Technical Manual · Thermal Lab
Liquid-to-Chip System Modelling Lab — Methodology & Formulas
Every input, equation, constant, output, and reference behind the LTC steady-state solver. All math is executed by the deterministic engine js/ltc-system-modelling-lab.js (function computeModel) — no back-solved constants, no random values. This is a SIMULATED / educational model; it is not a substitute for site-specific hydraulic or thermal commissioning data.
01 Purpose & engineering basis
The LTC System Modelling Lab answers five design questions for a liquid-to-chip cooled AI/HPC data center: what coolant flow is needed, what pump power does that cost, what PUE and system COP result, how does the design score against ASHRAE / ANSI / ISO / NFPA / Uptime Institute criteria, and how sensitive are those results to each input parameter.
The solver is a steady-state energy balance with no transient dynamics: at each solver call, Q_in = Q_cooling + Q_aux (losses), and the model reports the steady-state operating point for the given inputs. This is an engineering pre-design and education aid. Final system design must be validated by site-specific thermal and hydraulic modelling and commissioned against real telemetry. All outputs are labelled SIMULATED.
02 Inputs
The lab exposes a wide set of parameters. The five primary interactive sliders (flow-driving tier) are highlighted below; the remaining parameters are set via the architecture preset or manually. Ranges are enforced by clamp() in gatherInputs().
| Field | Symbol | Unit | Range / default | Meaning |
|---|---|---|---|---|
IT Load inItLoad | itLoadMw | MW | 0.5–80 · default 12 | Total IT electrical load driving the thermal calculation. itKw = itLoadMw × 1000. |
Liquid Capture % inLiquidCapture | liquidCapture | % | 0–100 · default 85 | Share of IT heat removed by the liquid loop. Drives liquidKw and thereby mass flow. |
Supply Temperature inSupplyTemp | supplyTemp | °C | 16–42 · default 32.5 | Entering liquid coolant temperature (liquid, not supply-air). Warm-water LTC designs typically run high-20s to low-30s °C. |
Return Temperature inReturnTemp | returnTemp | °C | supplyTemp+3 min · default 40.5 | Leaving liquid coolant temperature. Together with supply temp, sets baseDeltaT. |
Pump Head inPumpHead | pumpHead | m | 5–90 · default 28 | Nominal hydraulic head for the loop. Corrected for pipe-loss multiplier and density stress. |
Pump Efficiency inPumpEff | pumpEff | % | 35–95 · default 78 | Net pump efficiency converting hydraulic to electrical power. |
Architecture preset inCoolingArchitecture | — | enum | direct_liquid / hybrid / air_inrow_dahu | Auto-loads supply/return temps, capture %, airCOP, fan power, and pipe-loss for a representative profile. |
HX type / Coolant inCoolant | coolantKey | enum | water / pg20 / pg30 | Selects Cp and density (ρ) for the coolant. Water: Cp=4.186 kJ/kg·K, ρ=997 kg/m³; PG-20: Cp=3.92, ρ=1025; PG-30: Cp=3.75, ρ=1038. |
Economizer availability inEconomizerHours | economizerHours | % of year | 0–95 · default 34 | Share of annual hours under economizer conditions. Scales air-side COP and WUE. |
Facility fan power inFanPower | fanPower | % of IT | 0.5–12 · default 2.8 | Residual CRAH/DAHU fan overhead before liquid-capture and control reductions. |
UPS efficiency inUpsEff | upsEff | % | 90–99.5 · default 96.5 | UPS conversion efficiency. Loss = itKw / upsEff − itKw. |
Target PUE inTargetPue | targetPue | — | ≥1.05 · default 1.20 | Design target used by gap analysis and optimizer. Does not affect the solver result. |
03 Calculation methodology
The solver runs in one deterministic pass with no iteration loops. Function names map one-to-one to js/ltc-system-modelling-lab.js (computeModel).
Steady-state energy balance (conceptual)
Supply temperature rise & mass flow
Hydraulic pump power (affinity-law corrected)
fanKw = itKw × (fanPower%) × (1 − effectiveCapture/100 × 0.55) × (1 − controlBonus × 0.18) — residual fan demand after liquid-capture and control reductions.HX Institute · pump affinity laws · inline computeModel
HX effectiveness & liquid cooling COP
PUE impact (facility + CDU pump)
System COP
WUE and annual energy
04 Constants & data sources
All constants are declared in the top of initCalculator() in js/ltc-system-modelling-lab.js. Coolant property block:
| Coolant | Cp (kJ/kg·K) | ρ (kg/m³) | Typical use |
|---|---|---|---|
Water (water) | 4.186 | 997 | Standard warm-water DLC loops. |
Propylene glycol 20% (pg20) | 3.92 | 1025 | Light freeze protection; moderate Cp penalty. |
Propylene glycol 30% (pg30) | 3.75 | 1038 | Full freeze protection; higher density, lower Cp. |
| Rack profile | Typical density | LiquidBias | AirResidual | Notes |
|---|---|---|---|---|
| AI/HPC direct liquid | 50–100 kW/rack | 1.15 | 0.12 | GPU/TPU clusters; dominant liquid capture. |
| Enterprise mixed | 15–30 kW/rack | 0.82 | 0.45 | Mixed workloads; hybrid liquid + air. |
| Immersion (single-phase) | 80–120 kW/rack | 1.28 | 0.05 | Full immersion; near-total liquid capture. |
| Immersion (two-phase) | 80–120 kW/rack | 1.36 | 0.08 | Two-phase; highest capture bias. |
| Legacy air + RDHx | 10–25 kW/rack | 0.62 | 0.72 | Rear-door HX hybrid; mostly air-side. |
Hard guardrails: deltaT must be ≥3 °C (hard-stop below 3 °C); deltaT <6 °C triggers a design warning (typical target is ≥6–10 °C). Pump efficiency below 45% is a hard-stop; below 65% is a warning. Risk index is clamped to [5, 95] and blocked above 70 for optimizer/stochastic runs.
05 Outputs
| Output | Formula / derivation | Unit | Interpretation |
|---|---|---|---|
| Design flow | flowLPM | L/min | Pump sizing flow including redundancy, margin, and pipe factor. |
| Pump power | pumpPowerKw | kW | Electrical power to CDU pump; contributes directly to PUE. |
| PUE | totalFacilityKw / itKw | — | Overall facility efficiency. Typical hyperscale target 1.10–1.25. |
| System COP | itKw / totalCoolingKw | — | Cooling-side performance; higher = better. |
| WUE | climate-adjusted | L/kWh | Water consumption per IT energy unit. |
| Annual energy | totalFacilityKw × 8760 | GWh/year | Full-facility energy footprint at stated load. |
| Net OPEX | energy cost + water − heat-reuse credit | USD/year | Annual operating cost after any waste-heat recovery credit. |
| Net carbon | annualKWh × CI − avoidedCarbon | t CO₂e/year | Gross minus heat-reuse displacement; carbon intensity is site-specific. |
| Thermal delta-T | deltaT | °C | Effective liquid loop temperature rise after density-stress correction. |
| Compliance scores | ASHRAE / ANSI / ISO / NFPA / Uptime | 0–100 | Weighted standards-alignment index per protocol. |
| Risk index | additive penalty model | 0–100 | Composite resilience risk; <35 = low, 35–60 = moderate, >60 = high. |
| CDU count | ceil(liquidKw / cduUnit) | count | Number of CDU units at stated kW capacity. |
06 Worked example
Default scenario: 12 MW IT load, direct-liquid architecture (85% capture), water coolant, supply 32.5 °C, return 40.5 °C, pump head 28 m, pump efficiency 78%, hydraulic margin 12%, pipe-loss ×1.0, N+1 redundancy. Numbers reproduce the live solver output at default settings.
- IT load:
itKw = 12 × 1000 =12 000 kW - Liquid-side load:
liquidKw = 12 000 × 0.85 =10 200 kW - baseDeltaT:
40.5 − 32.5 =8.0 °C (within [3, 20] — valid design range) - Mass flow:
m = 10 200 / (4.186 × 8.0) =304.7 kg/s - Base volume flow:
304.7 / 997 =0.3056 m³/s - Design flow (N+1, 12% margin, ×1.0 pipe):
0.3056 × 1.15 × 1.12 × 1.0 =0.3936 m³/s → 23 616 LPM - Effective head:
28 × 1.0 × (1 + (densityStress−1) × 0.22) ≈~28.8 m (density stress ≈ 1.14 for 35 kW/rack default) - Hydraulic power:
P_hyd = 997 × 9.81 × 28.8 × 0.3936 / 1000 =~111 kW - Pump electrical power:
111 / 0.78 =~142 kW - PUE (simplified): liquid cooling + pump + air fan + UPS loss + dist loss + aux ÷ IT → ~1.27 (varies with climate / control settings)
07 References & standards
- ASHRAE TC9.9 Liquid Cooling Design Guide — Liquid cooling system design, coolant selection, temperature ranges, flow sizing methodology for data centers.
- HX Institute Standards — Heat exchanger thermal performance, approach temperature, effectiveness-NTU method, and hydraulic sizing.
- Pump affinity laws (centrifugal) — Flow ∝ speed; head ∝ speed²; power ∝ speed³. Used in fan-power modelling (fanKw ∝ flow³ scaling with control reduction).
- ISO 14644 / ISO 30134-2 — Cleanroom and data center classification; WUE metric definition; energy efficiency governance.
- ANSI/BICSI 002 — Data center design and implementation best practices; redundancy configurations.
- Uptime Institute Tier Standard — Availability tiers (N, N+1, 2N) and their concurrently-maintainable requirements.
- ASHRAE 90.4 / Green Grid — PUE and system COP definitions and reporting methodology.
- Engine source —
js/ltc-system-modelling-lab.jsfunctioncomputeModel(input). All formula line-numbers are verifiable in that file.
08 Assumptions & limitations
The model assumes a well-mixed, single-pass steady-state loop at the stated supply and return temperatures. Pipe-loss multiplier (coefPipeLoss) is a network-complexity factor applied uniformly — it is not a pressure-drop simulation. CDU loss is a fixed percentage of liquid heat load (default 1.8%). Coolant properties are constant (no temperature-dependent Cp or ρ). Future-tech coefficient (coefFutureTech) is a linear efficiency multiplier without underlying technology model. Heat-reuse credit is illustrative and varies heavily by site.
This manual and the LTC lab are engineering education and pre-design aids only. Outputs are clearly labelled SIMULATED. No cross-page Rule-1 consistency is asserted (this tool is self-contained). Detailed system design must be performed by qualified mechanical and electrical engineers using site-specific data and vendor curves.