v2: Toy Cooling Tower Prompt

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Start using notebook tools immediately. Do not narrate a plan or inspect unrelated cells. Create the requested cells, run them in order, make only essential corrections, and leave the finished dashboard visible.

# Goal

Create a fast, visually compelling conceptual study titled:

**Can a Flooded Mine Make Data Centers More Water-Efficient?**

Compare cooling-tower water recovery in hot-dry and hot-humid weather for a 10 MW data center.

This is a fictional educational model—not an engineering design, site assessment, financial analysis, or performance claim.

# Priorities

1. Reliability during a live phone demo
2. Complete within the configured ten agent steps
3. Execute in under eight seconds after kernels are ready
4. Produce clear, phone-readable results
5. Use physically defensible first-order assumptions
6. Keep cells and textual output concise

Use no network requests, package installation, external data, pandas, Matplotlib, Plotly imports, numerical optimizers, or unnecessary dependencies.

Use only:

- Bundled NumPy
- Python’s standard library
- SciREPL’s built-in `mplot`
- Bundled SWI-Prolog
- SharedVFS paths under `/shared`

# Notebook structure

Create exactly four cells in this order:

1. Markdown introduction
2. Python simulation
3. Prolog classification
4. Python dashboard

Do not create diagnostic or scratch cells.

## Cell 1 — Markdown introduction

Write no more than 110 words.

Explain that the toy system contains:

- A 10 MW liquid-cooled data center
- An induced-draft evaporative cooling tower
- A plenum capturing the warm, nearly saturated tower exhaust before ambient dilution
- Widely spaced, corrosion-resistant finned-tube condenser coils
- A closed secondary loop connected to a flooded-mine thermal reservoir
- Recovered condensate returned as tower makeup water
- A conditional heat pump used only when passive cooling cannot meet an illustrative facility-loop supply limit

Clearly state:

- The GPU primary loop transfers heat to a separate facility loop through a heat exchanger.
- The facility and tower-water circuits exchange heat without mixing.
- Mine water remains inside its own closed secondary loop.
- Mine water never contacts tower water or recovered condensate.

Say that the study explores water savings versus fan, pump, and heat-pump electricity under different humidity conditions.

## Cell 2 — Python simulation

Use NumPy and the standard library. Use a fixed random seed and simulate two independent seven-day hourly cases with smooth diurnal cycles.

Both cases must have identical:

- IT-load and dry-bulb schedules
- Cooling-tower design
- Induced-draft fan schedule
- Water and dry-air design flows
- Finned-coil area, spacing, UA, and pressure drop
- Mine-water starting temperature and effective reservoir volume
- Facility-loop temperature limit
- Heat-pump model

They must differ only in atmospheric moisture:

- `hot_dry`: relative humidity approximately 20–35%
- `hot_humid`: relative humidity approximately 55–75%

Declare all illustrative constants together near the top and avoid false precision.

Implement compact functions for:

- Saturation vapour pressure
- Humidity ratio
- Dew-point temperature
- Wet-bulb temperature using a documented approximation
- Moist-air enthalpy

Use approximately 101.3 kPa atmospheric pressure.

### Induced-draft tower

Set dry-air mass flow from fan operation and IT load using one simple declared relationship. Use the same relationship in both cases.

Do not derive airflow from boiling, buoyancy, or natural draft. Tower water must remain within a plausible liquid range of approximately 10–50°C and never approach boiling.

Use a constant design effectiveness:

`tower_effectiveness = (hot_water_temp - cold_water_temp) / (hot_water_temp - wet_bulb_temp)`

Calculate the water-temperature range from heat rejection, water flow, and water heat capacity. Derive cold- and hot-water temperatures consistently from wet bulb, range, and effectiveness.

Estimate the captured, nearly saturated exhaust state with a moist-air energy balance. A short fixed-iteration bisection is acceptable; do not use an optimizer.

Calculate:

- Evaporation from dry-air flow and humidity-ratio increase
- Drift separately
- Blowdown using five cycles of concentration
- Baseline makeup as evaporation plus drift plus blowdown

### Facility cooling and conditional heat pump

Treat the GPU primary loop, facility loop, and tower-water circuit as thermally coupled but non-mixing circuits.

Declare an illustrative facility supply-temperature limit and heat-exchanger approach.

- Use passive heat exchange when tower cold-water temperature plus the approach meets the limit.
- Otherwise activate a simple heat-pump/chiller model.
- Use a bounded COP between 3 and 6 that decreases with temperature lift.
- Include compressor power.
- Add compressor power to the heat rejected into the tower circuit.
- Recalculate the tower range once after activating the heat pump; do not create a convergence loop.
- Never run the heat pump when passive cooling is sufficient.
- Do not use the heat pump to boil tower water or generate airflow.

### Plume condenser and mine loop

Pass the captured, undiluted tower exhaust through downstream finned-tube coils. Mine-loop fluid flows inside the tubes; plume air and condensate remain outside.

Use a fixed, widely spaced coil design to reduce fouling and pressure drop. Do not optimize fin geometry.

Represent finite heat transfer with a compact UA/effectiveness relation such as:

`condenser_effectiveness = 1 - exp(-UA / C_min)`

Use mine-loop temperature plus a declared coil approach to estimate effective condensing-surface temperature.

Condensation must depend on:

- Plume dew point
- Coil surface temperature
- Finite condenser effectiveness
- Dry-air mass flow
- Inlet and outlet humidity ratios

Condense water only when the plume can be cooled below its dew point. Compute recovered water from the humidity-ratio reduction and clamp it between zero and tower evaporation.

Return condensate as makeup water:

`makeup_after_recovery = max(0, baseline_makeup - recovered_condensate)`

Transfer condenser sensible and latent heat into the closed mine-water reservoir. Update mine-water temperature using lumped thermal capacitance and a small heat-loss or recharge term representing surrounding rock and groundwater.

Additional electrical power must include:

- The fan penalty caused by condenser-coil pressure drop
- Mine-loop pump power
- Conditional heat-pump compressor power

Treat the ordinary tower fan as baseline power; count only the condenser pressure-drop penalty as additional power.

Flag hours when mine water is too warm to allow condensation.

### Results

Track hourly values for both cases:

- Ambient dry-bulb temperature and relative humidity
- Wet-bulb temperature
- Tower cold- and hot-water temperatures
- Plume dew point
- Mine-water temperature
- Baseline makeup
- Makeup after recovery
- Recovered condensate
- Condenser fan penalty
- Mine-loop pump power
- Heat-pump power
- Total additional power
- Heat-pump-active flag
- Condensation-available flag

Calculate:

- Total baseline makeup water
- Total recovered water
- Makeup-water reduction percentage
- Baseline and post-recovery Water Usage Effectiveness in litres per IT-kWh
- Additional energy as a percentage of IT energy
- Maximum mine-water temperature
- Condensation-available hours
- Heat-pump operating hours

Save hourly results for both cases to:

`/shared/mine_cooling.csv`

Write concise Prolog facts to:

`/shared/mine_cooling_status.pl`

Use:

`case_result(Case, WaterSavingPercent, ExtraEnergyPercent, MaxMineTempC, CondensationHours).`

Print no tables, arrays, generated code, or CSV contents. Print no more than two short summary lines.

## Cell 3 — Prolog classification

Consult:

`/shared/mine_cooling_status.pl`

Define deterministic rules that classify each case as exactly one of:

- `no_condensation`
- `thermal_limit`
- `marginal`
- `promising_toy_result`

Apply these rules in order:

1. `no_condensation` if condensation was possible for fewer than 5% of simulated hours
2. `thermal_limit` if maximum mine-water temperature reached or exceeded 28°C
3. `marginal` if water savings were below 10% or additional energy exceeded 5%
4. `promising_toy_result` otherwise

Use cuts or if-then-else logic so each case produces exactly one solution.

Print exactly one short line per case containing:

- Case name
- Classification
- Water-saving percentage
- Additional-energy percentage

## Cell 4 — Python dashboard

Use the simulation variables already created by Cell 2.

Use SciREPL’s built-in `mplot`; do not import another plotting package.

Create and render two phone-readable interactive charts:

1. A grouped comparison for `hot_dry` and `hot_humid` showing:
   - Baseline makeup water
   - Makeup after recovery
   - Recovered condensate

   Include each case’s water-saving and additional-energy percentages concisely in its label or annotation.

2. An hourly temperature chart showing, for both cases:
   - Plume dew-point temperature
   - Mine-water temperature

Use high-contrast colours, concise titles, labelled axes, units, and compact legends.

Add this final annotation:

“Toy model: results depend on weather, heat-exchanger design, mine hydraulics, fan and heat-pump assumptions, and long-term thermal recharge.”

# Completion behaviour

- Create exactly the four requested cells.
- Run each cell once in order.
- If a cell fails, make the smallest necessary correction and rerun it.
- Do not add diagnostic cells.
- Do not dump source code, arrays, or long explanations into outputs.
- Do not force either scenario to produce a favourable result.
- Prefer a working simplified model over extra complexity.
- Leave the final dashboard cell visible.
- Reply with one brief completion sentence.