IEEE Circuits and Systems Magazine - Q1 2023 - 53

temperature both in Modelica and in 3D-ICE, avoiding
the burden of keeping those values in sync.
IX. Simulation Examples
We have established that nowadays, for high-performance
systems, the design of the cooling circuit must
often be tailor-made. We have also established that the
said circuit needs assessing prior to facing potentially
destructive stress, by joint simulation with the chip and
the policies aboard. However, when designing the cooling
circuit, sizing its components and setting up its controls,
the above joint simulation is quite often not necessary
owing to the band separation between on-silicon
and circuit dynamics. It is apparently desirable that the
same cooling circuit models can be used for any of the
above activities, i.e., both with and without a connection
to chip simulation codes like 3D-ICE.
Said otherwise, the workflow for designing a cooling
system should start by concentrating on sizing heat
sinks and hydraulic components, having in this initial
phase the chips to cool just represented as prescribed
thermal powers. Then, once the above and its controls
are assessed, the obtained model needs to be connected
to detailed chip simulators to investigate the behavior of
on-chip policies and perform the necessary fine tuning.
In this section we show a few examples to demonstrate
how our approach-and as a consequence the
presented library do fully support such a workflow,
that needs to concentrate sometimes on the chip alone,
sometimes on the cooling alone, and sometimes on the
compound of the two.
We would like to point out that the models here presented
are custom cooling loops built with parts that
have not yet been manufactured. Therefore, the reported
examples demonstrate one of the major strong points
of component-based simulation, i.e., the possibility to
assess the performance of new solutions prior to their
realization. The reader interested in how our models are
validated, and which accuracy can be achieved, can refer
to the previous work [9]. In the research presented
therein we modeled a specific water block, using the
same approach and equations adopted in the following
examples. In that case we could carry out a laboratory
validation, and the average temperature error observed
was 0.9 °C, while the maximum error-temporary and
during a transient -5 °C. Such a result is more than adequate
for the intended purpose.
A. Example 1
We start with an all-Modelica example (i.e., no chip simulator
is involved) to show the approach capability to
address quite complex cooling circuit models including
FIRST QUARTER 2023
Figure 10. Example 1-Modelica diagram.
controls. The used model is shown in Fig. 10: a centrifugal
pump (a) feeds three modulating valves (b) to govern
the flow rate through three waterblocks (c) connected
each to one of three CPUspreader compounds (d);
three water-air exchangers (e) and a vented storage tank
(f) close the circuit. Three PI regulators (g) control the
three spreader temperatures, also governing the pump
speed based on the water request. Boundary conditions
are the external air temperature (h) and the power traces
for the three CPUs (i). The DAE model corresponding
to the scheme in Fig. 10 has 1901 equations and 207 state
variables.
As said, CPUs are modeled as prescribed powers,
and only a spreader layer is represented: the relevant
thermal characteristics and the TDP (91 W) were taken
from an Intel Core i5-6600K. Application traces have
been collected using an Intel Core i5-6600K processor
instrumented with a shunt resistor between the 12V
power supply and the connector on the motherboard
dedicated to powering the CPU, thus excluding interference
from the RAM and motherboard power consumption.
Power traces were collected while running the
Cloverleaf mini-application [33] from the UK Mini-App
Consortium, which employs an explicit second order
method for the resolution of compressible Euler equations,
a representative application for the high-performance
computing domain.
Thermal simulations were instead performed on
an Intel Core i9-12900K running Ubuntu 20.04.4, using
OpenModelica 1.20.0 dev-155-g379c110. The simulation
IEEE CIRCUITS AND SYSTEMS MAGAZINE
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