Dane Sabo
943066540c
M .task/backlog.data M .task/completed.data M .task/pending.data M .task/undo.data A Class_Work/nuce2101/exam2/NUCE2101_SABO/Submission.pdf A Class_Work/nuce2101/exam2/NUCE2101_SABO/problem1.py A Class_Work/nuce2101/exam2/NUCE2101_SABO/problem1_equal_loading.png A Class_Work/nuce2101/exam2/NUCE2101_SABO/problem1_unequal_loading.png
100 lines
3.6 KiB
Python
100 lines
3.6 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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# Problem 4: PWR Power Increase Transient (25% → 50% Steam Load)
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print("=" * 70)
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print("Problem 4: PWR Power Increase Transient")
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print("=" * 70)
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# Given Initial Conditions (25% power steady state)
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T_ave_initial = 500 # °F - Average temperature
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T_h_initial = 510 # °F - Hot leg temperature
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T_c_initial = 490 # °F - Cold leg temperature
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P_initial = 25 # % - Initial power level
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P_final = 50 # % - Final power level
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print("\n--- Initial Conditions (25% Power) ---")
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print(f"T_ave = {T_ave_initial} °F")
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print(f"T_h = {T_h_initial} °F")
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print(f"T_c = {T_c_initial} °F")
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print(f"Power = {P_initial}%")
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# Calculate initial ΔT across core
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DeltaT_initial = T_h_initial - T_c_initial
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print(f"ΔT across core = {DeltaT_initial} °F")
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print("\n" + "=" * 70)
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print("Part A: Chronological Physical Impacts")
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print("=" * 70)
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print("\n" + "=" * 70)
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print("Part B: Final State Comparison")
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print("=" * 70)
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# For a PWR at steady state:
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# Power ∝ mass flow rate × Cp × ΔT
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# If flow rate is constant (no pump speed change):
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# P_new / P_old = ΔT_new / ΔT_old
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# Calculate new ΔT
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DeltaT_final = DeltaT_initial * (P_final / P_initial)
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print(f"\nΔT calculation:")
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print(f"ΔT_initial = {DeltaT_initial} °F at {P_initial}% power")
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print(f"ΔT_final = ΔT_initial × (P_final/P_initial)")
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print(f"ΔT_final = {DeltaT_initial} × ({P_final}/{P_initial}) = {DeltaT_final} °F")
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# Estimate final temperatures
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# Assume T_ave returns to approximately initial value (no automatic control,
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# but moderator feedback will drive it back toward equilibrium)
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# This is a simplification - in reality, T_ave might be slightly different
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# Method 1: Assume T_ave = constant (strong moderator feedback)
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T_ave_final_method1 = T_ave_initial
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T_h_final_method1 = T_ave_final_method1 + DeltaT_final / 2
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T_c_final_method1 = T_ave_final_method1 - DeltaT_final / 2
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print(f"\n--- Method 1: Assume T_ave constant (strong moderator feedback) ---")
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print(f"T_ave_final = {T_ave_final_method1} °F")
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print(
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f"T_h_final = T_ave + ΔT/2 = {T_ave_final_method1} + {DeltaT_final/2} = {T_h_final_method1} °F"
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)
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print(
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f"T_c_final = T_ave - ΔT/2 = {T_ave_final_method1} - {DeltaT_final/2} = {T_c_final_method1} °F"
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)
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# Method 2: More realistic - Tc drops somewhat, Th rises more
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# The SG cooling will lower Tc, but not back to initial Tc
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# Let's estimate Tc drops by ~5-10°F, then Th rises to accommodate ΔT
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T_c_drop = 5 # °F - estimated drop in Tc due to increased SG cooling
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T_c_final_method2 = T_c_initial - T_c_drop
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T_h_final_method2 = T_c_final_method2 + DeltaT_final
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T_ave_final_method2 = (T_h_final_method2 + T_c_final_method2) / 2
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print(f"\n--- Method 2: Estimate Tc drop due to SG cooling ---")
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print(f"Assume Tc drops by ~{T_c_drop}°F due to increased steam flow")
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print(f"T_c_final = {T_c_final_method2} °F")
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print(
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f"T_h_final = T_c + ΔT = {T_c_final_method2} + {DeltaT_final} = {T_h_final_method2} °F"
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)
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print(f"T_ave_final = {T_ave_final_method2} °F")
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print(f"\n--- Comparison Table ---")
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print(
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f"{'Parameter':<20} {'Initial (25%)':<20} {'Final (50%) M1':<20} {'Final (50%) M2':<20}"
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)
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print(f"{'-'*80}")
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print(f"{'Power':<20} {P_initial:<20} {P_final:<20} {P_final:<20}")
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print(
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f"{'T_h (°F)':<20} {T_h_initial:<20} {T_h_final_method1:<20.1f} {T_h_final_method2:<20.1f}"
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)
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print(
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f"{'T_c (°F)':<20} {T_c_initial:<20} {T_c_final_method1:<20.1f} {T_c_final_method2:<20.1f}"
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)
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print(
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f"{'T_ave (°F)':<20} {T_ave_initial:<20} {T_ave_final_method1:<20.1f} {T_ave_final_method2:<20.1f}"
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)
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print(
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f"{'ΔT (°F)':<20} {DeltaT_initial:<20} {DeltaT_final:<20.1f} {DeltaT_final:<20.1f}"
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)
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