more writeup updates

dynamic_model/pump_transient_benchmark/pump_transients.ipynb

@@ -4,7 +4,21 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Imports"
+    "# MSRE Pump Transient Benchmark"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This notebook simulates pump transients for the MSRE at zero power (10W). A dynamical system representing the MSRE is built using the [msrDynamics](https://github.com/LukeLabrie/msrDynamics) tool. The system is run at steady-state until $t = 2500$, where the fuel and coolant pumps are spun down at the rate defined by the ORNL data. After allowing the system to settle to a new equilibrium, at $t = 7500$, the pumps are spun up again. The model includes a reactivity response, `rho_control`, which models the response of the MSRE control rod to maintain constant power. It is modeled as a pure integrator of $\\frac{dn}{dt}$ from the point-kinetics equations with a coefficient of -1.0, i.e. it tries to exactly cancel reactivity changes introduced by flow changes, with the caveat that changes are limited to $\\pm$29 pcm/s, which was the maximum rate achievable by the MSRE control rods. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Imports"
    ]
   },
   {
@@ -26,7 +40,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This notebook simulates pump transients for the MSRE at zero power (10W). A dynamical system representing the MSRE is built using the [msrDynamics](https://github.com/LukeLabrie/msrDynamics) tool. The system is run at steady-state until $t = 2500$, where the fuel and coolant pumps are spun down at the rate defined by the ORNL data. After allowing the system to settle to a new equilibrium, at $t = 7500$, the pumps are spun up again. The model includes a reactivity response, `rho_control`, which models the response of the MSRE control rod to maintain constant power. It is modeled as a pure integrator of $\\frac{dn}{dt}$ from the point-kinetics equations with a coefficient of -1.0, i.e. it tries to exactly cancel reactivity changes introduced by flow changes, with the caveat that changes are limited to $\\pm$29 pcm/s, which was the maximum rate achievable by the MSRE control rods. "
+    "## Plotting Style "
    ]
   },
   {
@@ -52,6 +66,13 @@
     "    ax.tick_params(axis='y', which='both', left=True, right=False, labelleft=True)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Sytem Definition using `msrDynamics`"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -70,6 +91,7 @@
     "t_spindown = 2500\n",
     "t_spinup = 7500\n",
     "\n",
+    "# defining flow events\n",
     "def flow_fac(t):\n",
     "    if (t <= t_spindown):\n",
     "        return 1.0\n",
@@ -82,15 +104,8 @@
     "    else:\n",
     "        return 1.0\n",
     "\n",
-    "flow_pct = MSRE.add_input(flow_fac, T, max_anchors = 5000, input_tol = 32)"
+    "flow_pct = MSRE.add_input(flow_fac, T, max_anchors = 5000, input_tol = 32)\n",
-   ]
+    "\n",
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
     "# define nodes\n",
     "\n",
     "# radiator\n",
@@ -192,6 +207,13 @@
     "rho.set_drdt(sources = [T_cf1.dydt, T_cg.dydt], coeffs = [a_f,a_g])"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,