A digital-twin and machine-learning framework for precise heat and energy management of data-centers

Abstract

The massive growth in data-centers has led to increased interest and regulations for management of waste heat and its utilization. This work seeks to develop a combined Digital-Twin and Machine-Learning framework to optimize such systems by controlling both the ventilation and the cooling of the bases of data units/processors in the system. This framework ascertains optimal cooling strategies to deliver a target temperature in the system using a minimum amount of energy. A model problem is constructed for a data-center, where the design variables are the flow rates and air-cooling at multiple ventilation ports and ground-level conduction-based base-cooling of processors. A thermo-fluid model, based on the Navier–Stokes equations and the first law of thermodynamics, for the data-center is constructed and a rapid, stencil-based, iterative solution method is developed. This is then combined with a genomic-based machine-learning algorithm to develop a digital-twin (digital-replica) of the system that can run in real-time or faster than the actual physical system, making it suitable as either a design tool or an adaptive controller. Numerical examples are provided to illustrate the framework.

Appendices

Appendix: Related websites

• 1. https://www.datacenterdynamics.com/en/analysis/taking-next-steps-stockholm-circular-city/

• 2. https://www.google.com/about/datacenters/efficiency/

• 3. https://en.wikipedia.org/wiki/Data_center

• 4. https://eta.lbl.gov/publications/united-states-data-center-energy

• 5. https://energyinnovation.org/2020/03/17/how-much-energy-do-data-centers-really-use/

• 6. https://www.nature.com/articles/d41586-018-06610-y

• 7. https://www.energy.gov/eere/buildings/data-centers-and-servers

• 8. https://www.vxchnge.com/blog/growing-energy-demands-of-data-centers

• 9. https://www.sciencedirect.com/science/article/pii/S0306261921003019

• 10. https://www.wsj.com/articles/data-center-company-aligned-energy-raises-1-25-billion-in-debt-to-fund-sustainable-facilities-11629407307 mod=hp_minor_pos4

• 11. https://datacenterfrontier.com/waste-heat-utilization-data-center-industry/

Appendix: Further discussion on fluid mechanics models

Although we considered an incompressible thermally-insensitive fluid in the body of the work, for completeness, we briefly discuss enhancements to such models.

1.1 Pressure-density approximation

There are a variety of possible Equations of State that connect the density to the pressure, such as a Boussinesq-like relation, which is adequate to describe dense gases and fluids, derived from³

$$\begin{aligned} \rho \approx \rho _{o}(P_o)+\frac{\partial \rho }{\partial P}\Delta P, \end{aligned}$$

(8.1)

where $\rho _{o}$ and $P_o$ are reference values and $\Delta P=P-P_o$. We define the bulk (compressibility) modulus by $\zeta {\mathop {=}\limits ^\mathrm{def}}\rho \frac{\partial P}{\partial \rho }$, yielding

$$\begin{aligned} \rho \approx \rho _{o}\left( 1+\frac{1}{\zeta } \Delta P\right) \Rightarrow P\approx P_o+\zeta \left( \frac{\rho }{\rho _{o}}-1\right) . \end{aligned}$$

(8.2)

For a constant density case, $\rho =\rho _{o}$, and utilizing the Boussinesq-like relation, $P=P_o$.

1.2 Buoyancy

Although we will not consider buoyancy in the present analysis, for completeness we illustrate a typical model. Consider the following decomposition of the body forces:

$$\begin{aligned} \varvec{f}=\rho \varvec{g}=\rho _o\varvec{g}+(\rho -\rho _o)\varvec{g}. \end{aligned}$$

(8.3)

Now we approximate

$$\begin{aligned} (\rho -\rho _o)\varvec{g}\approx -\rho _o\beta (\theta -\theta _o)\varvec{g}, \end{aligned}$$

(8.4)

where $\beta$ is the thermal expansion coefficient. Thus,

$$\begin{aligned} \Delta \rho =(\rho -\rho _o) \approx -\rho _o\beta (\theta -\theta _o), \end{aligned}$$

(8.5)

thus

$$\begin{aligned} \rho \approx \rho _o(1-\beta (\theta -\theta _o)). \end{aligned}$$

(8.6)

A generalization

$$\begin{aligned} \rho \approx \rho _oe^{-\beta (\theta -\theta _o)}\approx \rho _o(1-\beta (\theta -\theta _o))+\cdots \end{aligned}$$

(8.7)