From a011e2e0d39ba9a8fcd11d887af92f5bbe1f01de Mon Sep 17 00:00:00 2001 From: Dane Sabo Date: Tue, 8 Oct 2024 16:13:20 -0400 Subject: [PATCH] done w midterm nuce 2100 --- .../NUCE 2100 Midterm 1-checkpoint.ipynb | 180 +++++++++- NUCE_2100/NUCE 2100 Midterm 1.ipynb | 323 +++++++++++++++--- 2 files changed, 439 insertions(+), 64 deletions(-) diff --git a/NUCE_2100/.ipynb_checkpoints/NUCE 2100 Midterm 1-checkpoint.ipynb b/NUCE_2100/.ipynb_checkpoints/NUCE 2100 Midterm 1-checkpoint.ipynb index 4c5ad95..a81321a 100644 --- a/NUCE_2100/.ipynb_checkpoints/NUCE 2100 Midterm 1-checkpoint.ipynb +++ b/NUCE_2100/.ipynb_checkpoints/NUCE 2100 Midterm 1-checkpoint.ipynb @@ -420,10 +420,33 @@ "![Screenshot from 2024-10-07 10-41-57.png](attachment:8e28c362-fbb6-4270-950f-0644c54d7858.png)" ] }, + { + "cell_type": "code", + "execution_count": 9, + "id": "6ba0ed78-d681-49d6-a662-9548abd61e22", + "metadata": {}, + "outputs": [], + "source": [ + "# Part A\n", + "Phi_times_Sigma_f = 3.9e13 #fission/cm^3/s\n", + "E_r = 200 * 1.60218e-13 #J/fission\n", + "a = 40 #cm" + ] + }, + { + "cell_type": "markdown", + "id": "80ce855c-127a-4cdd-93b8-dddb5531c1e6", + "metadata": {}, + "source": [ + "$$\\phi(8) = \\frac{P \\pi}{2a E_r \\Sigma_f} \\cos\\left(\\frac{\\pi 8}{40}\\right)$$\n", + "\n", + "$$\\frac{ \\phi(8) \\Sigma_f E_r 2 a}{\\pi \\cos \\left( \\frac{\\pi 8}{40} \\right)} = P$$" + ] + }, { "cell_type": "code", "execution_count": 10, - "id": "efab76fa-fbc8-4ea4-9d4f-f5790b0cfeb1", + "id": "24dbc2ce-fcf2-49d8-9a01-044c468bc223", "metadata": {}, "outputs": [ { @@ -433,21 +456,72 @@ "\n", "=========FINAL ANSWER=========\n", "Question 6a:\n", - "1.249700e+03 J\n", + "3.933584e+04 W/cm^2\n", "=========FINAL ANSWER=========\n", "\n" ] } ], "source": [ - "# Part A\n", - "F_dot = 3.9e13 #fission/cm^3/s\n", - "E_r = 200 * 1.60218e-13 #J\n", - "#According to INL: https://mooseframework.inl.gov/bison/theory/power_burnup.html\n", - "P_local = F_dot * E_r\n", - "answer_print('Question 6a', f'{P_local:4e} J')\n", + "P = Phi_times_Sigma_f * E_r * 2 * a / np.pi / np.cos(np.pi*8/40)\n", + "answer_print('Question 6a', f'{P:4e} W/cm^2')" + ] + }, + { + "cell_type": "markdown", + "id": "f68df535-4c3a-4e1c-a413-98c8154eb041", + "metadata": {}, + "source": [ + "**Part B**\n", + "$$ \\phi(20) \\Sigma_f = \\frac{P \\pi}{2a E_r} \\cos \\left( \\frac{\\pi}{2} \\right) $$\n", + "$$ \\phi(20) \\Sigma_f = \\frac{P \\pi}{2a E_r} \\times 0 $$\n", "\n", - "# Part B\n" + "\n", + "========FINAL ANSWER==========\n", + "\n", + "$\\phi(20) \\Sigma_f = 0$\n", + "\n", + "========FINAL ANSWER==========\n" + ] + }, + { + "cell_type": "markdown", + "id": "dd015a5c-da4d-446d-81a9-67bcff242a1f", + "metadata": {}, + "source": [ + "**Part C**\n", + "\n", + "$$P(x) = \\phi(x) \\Sigma_f E_r = \\frac{P \\pi}{2a E_r} \\cos \\left( \\frac{\\pi x}{a} \\right) \\times E_r $$\n", + "$$P(x) = \\frac{P \\pi}{2a} \\cos \\left( \\frac{\\pi x}{a} \\right) $$\n", + "\n", + "========FINAL ANSWER==========\n", + "\n", + "$P(x) = \\frac{P \\pi}{2a} \\cos \\left( \\frac{\\pi x}{a} \\right) $\n", + "\n", + "where\n", + "\n", + "$P = 3933.6 \\frac{\\text{W}}{\\text{cm}^2}$\n", + "\n", + "$a = 40 \\text{cm}$\n", + "\n", + "$E_r = 200 \\text{MeV} \\times 1.60218\\times 10^{-13} \\frac{\\text{J}}{\\text{MeV}}$\n", + "\n", + "========FINAL ANSWER==========" + ] + }, + { + "cell_type": "markdown", + "id": "8166199c-3072-429c-85da-4fd93e06bb11", + "metadata": {}, + "source": [ + "**Part D**\n", + "\n", + "\n", + "========FINAL ANSWER==========\n", + "\n", + "I should get the value I obtained in Part A!\n", + "\n", + "========FINAL ANSWER==========" ] }, { @@ -465,7 +539,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 11, "id": "e669dab3-ef9a-460e-8fbc-9a99bbad623b", "metadata": {}, "outputs": [ @@ -522,7 +596,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 12, "id": "f3570a43-0a14-44c4-9237-e3e1f595535d", "metadata": {}, "outputs": [ @@ -535,6 +609,12 @@ "Question 8a:\n", "The atomic density of Pu239 in this reactor is 3.3757e+22 atoms/cm^3.\n", "=========FINAL ANSWER=========\n", + "\n", + "\n", + "=========FINAL ANSWER=========\n", + "Question 8b:\n", + "6.940e-02 1/cm^2\n", + "=========FINAL ANSWER=========\n", "\n" ] } @@ -542,13 +622,83 @@ "source": [ "Pu239_density = 13.4 #g/cm^3\n", "v = 2.88\n", - "Sigma_f = 1.8 #barns\n", - "Sigma_a = 2.1 #barns\n", + "sigma_f = 1.8e-24 #cm^2\n", + "sigma_a = 2.1e-24 #cm^2\n", "D = 1.5 #cm\n", "\n", "# Part A\n", "N_Pu239 = 100/100*Pu239_density*6.0221409e23/Pu239_mass\n", - "answer_print('Question 8a', f'The atomic density of Pu239 in this reactor is {N_Pu239:.4e} atoms/cm^3.')\n" + "answer_print('Question 8a', f'The atomic density of Pu239 in this reactor is {N_Pu239:.4e} atoms/cm^3.')\n", + "\n", + "# Part B\n", + "Sigma_f = sigma_f*N_Pu239 #1/cm\n", + "Sigma_a = sigma_a*N_Pu239 #1/cm\n", + "B_m_squared = (v*Sigma_f - Sigma_a)/D \n", + "answer_print('Question 8b', f'{B_m_squared:.3e} 1/cm^2')" + ] + }, + { + "cell_type": "markdown", + "id": "d1f1ccd1-c3d5-4148-8bdc-98c217239698", + "metadata": {}, + "source": [ + "**Part C:**\n", + "\n", + "For K = 1, $B_g^2 = B_m^2$:\n", + "$$ \\left( \\frac{\\pi}{R} \\right)^2 = \\frac{v \\Sigma_f - \\Sigma_a}{D} $$\n", + "$$ \\left( \\frac{\\pi}{R} \\right) = \\sqrt{ \\frac{v \\Sigma_f - \\Sigma_a}{D} }$$\n", + "$$ R = \\frac{\\pi} {\\sqrt{ \\frac{v \\Sigma_f - \\Sigma_a}{D} }}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "31086745-dd3a-401a-b4f4-a65b4e6214d0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 8c:\n", + "1.192e+01 cm\n", + "=========FINAL ANSWER=========\n", + "\n", + "\n", + "=========FINAL ANSWER=========\n", + "Question 8d:\n", + "9.518e+04 kg\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ + "R = np.pi/(B_m_squared)**(1/2)\n", + "answer_print('Question 8c', f'{R:.3e} cm')\n", + "\n", + "# Part D\n", + "critical_mass = Pu239_density*(4/3*np.pi*R**3)\n", + "answer_print('Question 8d', f'{critical_mass:.3e} kg')" + ] + }, + { + "cell_type": "markdown", + "id": "5e3c047b-ada8-4893-b670-00bca9e02741", + "metadata": {}, + "source": [ + "========FINAL ANSWER==========\n", + "\n", + "**Part E**\n", + "\n", + "If radius decreases:\n", + "1. Mateiral buckling will **stay the same**.\n", + "2. Geometric buckling will **increase**.\n", + "3. Multiplication factor will **decrease**. \n", + "\n", + "========FINAL ANSWER==========" ] }, { @@ -566,7 +716,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 14, "id": "c0c96c53-4ef8-4367-9d7c-0d9688aff15d", "metadata": {}, "outputs": [ diff --git a/NUCE_2100/NUCE 2100 Midterm 1.ipynb b/NUCE_2100/NUCE 2100 Midterm 1.ipynb index 4c5ad95..734ad33 100644 --- a/NUCE_2100/NUCE 2100 Midterm 1.ipynb +++ b/NUCE_2100/NUCE 2100 Midterm 1.ipynb @@ -220,7 +220,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "2f9c5cdb-d0ca-4eb9-9b6f-a1c6617db5d1", + "id": "8321b879-f036-4bf7-a1de-25ae9c496e11", "metadata": {}, "outputs": [ { @@ -232,20 +232,6 @@ "Question 3a:\n", "7.06700e-03 amu\n", "=========FINAL ANSWER=========\n", - "\n", - "\n", - "=========FINAL ANSWER=========\n", - "Question 3b:\n", - "The kinetic energy is 6.58291e+00 MeV. \n", - "This reaction releases energy.\n", - "=========FINAL ANSWER=========\n", - "\n", - "\n", - "=========FINAL ANSWER=========\n", - "Question 3c:\n", - "The difference is significant. Without electrons, the result is 7.60570e+00 MeV. \n", - "There is 15.54% difference between the two answers.\n", - "=========FINAL ANSWER=========\n", "\n" ] } @@ -261,18 +247,62 @@ "reactants = 1*U238_mass + 1*neutron_mass\n", "change_in_mass = reactants - products\n", "\n", - "answer_print('Question 3a', f'{change_in_mass:.5e} amu')\n", - "\n", + "answer_print('Question 3a', f'{change_in_mass:.5e} amu')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "71567a2c-c14b-45f6-88da-d96d51310c7c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 3b:\n", + "The kinetic energy is 6.58291e+00 MeV. \n", + "This reaction releases energy.\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ "# Part B\n", "Q = change_in_mass * 931.5 #MeV\n", - "answer_print('Question 3b', f'The kinetic energy is {Q:.5e} MeV. \\nThis reaction releases energy.')\n", - "\n", + "answer_print('Question 3b', f'The kinetic energy is {Q:.5e} MeV. \\nThis reaction releases energy.')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "63b91372-56d8-4433-9885-1f06a99d5435", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 3c:\n", + "The difference is significant. Without electrons, the result is 7.60570e+00 MeV. \n", + "There is 15.54% difference between the two answers.\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ "# Part C\n", "new_change_in_mass = reactants - 1*Pu239_mass #amu\n", "new_Q = new_change_in_mass * 931.5 #MeV\n", "percent_difference = (new_Q - Q)/Q *100\n", "\n", - "answer_print('Question 3c', f'The difference is significant. Without electrons, the result is {new_Q:.5e} MeV. \\nThere is {percent_difference:.2f}% difference between the two answers.')\n" + "answer_print('Question 3c', f'The difference is significant. Without electrons, the result is {new_Q:.5e} MeV. \\nThere is {percent_difference:.2f}% difference between the two answers.')" ] }, { @@ -290,7 +320,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "id": "8d9faf3b-aac3-4a1f-9d07-464ea77d3290", "metadata": {}, "outputs": [ @@ -356,8 +386,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "2612afc1-e0dc-4078-a792-b83e946af822", + "execution_count": 10, + "id": "b328c58b-948b-4b5d-ae2a-fdd59d77208b", "metadata": {}, "outputs": [ { @@ -371,12 +401,6 @@ "Beryllium-9 Binding Energy: 8.4417e+03MeV\n", "Helium-4 Binding Energy: 2.8296e+01MeV\n", "=========FINAL ANSWER=========\n", - "\n", - "\n", - "=========FINAL ANSWER=========\n", - "Question 5b:\n", - "8.3814e+03 MeV\n", - "=========FINAL ANSWER=========\n", "\n" ] } @@ -397,14 +421,35 @@ "answer_print('Question 5a',\n", " f'Lithium-6 Binding Energy: {binding_energy(3, 3, Li6_mass):.4e} MeV\\n'+\n", " f'Beryllium-9 Binding Energy: {binding_energy(4, 5, Be9_mass):.4e}MeV\\n'+\n", - " f'Helium-4 Binding Energy: {binding_energy(2, 2, He4_mass):.4e}MeV')\n", - "\n", + " f'Helium-4 Binding Energy: {binding_energy(2, 2, He4_mass):.4e}MeV')" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "cc50b7a9-75ce-4095-b0c7-d35fad787c10", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 5b:\n", + "8.3814e+03 MeV\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ "# Part B\n", "reactants = binding_energy(3, 3, Li6_mass) + binding_energy(2, 2, He4_mass)\n", "products = binding_energy(4, 5, Be9_mass)\n", "Q = products - reactants\n", "\n", - "answer_print('Question 5b', f'{Q:.4e} MeV')\n" + "answer_print('Question 5b', f'{Q:.4e} MeV')" ] }, { @@ -422,8 +467,31 @@ }, { "cell_type": "code", - "execution_count": 10, - "id": "efab76fa-fbc8-4ea4-9d4f-f5790b0cfeb1", + "execution_count": 12, + "id": "6ba0ed78-d681-49d6-a662-9548abd61e22", + "metadata": {}, + "outputs": [], + "source": [ + "# Part A\n", + "Phi_times_Sigma_f = 3.9e13 #fission/cm^3/s\n", + "E_r = 200 * 1.60218e-13 #J/fission\n", + "a = 40 #cm" + ] + }, + { + "cell_type": "markdown", + "id": "80ce855c-127a-4cdd-93b8-dddb5531c1e6", + "metadata": {}, + "source": [ + "$$\\phi(8) = \\frac{P \\pi}{2a E_r \\Sigma_f} \\cos\\left(\\frac{\\pi 8}{40}\\right)$$\n", + "\n", + "$$\\frac{ \\phi(8) \\Sigma_f E_r 2 a}{\\pi \\cos \\left( \\frac{\\pi 8}{40} \\right)} = P$$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "24dbc2ce-fcf2-49d8-9a01-044c468bc223", "metadata": {}, "outputs": [ { @@ -433,21 +501,72 @@ "\n", "=========FINAL ANSWER=========\n", "Question 6a:\n", - "1.249700e+03 J\n", + "3.933584e+04 W/cm^2\n", "=========FINAL ANSWER=========\n", "\n" ] } ], "source": [ - "# Part A\n", - "F_dot = 3.9e13 #fission/cm^3/s\n", - "E_r = 200 * 1.60218e-13 #J\n", - "#According to INL: https://mooseframework.inl.gov/bison/theory/power_burnup.html\n", - "P_local = F_dot * E_r\n", - "answer_print('Question 6a', f'{P_local:4e} J')\n", + "P = Phi_times_Sigma_f * E_r * 2 * a / np.pi / np.cos(np.pi*8/40)\n", + "answer_print('Question 6a', f'{P:4e} W/cm^2')" + ] + }, + { + "cell_type": "markdown", + "id": "f68df535-4c3a-4e1c-a413-98c8154eb041", + "metadata": {}, + "source": [ + "**Part B**\n", + "$$ \\phi(20) \\Sigma_f = \\frac{P \\pi}{2a E_r} \\cos \\left( \\frac{\\pi}{2} \\right) $$\n", + "$$ \\phi(20) \\Sigma_f = \\frac{P \\pi}{2a E_r} \\times 0 $$\n", "\n", - "# Part B\n" + "\n", + "========FINAL ANSWER==========\n", + "\n", + "$\\phi(20) \\Sigma_f = 0$\n", + "\n", + "========FINAL ANSWER==========\n" + ] + }, + { + "cell_type": "markdown", + "id": "dd015a5c-da4d-446d-81a9-67bcff242a1f", + "metadata": {}, + "source": [ + "**Part C**\n", + "\n", + "$$P(x) = \\phi(x) \\Sigma_f E_r = \\frac{P \\pi}{2a E_r} \\cos \\left( \\frac{\\pi x}{a} \\right) \\times E_r $$\n", + "$$P(x) = \\frac{P \\pi}{2a} \\cos \\left( \\frac{\\pi x}{a} \\right) $$\n", + "\n", + "========FINAL ANSWER==========\n", + "\n", + "$P(x) = \\frac{P \\pi}{2a} \\cos \\left( \\frac{\\pi x}{a} \\right)$\n", + "\n", + "where\n", + "\n", + "$P = 3933.6 \\frac{\\text{W}}{\\text{cm}^2}$\n", + "\n", + "$a = 40 \\text{cm}$\n", + "\n", + "$E_r = 200 \\text{MeV} \\times 1.60218\\times 10^{-13} \\frac{\\text{J}}{\\text{MeV}}$\n", + "\n", + "========FINAL ANSWER==========" + ] + }, + { + "cell_type": "markdown", + "id": "8166199c-3072-429c-85da-4fd93e06bb11", + "metadata": {}, + "source": [ + "**Part D**\n", + "\n", + "\n", + "========FINAL ANSWER==========\n", + "\n", + "I should get the value I obtained in Part A!\n", + "\n", + "========FINAL ANSWER==========" ] }, { @@ -465,7 +584,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 14, "id": "e669dab3-ef9a-460e-8fbc-9a99bbad623b", "metadata": {}, "outputs": [ @@ -522,8 +641,8 @@ }, { "cell_type": "code", - "execution_count": 29, - "id": "f3570a43-0a14-44c4-9237-e3e1f595535d", + "execution_count": 15, + "id": "3ab2c1cd-b8d0-488a-8e5a-c90e1efddeec", "metadata": {}, "outputs": [ { @@ -542,13 +661,119 @@ "source": [ "Pu239_density = 13.4 #g/cm^3\n", "v = 2.88\n", - "Sigma_f = 1.8 #barns\n", - "Sigma_a = 2.1 #barns\n", + "sigma_f = 1.8e-24 #cm^2\n", + "sigma_a = 2.1e-24 #cm^2\n", "D = 1.5 #cm\n", "\n", "# Part A\n", "N_Pu239 = 100/100*Pu239_density*6.0221409e23/Pu239_mass\n", - "answer_print('Question 8a', f'The atomic density of Pu239 in this reactor is {N_Pu239:.4e} atoms/cm^3.')\n" + "answer_print('Question 8a', f'The atomic density of Pu239 in this reactor is {N_Pu239:.4e} atoms/cm^3.')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "bd9ae0ce-d115-4842-8bb5-b4e049f74fd3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 8b:\n", + "6.940e-02 1/cm^2\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ + "# Part B\n", + "Sigma_f = sigma_f*N_Pu239 #1/cm\n", + "Sigma_a = sigma_a*N_Pu239 #1/cm\n", + "B_m_squared = (v*Sigma_f - Sigma_a)/D \n", + "answer_print('Question 8b', f'{B_m_squared:.3e} 1/cm^2')" + ] + }, + { + "cell_type": "markdown", + "id": "d1f1ccd1-c3d5-4148-8bdc-98c217239698", + "metadata": {}, + "source": [ + "**Part C:**\n", + "\n", + "For K = 1, $B_g^2 = B_m^2$:\n", + "$$ \\left( \\frac{\\pi}{R} \\right)^2 = \\frac{v \\Sigma_f - \\Sigma_a}{D} $$\n", + "$$ \\left( \\frac{\\pi}{R} \\right) = \\sqrt{ \\frac{v \\Sigma_f - \\Sigma_a}{D} }$$\n", + "$$ R = \\frac{\\pi} {\\sqrt{ \\frac{v \\Sigma_f - \\Sigma_a}{D} }}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "4fd471e0-69f4-42d3-a0d1-0e2c08ac7c4d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 8c:\n", + "1.192e+01 cm\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ + "R = np.pi/(B_m_squared)**(1/2)\n", + "answer_print('Question 8c', f'{R:.3e} cm')" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "fe2be15c-3e0f-45ce-9d4d-183aff3b2754", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "=========FINAL ANSWER=========\n", + "Question 8d:\n", + "9.518e+04 kg\n", + "=========FINAL ANSWER=========\n", + "\n" + ] + } + ], + "source": [ + "# Part D\n", + "critical_mass = Pu239_density*(4/3*np.pi*R**3)\n", + "answer_print('Question 8d', f'{critical_mass:.3e} kg')" + ] + }, + { + "cell_type": "markdown", + "id": "5e3c047b-ada8-4893-b670-00bca9e02741", + "metadata": {}, + "source": [ + "**Part E**\n", + "\n", + "========FINAL ANSWER==========\n", + "\n", + "If radius decreases:\n", + "1. Mateiral buckling will **stay the same**.\n", + "2. Geometric buckling will **increase**.\n", + "3. Multiplication factor will **decrease**. \n", + "\n", + "========FINAL ANSWER==========" ] }, { @@ -566,7 +791,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "id": "c0c96c53-4ef8-4367-9d7c-0d9688aff15d", "metadata": {}, "outputs": [