{ "cells": [ { "cell_type": "markdown", "id": "82e7156b-15bb-4000-928d-a904e76fe1fe", "metadata": {}, "source": [ "Homework 7 - NUCE 2100\n", "\n", "**Dane Sabo**\n", "\n", "*November 5th, 2024*" ] }, { "cell_type": "code", "execution_count": 1, "id": "af61cdf6-cb10-43e3-81b5-703acbc893a0", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import sympy as sm\n", "\n", "def answer_print(question,string):\n", " print('\\n=========FINAL ANSWER=========')\n", " print(question+':')\n", " print(string)\n", " print('=========FINAL ANSWER=========\\n')" ] }, { "cell_type": "markdown", "id": "dd8f8915-17e4-414a-8465-b8b66d66c673", "metadata": {}, "source": [ "# Problem 1" ] }, { "attachments": { "157098bb-2458-4cb5-87e1-6691918ea097.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "85659983-530e-4882-bf0b-13c15a1b05b6", "metadata": {}, "source": [ "![image.png](attachment:157098bb-2458-4cb5-87e1-6691918ea097.png)" ] }, { "cell_type": "code", "execution_count": 2, "id": "517f0fc3-ddd4-4713-adf7-c30d0649b851", "metadata": {}, "outputs": [], "source": [ "# Given Information\n", "n = 0.03\n", "D = 0.37/12 #in to ft\n", "t_cladding = 0.026/12 #in to ft\n", "t_gap = 2e-3/12 #in to ft\n", "q_prime = 13.5*3.412e3 #kW/ft to BTU/hr/ft\n", "T_bulk = 580 #F\n", "k_fuel = 1.2 #BTU/hr/ft/F\n", "k_cladding = 10.5 #BTU/hr/ft/F\n", "k_gap = 0.19 #BTU/hr/ft/F\n", "h = 6500 #BTU/hr/ft^2/F" ] }, { "cell_type": "code", "execution_count": 3, "id": "15a7a1c5-f424-46d9-8c59-2e9a6e6243d7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "=========FINAL ANSWER=========\n", "Problem 1:\n", " The centerline temperature is 4095.69 F\n", "=========FINAL ANSWER=========\n", "\n" ] } ], "source": [ "#Assuming constant heat generation and fuel thermal conductivity:\n", "R_cladding_outer = D/2 + t_gap + t_cladding #ft\n", "R_cladding_inner = D/2 + t_gap #ft\n", "R_pellet = D/2 #ft\n", "h_gap = k_gap / (R_cladding_inner - D/2 + 14.4e-6) #BTU/hr/ft^2/F\n", "\n", "#Find f\n", "f = 0.96 #From slides\n", "\n", "\n", "T_max = f*q_prime*(1/2/np.pi/R_cladding_outer/h + \\\n", " np.log(R_cladding_outer/R_cladding_inner)/2/np.pi/k_cladding + \\\n", " 1/2/np.pi/R_pellet/h_gap + \\\n", " 1/4/np.pi/k_fuel) \\\n", "+ T_bulk\n", "\n", "answer_print('Problem 1', f' The centerline temperature is {T_max:.2f} F')" ] }, { "attachments": { "650c587e-4e69-4294-8fa1-5139a4365804.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "0e7e0092-2b89-466f-85fb-09862610a0f2", "metadata": {}, "source": [ "# Problem 2\n", "![image.png](attachment:650c587e-4e69-4294-8fa1-5139a4365804.png)" ] }, { "cell_type": "code", "execution_count": 4, "id": "c7a6e14a-5694-4aa8-bd44-5b1ea1c095a8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The surface temperature is 628.50 C\n" ] } ], "source": [ "#First, let's get to the temperature at the fuel pellet surface\n", "\n", "T_surf = f*q_prime*(1/2/np.pi/R_cladding_outer/h +\\\n", " np.log(R_cladding_outer/R_cladding_inner)/2/np.pi/k_cladding +\\\n", " 1/2/np.pi/R_pellet/h_gap) +\\\n", "T_bulk\n", "\n", "print(f'The surface temperature is {(T_surf-32)*5/9:.2f} C')" ] }, { "cell_type": "markdown", "id": "a7a4b53f-d223-46f6-82e4-468c9c664e34", "metadata": {}, "source": [ "$$ \\int_{T_{surf}}^{T_{max}} k_f dT = \\frac{f q'}{4 \\pi} $$\n", "\n", "$$ \\int_{0}^{T_{max}} k_f dT - \\int_0^{T_{surf}} k_f dT = \\frac{f q'}{4 \\pi} $$\n", "\n", "$$ \\int_{0}^{T_{max}} k_f dT = \\frac{f q'}{4 \\pi} + \\int_0^{T_{surf}} k_f dT$$" ] }, { "cell_type": "code", "execution_count": 5, "id": "2db67093-bec9-495d-8250-9b401e44d2b1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The Lyon integral value for the maximum temperature is 98 W/cm\n", "\n", "=========FINAL ANSWER=========\n", "Problem 2:\n", "The max temperature is approximately 5072 F\n", "=========FINAL ANSWER=========\n", "\n" ] } ], "source": [ "#Lyon's Integral Values pulled from the slides given T_surf\n", "lyon_surf = 37.5*57.818 #W/cm -> BTU/hr/ft\n", "lyon_max = f*q_prime/4/np.pi + lyon_surf\n", "print(f'The Lyon integral value for the maximum temperature is {lyon_max/57.818:.0f} W/cm')\n", "\n", "answer_print('Problem 2', f'The max temperature is approximately {2800*9/5+32:.0f} F') #From slides, converted to F" ] }, { "attachments": { "802911f2-5ab1-4743-8183-a4c3cf5e52fc.png": { "image/png": "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" } }, "cell_type": "markdown", "id": "db5b8c2b-fef7-4704-b435-453cd75a1191", "metadata": {}, "source": [ "# Problem 3\n", "![image.png](attachment:802911f2-5ab1-4743-8183-a4c3cf5e52fc.png)" ] }, { "cell_type": "code", "execution_count": 6, "id": "196cdf97-6ef8-467b-8f7e-564db35115c9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The surface temperature is 405.09 C\n", "The lyon integral value for the maximum temperature is 86 W/cm\n", "\n", "=========FINAL ANSWER=========\n", "Problem 3:\n", "The max temperature is approximately 4667 F\n", "=========FINAL ANSWER=========\n", "\n" ] } ], "source": [ "h_gap_closed = 0.68*1e3 + k_gap/14.4e-6\n", "\n", "T_surf = f*q_prime*(1/2/np.pi/R_cladding_outer/h +\\\n", " np.log(R_cladding_outer/R_cladding_inner)/2/np.pi/k_cladding +\\\n", " 1/2/np.pi/R_pellet/h_gap_closed) +\\\n", "T_bulk\n", "\n", "print(f'The surface temperature is {(T_surf-32)*5/9:.2f} C')\n", "\n", "lyon_surf = 24.75*57.818 #W/cm -> BTU/hr/ft\n", "lyon_max = f*q_prime/4/np.pi + lyon_surf\n", "print(f'The lyon integral value for the maximum temperature is {lyon_max/57.818:.0f} W/cm')\n", "\n", "answer_print('Problem 3', f'The max temperature is approximately {2575*9/5+32:.0f} F')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }