Dane Sabo
dfca8eab77
M .task/backlog.data M .task/completed.data M .task/pending.data M .task/undo.data A Class_Work/nuce2101/final/latex/SABO_NUCE2101_FINAL.pdf M Class_Work/nuce2101/final/latex/main.aux M Class_Work/nuce2101/final/latex/main.fdb_latexmk M Class_Work/nuce2101/final/latex/main.fls
55 lines
1.8 KiB
Python
55 lines
1.8 KiB
Python
import sympy as sp
|
|
|
|
# Define symbolic variable
|
|
alpha_f = sp.Symbol('alpha_f', real=True)
|
|
|
|
# Given values from graphs at t = 17.2s
|
|
Delta_T_ave = 11.0 # degrees F
|
|
d_Delta_T_dt = 1.0 # degrees F/s
|
|
lambda_eff = 0.13 # s^-1
|
|
dot_lambda_eff = 0.081 # s^-2
|
|
|
|
# Known parameters
|
|
rho_0 = 0.008451 # initial reactivity (845.1 pcm)
|
|
alpha_m = -10.6e-5 # in absolute units (-10.6 pcm/F = -10.6e-5 per F)
|
|
beta = 0.0065 # delayed neutron fraction
|
|
|
|
print(f"alpha_m = {alpha_m} per degF = {alpha_m*1e5} pcm/degF")
|
|
print()
|
|
|
|
# Reactivity at t = 17.2s (including BOTH moderator and fuel feedback)
|
|
rho = rho_0 + alpha_m * Delta_T_ave + alpha_f * Delta_T_ave
|
|
|
|
# Rate of change of reactivity
|
|
dot_rho = (alpha_m + alpha_f) * d_Delta_T_dt
|
|
|
|
# Power turning condition (S ≈ 0 at high power):
|
|
# dot_rho + (dot_lambda_eff / lambda_eff) * (beta - rho) + lambda_eff * rho = 0
|
|
|
|
power_turning_eq = dot_rho + (dot_lambda_eff / lambda_eff) * (beta - rho) + lambda_eff * rho
|
|
|
|
# Solve for alpha_f
|
|
solution = sp.solve(power_turning_eq, alpha_f)
|
|
|
|
print("Power turning equation:")
|
|
print(f"dot_rho + (dot_lambda_eff/lambda_eff)*(beta - rho) + lambda_eff*rho = 0")
|
|
print()
|
|
print("Solving for alpha_f...")
|
|
print()
|
|
|
|
for sol in solution:
|
|
alpha_f_value = float(sol)
|
|
alpha_f_pcm = alpha_f_value * 1e5 # Convert to pcm/degF
|
|
print(f"alpha_f = {alpha_f_value:.6e} per degF")
|
|
print(f"alpha_f = {alpha_f_pcm:.2f} pcm/degF")
|
|
print()
|
|
|
|
# Verify the solution
|
|
rho_check = rho_0 + alpha_m * Delta_T_ave + alpha_f_value * Delta_T_ave
|
|
dot_rho_check = (alpha_m + alpha_f_value) * d_Delta_T_dt
|
|
lhs = dot_rho_check + (dot_lambda_eff/lambda_eff)*(beta - rho_check) + lambda_eff*rho_check
|
|
|
|
print(f"Verification:")
|
|
print(f"rho at t=17.2s = {rho_check:.6f} ({rho_check*1e5:.1f} pcm)")
|
|
print(f"Power turning equation LHS = {lhs:.6e} (should be ~0)")
|