# Cooling Effectiveness of a Data Center Room under Overhead Airflow via Entropy Generation Assessment in Transient Scenarios

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## Abstract

**:**

## 1. Introduction

## 2. Motivation and Goals

## 3. Mathematical Model and Numerical Implementation

- The room transfers no heat to the outside (adiabatic walls),
- Fully-contained aisle, in other words, air only flows through servers and heat exchangers,
- Heat conduction allowed through the aisle containment walls,
- Fluid flow in the turbulent regime,
- Constant server heat dissipation of 1 kW, for a total of 100 kW of required overhead cooling.

#### 3.1. Airside

#### 3.2. Server Transient Model

#### 3.3. Heat Exchanger Transient Model

#### 3.4. Entropy Generation

- Servers: heat transfer between the electronics and the cooling air; pressure drop as the air flows through the server, undergoing significant impedance
- Overhead heat exchangers: heat transfer between the chilled water and the airflow
- Airside: the temperature difference between the room and the aisle induces heat transfer through the containment walls; turbulent viscous dissipation of momentum becomes non-negligible

- ${\dot{S}}_{\mathrm{gen},\overline{\mathrm{D}}}^{\u2034}$: Entropy Generation by direct dissipation.
- ${\dot{S}}_{\mathrm{gen},{\mathrm{D}}^{\prime}}^{\u2034}$: Entropy Generation by turbulent dissipation.
- ${\dot{S}}_{\mathrm{gen},\overline{\mathrm{C}}}^{\u2034}$: Entropy Generation by heat conduction.
- ${\dot{S}}_{\mathrm{gen},{\mathrm{C}}^{\prime}}^{\u2034}$: Entropy Generation by heat transfer with fluctuating temperature gradients.

#### 3.5. Numerical Procedure

^{TM}. The velocity and pressure fields were coupled using the SIMPLE algorithm, and the nodes were interpolated via a second order upwind scheme.

^{TM}. We considered air as an ideal gas and assumed both the impedance and fan curves as a quadratic function of the mass flow rate, obtaining server volumetric flow rates of approximately 50 CFM.

- Fluent computes the Airside turbulent flow and moves the solution forward by one time step
- The airflow data are used as inputs to the servers and heat exchangers
- MATLAB solves the servers and heat exchangers
- MATLAB output data become inlet boundary conditions for Fluent, and the fluid flow is updated
- Go back to Step 1 under these new conditions

#### 3.6. Grid Independence

## 4. Steady State Analysis

#### Entropy Generation in an Idealized Case

## 5. Unsteady Behavior during the Cooling Process

## 6. Conclusions

- The server temperature distributed uniformly throughout the racks. The positioning of the overhead heat exchangers allowed for the cooling airflow to undergo less resistance than the common perforated tile flow. This led to a uniform distribution of cold fluid entering the servers.
- Aisle containment reduced the Entropy Generation in the Airside to negligible levels when compared to previous results from a legacy data center.
- Using a second law analysis, we determined the room cooling efficacy, which quantified the deviation of server thermal management from optimum operation.
- In terms of cooling performance, the OUF and the ODF approaches showed nearly identical results (under the constraints of our idealized analysis); selecting the correct scheme might potentially depend on other aspects, e.g., geometrical, mechanical, economical.
- The unsteady first and second law metrics presented in this numerical study show promise towards the grand goal of providing instantaneous thermal management as the data center demands it.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the room and boundary conditions for the two approaches: (

**a**) downward flow and (

**b**) upward flow.

**Figure 3.**Schematic representation of the phenomena that destroys entropy during the cooling process.

**Figure 6.**Conduction and Dissipation Entropy Generation distribution inside the room for the two approaches. Arrow indicates flow direction in the overhead heat exchanger.

**Figure 7.**Entropy Generation Number ${N}_{S}$ as a function of the effectiveness ratio ${\xi}_{s}/{\xi}_{\mathit{HX}}$.

N of Nodes | ${\dot{\mathit{S}}}_{\mathbf{gen},\mathit{s}}$ (Servers) | ${\dot{\mathit{S}}}_{\mathbf{gen},\mathbf{airside}}$ (Room + Aisle) | |
---|---|---|---|

Mesh 1 | 108,573 | 203.5 | 0.059 |

Mesh 2 | 167,493 | 203.4 | 0.062 |

Mesh 3 | 315,671 | 203.3 | 0.073 |

Mesh 4 | 563,859 | 203.9 | 0.075 |

**Table 2.**Total Entropy Generation (W/K) for racks, overhead heat exchangers, and the Airside (room-aisle).

Servers | Overhead Heat Exchangers | Airside | |
---|---|---|---|

ODF | 190.9 | 17.65 | 0.318 |

OUF | 203.4 | 18.55 | 0.062 |

ODF | OUF | |
---|---|---|

$\overline{\eta}$ | 0.66 | 0.68 |

${\sigma}_{\eta}$ | 0.0012 | 0.0006 |

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**MDPI and ACS Style**

Silva-Llanca, L.; del Valle, M.; Ortega, A.; Díaz, A.J.
Cooling Effectiveness of a Data Center Room under Overhead Airflow via Entropy Generation Assessment in Transient Scenarios. *Entropy* **2019**, *21*, 98.
https://doi.org/10.3390/e21010098

**AMA Style**

Silva-Llanca L, del Valle M, Ortega A, Díaz AJ.
Cooling Effectiveness of a Data Center Room under Overhead Airflow via Entropy Generation Assessment in Transient Scenarios. *Entropy*. 2019; 21(1):98.
https://doi.org/10.3390/e21010098

**Chicago/Turabian Style**

Silva-Llanca, Luis, Marcelo del Valle, Alfonso Ortega, and Andrés J. Díaz.
2019. "Cooling Effectiveness of a Data Center Room under Overhead Airflow via Entropy Generation Assessment in Transient Scenarios" *Entropy* 21, no. 1: 98.
https://doi.org/10.3390/e21010098