Investigation of a Gas-Pump-Driven Loop Heat Pipe

Abstract

A loop heat pipe (LHP) is an efficient method of conserving energy in data center cooling applications. In scenarios where the installation is constrained by height or distance limitations, pump driving is needed. This paper examines the performance changes induced by a gas pump both experimentally and theoretically. An adjustable, oil-free linear compressor is utilized as a gas pump. The evaporator is a finned-tube heat exchanger and the condenser is a water-cooled plate heat exchanger. When the filling ratio of the working fluid is insufficient, employing a gas pump can enhance the heat transfer performance. However, when the filling ratio of the working fluid is sufficient, while the gas pump can increase the flowrate of the working fluid, the heat transfer rate (HTR) does not change significantly. In fact, it may reduce the energy efficiency ratio of the heat pipe. Infrared thermography has proven to be an efficient tool for estimating the area ratio of different zones within the evaporator, which is crucial for the output regulation of the compressor. The area ratio of the two-phase zone is nearly linear to the HTR. Through the establishment of a physical model of a gas-pump-driven loop heat pipe (GPLHP), the impacts of the LHP size and gas pump operation on the heat transfer performance are analyzed. It is found that the gas pump can extend the application range of the LHP, although it has a minimal impact on the maximum HTR. How to select a gas pump for an LHP is discussed.

1. Introduction

The number and scale of data centers has increased in recent years due to the development of advanced information technologies, including artificial intelligence. Accordingly, the electricity consumption of these data centers has soared. In China, the annual electricity consumption of data centers is estimated to account for 2% of the total national electricity consumption [1]. In a typical data center, 45% of the electricity may be used by the thermal management system. To promote energy efficiency and reduce the power usage effectiveness (PUE) of the data center, various advanced cooling technologies are being implemented and studied. These include direct and indirect natural cooling, liquid-cooling cold plates, submersion, heat pipes, and thermosiphon-based systems [2].

A loop heat pipe (LHP) is an advanced two-phase heat transfer device that efficiently transports thermal energy over long distances, typically up to several meters. As a highly efficient cooling solution for cooling data centers, it has been a hot topic in recent years [3]. The driving force for an LHP can be gravity, as shown in Figure 1a, but some problems may exist, such as a slow start-up, a necessary height difference between the evaporator and the condenser, and poor system performance when handling a high heat flux, large room, long pipelines and multiple branches [1]. To increase the driving force, either a liquid pump or a gas pump may be employed, as shown in Figure 1b,c. These are also called mechanically driven two-phase cooling loops.

There have been numerous studies about the testing, application, modelling and economic analysis of liquid-pump-driven loop heat pipes (LPLHPs). Zhang et al. found that there is an approximately linear relationship between the capacity and the temperature difference for an LPLHP, and that there are no significant changes in the heat transfer capacity when the mass flow rate of the working fluid varies within a certain range, i.e., when the gasification rate of the working fluid is 2% and 50% [4]. Wang et al. studied the effects of influencing factors on the performance of a pump-driven loop heat pipe and found that there exists an optimum mass flow rate of the working fluid. They also discovered that R32 performs better than R152a and R22 [5]. Ma et al. conducted an energy saving analysis based on the curve fitting of the in situ energy efficiency ratio (EER) and achieved a high energy saving ratio compared with air conditioners for a data center in Beijing. When the temperature differences between the indoors and outdoors were 10 °C and 25 °C, the EER of the LPLHP were 12.9 and 29.7, respectively [6,7,8]. Zhou et al. further investigated the energy savings and payback periods of the LPLHP system for different cities in China and found that LPLHPs are suitable for about 74.2% of these cities, bringing an annual energy saving ratio of over 30% [9]. Xue et al. evaluated the performance of a GPLHP unit installed in a small data center in Beijing, and estimated an annual energy saving rate of 25.78% compared to the original air conditioning [10]. Kokate and Park developed a comprehensive thermal–hydraulic flow network model for an LPLHP to study the system performance characteristics. Their study highlights the trade-off between the total system thermal resistance reduction and the increased pumping power [11]. It was found that smaller microchannels in the evaporator had a significant heat transfer enhancement but poor system performance. Middelhuis et al. developed a model of an LPLHP with multiple evaporators and checked it with experiments. The pressure and flow predictions were in agreement with the measurements in a qualitative manner, but the peak values were consistently underestimated [12]. The economy, convenience and flexibility of using an LPLHP for heat dissipation have been demonstrated by these studies.

Compared to LPLHPs, gas-pump-driven loop heat pipes (GPLHPs) can achieve a higher condensing temperature and lower evaporating temperature at the same mass flow rate, thus leading to a better performance [13]. Currently, most of the test studies about GPLHPs are conducted with refrigeration compressors. Wei et al. tested a GPLHP for communication base stations and obtained an EER of 7.705 when the temperature difference was 30 °C and a sliding vane compressor was used [14]. Shi et al. tested a GPLHP integrated with a R410a air conditioner. The refrigeration compressor was also used as a gas pump. Compared to the conventional air conditioner, the annual energy efficiency ratio of the composite system increased by 40% [15]. The phenomenon of over-compression was observed in their studies. Zhang et al. conducted a comparative study between gravity-assisted LHPs and GPLHPs, and concluded that gas-side driving can improve the performance noticeably only when the performance of the LHP deviates significantly from the “ideal cycle”, and the performance upper limit is the performance of the “ideal cycle”. Compared with liquid-side driving, gas-side driving increases the condensing temperature and decreases the evaporating temperature, thus enhancing the heat transfer performance [16]. Li et al. developed an improved rotary booster with a small pressure ratio for a GPLHP and obtained an EER improvement of 104.7% compared to an LPLHP when the temperature difference was 10 °C [17]. Wang and Shao tested and analyzed a GPLHP integrated with an air conditioner used in a data center [18]. For three types of compressors, namely, an inverter scroll compressor, inverter rotary compressor and maglev compressor, the PUE values were less than 1.25, 1.3, 1.2, respectively. It can be noted that the application and research of GPLHPs are not as extensive as those of LPLHPs. This may be for two reasons: (1) a gas pump is larger than a liquid pump, which may be inconvenient for installation; and (2) there is a lack of an appropriate commercial gas pump product that is suitable for GPLHP application.

Compared to LPLHPs, GPLHPs possess distinct advantages when properly designed and operated. To learn more about the design and control of GPLHPs, experimental and theoretical investigations were conducted in this study. A GPLHP that employed a linear compressor and cooled a cabinet was tested and modeled. Infrared thermography technology was employed to assess the evaporator operation. The impact of the gas pump on the heat transfer performance of the GPLHP was analyzed, and the selection and control of the gas pump were discussed.

2. Experiment

The schematic diagram and a photo of the experimental system are shown in Figure 2; the system was transformed from the setup utilized in a previous study [19]. The orientation of the evaporator and condenser in the setup is identical to that at the engineering site. The part enclosed by the rectangular dashed line is the loop heat pipe. R134a is chosen as the working fluid due to its widespread use and its zero ozone depletion potential [2]. However, because of its moderate Global Warming Potential (GWP), there is a growing shift towards phasing out R134a in favor of more eco-friendly alternatives. R134a is charged into the LHP as follows: (1) the LHP is vacuumed to below 100Pa for over half an hour; (2) R134a in a storage tank is filled into the LHP through the filling port; and (3) the charged amount is determined by the weight difference in the tank before and after the charge. The cooling water of the LHP is provided by a water-cooled chiller. The experimental system can run in two modes: using a gravity-assisted LHP and GPLHP; these are switched by the open/close of three valves, V1, V2 and V3. An oil-free linear compressor (Embraco, WMD7H) is used as the gas pump. Its operation can be regulated with a specific inverter that outputs a voltage of 110–135Hz. The pressure lift afforded by the gas pump is partially offset by the V3 valve according to the test requirements. The evaporator of the LHP is a finned-tube heat exchanger that has four rows of tubes. Fourteen inverter fans blow air through the evaporator. The condenser of the SHP is a plate heat exchanger. The bottom of the condenser is 0.6m higher than the top of the evaporator. Detailed information about the evaporator and the condenser is given in

Table 1. Detailed information about the evaporator and the condenser.

Parameter	Value
Evaporator
Inner diameter of liquid inlet line (mm)	15.88
Inner diameter of gas outlet line (mm)	19.05
Space between neighbored columns (mm)	18
Space between neighbored rows (mm)	18
Thickness of corrugated fin (mm)	0.11
Space between neighbored fins (mm)	1.5
Tube size (mm)	∅7 × 0.24
Tube length (mm)	1800
Number of tube rows	4
Column number of tube	17
Fan number	14
Condenser
Length of the plate (mm)	525
Width of the plate (mm)	107
Thickness of the plate (mm)	0.4
Chevron angle of the plate (°)	65
Hydraulic diameter (mm)	4.2
Flow area of single channel (mm2)	206
Heat transfer area (m2)	1.25

. The riser has a length of 6 m and an inner diameter of 17 mm. The downcomer has a length of 6.7 m and an inner diameter of 14 mm. Four electric heaters that have a total of 8 kW of heating power are placed evenly in the cabinet to serve as the dummy load.

The parameters of the cooling water, the working fluid of the LHP and the air, and the electricity consumption were measured by sensors, whose information is listed in

Table 2. Detailed information about the sensors.

Item	Type	Range	Precision
Temperature	PT100 platinum resistor (Xiamen Mingcon Instrument Co., Ltd., Xiamen, China)	−50~500 °C	±0.1 °C
Pressure	Pressure transmitter (Xuan Sheng Instrument Technology Co., Ltd., Suzhou, China)	0~5 MPa	±0.2%
Pressure difference	EJA110E pressure difference transducer (Yokogawa China Co., Ltd., Shanghai, China)	0~100 kPa	±0.075%
Air velocity	Hot wire anemometer (Testo SE & Co., KGaA, Shenzhen, China)	0~30 m/s	±0.1 m/s
Refrigerant mass flow rate	Coriolis mass flowmeter (MicroMotion, Inc., Boulder, CO, USA)	0~0.378 kg/s	±0.2%
Water flow rate	Electromagnetic flowmeter (Shanghai Micro Condition Measurement and Control Technology Co., Ltd., Shanghai, China)	0~17.671 m3/h	±0.2%
Electricity power	Power meter (Ningbo Gigh-tech Zone Xincheng Electronics Co., Ltd., Ningbo, China)	0~2500 W	±0.1%

. The signals of the sensors are acquired by a data acquisition unit, Agilent 34970a. BenchLink Data Logger, a software accompanied by an instrument, is used to collect the data. An infrared imager (Tix660, Fluke Corporation, Everett, USA) is employed to snapshot the evaporator. Detailed information about the infrared imager is shown in

Table 3. Detailed information about the infrared imager.

Parameter	Value
Temperature range	−40~+1200 °C
Measurement accuracy	±1.5 °C or ±1.5%
Image resolution	640 × 480 Pixels
NETD	0.03 °C
Wavelength range	7.5~14 μm

.

The experimental system, with the exception of the cooling tower and the water pump, is installed in an air-conditioned room. The heat transfer rate of the LHP is calculated using the following water-side parameters:

$$\mathrm{Q}=C_w{\rho }_w{V}_w\left(T_{wo}-T_{wi}\right)$$

(1)

The EER of the SHP is estimated by the following formula:

$$\mathrm{E}\mathrm{E}\mathrm{R}={\displaystyle \frac{Q}{W_{fan}+W_{pump}}}$$

(2)

The thermal resistance of the LHP is defined as follows:

$${\mathsf{\Omega }}_{sys}={\displaystyle \frac{T_{ai}-(T_{wo}+T_{wi})/2}{Q}}$$

(3)

The thermal conductance of the LHP is the reciprocal of ${\mathsf{\Omega }}_{sys}$:

$${\mathsf{\Pi }}_{sys}=1/{\mathsf{\Omega }}_{sys}$$

(4)

The maximum measurement uncertainties for the heat transfer rate, the thermal resistance, and the EER are calculated by the following equations:

$${\displaystyle \frac{\Delta Q}{Q}}=\sqrt{{\left({\displaystyle \frac{\Delta V_w}{V_w}}\right)}^2+{\displaystyle \frac{{\left(\Delta T_{wo}\right)}^2+{\left(\Delta T_{wi}\right)}^2}{{\left(T_{wo}-T_{wi}\right)}^2}}}$$

(5)

$${\displaystyle \frac{{\Delta \mathsf{\Omega }}_{sys}}{{\mathsf{\Omega }}_{sys}}}=\sqrt{{\left({\displaystyle \frac{\Delta Q}{Q}}\right)}^2+{\displaystyle \frac{{\left(\Delta T_{ai}\right)}^2+{\left(0.5\Delta T_{wi}\right)}^2+{\left(0.5\Delta T_{wo}\right)}^2}{{\left[T_{ai}-(T_{wo}+T_{wi})/2\right]}^2}}}$$

(6)

$${\displaystyle \frac{\Delta EER}{EER}}=\sqrt{{\left({\displaystyle \frac{\Delta Q}{Q}}\right)}^2+{\displaystyle \frac{{\left(\Delta W_{fan}\right)}^2+{\left(\Delta W_{pump}\right)}^2}{{\left(W_{fan}+W_{pump}\right)}^2}}}$$

(7)

The corresponding uncertainties are 2.81%, 2.96%, and 2.98%, respectively.

3. Modelling and Solving

The mathematical model for a gravity-assisted LHP was established in our previous study [19]. Based upon this model, a mathematical model for a GPLHP is established here. The details of the model and its solution are explained as follows.

3.1. Model Assumption

Some brief assumptions about the model are as follows: (1) there is no heat exchange between the riser, the downcomer, the condenser and the environment; (2) in the evaporator, the working fluid is evenly distributed across the parallel tubes on the same row; (3) the air flows uniformly through the evaporator; (4) the pressure drops caused by flow turns in the flexible riser and downcomer tubes are considered negligible; (5) the downcomer is filled with liquid working fluid; and (6) the pipelines of the riser and the downcomer are straight.

3.2. Model

3.2.1. Single-Phase Heat Transfer

For the single-phase heat transfer of working fluid in a round tube, Hausen, Gnielinski, and Dittus–Boelter correlations are applied according to the value of the Renold number [20].

$$\mathrm{N}\mathrm{u}=3.65+{\displaystyle \frac{0.0668(\mathrm{D}/\mathrm{L})\mathrm{R}\mathrm{e}\mathrm{P}\mathrm{r}}{1+0.04\left[\right(\mathrm{D}/\mathrm{L})\mathrm{RePr}{]}^{2/3}}},\mathrm{R}\mathrm{e}<2300$$

(8)

$$\mathrm{N}\mathrm{u}={\displaystyle \frac{\mathsf{\xi }\left(\mathrm{R}\mathrm{e}-1000\right)\mathrm{P}\mathrm{r}}{1+12.7\sqrt{\mathsf{\xi }}\left({\mathrm{P}\mathrm{r}}^{2/3}-1\right)}},\xi ={\displaystyle \frac{1}{8{\left[1.82\log \left(Re\right)-1.64\right]}^2}},2300\le \mathrm{R}\mathrm{e}\le \mathrm{10,000}$$

(9)

$$Nu=0.023{\mathit{Re}}^{0.8}{Pr}^{0.4},\mathrm{R}\mathrm{e}>\mathrm{10,000}$$

(10)

For single-phase heat transfer in a plate heat exchanger, the correlation proposed by Roetzel et al. is adopted [21]:

$$\mathrm{Nu}=0.317{\mathrm{R}\mathrm{e}}^{0.703}{\mathrm{P}\mathrm{r}}^{1/3}$$

(11)

To determine the heat transfer coefficient on the air side, the correlation for plain flat fins on staggered tube bundles is taken from reference [22]:

$$\mathrm{N}\mathrm{u}=\mathrm{C}\times {Re}^n{\left({\displaystyle \frac{{\mathrm{L}}_{fin}}{{\mathrm{d}}_{\mathrm{e}\mathrm{q}}}}\right)}^{\mathrm{m}}$$

(12)

where m and C are the functions of Re, and n is a function of $L_{fin}/d_{eq}$.

3.2.2. Two-Phase Heat Transfer

For the evaporative heat transfer of the working fluid in a round tube where the fluid quality is less than 90%, the Gungor–Winterton correlation is adopted [23].

For evaporative heat transfer where the fluid quality is greater than 90%, the formula suggested by Bensafi et al. is used [24]:

$${\mathrm{h}}_{\mathrm{x}}=10\left[\left(1-\mathrm{x}\right){\mathrm{h}}_{0.9}+\left(\mathrm{x}-0.9\right){\mathrm{h}}_{\mathrm{v}\mathrm{a}\mathrm{p}}\right]$$

(13)

For the condensation heat transfer of the working fluid in a plate heat exchanger, a correlation from a technical manual is employed [25]:

$${\mathsf{\alpha }}_{\mathrm{tp}}=6.43{\left({\displaystyle \frac{{\mathsf{\lambda }}_{\mathrm{l}}^3{{\mathsf{\rho }}_{\mathrm{l}}}^2\mathrm{g}}{{{\mathsf{\mu }}_{\mathrm{l}}}^2}}\right)}^{1/3}\times {{\mathrm{Re}}_{\mathrm{tp}}}^{1/3}$$

(14)

3.2.3. Single Phase Pressure Drop

The frictional pressure drop for subcooled liquid and superheated vapor flowing within a round tube can be calculated by the following:

$$\mathsf{\Delta }{\mathrm{P}}_{\mathrm{f}}=\mathrm{f}{\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{r}}{\mathrm{v}}_{\mathrm{r}}^2}{2}}{\displaystyle \frac{\mathrm{L}}{D}}$$

(15)

where $f$ is estimated by the Poiseuille correlation when $Re<2100$ and the Blasius correlation when $2100\le Re<\mathrm{10,000}$, as follows [26]:

$$\mathrm{f}={\displaystyle \frac{16}{Re}}\mathrm{Re}<2100$$

(16)

$$f=0.079/{Re}^{0.25}2100\le Re<\mathrm{10,000}$$

(17)

For the single-phase flow of gas or liquid in a plate heat exchanger, the correlation proposed by Muley and Manglik, which considers the effects of the chevron angle and surface area enlargement factor, is adopted for the calculation of the frictional pressure drop [27].

For air flow through a tube array with plain flat fins, the pressure drop is calculated by a correlation provided in reference [22].

$$\Delta P_{air}=11.772A{\displaystyle \frac{{\mathrm{L}}_{fin}}{{\mathrm{d}}_{\mathrm{e}\mathrm{q}}}}{\left(\mathsf{\rho }{\mathrm{u}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)}^{1.7}$$

(18)

where constant A equals 0.0113 for a rough surface.

3.2.4. Two-Phase Pressure Drop

For two-phase flow, the total pressure drop may be calculated by the following:

$$\mathsf{\Delta }{\mathrm{P}}_{\mathrm{t}\mathrm{p}}=\mathsf{\Delta }{\mathrm{P}}_{\mathrm{f}}+\mathsf{\Delta }{\mathrm{P}}_{\mathrm{g}}+\mathsf{\Delta }{\mathrm{P}}_{\mathrm{a}}$$

(19)

where $\mathsf{\Delta }{P}_a$ is estimated by the following:

$$\mathsf{\Delta }{\mathrm{P}}_{\mathrm{a}}={\mathrm{G}}^2{\left[{\displaystyle \frac{{\mathrm{x}}^2}{{\mathsf{\rho }}_{\mathrm{v}}\mathsf{\alpha }}}+{\displaystyle \frac{{\left(1-\mathrm{x}\right)}^2}{{\mathsf{\rho }}_{\mathrm{l}}\left(1-\mathsf{\alpha }\right)}}\right]}_{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{G}}^2{\left[{\displaystyle \frac{{\mathrm{x}}^2}{{\mathsf{\rho }}_{\mathrm{v}}\mathsf{\alpha }}}+{\displaystyle \frac{{\left(1-\mathrm{x}\right)}^2}{{\mathsf{\rho }}_{\mathrm{l}}\left(1-\mathsf{\alpha }\right)}}\right]}_{\mathrm{i}\mathrm{n}}$$

(20)

in which the subscript “out” denotes the outlet of the two-phase zone, subscript “in” denotes the inlet of the two-phase zone, and $\alpha$ is the void fraction evaluated by the Zivi model [28]:

$$\mathsf{\alpha }={\displaystyle \frac{\mathrm{x}{\mathsf{\rho }}_{\mathrm{l}}}{\mathrm{x}{\mathsf{\rho }}_{\mathrm{l}}+\mathrm{S}\left(1-\mathrm{x}\right){\mathsf{\rho }}_{\mathrm{g}}}}$$

(21)

$$\mathrm{S}={\left({\mathsf{\rho }}_{\mathrm{l}}/{\mathsf{\rho }}_{\mathrm{g}}\right)}^{1/3}$$

(22)

$\mathsf{\Delta }{P}_g$ is calculated by the following:

$$\mathsf{\Delta }{\mathrm{P}}_{\mathrm{g}}=\left[\mathsf{\alpha }{\mathsf{\rho }}_{\mathrm{g}}+\left(1-\mathsf{\alpha }\right){\mathsf{\rho }}_{\mathrm{l}}\right]\mathrm{g}{L}_{tp}$$

(23)

There are two cases for the calculation of $\mathsf{\Delta }{P}_f$. One case is evaporative flow in a round tube, for which $\mathsf{\Delta }{P}_f$ is calculated by the Friedel correlation [29]. The other case is the condensation flow in a plate heat exchanger, for which $\Delta P_f$ is calculated by the formula proposed by Han et al. [30].

3.2.5. Fan and Gas Pump

The power consumption of the fan is calculated by the following:

$${\mathrm{W}}_{fan}=\Delta {\mathrm{p}}_{fan}\dot{\mathrm{F}}/\mathsf{\eta }$$

(24)

where $\eta$, the fan efficiency, is set at 0.7. The pressure lift is estimated with a quadratic model:

$$\Delta {\mathrm{p}}_{fan}=\Delta {\mathrm{p}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\Delta {\mathrm{p}}_{\mathrm{m}\mathrm{a}\mathrm{x}}{\left({\displaystyle \frac{\dot{\mathrm{F}}}{{\dot{\mathrm{F}}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)}^2$$

(25)

The power consumption of the gas pump is estimated with a specific model for the oil-free linear compressor [31]:

$$W_{pump}=\dot{m_r}(h_{pump,out}-h_{pump,in})/\left({\eta }_m{\eta }_s{\eta }_v\right)$$

(26)

$${{\eta }_t=\eta }_m{\eta }_s{\eta }_v$$

(27)

$$s_{pump,out}=s_{pump,in}$$

(28)

$${{\Delta p}_{pump}=p}_{pump,out}-p_{pump,in}$$

(29)

3.2.6. Mass Balance

The total amount of working fluid within the LHP should equal the initial charge:

$${\mathrm{m}}_0={\mathrm{m}}_{\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}+{\mathrm{m}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}+{\mathrm{m}}_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}+{\mathrm{m}}_{\mathrm{d}\mathrm{o}\mathrm{w}\mathrm{n}}$$

(30)

when the mass in the two-phase zone of the evaporator or condenser is estimated, the involved void fraction is evaluated by the Zivi model [28].

The filling ratio of the LHP is defined as follows:

$$\mathsf{\phi }={\displaystyle \frac{m_0}{{{\rho }_l\mathrm{V}}_{\mathrm{e}\mathrm{v}\mathrm{a}\mathrm{p}}}}$$

(31)

All the fluid physical properties are obtained through calling the REFPROP (version 9.1) program of NIST [32].

3.3. Model Solving

Assuming that the configuration of the GPLHP (including the structure of the evaporator and the condenser, the length and diameter of the riser and downcomer, the type of gas pump, and the height difference between the evaporator and the condenser), the inlet air parameters of the evaporator, the inlet water parameters of the condenser and the filling ratio of the working fluid are known, the performance curve of the GPLHP may be predicted by solving the aforementioned equations, which describe mass, energy and momentum conservations, and heat transfer and fluid flow characteristics. The evaporator is segmented in the same way as our previous study [19]. The solving procedure shown in Figure 3a is described briefly as follows: (1) input the known parameters, including the size of each component of the GPLHP, the inlet parameters, the flowrate of the cooling water, the flowrate of the working fluid and the working fluid charge; (2) assume the thermodynamic state of the working fluid at the evaporator inlet and the flowrate of the working fluid; (3) calculate the heat transfer and the fluid flow in the evaporator row by row and adjust the flow distribution of the working fluid between rows to ensure pressure drop balance, as shown in Figure 3b; (4) calculate the flow process in the riser; (5) calculate the thermodynamic process in the gas pump; (6) calculate the heat transfer and fluid flow processes in the condenser and the downcomer; (7) compare the calculated working fluid charge and the assumed charge, the calculated and assumed inlet state parameters of the evaporator, and adjust the flowrate of the working fluid, the inlet pressure and the subcooling of the evaporator; (8) repeat (2)~(7) until convergence ($\Delta <\epsilon ,\epsilon ={10}^{-5}$) is reached; and (9) output the results, including the outlet parameters on both sides of the evaporator and the condenser, the heat transfer rate, the pressure drop on the air side, and the fan power and pump power.

4. Results and Discussions

Both experimental and numerical investigations have been carried out for the specified GPLHP. In this part, experimental results about the influences of pressure lift are presented first. A finding regarding the relationship between the heat conductance of the LHP and area ratio of the two-phase zone is reported. Secondly, with the help of numerical analysis, the effects of the pressure lift of the gas pump on the performance of the LHP under cases of unfavorable installation conditions are disclosed. Finally, the configuration of the gas pump and operation debugging of the GPLHP are discussed.

4.1. Experimental Results

Figure 4, Figure 5, Figure 6 and Figure 7 illustrate the influence of pressure lift on the mass flowrate of the working fluid, the heat transfer rate, the heat conductance and the EER of the LHP under three filling ratio scenarios: 0.755, 0.971, 1.078, representing insufficient charge, appropriate charge and overcharge, respectively. The selection of these three filling ratios was based on our previous study [19]. Zero pressure lift corresponds to the gravity-assisted situation. The experiments were carried out under the following conditions: the inlet cooling water temperature of the condenser was fixed at 16, the simulated load was fixed at 8 kW, and the fan speed was fixed at 3500 rpm. The pressure lift was varied by regulating the input frequency of the gas pump, from 108 Hz to 118 Hz.

As depicted in Figure 4, when the pressure lift afforded by the gas pump increases, the mass flowrate of the working fluid increases to varying degrees for three filling ratio scenarios. For the same pressure lift, the increment in the mass flowrate for $\phi =0.971$ is the largest, while the increment in the mass flowrate for $\phi =0.755$ is the smallest. The increase in the mass flowrate does not mean the improvement of heat transfer. As shown in Figure 5, for the scenario of insufficient charge, the heat transfer rate increases from 5.151 kW to 6.423 kW when the pressure lift rises from 0 to 4.37 kPa, but remains relatively constant with the further elevation of the pressure lift; for the scenario of overcharge, a minor positive effect of pressure lift is observed; a pressure lift of 9.16 kPa only results in a 3.3% change in the heat transfer rate. For the scenario of appropriate charge, an adverse effect of pressure lift is observed; a pressure lift of 8.31 kPa leads to a 2.2% reduction in the heat transfer rate. The thermal conductance of the LHP for the three filling ratio scenarios has a similar trend to that of the heat transfer rate, as shown in Figure 6. It is not surprising that the EER of the LHP decreases when a gas pump is employed in the scenarios of appropriate charge and overcharge. For the scenario of appropriate charge, the EER decreases from 20.8 to 15.2 as the pressure lift increases from 0 to 8.31 kPa. For the scenario of overcharge, the EER decreases from 19.5 to 14.8 as the pressure lift increases from 0 to 9.16 kPa. For the scenario of insufficient charge, as the pressure lift increases from 0 to 6.14 kPa, the EER initially increases and then decreases, reaching a maximum of 18.11 at a pressure lift of 3.89 kPa.

Figure 8 displays an image of the evaporator recorded by an infrared thermal imager, with the superheat zone, two-phase zone and subcooled zone labelled. The area ratio of the two-phase zone has been estimated using the method outlined in reference [33]. Through an analysis of the experimental datapoints obtained under different filling ratios and inlet cooling water temperatures, it was found that an approximately linear relationship exists between the heat conductance of the LHP and the area ratio of the two-phase zone, as shown in Figure 9. The relationship is expressed as follows:

$${\mathsf{\Pi }}_{sys}=0.1699\mathsf{\Theta }+0.2203$$

(32)

with fitting degree R² = 0.9729. From this relationship, it appears that the largest heat conductance of the LHP may reach 0.3902 kW/°C.

4.2. Numerical Results

Figure 10 presents a comparison of the heat transfer rates of the LHP, as derived from the numerical simulation and experimental data when the filling ratio is 0.971 and the pressure lift equals zero. The maximum discrepancy is 10.3%, and the average discrepancy is 5.1%. Figure 11 gives a comparison between the numerical and experimental results for the heat transfer rate of the LHP at different pressure lifts at different filling ratios. The numerical results in Figure 11 (also for Figure 10) were obtained in experimental conditions. The maximum discrepancy is 9.6%, and the average discrepancy is 5.7%. Overall, these comparisons indicate good consistency between the numerical predictions and the experimental outcomes.

With the help of numerical analysis, the impact of the configuration of the gas pump on the performance of the LHP under unfavorable installation conditions may be quantitatively revealed. In engineering practice, the common unfavorable conditions include an insufficient height difference between the evaporator and the condenser due to space limitations, and an overly long distance between the condenser and the evaporator due to the dimensions of the computer room. Figure 12 illustrates the influence of pressure lift on Q and the EER for the former case, with a filling ratio of 0.971 and a cooling water inlet temperature of 16 °C. With the pressure lift afforded by the gas pump, the heat transfer rate initially increases with the pump power, then comes to a stable value. Therefore, there exists an optimal point at which the EER of the LHP reaches its highest value. For height differences of 0.1 m, 0.3 m and 0.5 m, the optimal power inputs are 60 W, 40 W and 20 W, respectively. Figure 13 demonstrates the influence of pressure lift on the Q and EER for the latter case of long distance. Similarly, the use of a gas pump can improve the heat transfer rate. For a pipe length of 12 m, the input of 100 W of power from the gas pump can raise the heat transfer rate by 37.2%, from 5.162 kW to 7.084 kW. However, for a pipe length of 6 m, the same power input can raise the heat transfer rate only by 3.6%. To achieve the highest EER, the optimal power inputs are 40 W and 20 W, respectively, for pipe lengths of 9 m and 12 m. For a pipe length of 6 m, the EER just decreases monotonically with the pump power. Consequently, 9 m and 12 m, not 6 m, are overly long distances for the case investigated here.

4.3. Discussions

Although numerous studies have been conducted on GPLHPs, the majority focus on the application effects and economic benefits. Comparatively, little attention has been paid to the mechanism that guides the selection of gas pumps. The use of a gas pump can lift the mass flowrate of the LHP; nevertheless, this does not necessarily lead to an increase in the heat transfer rate. The effects of pressure lift afforded by the gas pump depend on the installation condition (height difference and distance between the evaporator and the condenser) and the filling ratio of the working fluid.

Table 4. The effect of pressure lift on the heat transfer rate.

Installation Condition	Filling Ratio	Effect (Positive/Negative)
Appropriate height difference and distance	Appropriate	negative
Appropriate height difference and distance	insufficient	Positive
Appropriate height difference and distance	Too high	Positive
Too long distance	Appropriate	Positive
Too small height difference	Appropriate	Positive

lists the observed effects in this study. The limited function of the gas pump was also discussed by Zhang et al. [16,34]. They put forward a concept called “ideal cycle”, which is a cycle with no overheating, subcooling, and pressure loss. The performance of the “ideal cycle” is the upper limit of the pumped LHP cycle. Although the assumption behind the “ideal cycle” does not exactly reflect the reality of the commercial-scale LHP investigated here, the existence of the upper limit is verified by this study. With the help of numerical simulation, the influence of the gas pump on the heat transfer rate and EER can be quantitatively evaluated, thereby aiding in the selection of gas pumps for engineering GPLHP applications. The gas pump employed in this instance is an oil-free linear compressor that was originally designed for home refrigerators, and is not necessarily characterized by high efficiency. For the present GPLHP, a gas pump that can match the desired pressure lift and corresponding mass/volume flowrate is needed.

Infrared thermography is employed to monitor the operation of the evaporator in this study. As infrared thermal imagers become cheaper and better, this equipment is increasingly found in investigations on heat exchangers, from the measurement of the heat transfer coefficient to the fluid flow distribution [35,36,37]. However, there have been few studies on the monitoring of LHPs. Zhang et al. captured thermal images of the evaporator of a co₂ LHP and observed that the superheated region diminishes and eventually vanishes as the filling ratio increases [38]. In this study, a quantitative analysis of thermal images was attempted based on the existing literature and the author’s experience [33,39]. The finding of an approximately linear relationship between the heat conductance of the LHP and the area ratio of the two-phase zone can aid in the debugging of the LHP. Based on a few field-measured points of paired heat conductance and area ratio, a relationship like Equation (29) can be established, allowing for the inference of the maximum heat conductance of the LHP. Therefore, infrared thermography has been demonstrated to be a powerful tool for debugging the operational performance of the LHP.

5. Conclusions

GPLHPs are an important alternative to implementing LHPs in unfavored situations. In order to explore the impact of pressure lift upon the performance of the LHP, both experimental and numerical studies have been carried out. The main results may be concluded as follows:

(1)

The gas pump can enhance the heat transfer of the LHP depending on the installation condition (height difference and distance between the evaporator and the condenser) and the filling ratio of the working fluid.

(2)

A positive effect can be achieved under the following situations: an insufficient change in the working fluid, an insufficient height difference between the evaporator and the condenser, an overly long distance between the evaporator and the condenser.

(3)

There exists an approximately linear relationship between the heat conductance of the LHP and area ratio of two-phase zone of the evaporator when the cooling conditions on the condenser side are fixed. Maximum heat conductance may be derived from a few measurements.

In order to promote the application of GPLHPs in data centers, the further development of specialized gas pumps is anticipated.