Issue 912 tab cooling

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Features
 
+-   Added tab, edge, and surface cooling ([#965](https://github.com/pybamm-team/PyBaMM/pull/965))
 -   Added functionality to solver to automatically discretise a 0D model ([#947](https://github.com/pybamm-team/PyBaMM/pull/947))
 -   Added sensitivity to `CasadiAlgebraicSolver` ([#940](https://github.com/pybamm-team/PyBaMM/pull/940))
 -   Added `ProcessedSymbolicVariable` class, which can handle symbolic variables (i.e. variables for which the inputs are symbolic) ([#940](https://github.com/pybamm-team/PyBaMM/pull/940))

examples/notebooks/using-model-options_thermal-example.ipynb

@@ -65,7 +65,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We choose to use the parameters from [1]. We then update the heat transfer coefficient to be 0.1 [W/m^2/K] (see the [Parameter Values notebook](./parameter-values.ipynb) for more details)"
+    "We choose to use the parameters from [1]. We then update the heat transfer coefficients (see the [Parameter Values notebook](./parameter-values.ipynb) for more details)"
    ]
   },
   {
@@ -75,7 +75,17 @@
    "outputs": [],
    "source": [
     "param = pybamm.ParameterValues(chemistry=pybamm.parameter_sets.Marquis2019)\n",
-    "param.update({\"Heat transfer coefficient [W.m-2.K-1]\": 0.1})"
+    "param.update(\n",
+    "    {\n",
+    "        \"Negative current collector\"\n",
+    "        + \" surface heat transfer coefficient [W.m-2.K-1]\": 5,\n",
+    "        \"Positive current collector\"\n",
+    "        + \" surface heat transfer coefficient [W.m-2.K-1]\": 5,\n",
+    "        \"Negative tab heat transfer coefficient [W.m-2.K-1]\": 0,\n",
+    "        \"Positive tab heat transfer coefficient [W.m-2.K-1]\": 0,\n",
+    "        \"Edge heat transfer coefficient [W.m-2.K-1]\": 0,\n",
+    "    }\n",
+    ")"
    ]
   },
   {
@@ -121,7 +131,7 @@
    "source": [
     "# solve model\n",
     "solver = model.default_solver\n",
-    "t_eval = np.linspace(0, 1, 250)\n",
+    "t_eval = np.linspace(0, 3600, 250)\n",
     "solution = solver.solve(model, t_eval)"
    ]
   },
@@ -140,12 +150,12 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "c3d04dd597c24caf83c370bd01fe6131",
+       "model_id": "115696cc7c7e4297bb6d85a9f8220a82",
        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "interactive(children=(FloatSlider(value=0.0, description='t', max=1.0, step=0.01), Output()), _dom_classes=('w…"
+       "interactive(children=(FloatSlider(value=0.0, description='t', max=3599.9999999999995, step=35.99999999999999),…"
       ]
      },
      "metadata": {},
@@ -202,9 +212,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 2
-}
+}

examples/scripts/thermal_lithium_ion.py

@@ -18,7 +18,20 @@
 
 # load parameter values and process models and geometry
 param = models[0].default_parameter_values
-param.update({"Heat transfer coefficient [W.m-2.K-1]": 1})
+
+# for x-full, cooling is only implemented on the surfaces
+# so set other forms of cooling to zero for comparison.
+param.update(
+    {
+        "Negative current collector"
+        + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+        "Positive current collector"
+        + " surface heat transfer coefficient [W.m-2.K-1]": 5,
+        "Negative tab heat transfer coefficient [W.m-2.K-1]": 0,
+        "Positive tab heat transfer coefficient [W.m-2.K-1]": 0,
+        "Edge heat transfer coefficient [W.m-2.K-1]": 0,
+    }
+)
 
 for model in models:
     param.process_model(model)

pybamm/input/parameters/lead-acid/experiments/1C_discharge_from_full/parameters.csv

@@ -5,8 +5,11 @@ Name [units],Value,Reference,Notes
 Reference temperature [K],294.85,Room temperature,
 Maximum temperature [K],333.15,,
 Ambient temperature [K], 294.85,,
-Heat transfer coefficient [W.m-2.K-1],10,,
-Initial temperature [K],294.85,Room temperature,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],10,,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 
 ,,,
 # Electrical
@@ -18,3 +21,4 @@ Upper voltage cut-off [V],2.44,(just over) 14.5V across 6-cell battery,
 # Initial conditions
 Initial State of Charge,1,-,
 Initial oxygen concentration [mol.m-3],0,,
+Initial temperature [K],294.85,Room temperature,

pybamm/input/parameters/lithium-ion/experiments/1C_charge_from_empty_Mohtat2020/parameters.csv

@@ -3,10 +3,14 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],298.15,25C,
-Heat transfer coefficient [W.m-2.K-1],5,Peyman MPM,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],0,,
+Positive tab heat transfer coefficient [W.m-2.K-1],0,,
+Edge heat transfer coefficient [W.m-2.K-1],5,Peyman MPM,
 Ambient temperature [K], 298.15,,
 ,,,
-# Electrical			
+# Electrical
 Number of electrodes connected in parallel to make a cell,1,,
 Number of cells connected in series to make a battery,1,,
 Lower voltage cut-off [V],2.5,,

pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Chen2020/parameters.csv

@@ -3,11 +3,15 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],298.15,25C,
-Heat transfer coefficient [W.m-2.K-1],10,,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],10,,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 Ambient temperature [K], 298.15,,
 
 ,,,
-# Electrical			
+# Electrical
 Number of electrodes connected in parallel to make a cell,1,,
 Number of cells connected in series to make a battery,1,,
 Lower voltage cut-off [V],2.5,,

pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Ecker2015/parameters.csv

@@ -3,7 +3,11 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],296.15,23C,
-Heat transfer coefficient [W.m-2.K-1],10, The paper does not consider thermal effects so a typical value is chosen,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,Paper does not consider thermal effects
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,Paper does not consider thermal effects
+Negative tab heat transfer coefficient [W.m-2.K-1],10,Paper does not consider thermal effects,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,Paper does not consider thermal effects,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,Paper does not consider thermal effects,
 Ambient temperature [K], 298.15,,
 
 ,,,

pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Kim2011/parameters.csv

@@ -3,7 +3,11 @@ Name [units],Value,Reference,Notes
 ,,,
 # Temperature
 Reference temperature [K],298.15,25C,
-Heat transfer coefficient [W.m-2.K-1],25,,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],25,,
+Positive tab heat transfer coefficient [W.m-2.K-1],25,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 Ambient temperature [K], 298.15,,
 
 ,,,

pybamm/input/parameters/lithium-ion/experiments/1C_discharge_from_full_Marquis2019/parameters.csv

@@ -4,9 +4,13 @@ Name [units],Value,Reference,Notes
 # Temperature
 Reference temperature [K],298.15,25C,
 Ambient temperature [K], 298.15,,
-Heat transfer coefficient [W.m-2.K-1],10,,
+Negative current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Positive current collector surface heat transfer coefficient [W.m-2.K-1],0,,
+Negative tab heat transfer coefficient [W.m-2.K-1],10,,
+Positive tab heat transfer coefficient [W.m-2.K-1],10,,
+Edge heat transfer coefficient [W.m-2.K-1],0.3,,
 ,,,
-# Electrical			
+# Electrical
 Number of electrodes connected in parallel to make a cell,1,,
 Number of cells connected in series to make a battery,1,,
 Lower voltage cut-off [V],3.105,,

pybamm/models/submodels/thermal/lumped.py

@@ -53,12 +53,47 @@ def set_rhs(self, variables):
         # the choice of non-dimensionalisation.
         # TODO: allow for arbitrary surface area to volume ratio in order to model
         # different cell geometries (see #718)
-        A = self.param.l_y * self.param.l_z
-        V = self.param.l * self.param.l_y * self.param.l_z
-        cooling_coeff = -2 * self.param.h * A / V / (self.param.delta ** 2)
+        cell_volume = self.param.l * self.param.l_y * self.param.l_z
+
+        yz_cell_surface_area = self.param.l_y * self.param.l_z
+        yz_surface_cooling_coefficient = (
+            -(self.param.h_cn + self.param.h_cp)
+            * yz_cell_surface_area
+            / cell_volume
+            / (self.param.delta ** 2)
+        )
+
+        negative_tab_area = self.param.l_tab_n * self.param.l_cn
+        negative_tab_cooling_coefficient = (
+            -self.param.h_tab_n * negative_tab_area / cell_volume / self.param.delta
+        )
+
+        positive_tab_area = self.param.l_tab_p * self.param.l_cp
+        positive_tab_cooling_coefficient = (
+            -self.param.h_tab_p * positive_tab_area / cell_volume / self.param.delta
+        )
+
+        edge_area = (
+            2 * self.param.l_y * self.param.l
+            + 2 * self.param.l_z * self.param.l
+            - negative_tab_area
+            - positive_tab_area
+        )
+        edge_cooling_coefficient = (
+            -self.param.h_edge * edge_area / cell_volume / self.param.delta
+        )
+
+        total_cooling_coefficient = (
+            yz_surface_cooling_coefficient
+            + negative_tab_cooling_coefficient
+            + positive_tab_cooling_coefficient
+            + edge_cooling_coefficient
+        )
 
         self.rhs = {
-            T_vol_av: (self.param.B * Q_vol_av + cooling_coeff * (T_vol_av - T_amb))
+            T_vol_av: (
+                self.param.B * Q_vol_av + total_cooling_coefficient * (T_vol_av - T_amb)
+            )
             / (self.param.C_th * self.param.rho)
         }
 

pybamm/models/submodels/thermal/pouch_cell/pouch_cell_1D_current_collectors.py

@@ -60,40 +60,82 @@ def set_rhs(self, variables):
         # Account for surface area to volume ratio of pouch cell in cooling
         # coefficient. Note: the factor 1/delta^2 comes from the choice of
         # non-dimensionalisation
-        A = self.param.l_y * self.param.l_z
-        V = self.param.l * self.param.l_y * self.param.l_z
-        cooling_coeff = -2 * self.param.h * A / V / (self.param.delta ** 2)
+        cell_volume = self.param.l * self.param.l_y * self.param.l_z
+
+        yz_surface_area = self.param.l_y * self.param.l_z
+        yz_surface_cooling_coefficient = (
+            -(self.param.h_cn + self.param.h_cp)
+            * yz_surface_area
+            / cell_volume
+            / (self.param.delta ** 2)
+        )
+
+        side_edge_area = 2 * self.param.l_z * self.param.l
+        side_edge_cooling_coefficient = (
+            -self.param.h_edge * side_edge_area / cell_volume / self.param.delta
+        )
+
+        total_cooling_coefficient = (
+            yz_surface_cooling_coefficient + side_edge_cooling_coefficient
+        )
 
         self.rhs = {
             T_av: (
                 pybamm.laplacian(T_av)
                 + self.param.B * Q_av
-                + cooling_coeff * (T_av - T_amb)
+                + total_cooling_coefficient * (T_av - T_amb)
             )
             / (self.param.C_th * self.param.rho)
         }
 
     def set_boundary_conditions(self, variables):
         T_amb = variables["Ambient temperature"]
         T_av = variables["X-averaged cell temperature"]
-        T_av_left = pybamm.boundary_value(T_av, "negative tab")
-        T_av_right = pybamm.boundary_value(T_av, "positive tab")
+        T_av_top = pybamm.boundary_value(T_av, "right")
+        T_av_bottom = pybamm.boundary_value(T_av, "left")
+
+        # Tab cooling only implemented for both tabs at the top.
+        negative_tab_area = self.param.l_tab_n * self.param.l_cn
+        positive_tab_area = self.param.l_tab_p * self.param.l_cp
+        total_top_area = self.param.l * self.param.l_y
+        non_tab_top_area = total_top_area - negative_tab_area - positive_tab_area
+
+        negative_tab_cooling_coefficient = (
+            self.param.h_tab_n / self.param.delta * negative_tab_area / total_top_area
+        )
+        positive_tab_cooling_coefficient = (
+            self.param.h_tab_p / self.param.delta * positive_tab_area / total_top_area
+        )
+
+        top_edge_cooling_coefficient = (
+            self.param.h_edge / self.param.delta * non_tab_top_area / total_top_area
+        )
+
+        bottom_edge_cooling_coefficient = (
+            self.param.h_edge / self.param.delta * total_top_area / total_top_area
+        )
+
+        total_top_cooling_coefficient = (
+            negative_tab_cooling_coefficient
+            + positive_tab_cooling_coefficient
+            + top_edge_cooling_coefficient
+        )
+
+        total_bottom_cooling_coefficient = bottom_edge_cooling_coefficient
 
-        # Three boundary conditions here to handle the cases of both tabs at
-        # the same side (top or bottom), or one either side. For both tabs on the
-        # same side, T_av_left and T_av_right are equal, and the boundary condition
-        # "no tab" is used on the other side.
+        # just use left and right for clarity
+        # left = bottom of cell (z=0)
+        # right = top of cell (z=L_z)
         self.boundary_conditions = {
             T_av: {
-                "negative tab": (
-                    self.param.h * (T_av_left - T_amb) / self.param.delta,
+                "left": (
+                    total_bottom_cooling_coefficient * (T_av_bottom - T_amb),
                     "Neumann",
                 ),
-                "positive tab": (
-                    -self.param.h * (T_av_right - T_amb) / self.param.delta,
+                "right": (
+                    -total_top_cooling_coefficient * (T_av_top - T_amb),
                     "Neumann",
                 ),
-                "no tab": (pybamm.Scalar(0), "Neumann"),
             }
         }