HW9 NUCE 2100
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@ -44,7 +44,7 @@
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"cell_type": "code",
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"execution_count": 26,
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"execution_count": 2,
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"id": "3aec147b-37b2-4938-9f33-db77c6836747",
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"metadata": {},
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"outputs": [],
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@ -56,6 +56,7 @@
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"C_p = 1.322 #BTU/lbm/F\n",
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"k = 0.3188 #BTU/hr/ft/F\n",
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"mu = 0.2188 #lbm/ft/hr\n",
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"mu = mu/60/60 #lbm/ft/s\n",
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"\n",
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"d_fuel = 0.422 #in\n",
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"pitch_rod = 0.563 #in\n",
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@ -98,7 +99,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"execution_count": 3,
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"id": "27fe2439-e64e-48e7-a62b-62db8e37f4ca",
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"metadata": {},
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"outputs": [],
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@ -108,7 +109,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"execution_count": 4,
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"id": "9acf4d43-b27d-4019-9b13-b0e3539518bf",
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"metadata": {},
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"outputs": [
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@ -121,7 +122,7 @@
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"Eq(0, g*(-z_1 + z_2)/g_c + w_loss + (-P_1 + P_2)/rho + (-V_1**2/2 + V_2**2/2)/g_c)"
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]
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},
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"execution_count": 28,
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -151,7 +152,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 32,
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"execution_count": 5,
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"id": "06dd7077-b3a9-479b-a3fb-81b82cf7f4a0",
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"metadata": {},
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"outputs": [
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@ -176,7 +177,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 33,
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"execution_count": 6,
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"id": "7abbca89-f46b-407d-9e47-d8c4ceb1de83",
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"metadata": {},
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"outputs": [
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@ -184,7 +185,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Reynolds Number in Nozzle: 2.368e+01\n"
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"Reynolds Number in Nozzle: 8.525e+04\n"
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]
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}
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],
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@ -203,7 +204,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 34,
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"execution_count": 7,
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"id": "2fe8daf0-d0c3-47ef-996d-9178ddc29902",
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"metadata": {},
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"outputs": [
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@ -211,7 +212,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Moody Friction Factor (Nozzle): 1.432e-01\n"
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"Moody Friction Factor (Nozzle): 1.849e-02\n"
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]
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}
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],
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@ -230,7 +231,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"execution_count": 8,
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"id": "35e3e19b-2bc0-4f59-9452-9b78506eab7d",
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"metadata": {},
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"outputs": [
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@ -238,7 +239,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Lost work is 5.071e-06 (lbf-ft/lbm)\n"
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"Lost work is 5.058e-06 (lbf-ft/lbm)\n"
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]
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}
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],
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@ -257,7 +258,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"execution_count": 9,
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"id": "134f9720-57e3-4038-87bc-c427fe27eafc",
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"metadata": {},
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"outputs": [
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@ -270,7 +271,7 @@
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"Eq(-P_1 + P_2, rho*(V_1**2 - V_2**2 + 2*g*z_1 - 2*g*z_2 - 2*g_c*w_loss)/(2*g_c))"
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]
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},
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"execution_count": 36,
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -281,7 +282,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"execution_count": 10,
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"id": "7cf0e686-49d3-4c65-a637-4c5244274c22",
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"metadata": {},
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"outputs": [
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@ -289,14 +290,17 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The pressure drop from the inlet is -1.897e+02 psia\n"
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"The pressure drop from the inlet is -1.317e+00 psia\n"
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]
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}
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],
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"source": [
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"delta_P_inlet = rho_value*((G_nozzle/rho_value)**2 - (G/rho_value)**2 + 2*g_value*(-0.5) - 2*g_c_value*w_loss_12) \\\n",
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" /2/g_c_value\n",
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"print(f'The pressure drop from the inlet is {delta_P_inlet:.3e} psia')"
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" /2/g_c_value #lb/ft^2\n",
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"\n",
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"lb_ft2_to_psi = 1/12/12\n",
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"\n",
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"print(f'The pressure drop from the inlet is {delta_P_inlet*lb_ft2_to_psi:.3e} psia')\n"
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]
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},
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{
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@ -309,7 +313,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"execution_count": 11,
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"id": "f27293d3-f93a-43e9-81ed-e89510c7e15d",
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"metadata": {},
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"outputs": [],
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@ -319,7 +323,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 41,
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"execution_count": 12,
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"id": "48a692db-07f3-47cc-a678-143c36d5ba53",
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"metadata": {},
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"outputs": [
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@ -332,7 +336,7 @@
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"Eq(0, g*(-z_2 + z_3)/g_c + w_loss_23 + (-P_2 + P_3)/rho + (-V_2**2/2 + V_3**2/2)/g_c)"
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]
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},
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"execution_count": 41,
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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@ -342,13 +346,311 @@
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"P23"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f89bdf25-e3db-4f53-b183-96fc7b1c80c8",
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"metadata": {},
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"source": [
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"But we know the velocity is just about constant at points 2 and 3:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "1b084d11-2065-4461-8ef7-1004c095132b",
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"execution_count": 13,
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"id": "2597141b-2f11-4590-95ff-6e6067f2290a",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 0 = \\frac{g \\left(- z_{2} + z_{3}\\right)}{g_{c}} + w_{loss 23} + \\frac{- P_{2} + P_{3}}{\\rho}$"
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],
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"text/plain": [
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"Eq(0, g*(-z_2 + z_3)/g_c + w_loss_23 + (-P_2 + P_3)/rho)"
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]
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},
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"execution_count": 13,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"P23 = P23.subs({V_2: V_3})\n",
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"P23"
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]
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},
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{
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"cell_type": "markdown",
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"id": "49253657-a0e7-42e2-8f97-7ade8a1a463d",
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"metadata": {},
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"source": [
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"We know all of these terms except for the loss. In this section, there are friction losses from the rods, and form losses from the spacer grids."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"id": "c84ab700-ddf0-459b-b4e1-32feda6a917a",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Reynolds Nmber in rodded area: 3.142e+06\n",
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"Moody Friction Factor (Rodded): 9.500e-03\n",
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"Loss in rodded section from friction: 1.547e+00 (lbf-ft/lbm)\n",
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"Loss in rodded section from form: 6.116e+01 (lbf-ft/lbm)\n"
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]
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}
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],
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"source": [
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"#Friction Losses\n",
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"Re_rodded = G*D_rodded/mu\n",
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"print(f'Reynolds Nmber in rodded area: {Re_rodded:.3e}')\n",
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"\n",
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"#Friction Factor Taken From Chart (Smooth Pipe)\n",
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"f_m = 0.0095\n",
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"print(f'Moody Friction Factor (Rodded): {f_m:.3e}')\n",
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"\n",
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"friction_loss = f_m*(12)/D_rodded*(G/rho_value)**2/2/g_c_value\n",
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"print(f'Loss in rodded section from friction: {friction_loss:.3e} (lbf-ft/lbm)')\n",
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"\n",
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"#Finding Form Losses\n",
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"#Find K for egg-crate style\n",
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"k_egg = 1.4*c_v*(epsilon_egg+0)**2\n",
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"\n",
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"#Find K for mixing-vane style\n",
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"k_mix = 1.4*c_v*(epsilon_mix_grid + epsilon_mix_vane)**2\n",
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"\n",
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"#Calculate form losses\n",
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"form_loss = (2*k_egg + 6*k_mix)*(G/rho_value)**2/2/g_c_value\n",
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"print(f'Loss in rodded section from form: {form_loss:.3e} (lbf-ft/lbm)')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "715fb35e-e211-4e42-9f91-5148d63d5380",
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"metadata": {},
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"source": [
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"Now we can calculate the pressure drop in the rodded section:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "ac4de5cf-7fde-4cb5-abba-6c2102221f2f",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle - P_{2} + P_{3} = \\frac{\\rho \\left(g z_{2} - g z_{3} - g_{c} w_{loss 23}\\right)}{g_{c}}$"
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],
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"text/plain": [
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"Eq(-P_2 + P_3, rho*(g*z_2 - g*z_3 - g_c*w_loss_23)/g_c)"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sm.Eq(P_3-P_2, sm.solve(P23,P_3-P_2)[0])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "033a4399-abff-474e-9558-17e0ec43ff5e",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"The pressure drop in the rodded section is -2.325e+01 psia\n"
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]
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}
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],
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"source": [
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"delta_p_rodded = rho_value*(g_value*(-12))/g_c_value - rho_value*(form_loss+friction_loss) #lb/ft^2\n",
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"print(f'The pressure drop in the rodded section is {delta_p_rodded*lb_ft2_to_psi:.3e} psia')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7548d77c-3f3a-4895-85f2-4b89cbf82e83",
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"metadata": {},
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"source": [
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"And now we find the pressure drop in the outlet nozzle:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"id": "1d8fa9b6-ce56-43c6-be42-12f487c3942c",
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"metadata": {},
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"outputs": [],
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"source": []
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"source": [
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"V_3, V_4, g_c, g, z_3, z_4, P_3, P_4, rho, w_loss = sm.symbols('V_3, V_4, g_c, g, z_3, z_4, P_4, P_3, rho, w_loss')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "4a81f970-a5cf-4646-8745-b0aae22bb685",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle 0 = \\frac{g \\left(- z_{3} + z_{4}\\right)}{g_{c}} + w_{loss} + \\frac{P_{3} - P_{4}}{\\rho} + \\frac{- \\frac{V_{3}^{2}}{2} + \\frac{V_{4}^{2}}{2}}{g_{c}}$"
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],
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"text/plain": [
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"Eq(0, g*(-z_3 + z_4)/g_c + w_loss + (P_3 - P_4)/rho + (-V_3**2/2 + V_4**2/2)/g_c)"
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"P34 = sm.Eq(0, (V_4**2 - V_3**2)/2/g_c + g/g_c*(z_4 - z_3) + (P_4 - P_3)/rho + w_loss)\n",
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"P34"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"id": "a057320a-e37e-4afa-9069-389ed0377bb8",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Moody Friction Factor (Nozzle): 1.849e-02\n"
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]
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}
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],
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"source": [
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"f_m = 0.316*Re_nozzle**(-0.25)\n",
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"print(f'Moody Friction Factor (Nozzle): {f_m:.3e}')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "44f14409-0134-48ea-a361-77ae52241599",
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"metadata": {},
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"source": [
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"The outlet nozzle has very similar lost work as the inlet nozzle, except for a form factor difference:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "1a926053-b6d4-4267-bf80-b2c7c6f8877c",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Lost work is 4.047e-06 (lbf-ft/lbm)\n"
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]
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}
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],
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"source": [
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"w_loss_34 = f_m*(0.5)/D_nozzle*(G_nozzle/rho_value)**2/2/g_c_value + k_exit*(G_nozzle/rho_value)**2/2/g_c_value #lbf-ft/lbm\n",
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"print(f'Lost work is {w_loss_34:.3e} (lbf-ft/lbm)')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "08e477a6-460f-432a-ae65-7e4036b7ac70",
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"metadata": {},
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"source": [
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"And now we can find the pressure loss of the whole inlet nozzle:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "85611fe7-0749-4090-a532-cd1eba07a715",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\displaystyle P_{3} - P_{4} = \\frac{\\rho \\left(V_{3}^{2} - V_{4}^{2} + 2 g z_{3} - 2 g z_{4} - 2 g_{c} w_{loss}\\right)}{2 g_{c}}$"
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],
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"text/plain": [
|
||||
"Eq(P_3 - P_4, rho*(V_3**2 - V_4**2 + 2*g*z_3 - 2*g*z_4 - 2*g_c*w_loss)/(2*g_c))"
|
||||
]
|
||||
},
|
||||
"execution_count": 21,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"sm.Eq(P_4-P_3,sm.solve(P34,P_4-P_3)[0])"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"id": "4a3b7a81-1644-4f5b-bd3b-b4dd77a6ae00",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"The pressure drop from the outlet is 1.006e+00 psia\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"delta_P_outlet = rho_value*((G/rho_value)**2 - (G_nozzle/rho_value)**2 + 2*g_value*(-0.5) - 2*g_c_value*w_loss_34) \\\n",
|
||||
" /2/g_c_value #lb/ft^2\n",
|
||||
"print(f'The pressure drop from the outlet is {delta_P_outlet*lb_ft2_to_psi:.3e} psia')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "f16b4f27-acb0-40e9-868a-be7c19c33d93",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We add these pressure changes together to get the total pressure drop across the reactor:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"id": "1145f10a-cffc-4453-9beb-6cbc43335427",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"Problem 1::\n",
|
||||
"The total pressure change from point 1 to 4 is -2.356e+01 psia\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"Delta_P = delta_P_inlet + delta_p_rodded + delta_P_outlet #lb/ft^2\n",
|
||||
"answer_print('Problem 1:',f'The total pressure change from point 1 to 4 is {Delta_P*lb_ft2_to_psi:.3e} psia')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
@ -362,6 +664,64 @@
|
||||
"source": [
|
||||
""
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"id": "4dd972ef-38b7-4746-9f8a-8eb63ed7ec69",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"2a:\n",
|
||||
"1.414e+4 W/ft\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Find Thermal Power Ouput\n",
|
||||
"Q = 90e6/0.303 #W\n",
|
||||
"\n",
|
||||
"#Find power per rod\n",
|
||||
"q = Q/9e3 #W/(rod)\n",
|
||||
"\n",
|
||||
"#Set up equation to find q_prime_max\n",
|
||||
"z, q_prime_max = sm.symbols('z, q_prime_max')\n",
|
||||
"q_balance = sm.Eq(q, sm.integrate(q_prime_max*z**2/16, (z, 0, 4)) + (q_prime_max*2)/2)\n",
|
||||
"q_prime_max_value = sm.solve(q_balance, q_prime_max)\n",
|
||||
"\n",
|
||||
"answer_print('2a', f'{q_prime_max_value[0]:.3e} W/ft')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"id": "b8e4782c-98a5-4558-96a3-eae23fee99ca",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"2b:\n",
|
||||
"2.571e+0\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Calculate axial peaking factor:\n",
|
||||
"answer_print('2b', f'{q_prime_max_value[0]/(q/6):.3e}')"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
||||
@ -44,7 +44,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 26,
|
||||
"execution_count": 2,
|
||||
"id": "3aec147b-37b2-4938-9f33-db77c6836747",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
@ -56,6 +56,7 @@
|
||||
"C_p = 1.322 #BTU/lbm/F\n",
|
||||
"k = 0.3188 #BTU/hr/ft/F\n",
|
||||
"mu = 0.2188 #lbm/ft/hr\n",
|
||||
"mu = mu/60/60 #lbm/ft/s\n",
|
||||
"\n",
|
||||
"d_fuel = 0.422 #in\n",
|
||||
"pitch_rod = 0.563 #in\n",
|
||||
@ -98,7 +99,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 27,
|
||||
"execution_count": 3,
|
||||
"id": "27fe2439-e64e-48e7-a62b-62db8e37f4ca",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
@ -108,7 +109,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"execution_count": 4,
|
||||
"id": "9acf4d43-b27d-4019-9b13-b0e3539518bf",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -121,7 +122,7 @@
|
||||
"Eq(0, g*(-z_1 + z_2)/g_c + w_loss + (-P_1 + P_2)/rho + (-V_1**2/2 + V_2**2/2)/g_c)"
|
||||
]
|
||||
},
|
||||
"execution_count": 28,
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@ -151,7 +152,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"execution_count": 5,
|
||||
"id": "06dd7077-b3a9-479b-a3fb-81b82cf7f4a0",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -176,7 +177,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"execution_count": 6,
|
||||
"id": "7abbca89-f46b-407d-9e47-d8c4ceb1de83",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -184,7 +185,7 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Reynolds Number in Nozzle: 2.368e+01\n"
|
||||
"Reynolds Number in Nozzle: 8.525e+04\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@ -203,7 +204,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"execution_count": 7,
|
||||
"id": "2fe8daf0-d0c3-47ef-996d-9178ddc29902",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -211,7 +212,7 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Moody Friction Factor (Nozzle): 1.432e-01\n"
|
||||
"Moody Friction Factor (Nozzle): 1.849e-02\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@ -230,7 +231,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 35,
|
||||
"execution_count": 8,
|
||||
"id": "35e3e19b-2bc0-4f59-9452-9b78506eab7d",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -238,7 +239,7 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Lost work is 5.071e-06 (lbf-ft/lbm)\n"
|
||||
"Lost work is 5.058e-06 (lbf-ft/lbm)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@ -257,7 +258,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 36,
|
||||
"execution_count": 9,
|
||||
"id": "134f9720-57e3-4038-87bc-c427fe27eafc",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -270,7 +271,7 @@
|
||||
"Eq(-P_1 + P_2, rho*(V_1**2 - V_2**2 + 2*g*z_1 - 2*g*z_2 - 2*g_c*w_loss)/(2*g_c))"
|
||||
]
|
||||
},
|
||||
"execution_count": 36,
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@ -281,7 +282,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"execution_count": 10,
|
||||
"id": "7cf0e686-49d3-4c65-a637-4c5244274c22",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -289,14 +290,17 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"The pressure drop from the inlet is -1.897e+02 psia\n"
|
||||
"The pressure drop from the inlet is -1.317e+00 psia\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"delta_P_inlet = rho_value*((G_nozzle/rho_value)**2 - (G/rho_value)**2 + 2*g_value*(-0.5) - 2*g_c_value*w_loss_12) \\\n",
|
||||
" /2/g_c_value\n",
|
||||
"print(f'The pressure drop from the inlet is {delta_P_inlet:.3e} psia')"
|
||||
" /2/g_c_value #lb/ft^2\n",
|
||||
"\n",
|
||||
"lb_ft2_to_psi = 1/12/12\n",
|
||||
"\n",
|
||||
"print(f'The pressure drop from the inlet is {delta_P_inlet*lb_ft2_to_psi:.3e} psia')\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@ -309,7 +313,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 40,
|
||||
"execution_count": 11,
|
||||
"id": "f27293d3-f93a-43e9-81ed-e89510c7e15d",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
@ -319,7 +323,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 41,
|
||||
"execution_count": 12,
|
||||
"id": "48a692db-07f3-47cc-a678-143c36d5ba53",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
@ -332,7 +336,7 @@
|
||||
"Eq(0, g*(-z_2 + z_3)/g_c + w_loss_23 + (-P_2 + P_3)/rho + (-V_2**2/2 + V_3**2/2)/g_c)"
|
||||
]
|
||||
},
|
||||
"execution_count": 41,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@ -342,13 +346,311 @@
|
||||
"P23"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "f89bdf25-e3db-4f53-b183-96fc7b1c80c8",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"But we know the velocity is just about constant at points 2 and 3:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "1b084d11-2065-4461-8ef7-1004c095132b",
|
||||
"execution_count": 13,
|
||||
"id": "2597141b-2f11-4590-95ff-6e6067f2290a",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/latex": [
|
||||
"$\\displaystyle 0 = \\frac{g \\left(- z_{2} + z_{3}\\right)}{g_{c}} + w_{loss 23} + \\frac{- P_{2} + P_{3}}{\\rho}$"
|
||||
],
|
||||
"text/plain": [
|
||||
"Eq(0, g*(-z_2 + z_3)/g_c + w_loss_23 + (-P_2 + P_3)/rho)"
|
||||
]
|
||||
},
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"P23 = P23.subs({V_2: V_3})\n",
|
||||
"P23"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "49253657-a0e7-42e2-8f97-7ade8a1a463d",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We know all of these terms except for the loss. In this section, there are friction losses from the rods, and form losses from the spacer grids."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"id": "c84ab700-ddf0-459b-b4e1-32feda6a917a",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Reynolds Nmber in rodded area: 3.142e+06\n",
|
||||
"Moody Friction Factor (Rodded): 9.500e-03\n",
|
||||
"Loss in rodded section from friction: 1.547e+00 (lbf-ft/lbm)\n",
|
||||
"Loss in rodded section from form: 6.116e+01 (lbf-ft/lbm)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Friction Losses\n",
|
||||
"Re_rodded = G*D_rodded/mu\n",
|
||||
"print(f'Reynolds Nmber in rodded area: {Re_rodded:.3e}')\n",
|
||||
"\n",
|
||||
"#Friction Factor Taken From Chart (Smooth Pipe)\n",
|
||||
"f_m = 0.0095\n",
|
||||
"print(f'Moody Friction Factor (Rodded): {f_m:.3e}')\n",
|
||||
"\n",
|
||||
"friction_loss = f_m*(12)/D_rodded*(G/rho_value)**2/2/g_c_value\n",
|
||||
"print(f'Loss in rodded section from friction: {friction_loss:.3e} (lbf-ft/lbm)')\n",
|
||||
"\n",
|
||||
"#Finding Form Losses\n",
|
||||
"#Find K for egg-crate style\n",
|
||||
"k_egg = 1.4*c_v*(epsilon_egg+0)**2\n",
|
||||
"\n",
|
||||
"#Find K for mixing-vane style\n",
|
||||
"k_mix = 1.4*c_v*(epsilon_mix_grid + epsilon_mix_vane)**2\n",
|
||||
"\n",
|
||||
"#Calculate form losses\n",
|
||||
"form_loss = (2*k_egg + 6*k_mix)*(G/rho_value)**2/2/g_c_value\n",
|
||||
"print(f'Loss in rodded section from form: {form_loss:.3e} (lbf-ft/lbm)')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "715fb35e-e211-4e42-9f91-5148d63d5380",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Now we can calculate the pressure drop in the rodded section:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"id": "ac4de5cf-7fde-4cb5-abba-6c2102221f2f",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/latex": [
|
||||
"$\\displaystyle - P_{2} + P_{3} = \\frac{\\rho \\left(g z_{2} - g z_{3} - g_{c} w_{loss 23}\\right)}{g_{c}}$"
|
||||
],
|
||||
"text/plain": [
|
||||
"Eq(-P_2 + P_3, rho*(g*z_2 - g*z_3 - g_c*w_loss_23)/g_c)"
|
||||
]
|
||||
},
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"sm.Eq(P_3-P_2, sm.solve(P23,P_3-P_2)[0])"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"id": "033a4399-abff-474e-9558-17e0ec43ff5e",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"The pressure drop in the rodded section is -2.325e+01 psia\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"delta_p_rodded = rho_value*(g_value*(-12))/g_c_value - rho_value*(form_loss+friction_loss) #lb/ft^2\n",
|
||||
"print(f'The pressure drop in the rodded section is {delta_p_rodded*lb_ft2_to_psi:.3e} psia')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "7548d77c-3f3a-4895-85f2-4b89cbf82e83",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"And now we find the pressure drop in the outlet nozzle:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 17,
|
||||
"id": "1d8fa9b6-ce56-43c6-be42-12f487c3942c",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
"source": [
|
||||
"V_3, V_4, g_c, g, z_3, z_4, P_3, P_4, rho, w_loss = sm.symbols('V_3, V_4, g_c, g, z_3, z_4, P_4, P_3, rho, w_loss')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 18,
|
||||
"id": "4a81f970-a5cf-4646-8745-b0aae22bb685",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/latex": [
|
||||
"$\\displaystyle 0 = \\frac{g \\left(- z_{3} + z_{4}\\right)}{g_{c}} + w_{loss} + \\frac{P_{3} - P_{4}}{\\rho} + \\frac{- \\frac{V_{3}^{2}}{2} + \\frac{V_{4}^{2}}{2}}{g_{c}}$"
|
||||
],
|
||||
"text/plain": [
|
||||
"Eq(0, g*(-z_3 + z_4)/g_c + w_loss + (P_3 - P_4)/rho + (-V_3**2/2 + V_4**2/2)/g_c)"
|
||||
]
|
||||
},
|
||||
"execution_count": 18,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"P34 = sm.Eq(0, (V_4**2 - V_3**2)/2/g_c + g/g_c*(z_4 - z_3) + (P_4 - P_3)/rho + w_loss)\n",
|
||||
"P34"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 19,
|
||||
"id": "a057320a-e37e-4afa-9069-389ed0377bb8",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Moody Friction Factor (Nozzle): 1.849e-02\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"f_m = 0.316*Re_nozzle**(-0.25)\n",
|
||||
"print(f'Moody Friction Factor (Nozzle): {f_m:.3e}')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "44f14409-0134-48ea-a361-77ae52241599",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The outlet nozzle has very similar lost work as the inlet nozzle, except for a form factor difference:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 20,
|
||||
"id": "1a926053-b6d4-4267-bf80-b2c7c6f8877c",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Lost work is 4.047e-06 (lbf-ft/lbm)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"w_loss_34 = f_m*(0.5)/D_nozzle*(G_nozzle/rho_value)**2/2/g_c_value + k_exit*(G_nozzle/rho_value)**2/2/g_c_value #lbf-ft/lbm\n",
|
||||
"print(f'Lost work is {w_loss_34:.3e} (lbf-ft/lbm)')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "08e477a6-460f-432a-ae65-7e4036b7ac70",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"And now we can find the pressure loss of the whole inlet nozzle:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 21,
|
||||
"id": "85611fe7-0749-4090-a532-cd1eba07a715",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/latex": [
|
||||
"$\\displaystyle P_{3} - P_{4} = \\frac{\\rho \\left(V_{3}^{2} - V_{4}^{2} + 2 g z_{3} - 2 g z_{4} - 2 g_{c} w_{loss}\\right)}{2 g_{c}}$"
|
||||
],
|
||||
"text/plain": [
|
||||
"Eq(P_3 - P_4, rho*(V_3**2 - V_4**2 + 2*g*z_3 - 2*g*z_4 - 2*g_c*w_loss)/(2*g_c))"
|
||||
]
|
||||
},
|
||||
"execution_count": 21,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"sm.Eq(P_4-P_3,sm.solve(P34,P_4-P_3)[0])"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"id": "4a3b7a81-1644-4f5b-bd3b-b4dd77a6ae00",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"The pressure drop from the outlet is 1.006e+00 psia\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"delta_P_outlet = rho_value*((G/rho_value)**2 - (G_nozzle/rho_value)**2 + 2*g_value*(-0.5) - 2*g_c_value*w_loss_34) \\\n",
|
||||
" /2/g_c_value #lb/ft^2\n",
|
||||
"print(f'The pressure drop from the outlet is {delta_P_outlet*lb_ft2_to_psi:.3e} psia')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "f16b4f27-acb0-40e9-868a-be7c19c33d93",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We add these pressure changes together to get the total pressure drop across the reactor:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"id": "1145f10a-cffc-4453-9beb-6cbc43335427",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"Problem 1::\n",
|
||||
"The total pressure change from point 1 to 4 is -2.356e+01 psia\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"Delta_P = delta_P_inlet + delta_p_rodded + delta_P_outlet #lb/ft^2\n",
|
||||
"answer_print('Problem 1:',f'The total pressure change from point 1 to 4 is {Delta_P*lb_ft2_to_psi:.3e} psia')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
@ -362,6 +664,64 @@
|
||||
"source": [
|
||||
""
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"id": "4dd972ef-38b7-4746-9f8a-8eb63ed7ec69",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"2a:\n",
|
||||
"1.414e+4 W/ft\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Find Thermal Power Ouput\n",
|
||||
"Q = 90e6/0.303 #W\n",
|
||||
"\n",
|
||||
"#Find power per rod\n",
|
||||
"q = Q/9e3 #W/(rod)\n",
|
||||
"\n",
|
||||
"#Set up equation to find q_prime_max\n",
|
||||
"z, q_prime_max = sm.symbols('z, q_prime_max')\n",
|
||||
"q_balance = sm.Eq(q, sm.integrate(q_prime_max*z**2/16, (z, 0, 4)) + (q_prime_max*2)/2)\n",
|
||||
"q_prime_max_value = sm.solve(q_balance, q_prime_max)\n",
|
||||
"\n",
|
||||
"answer_print('2a', f'{q_prime_max_value[0]:.3e} W/ft')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"id": "b8e4782c-98a5-4558-96a3-eae23fee99ca",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"2b:\n",
|
||||
"2.571e+0\n",
|
||||
"=========FINAL ANSWER=========\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#Calculate axial peaking factor:\n",
|
||||
"answer_print('2b', f'{q_prime_max_value[0]/(q/6):.3e}')"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user