Dane Sabo
ed59b30dd0
D Presentations/ERLM/bouncing_ball_hybrid.png A Presentations/ERLM/images/4_research_approach/phase_portrait_sg1.png A Presentations/ERLM/images/4_research_approach/two_loop.png A Presentations/ERLM/images/7_broader_impacts/billion.jpg M Presentations/ERLM/main.aux M Presentations/ERLM/main.fdb_latexmk M Presentations/ERLM/main.fls M Presentations/ERLM/main.log
180 lines
6.6 KiB
Julia
180 lines
6.6 KiB
Julia
using DifferentialEquations
|
|
using Plots
|
|
|
|
"""
|
|
Two-Loop Reactor: SG1 Heat Removal Uncertainty
|
|
|
|
Simple, realistic scenario:
|
|
- SG2 efficiency is known: Q2 = 50.0
|
|
- SG1 efficiency is uncertain: Q1 ∈ [45, 55] (±10% due to fouling/conditions)
|
|
- Everything else is exact!
|
|
|
|
This shows how uncertainty in ONE component propagates through the system.
|
|
"""
|
|
|
|
println("=== Two-Loop Reactor: SG1 Heat Removal Uncertainty ===\n")
|
|
|
|
# Constants from Python script
|
|
const C_0 = 33.33 # Base Heat Capacity [%-sec/°F]
|
|
const τ_0 = 0.75 * C_0 # Base Time Constant [sec]
|
|
const μ = 0.6 # Fixed reactor water mass fraction
|
|
const P_r = 100.0 # Reactor power
|
|
const Q2 = 50.0 # SG2 heat removal (KNOWN)
|
|
|
|
println("=== Parameters ===")
|
|
println("C_0 = $C_0 %-sec/°F")
|
|
println("τ_0 = $τ_0 sec")
|
|
println("μ = $μ (fixed)")
|
|
println("P_r = $P_r")
|
|
println("Q2 = $Q2 (SG2 - KNOWN)")
|
|
|
|
# Initial conditions (non-equilibrium for interesting dynamics)
|
|
const T_hot_0 = 455.0 # Hot leg slightly elevated
|
|
const T_cold1_0 = 450.0 # Cold legs at reference
|
|
const T_cold2_0 = 450.0
|
|
|
|
println("\n=== Initial Conditions ===")
|
|
println("T_hot_0 = $T_hot_0 °F")
|
|
println("T_cold1_0 = $T_cold1_0 °F")
|
|
println("T_cold2_0 = $T_cold2_0 °F")
|
|
|
|
# Two-loop ODEs with Q1 as parameter
|
|
function two_loop!(du, u, p, t)
|
|
T_hot, T_cold1, T_cold2 = u
|
|
Q1 = p[1] # SG1 heat removal (UNCERTAIN)
|
|
|
|
# System parameters
|
|
C_r = μ * C_0
|
|
C_sg = (1 - μ) * C_0 / 2
|
|
W = C_0 / (2 * τ_0)
|
|
|
|
# Energy balances
|
|
du[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
|
|
du[2] = (W * (T_hot - T_cold1) - Q1) / C_sg # Q1 varies!
|
|
du[3] = (W * (T_hot - T_cold2) - Q2) / C_sg # Q2 fixed
|
|
|
|
return du
|
|
end
|
|
|
|
# Q1 uncertainty range
|
|
Q1_values = range(45.0, 55.0, length=40) # Fine sweep over ±10%
|
|
|
|
println("\n=== Q1 Uncertainty (SG1 Heat Removal) ===")
|
|
println("Q1 range: [45.0, 55.0] (±10% from nominal 50)")
|
|
println("Number of cases: $(length(Q1_values))")
|
|
println("\nPhysical meaning:")
|
|
println(" Q1 = 45: SG1 is 10% less efficient (fouling, poor heat transfer)")
|
|
println(" Q1 = 55: SG1 is 10% more efficient (better conditions)")
|
|
|
|
# Solve for all Q1 values
|
|
u0 = [T_hot_0, T_cold1_0, T_cold2_0]
|
|
tspan = (0.0, 30.0)
|
|
t_save = range(0, 30, length=300)
|
|
|
|
println("\nSolving...")
|
|
all_sols = []
|
|
for Q1 in Q1_values
|
|
p = [Q1]
|
|
prob = ODEProblem(two_loop!, u0, tspan, p)
|
|
sol = solve(prob, Tsit5(), saveat=t_save)
|
|
push!(all_sols, sol)
|
|
end
|
|
println("Done!")
|
|
|
|
# Extract data
|
|
times = all_sols[1].t
|
|
all_T_hot = [[sol.u[i][1] for i in 1:length(sol)] for sol in all_sols]
|
|
all_T_cold1 = [[sol.u[i][2] for i in 1:length(sol)] for sol in all_sols]
|
|
all_T_cold2 = [[sol.u[i][3] for i in 1:length(sol)] for sol in all_sols]
|
|
|
|
# Compute T_ave
|
|
all_T_ave = []
|
|
for (i, Q1) in enumerate(Q1_values)
|
|
T_ave = μ * all_T_hot[i] .+ (1 - μ) * (all_T_cold1[i] .+ all_T_cold2[i]) ./ 2
|
|
push!(all_T_ave, T_ave)
|
|
end
|
|
|
|
# Compute reach tube envelopes
|
|
T_hot_min = [minimum([all_T_hot[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
|
|
T_hot_max = [maximum([all_T_hot[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
|
|
T_cold1_min = [minimum([all_T_cold1[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
|
|
T_cold1_max = [maximum([all_T_cold1[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
|
|
T_ave_min = [minimum([all_T_ave[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
|
|
T_ave_max = [maximum([all_T_ave[i][j] for i in 1:length(Q1_values)]) for j in 1:length(times)]
|
|
|
|
println("\n=== Creating Plots ===")
|
|
|
|
# Plot 1: T_hot reach tube
|
|
p1 = plot(times, T_hot_min, fillrange=T_hot_max,
|
|
xlabel="Time (s)", ylabel="T_hot (°F)",
|
|
title="Hot Leg Temperature",
|
|
fillalpha=0.4, color=:red, lw=2.5,
|
|
label="Reach tube", legend=:topright)
|
|
|
|
# Plot 2: T_cold1 reach tube (affected by Q1 uncertainty)
|
|
p2 = plot(times, T_cold1_min, fillrange=T_cold1_max,
|
|
xlabel="Time (s)", ylabel="T_cold1 (°F)",
|
|
title="Cold Leg 1 (SG1 - Uncertain)",
|
|
fillalpha=0.4, color=:blue, lw=2.5,
|
|
label="Reach tube", legend=:topright)
|
|
|
|
# Plot 3: T_ave reach tube
|
|
p3 = plot(times, T_ave_min, fillrange=T_ave_max,
|
|
xlabel="Time (s)", ylabel="T_avg (°F)",
|
|
title="Average Primary Temperature",
|
|
fillalpha=0.4, color=:orange, lw=2.5,
|
|
label="Reach tube", legend=:topright)
|
|
|
|
# Plot 4: Phase portrait T_hot vs T_ave
|
|
p4 = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
|
|
title="Phase Portrait: T_hot vs T_avg",
|
|
legend=:topright)
|
|
|
|
# Plot envelope
|
|
plot!(p4, [T_ave_min; reverse(T_ave_max)], [T_hot_min; reverse(T_hot_max)],
|
|
seriestype=:shape, fillalpha=0.3, color=:purple,
|
|
label="Reachable region", lw=2.5)
|
|
|
|
# Mark extremes
|
|
plot!(p4, T_ave_min, T_hot_min, color=:blue, lw=2.5, label="Q1 = 45", linestyle=:dash)
|
|
plot!(p4, T_ave_max, T_hot_max, color=:red, lw=2.5, label="Q1 = 55", linestyle=:dash)
|
|
|
|
plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
|
|
plot_title="SG1 Heat Removal Uncertainty: Q1 ∈ [45, 55]")
|
|
savefig(plot_combined, "sg1_uncertainty.png")
|
|
println("Saved: sg1_uncertainty.png")
|
|
|
|
# Detailed phase portrait
|
|
p_phase = plot(xlabel="T_avg (°F)", ylabel="T_hot (°F)",
|
|
title="Phase Portrait: T_hot vs T_avg\n(SG1 efficiency uncertainty: Q1 ∈ [45, 55])",
|
|
size=(1000, 900), legend=:topright)
|
|
|
|
# Plot all trajectories
|
|
for (i, Q1) in enumerate(Q1_values)
|
|
color_val = (Q1 - minimum(Q1_values)) / (maximum(Q1_values) - minimum(Q1_values))
|
|
plot!(p_phase, all_T_ave[i], all_T_hot[i],
|
|
color=cgrad(:RdBu)[color_val], lw=1.5, alpha=0.3, label="")
|
|
end
|
|
|
|
# Add envelope
|
|
plot!(p_phase, [T_ave_min; reverse(T_ave_max)], [T_hot_min; reverse(T_hot_max)],
|
|
seriestype=:shape, fillalpha=0.25, color=:purple,
|
|
label="Reachable region", lw=3)
|
|
|
|
# Mark extremes
|
|
plot!(p_phase, all_T_ave[1], all_T_hot[1],
|
|
color=:blue, lw=3.5, label="Q1 = 45 (low efficiency)", linestyle=:dash)
|
|
plot!(p_phase, all_T_ave[end], all_T_hot[end],
|
|
color=:red, lw=3.5, label="Q1 = 55 (high efficiency)", linestyle=:dash)
|
|
|
|
savefig(p_phase, "phase_portrait_sg1.png")
|
|
println("Saved: phase_portrait_sg1.png")
|
|
|
|
println("\n✓ Complete!")
|
|
println("\n=== Results ===")
|
|
println("T_hot range: [$(round(minimum(T_hot_min), digits=1)), $(round(maximum(T_hot_max), digits=1))] °F")
|
|
println("T_avg range: [$(round(minimum(T_ave_min), digits=1)), $(round(maximum(T_ave_max), digits=1))] °F")
|
|
println("T_cold1 range: [$(round(minimum(T_cold1_min), digits=1)), $(round(maximum(T_cold1_max), digits=1))] °F")
|
|
println("\nΔT_hot = $(round(maximum(T_hot_max) - minimum(T_hot_min), digits=1)) °F")
|
|
println("ΔT_avg = $(round(maximum(T_ave_max) - minimum(T_ave_min), digits=1)) °F")
|