## Abstract

Cooling is one of the costly factors in data centers in terms of overall power consumption. Over the past few decades, traditional cooling approaches have maintained the facility's equipment during its operation. However, with the increasing demands of networking and computation, data centers are now facing substantial challenges in saving energy and reducing the power usage effectiveness. Many innovative strategies have been developed to respond to the demands. Several approaches relate to the change in the density of working gas. The locations of data centers are not limited to sea level. For example, the world's highest data center, the ALMA correlator located in the Andes of northern Chile, is more than 5,000 m above the sea level. The air density is only 60% compared with the air density at sea level, which can considerably affect the cooling capabilities because electronics cooling is related to the density of the working gas. Meanwhile, humidity and the types of working gas can affect both fan performance and electronics cooling capabilities. Theoretically, the effect of the density of the working gas on electronics cooling capabilities can be predicted by the ideal gas law, fan laws, and heat convection equations. In this study, we conducted an experimental study on the heat sink performance at a constant volumetric airflow rate under various pressure conditions and verified the effect of the change in the density of the working gas on electronics cooling performance. First, we measured the flow rate of different fan duties via AMCA 210 airflow bench. Second, we used an altitude chamber to simulate the environmental conditions of varying altitude levels. In the altitude chamber, we set up a heat sink and a fan connected serially in a duct. A heat sink was mounted on a dummy heater heated with a constant power of 165 W, and a fan set at constant speed was monitored during the test period. The correlations between CPU case temperature, outlet temperature, pressure drop, and environmental conditions were investigated.

## Introduction

Data centers need to be kept evolving to respond to the increasing demands of Ethernet speeds and computation while reducing management costs. One of the major costs of data centers is cooling management. Given that high temperature is harmful to the reliability and life cycles of equipment, thermal engineers need to predict the component temperatures under real conditions in data centers by means of simulations or experiments.

The environments of data centers are important to both IT and power equipment. Moreover, the locations of the data center are not limited to sea level anymore. Some data centers are located at high altitudes, whereas some data centers are located under the sea. Take, e.g., Microsoft's present project “Natick”; the emergence of the lights-out and self-sufficient underwater data center could be a feasible approach [1].

Thermofluidic behaviors of the electrical device are affected by the level of altitude. The altitude studies of heat transfer have been investigated in the past and have significant applications on designing products applied in high altitude levels, such as airships, unmanned aerial vehicles, and military electronics [2–4]. In 1984, Nelson [5] studied the electrical power components at high altitude. The results reveal that the relative air density decreases 10% with every 1,000 m gain from the sea level. He found that the thermal performance of electronic components reduced with the increase in altitude level. Besides, Ohadi and Qi [6] reviewed literature related to thermal management of electronic components in the harsh environment, and they proposed that the cooling efficiency of a heat sink is highly sensitive to altitude levels.

To rapidly predict the CPU case temperature as altitude varies, the density correction factor is often used to correct the temperature with respect to the temperature in the sea level scenario. However, the accuracy of the correction is unknown. In this study, we conducted experiments in an altitude chamber that we have fabricated. We measured the pressure drop across the heat sink and the case temperature of the dummy heater at a constant power of 165 W and constant airflow velocity as environmental pressure varies. The environmental conditions, the pressure drop across the heat sink, inlet temperature, outlet temperature, and CPU case temperature are all recorded during the test period.

### Altitude and Air Properties

At an ambient temperature of 20°C, the relationships between altitude levels, atmospheric pressure, and air densities are listed in Table I [7]. The density ratio is the relative density of air at sea level compared with the density at different altitude levels. The relationship between altitude and pressure can be described as a quadratic equation, as shown in Fig. 1.

## Experiment

### Heat Sink Dimensions

#### Fan Specifications

The fan used in this experiment is a DC brushless axial flow fan, and the fan motor is single phasing with four poles. The characteristics of the fan listed in Table III, except for the last item, are based on the fan tested at normal environmental conditions. The characteristics correspond to the environmental conditions 20° and 101.3 kPa.

#### Airflow Measurement Setup

The AMCA 210 airflow bench was used to conduct the airflow measurement, and the tested heat sink was placed in a duct connected to the airflow bench in series, as shown in Figs. 3 and 4. Afterward, we measured the airflow rate and fan speeds corresponding to varying fan duties. The results of airspeed through the heat sink channel versus fan speed are listed in Table IV.

#### Altitude Chamber Setup

The operating range of the air-cooled altitude chamber ranges from 20°C to 50°C for temperature and from 47 kPa to 200 kPa for pressure. The readings of the thermocouples, differential pressure, fan speed, fan power, and heater power are all monitored via externally connected instruments. The detailed setup of the altitude chamber and the test section are shown in Figs. 5 and 6, and the specifications of the altitude chamber are listed in Table V. Given that we measured the fan duty versus air velocity passing through the heat sink channel in the airflow measurement test in advance, we can establish the relationships between thermal properties corresponding to constant air velocity as elevation level varies.

## Theoretical Calculations of Pressure Drop

### Assumptions

Rectangular straight fin

Fins are integral to the base

Tip and bypass effects are neglected

Fully developed laminar flow, Re < 2,300

Incompressible, Newtonian, and steady flow conditions

### Nomenclature

#### Pressure Drop across the Heat Sink in a Duct

In this study, we applied an analytical method [8] to estimate the heat sink pressure drop as a function of heat sink geometries, flow velocity (*V*_{f}), apparent flow friction factor (*f*_{app}), the coefficient of contraction (*K*_{c}), coefficient of expansion (*K*_{e}), and air density (ρ). We compared the results of pressure drop calculation with the experiments in Fig. 7.

In eq. (1) [8], the first term is corresponding to major pressure loss; the second term is the contraction loss; and the third term is the expansion loss. In this equation, *f*_{app} is the apparent friction factor; *L* is the heat sink length; *D*_{H} is the hydraulic diameter defined in eq. (2) [8]; *K*_{c} is the pressure loss coefficient due to sudden contraction; *K*_{e} is the pressure loss coefficient due to sudden expansion; ρ is the air density, the values of air density corresponding to each altitude conditions referred to Table I; and *V*_{f} is the heat sink channel velocity defined in eq. (3).

where *D*_{H} is known as hydraulic diameter, defined as the ratio of four times of the cross-sectional area of the flow divided by the overall wetted perimeter of the cross-section [8].

where *V*_{f} is the heat sink channel velocity; *V* is the heat sink approach velocity; *A* is the total heat sink frontal area including the base; and *A*_{f} is the total free area that allows airflow to pass through.

#### Major Loss

The first term in eq. (1) is related to major losses, associated with air velocity through heat sink channels and heat sink geometries. The apparent friction factor (*f*_{app}) is defined in eq. (4) [8].

where friction factor f is a function of the aspect ratio of the heat sink gap (λ), channel Reynolds number (Re ^{−1}_{f}), and hydrodynamic development length of the heat sink (*L**) [8].

and the channel Reynolds number is defined in eq. (8).

#### Contraction Loss

The second term in eq. (1) represents the pressure loss due to contraction and is defined in eqs. (9) and (10) [8].

α is the ratio of the flow channels area to the area in which the flow approaches the heat sink.

#### Expansion Loss

## Experimental Results

In this experiment, we measure the pressure drop across the heat sink channel, CPU case temperature, and fan power at the altitude above the sea level at 0, 5,000, 10,000, and 15,000 ft corresponding to the absolute atmospheric pressure at 101.3, 84.3, 69.7, and 57.2 kPa, respectively. We have detailed the results in the following sections.

### Comparison of Theoretical Pressure Drop Calculation with Experimental Results

The theoretical models of pressure drop calculation are verified by the experimental results at constant heat sink channel air velocity of 8.71 m/s. Both the theoretical value and experimental results show that the pressure drop decreases linearly as altitude increases. However, at sea level, the theoretical pressure drop is 74.24 Pa, whereas the experimental pressure drop is 83 Pa. Besides, the maximum error between theoretical calculation and the experimental result happens at sea level. The maximum error is 10% and the error decreases as the elevation level increases. The errors between theoretical values and experimental data could be caused by the ideal assumptions of theoretical models. For example, in the experiment, clearances are observed between the heat sink and the test duct. Thus, the tip and bypass effects exist in real cases.

### Experimental Measurements—Constant Fan Duty

In many server cooling scenarios, stepwise fan speed control algorithm is often being applied, e.g., if the fan speed control algorithm refers to ambient temperature. The fan duty stays the same at constant ambient temperature regardless of the varying altitude levels.

Therefore, in this section, we discuss pressure drop, CPU case temperature, and fan characteristics at constant fan duty in the scenarios of different fan speeds and altitude levels. The results are shown in Figs. 8–11.

As shown in Fig. 8, given that the air density decreases with the increase in the altitude, according to eq. (1), the pressure drop decreases linearly as the altitude level increases. In the experiment, for the heat sink channel, air velocity of 8.71 m/s, the pressure drop is 83 Pa at sea level. Meanwhile, the pressure drop decreases to 54 Pa at the altitude level of 15,000 ft. In other words, the pressure drop at 15,000 ft is 35% compared with the pressure drop at sea level. For the heat sink channel, air velocity of 9.26 m/s, the pressure drop is 97 Pa at sea level. Meanwhile, the pressure drop decreases to 63 Pa at the altitude level of 15,000 ft. The pressure drop at 15,000 ft is 35% compared with the pressure drop at sea level as well.

Figs. 9 and 10 show the CPU case temperature and case-to-ambient thermal resistance, respectively. The definition of case-to-ambient thermal resistance is ψ_{ca} = (*T*_{case} − *T _{ambient}*)/ Power, where the power of the heater is 165 W in the experiments. As Figs. 9 and 10 show, both the CPU case temperature and the case-to-ambient thermal resistance increase linearly as altitude increases. Furthermore, the case-to-ambient thermal resistances at the velocity level at 8.71, 9.00, and 9.26 m/s all increase to 30% compared with the thermal resistances at sea level.

Figs. 11 and 12 show the fan current and fan power at various altitudes, fixed fan voltage, and constant rated voltage of 48 V, respectively.

Moreover, the fan current decreases by 25% at the channel air velocity of 8.71 m/s compared with the fan current at sea level. The fan current decreases even further by 27% as the air velocity increases to 9.26 m/s compared with the fan current at sea level.

### Experimental Measurements—Constant Fan Power

Considering data centers also care about power usage effectiveness (PUE), the most commonly used metric for evaluating the energy efficiency of data centers indicates the portion of power consumption used in computing equipment in contrast to noncomputing devices, such as cooling devices. In this section, we discuss the effect of constant fan power, indicating constant PUE, at different altitude levels on cooling performance.

Figs. 13 and 14 show the fan speeds and CPU case temperatures at the ambient temperature of 20°C and constant fan power of 7.3 W, respectively. The results indicate that, at constant fan power, even the fan speed increases as the altitude increases. Specifically, the CPU temperature increases from 63°C to 68°C as altitude increases from sea level to 15,000 ft at constant fan power. Therefore, considering constant PUE, the overall cooling abilities drop as altitude increases.

## Conclusions

In this study, we analyze the pressure drop across the heat sink channel, CPU case temperature, fan current, and fan power as altitude varies. The error between theoretical models and experiments is 10%, and the error decreases as the altitude increases. Given that the ambient pressure and air density decrease as the altitude increases, both CPU case temperature and case-to-ambient thermal resistances increase with the increase in the altitude. Meanwhile, both fan power and fan current decrease with the increase in altitude.

Considering the perspective of PUE, we also discuss the effects of constant fan power in different altitude levels on CPU case temperatures. For constant fan power at various altitudes, even the fan speed increases as the altitude increases and the CPU case temperature increases as the altitude increases, still getting worse than the cooling capabilities at sea level. As a result, the overall cooling abilities drop as the altitude increases.

## References

## Author notes

The original version of this paper was presented at IMAPS Advanced Technology Workshop and Tabletop Exhibit on *Thermal Management*, Los Gatos, CA, November 6–8, 2018.

Long Win Science & Technology Corporation, Taoyuan, Taiwan