From real system to verified solution

CDS-100 is a single-loop cooling demonstration system. Water stored in vessel V-101 (volume V = 5 m³) is continuously heated by a process heat load Qₙ and cooled by a shell-and-tube heat exchanger HX-101.

Energy balance — tank temperature

ρ · V · cₙ · dT/dt = Qₙ − Qₕₕₓₙ

• ρ = 1000 kg/m³ — water density
• cₙ = 4180 J/(kg·K) — specific heat
• V = 5 m³ — tank volume → thermal mass M·cₙ = 20.9 MJ/K
• Qₙ = adjustable heat load (50–400 kW)
• Qₕₕₓₙ = heat removed by HX-101

Flow

Each running pump delivers nominal flow Fₙ = 25 m³/h through CV-101. Two pumps in parallel double the flow. Flow is zero when no pump runs or CV-101 is fully closed.

F = nₘ · Fₙ · x𝐶𝑉    [kg/s]

Heat exchanger — NTU effectiveness method

HX-101 is modelled using the ε-NTU method for a single-pass heat exchanger with cooling water inlet temperature T𝑢 = 20°C:

UA = UA₀ · h𝑓 · (F/Fₙ)^0.8
ε = 1 − exp(−UA / Cₙ)
Qₕₕₓₙ = ε · Cₙ · (T − T𝑢)

• UA₀ = 13 333 W/K — design conductance at nominal flow
• h𝑓 = HX capacity factor (1.0 = clean, <1 = fouled)
• 0.8 exponent — Dittus-Boelter turbulent convection dependence
• Cₙ = F · cₙ — process stream heat capacity rate [W/K]

Alarms

• LAH-101: T ≥ 45°C — high temperature warning
• LAHH-101: T ≥ 55°C — high-high temperature, requires immediate action

Instrumentation

• TT-101: Process temperature in V-101. Primary input to TIC-101. Also displayed as a readout tag next to the transmitter circle in the P&ID.
• FT-101: Volumetric flow rate in the pump discharge header [m³/h]. Computed from pump count and CV-101 position.
• TT-102: Process return temperature after HX-101, computed as T₂ = T − Q_cool/(ṁ·c_p). Represents the temperature entering the top of V-101.

Cooling water side

The cooling water (CW) enters HX-101 at T_u = 20°C. The outlet temperature is estimated assuming a nominal CW circulation rate of 30 m³/h (8.33 kg/s):

T_CW,out = T_u + Q_cool / (ṁ_CW · c_p)

• At 200 kW cooling duty: T_CW,out ≈ 20 + 200 000 / (8.33 × 4180) ≈ 25.7°C
• CW outlet temperature is displayed in the P&ID next to the CW OUT arrow.

TIC-101 controls the tank temperature T by adjusting the position of control valve CV-101. The controller acts in reverse: when T rises above setpoint, the valve opens further to increase cooling flow.

PID equation (positional form, discrete)

u(t) = bias + Kₙ · e(t) + K𝑖 · ∫e dt + K𝑑 · de/dt

e(t) = T(t) − Tⱼₙ   (error, positive when too hot)

Parameters

Anti-windup

The simulator uses conditional integration: the integral accumulates only when the output u is within [0, 1]. When the valve is saturated (fully open or fully closed), the integral is frozen unless accumulating in that direction would reduce saturation. This prevents integral windup during pump trips and large setpoint steps.

Tuning guide

• Temperature oscillates slowly after a setpoint step → K𝑖 is too large. Reduce K𝑖 by 30–50%.
• Temperature never reaches setpoint (persistent offset) → K𝑖 is too small, or bias is far from the steady-state operating point. Increase K𝑖 or adjust bias.
• Valve hunts rapidly (high-frequency oscillation) → Kₙ is too large. Reduce Kₙ by 50%.
• Response is slow after a pump trip → Increase Kₙ. The large thermal mass (≈21 MJ/K) means the system is naturally slow.
• Derivative makes the valve jitter → Set K𝑑 = 0. The process has no significant measurement noise but K𝑑 > 0.01 will still interact poorly with the discrete integration step.