IEEE Circuits and Systems Magazine - Q1 2023 - 54

Figure 11. Example 1-simulation results.
results shown in Fig. 11 demonstrate the opportunity
of endowing modern cooling with controls, thanks to
which good temperature management is achieved on
the scale of some seconds; this cannot replace millisecond-scale
control, typically via DVFS, but certainly
helps. It is worth noticing that the 4-hour-long simulation
took only 84 seconds, which is approximately 170×
faster than real time.
B. Example 2
We now present an example including detailed chip simulation
with 3D-ICE. The simulated system is composed
of a waterblock heat exchanger fed by a chiller that provides
a constant water inlet temperature of 24 °C and a
flow rate of 0.12 liters/minute. The waterblock is modeled
in Modelica as a 1D cavity with a finned base of
3×3cm, in which turbulent water flow induces a convective
heat exchange ruled by the Dittus-Bölter equation
[34]. The waterblock Modelica model is connected, by
means of the 3D-ICE 3.0 co-simulation interface, with the
3D-ICE model of a square flip chip with a side of 1.024cm.
The chip floorplan features an array of 4×4 heat generation
areas, each split in two, so as to model our Thermal
Test Chip (TTC) platform [35].
Fig. 12 shows two steady-state chip temperature maps
with different heating patterns, both totaling a power of
60W. The upper temperature map comes from a uniform
power distribution across the 16 heating elements. In
this case, the maximum temperature of 66.7 °C is observed
in the central heating elements; temperatures in
the bottom part of the chip map are slightly lower as
this is where the water inlet is located.
54
IEEE CIRCUITS AND SYSTEMS MAGAZINE
Figure 12. Example 2-simulation results: steady-state chip
temperature maps with uniform (above) and chessboard
(below) power distribution.
The second simulation instead shows a hotspot scenario,
where the heating elements are turned on in a
chessboard pattern, and dissipate 7.5W each to still total
60W. As can be seen the steady-state temperatures are
higher, reaching a maximum of 79.1 °C, but also the temperature
distribution changes: the highest temperatures
are now at the corners, not at the center. The reason is
that central heating elements can effectively spread heat
laterally through the cold parts of the chip, thus reaching
a lower temperature than the elements at the corners.
Both simulations were performed on a Core i9-12900KF
server running Ubuntu 20.04.4 LTS, OpenModelica 1.20.0
dev-155-g379c110 and 3D-ICE 3.1. The simulation time is
72s: 95% is spent in 3D-ICE for the high-resolution chip
simulation, and only 5% by Modelica for the heat sink
simulation, thanks to the different spatial discretisation
granularities for the chip and the sink models [9].
FIRST QUARTER 2023

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