Dynamic system modeling of liquid-cooled AI data centers
The first chip-to-ambient transient model of a direct-to-chip liquid-cooled AI rack, run under real workloads and real weather.
Why dynamics
Data centers used about 415 TWh in 2024, roughly 1.5 % of global electricity, and cooling is around a third of a facility’s energy. Rack density has jumped from under 10 kW to 130 kW for a GB200 NVL72, and programs such as ARPA-E COOLERCHIPS target racks above 126 kW cooled with at most 5 % of IT load. Air cannot do that; direct-to-chip liquid cooling is the default.
Nearly all of the modeling behind those systems is steady state, and the two industry metrics, PUE and TUE, are steady-state constructs. But AI training swings facility power at 0.2–3 Hz, inference has 1.7–2.8× diurnal peaks, weather acts directly on the dry cooler, and grids increasingly want data centers to shed load on request. Warm-water-cooled chips throttle within tens of seconds of losing flow. Nobody had a rack-scale, chip-to-ambient transient model, and nobody had a formal transient metric.
The model
Built in MATLAB Simscape Fluids: about 37 000 blocks and 580 logged signals covering 126 compute packages, cold plates, 14 modular in-rack coolant distribution units (gear pump plus brazed-plate heat exchanger), 532 quick disconnects, a glycol primary loop and two dry coolers in series, with 16 PI control loops. The chip side is a four-node RC chain per package validated against a bench GPU transient to 0.57 K RMSE; the cold plate is the lab’s measured diamond pin-fin dataset; the dry cooler is calibrated to manufacturer duty and checked out of sample. A 56-check conservation audit runs on every result.
Around the model sits a transient performance framework: a temperature-budget regime map (actuator floor, regulated, saturated), an inventory of storage and transport time scales from the die at under a millisecond to loop turnover at minutes, six excitation families with protocol rules, and a four-axis scorecard covering thermal compliance with JEDEC and ASHRAE rate limits, windowed TUE split into static and dynamic excess, frequency response, and cycling wear.
The campaign so far: 215 cases and more than 1 000 wall-hours on a 96-core node, including 77 realistic AI workload days and 24 week-long runs under measured Champaign and Austin weather.
What it answers
The results are in write-up for the International Journal of Heat and Mass Transfer, so the numbers stay in the paper for now. The shape of the findings:
- Capacity derates linearly with ambient, and faster than a one-sided estimate, because the coolant supply temperature must fall with load.
- The plant settles in about two minutes. A measured steady-state map plus an integral therefore predicts a full week’s cooling energy to about one percent, which is the licence to size from steady data.
- A fluctuating load costs real energy versus a steady one at the same mean, and nearly all of that cost is curvature of the fan power curve rather than lag. Load smoothing, not faster control, is the lever.
- Pumps, not fans, dominate cooling power in this warm-water architecture.
- Demand-response sheds are thermally free; only the restore ramp matters, and a ten-minute ramp complies everywhere.
- A climate-based sizing rule and an annual lookup that replaces thousands of wall-hours of simulation.
A gray-box reduced-order model built with a colleague runs 20–100× faster, and a pilot pumped two-phase loop with R1233zd(E) is the first step toward the same analysis for two-phase direct-to-chip cooling.
Status
First-author manuscript in preparation with seven co-authors. Presented to Gamma Technologies, Trane and A. O. Smith in 2026, and at ACRC meetings.