7-45a4-b99a-5dd0958f8902.csv                                \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[20:29:01]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Saved to \u001b[35m/tmp/tmp1fkdwydy/\u001b[0m\u001b[95m197e50bd-f6d7-45a4-b99a-5dd0958f8902.csv\u001b[0m                                \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": "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",
      "text/plain": [
       "
"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "e722701f"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we can monitor the drag force on the hull and also compute the actuator disk thrust and torque. To do so, we need to dimensionalise the forces based on the case reference quantities like length, density, reference velocity and area. Note that here the reference velocity for actuator disk output is the reference velocity magnitude and if this is not defined, then, the velocity magintude. This is the case since we are using `LiquidOperationCondition`, if we use `AerospaceCondition` then the reference velocity is the speed of sound."
   ],
   "id": "d074f72d"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# Get the reference quantities\n",
    "length_unit = project.length_unit\n",
    "density = case.params.operating_condition.material.density\n",
    "U_ref = (\n",
    "    case.params.operating_condition.reference_velocity_magnitude\n",
    "    or case.params.operating_condition.velocity_magnitude\n",
    ")\n",
    "A_ref = case.params.reference_geometry.area\n",
    "\n",
    "# Body force coefficients\n",
    "body_forces = case.results.total_forces.as_dataframe().iloc[-1]\n",
    "CD = body_forces[\"CD\"]\n",
    "\n",
    "# Actuator disk force coefficients\n",
    "actuator_disk_output = case.results.actuator_disks.as_dataframe().iloc[-1]\n",
    "C_p = actuator_disk_output[\"Disk0_Power\"]\n",
    "C_t = actuator_disk_output[\"Disk0_Force\"]\n",
    "C_q = actuator_disk_output[\"Disk0_Moment\"]\n",
    "\n",
    "# Dimensionalise the forces\n",
    "drag_force = (CD * 0.5 * density * U_ref**2 * A_ref).to(\"N\")\n",
    "power = (C_p * density * U_ref**3 * length_unit**2).to(\"W\")\n",
    "thrust = (C_t * density * U_ref**2 * length_unit**2).to(\"N\")\n",
    "torque = (C_q * density * U_ref**2 * length_unit**3).to(\"N*m\")\n",
    "\n",
    "print(f\"Drag force: {drag_force}\")\n",
    "print(f\"Power: {power}\")\n",
    "print(f\"Thrust: {thrust}\")\n",
    "print(f\"Torque: {torque}\")"
   ],
   "execution_count": 15,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ad8c98e233314b0e943d9c64166cd61b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[20:29:04] INFO: Saved to /tmp/tmp1fkdwydy/de46f561-2831-4eda-91e6-3fcfeaf7a15d.csv                                \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[20:29:04]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Saved to \u001b[35m/tmp/tmp1fkdwydy/\u001b[0m\u001b[95mde46f561-2831-4eda-91e6-3fcfeaf7a15d.csv\u001b[0m                                \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "93cd62b9440444458b2de819804ecdb0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
\n"
      ],
      "text/plain": []
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[20:29:05] INFO: Saved to /tmp/tmp1fkdwydy/9ab4120a-1436-41fa-8acb-22bc902462f6.csv                                \n",
       "
\n"
      ],
      "text/plain": [
       "\u001b[2;36m[20:29:05]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Saved to \u001b[35m/tmp/tmp1fkdwydy/\u001b[0m\u001b[95m9ab4120a-1436-41fa-8acb-22bc902462f6.csv\u001b[0m                                \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "text": [
      "Drag force: 379.51182943493876 N\n",
      "Power: 10889.669869904938 W\n",
      "Thrust: 1998.5858964472352 N\n",
      "Torque: -99.929914791825 N*m\n"
     ],
     "name": "stdout"
    }
   ],
   "id": "2c796b8d"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "flow360",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}