Merge pull request #56 from FireDynamics/development

Development

Author: kriboe90

book/content/modelling/06_heat_transfer/02_heat_transfer_example.ipynb

@@ -15,7 +15,7 @@
    "source": [
     "## Introduction\n",
     "\n",
-    "Fire Dynamics Simulator (FDS) calculates the mechanisms of heat transfer taking into account the corresponding physical processes of convection and radiation. From the resulting heat flow onto a solid surface, the surface temperature as well as the temperature at a certain depth can be determined, depending on the material properties and the the respective boundary conditions. By default, FDS  only performs a transient, one-dimensional calculation of heat transfer. The objective of this exercise is to discuss the different influences of radiation and convection as well as the surface and material properties of a solid body on its heating in case of fire. The {download}`HeatTransfer.fds` input file should be used as a starting point."
+    "Fire Dynamics Simulator (FDS) calculates the mechanisms of heat transfer taking into account the corresponding physical processes of convection and radiation. From the resulting heat flux onto a solid surface, the surface temperature as well as the temperature at a certain depth can be determined, depending on the material properties and the the respective boundary conditions. By default, FDS  only performs a transient, one-dimensional calculation of heat transfer. The objective of this exercise is to discuss the different influences of radiation and convection as well as the surface and material properties of a solid body on its heating in case of fire. The {download}`HeatTransfer.fds` input file should be used as a starting point."
    ]
   },
   {
@@ -32,7 +32,7 @@
     "\n",
     "<img src=\"figs/fds.png\" width=\"100%\">\n",
     "\n",
-    "SMV visualization of the geometry. The surface patch `HEATER`, which has a constant surface temperature of $1000^\\circ C$ (`TMP_FRONT = 1000`) ,is colored redish. The orange and yellow `OBSTRUCTIONS` depict different surfaces (`SURF`). The gray heat shield covers thermocouples and devices from a radiative impact.  \n",
+    "SMV visualization of the geometry. The surface patch `HEATER`, which has a constant surface temperature of $1000^\\circ C$ (`TMP_FRONT = 1000`) ,is colored reddish. The orange and yellow obstructions (`OBST`) depict different surfaces (`SURF`). The gray heat shield covers thermocouples and devices from a radiative impact.  \n",
     ":::"
    ]
   },
@@ -42,16 +42,16 @@
    "metadata": {},
    "source": [
     "## Heat Flux\n",
-    "FDS provides several outputs quantities related to the thermal exposure of solid surfaces (See section 11.33 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)).\n",
+    "FDS provides several output quantities related to the thermal exposure of solid surfaces (See section 21.10.7 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)).\n",
     "\n",
     "\n",
-    "The sum of radiative and convective energy absorbed at a solid surface is expressed by the `TOTAL HEAT FLUX`:\n",
+    "The sum of radiative and convective energy absorbed at a solid surface is expressed by the `TOTAL HEAT FLUX` or `NET HEAT FLUX`:\n",
     "\n",
     "$$\\mf q_{\\rm net}'' = \\epsilon_{\\rm s} \\, \\left(q_{\\rm inc,rad}'' - \\sigma \\, T_{\\rm s}^4 \\right) + h \\, (T_{\\rm gas} - T_{\\rm s}) \\label{net_flux}$$\n",
     "\n",
     "where $\\mf \\dot{q}_{\\rm inc,rad}$ is the incident radiative heat flux (`INCIDENT HEAT FLUX`), $\\mf \\epsilon_{\\rm s}$ is the surface emissivity, h is the convective heat transfer coefficient, $\\mf T_{\\rm s}$ is the surface temperature, and $\\mf T_{\\rm gas}$ is the gas temperature in the vicinity of the surface. The convective heat transfer coefficient, h, is calculated by FDS using the specified surface properties and the calculated near-boundary flow characteristics.\n",
     "\n",
-    "The net radiative component can be evaluated separately by the `RADIATIVE HEAT FLUX` quantity:\n",
+    "The radiative component can be evaluated separately by the `RADIATIVE HEAT FLUX` quantity:\n",
     "\n",
     "\n",
     "$$\\mf q_{\\rm r}'' = \\epsilon_{\\rm s} \\, \\left( q_{\\rm inc,rad}'' - \\sigma \\, T_{\\rm s}^4 \\right)$$\n",
@@ -193,10 +193,10 @@
    "metadata": {},
    "source": [
     "## Task 1\n",
-    "The local gas phase temperature at a certain cell can be evaluated via a dimple `DEVC` with `QUANTITY = 'TEMPERATURE'`. The output of a thermocouple which lags the true gas temperature by an amount determined mainly by its size can be assessed by a `DEVC` with `QUANTITY = THERMOCOUPLE` that  also takes into account the heat transfer to a small sphere. For this purpose, it must be assigned an emissivity and a diameter.  The properties can be assigned to a `DEVICE` via the `PROP_ID` attribute (see also section 20.1 of [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf). For detailed information on how to model thermocouples in FDS please refer to section 21.10.6.\n",
+    "The local gas phase temperature at a certain cell can be evaluated via a simple `DEVC` with `QUANTITY = 'TEMPERATURE'`. The output of a thermocouple which lags the true gas temperature by an amount determined mainly by its size can be assessed by a `DEVC` with `QUANTITY = THERMOCOUPLE`. It takes into account the radiative and convective heat transfer to a small sphere. For this purpose, it must be assigned an emissivity and a diameter.  The properties can be assigned to a `DEVICE` via the `PROP_ID` attribute (see also section 20.1 of [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf). For detailed information on how to model thermocouples in FDS please refer to section 21.10.6.\n",
     "\n",
     "**Tasks**\n",
-    "1. Place simple devices with `QUANTITY = 'TEMPERATURE'` and thermocouples at X = 0, Y = 0.8 and heights z = 0.6 m (bottom), 2.6 m (behind heat shield), 4.4 m (top).  Run the simulation for 100 seconds and plot the temporal output of the devices. Discuss what effects lead to the differences between the two types of devices. For the thermocouples assume an `EMISSIVITY` of 0.9 and a diameter of d = 3 mm. \n",
+    "1. Place simple devices with `QUANTITY = 'TEMPERATURE'` and `THERMOCOUPLE` at X = 0, Y = 0.8 and heights z = 0.6 m (bottom), 2.6 m (behind heat shield), 4.4 m (top).  Run the simulation for at least 100 seconds and plot the temporal output of the devices. Discuss what effects lead to the differences between the two types of devices. For the thermocouples assume an `EMISSIVITY` of 0.9 and a diameter of d = 3 mm. \n",
     "\n",
     ":::{figure-md} heat-transfer-namelist-dependencies-prop\n",
     "\n",
@@ -208,7 +208,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 9,
    "id": "3396ebc0-f1d2-4437-a9e8-7cd3f2bff780",
    "metadata": {
     "tags": [
@@ -236,6 +236,7 @@
     "plt.ylabel(\"Temperature / $\\circ C$\")\n",
     "plt.legend(loc='best')\n",
     "plt.grid(True, linestyle='--', alpha=0.5)\n",
+    "plt.xlim(0,100)\n",
     "plt.savefig('figs/thermocouples.svg', bbox_inches='tight')\n",
     "plt.close()"
    ]
@@ -261,14 +262,14 @@
    "metadata": {},
    "source": [
     "## Task 2\n",
-    "In order to correctly represent the heat transfer within a component, the temperature-dependent material parameters thermal `CONDUCTIVITY`, `SPECIF_HEAT` and `DENSITY` must be known. A new material can be defined via the `MATL ID` attribute. The available parameters for describing the material properties can be found at section 22.14 of [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)). Another parameter influencing the heat conduction within a solid is its thermal effective `THICKNESS`. This is defined in the `SURF` line and is independent of the actual thickness of an obstruction.\n",
+    "In order to correctly compute the heat transfer within a solid obstruction, the thermal material properties `CONDUCTIVITY`, `SPECIF_HEAT` and `DENSITY` must be known. A new material can be defined via the `MATL` attribute. The available parameters for describing the material properties can be found at section 22.14 of [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)). Another parameter influencing the heat conduction within a solid is its thermal effective `THICKNESS`. This is defined on the `SURF` line and is independent from the actual thickness of an obstruction.\n",
     "\n",
     "The `EMISSIVITY` (default 0.9) can be set on the `SURF` or `MATL` line while the `MATL` parameter is given priority.\n",
     "\n",
     "The back side boundary conditions of a solid obstruction can be defined on the `SURF` line as:\n",
-    "- `EXPOSED`: calculates heat conduction through the wall into the space behind the wall (default)\n",
-    "- `INSULATED`: prevents any heat loss from the back side of the material\n",
-    "- `VOID`: always backs up to ambient temperature\n",
+    "- `EXPOSED`: Calculates heat conduction through the wall into the space behind the wall (default)\n",
+    "- `INSULATED`: Prevents any heat loss from the back side of the material\n",
+    "- `VOID`: Always backs up to ambient temperature\n",
     "\n",
     "::::{important}\n",
     "The `THICKNESS` of a `SURF` ought to be the actual thickness of the “wall” through which FDS performs a 1-D heat conduction calculation. It is independent from the mesh cell width. If the obstruction is on the boundary of the domain or is more than one cell thick, then it is automatically assumed to back up to an air gap at ambient temperature.\n",
@@ -282,7 +283,7 @@
     ":::\n",
     "\n",
     "**Tasks**\n",
-    "1. Define a new material \"Steel\" with the following material properties $\\mf c_p = 0.5~kJ~/kg~K$, $\\mf \\lambda = 45.3~W~/m~K $ and $\\mf \\rho=7854~kg~m^{-3}$. Assign the material to the \"SURF_1\" (yellow) and \"SURF_2\" (orange). On the `SURF` line change the back side boundary condition of one of the surfaces to `INSULATED` and on the other to `EXPOSED` (See section 11.33 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)). Assume a `THICKNESS` of 10 cm (0.1 m). Analyse the `WALL TEMPERATURE` (on front surface) as well as the `INSIDE WALL TEMPERATURE` at depths 25 and 75 mm and the `BACK WALL TEMPERATURE` (on back surface) (see 21.21.1 and 21.2.3 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)). For this purpose a respective`DEVC` must be placed on the front surface of the solid `OBSTRUCTION`. The parameter `IOR` (Index of Orientation) is required for any device that is placed on the surface of a solid. It indicates the direction that the device points at. For example, `IOR = -1` means that the device is mounted on a wall that faces in the negative x direction. Run the simulation for 600 s and plot the plot the indicated temperatures for both surfaces.\n",
+    "1. Define a new material \"Steel\" with the following material properties $\\mf c_p = 0.5~kJ~/kg~K$, $\\mf \\lambda = 45.3~W~/m~K $ and $\\mf \\rho=7854~kg~m^{-3}$. Assign the material to the \"SURF_1\" (yellow) and \"SURF_2\" (orange). On the `SURF` line change the back side boundary condition of one of the surfaces to `INSULATED` and on the other to `EXPOSED` (See section 11.3.3 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)). Assume a `THICKNESS` of 10 mm (0.1 m). Analyse the `WALL TEMPERATURE` (on front surface) as well as the `INSIDE WALL TEMPERATURE` at depths 2.5 mm and 7.5 mm and the `BACK WALL TEMPERATURE` (on back surface) (see 21.2.1 and 21.2.3 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)). For this purpose a respective `DEVC` must be placed on the front surface of the solid `OBSTRUCTION`. The parameter `IOR` (Index of Orientation) is required for any device that is placed on the surface of a solid. It indicates the direction that the device points at. For example, `IOR = -1` means that the device is mounted on a wall that faces in the negative x direction. Run the simulation for 600 s and plot the indicated temperatures for both surfaces.\n",
     "\n",
     "2. At which timestep does the difference between the `WALL TEMPERATURE` of both surfaces exceed a ratio of 5%?\n",
     "\n",
@@ -299,7 +300,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 8,
    "id": "8563beee-f96e-4a82-897e-480788383ea8",
    "metadata": {
     "tags": [
@@ -325,12 +326,12 @@
     "fig, ax1 = plt.subplots()\n",
     "\n",
     "ax1.plot(time, steel_exposed_front, label=\"Front, back. exposed\", color='blue')\n",
-    "ax1.plot(time, steel_exposed_025, label=\"d = 25 mm, back. exposed\", color='red')\n",
-    "ax1.plot(time, steel_exposed_075, label=\"d = 75 mm, back. exposed\", color='green')\n",
+    "ax1.plot(time, steel_exposed_025, label=\"d = 2.5 mm, back. exposed\", color='red')\n",
+    "ax1.plot(time, steel_exposed_075, label=\"d = 7.5 mm, back. exposed\", color='green')\n",
     "ax1.plot(time, steel_exposed_back, label=\"Back, back. exposed\", color='yellow')\n",
     "ax1.plot(time, steel_insulated_front, label=\"Front, back. insulated\", color='blue', linestyle='--')\n",
-    "ax1.plot(time, steel_insulated_025, label=\"25 mm, back. insulated\", color='red', linestyle='--')\n",
-    "ax1.plot(time, steel_insulated_075, label=\"75 mm, back. insulated\", color='green', linestyle='--')\n",
+    "ax1.plot(time, steel_insulated_025, label=\"2.5 mm, back. insulated\", color='red', linestyle='--')\n",
+    "ax1.plot(time, steel_insulated_075, label=\"7.5 mm, back. insulated\", color='green', linestyle='--')\n",
     "ax1.plot(time, steel_insulated_back, label=\"Back, back. insulated\", color='yellow', linestyle='--')\n",
     "\n",
     "ax1.set_xlabel(\"Time / s\")\n",
@@ -377,7 +378,7 @@
     "\n",
     "<img src=\"figs/backings_end.svg\" width=\"100%\">\n",
     "\n",
-    "`WALL TEMPERATURE` and `INSIDE WALL TEMPERATURE` at several depths inside the solid steel obstruction within the first 600 seconds seconds of heating phase. The blue line indicates the relative error between an insulated and exposed backing boundary condition. \n",
+    "`WALL TEMPERATURE` and `INSIDE WALL TEMPERATURE` at several depths inside the solid steel obstruction within the first 600 seconds seconds of heating phase. The purple line indicates the relative error between an insulated and exposed backing boundary condition. \n",
     ":::"
    ]
   },
@@ -541,7 +542,7 @@
     "\n",
     "The assumption of constant thermal material properties is a simplification that often is sufficiently accurate. In some cases, however, it may be necessary to consider the actual temperature-dependent properties of a material or component. This can be done in FDS by defining a RAMP function, which describes a material parameter as a function of temperature (see section 11.3.2 [FDS User's Guide](https://github.com/firemodels/fds/releases/download/FDS6.7.5/FDS_User_Guide.pdf)).\n",
     "\n",
-    "Figure 1-3 shows the temperature-dependent relationships for the specific heat capacity, thermal conductivity and density of concrete according to DIN EN 1992-1-2.\n",
+    "Figure {numref}`heat-transfer-density` - {numref}`heat-transfer-conductivity` shows the temperature-dependent relationships for the specific heat capacity, thermal conductivity and density of concrete according to DIN EN 1992-1-2.\n",
     "\n",
     "```{note}\n",
     "In FDS only the `SPECIFI_HEAT` and `CONDUCTIVITY` can be ramped while `DENSITY` and `EMISSIVITY` cannot.\n",
@@ -550,7 +551,7 @@
     "**Tasks**\n",
     "\n",
     "1. At 20°C, read the values from {numref}`heat-transfer-density` - {numref}`heat-transfer-conductivity` and define a new material \"concrete\" with the corresponding material properties. Define another material taking into account the variable material properties. Therefore roughly map the corresponding progression curves using a RAMP function (max. 7 datapoints each). Assign the two materials to \"SURF_1\"  and \"SURF_2\" in the FDS file. \n",
-    "2. Run the simulation for 600s and compare the `WALL TEMPERATURE` for both surfaces as well as the `INSIDE WALL TEMPERATURE` at d = 10 mm. Assume the wall to have a thickness of 20 cm.\n",
+    "2. Run the simulation for 600 s and compare the `WALL TEMPERATURE` for both surfaces as well as the `INSIDE WALL TEMPERATURE` at d = 10 mm. Assume the wall to have a thickness of 10 cm. Assume a humidity of 3 %. For the conductivity consider the upper limit.\n",
     ":::{figure-md} heat-transfer-namelist-dependencies-ramp\n",
     "\n",
     "<img src=\"figs/flow_chart_ramp.svg\" width=\"70%\">\n",