Application of an anti-gravity oscillating heat pipe on enhancement of waste heat recovery

Energy Conversion and Management 205 (2020) 112404

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Application of an anti-gravity oscillating heat pipe on enhancement of waste heat recovery

T

Xiangdong Liua, Xiaotian Hana, Zhaoyu Wangb, Guanqiu Haoc, Ziwen Zhangc, ⁎ Yongping Chena,b,c, a

College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, PR China Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, School of Environmental Science and Engineering, Suzhou University of Science and Technology, Suzhou 215009, PR China c Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, PR China b

ARTICLE INFO

ABSTRACT

Keywords: Anti-gravity oscillating heat pipe Heat recovery Conceptual facility Thermal performance

An anti-gravity oscillating heat pipe are introduced to enhance the waste heat recovery from an upper heat source to a lower object. A conceptual facility using an anti-gravity oscillating heat pipe as a core part of the heat conductor is set up for the recovery of waste heat from the upper high-temperature “exhaust” to preheat the diesel in a lower fuel tank. In order to verify this idea, a thermal experiment is conducted to investigate and compare the heat recovery performance of the conceptual facility based on four heat conductor designs. The results indicate that the current anti-gravity oscillating heat pipe with 35 turns and a filling ratio of 70% is able to effectively work under Bond number ranging from 0.814 to 0.986, exhibiting a much better heat-transfer performance along a distance of 0.83 m and only 58% weight relative to the pure copper with the same geometry. Significantly, the heat recovery efficiency of the conceptual facility using the anti-gravity oscillating heat pipe as the heat conductor is higher (about 1.66 times on average) than that using the traditional pure copper heat conductor, especially under a large heat load. Moreover, during the heat recovery process, the temperature uniformity of the diesel can be improved by increasing its effective thermal conductivity by filling a pure copper grating inside. This approach is also capable of enhancing the heat recovery efficiency of the anti-gravity oscillating heat pipe conceptual facility by an average of around 3.6% under the current experimental conditions.

1. Introduction Nowadays, with fast-growing global energy consumption and the consequent environmental and economic problems [1], efficient waste heat recovery during the energy production and conversion has attracted much attention because it is one of the most important approaches utilized to improve energy conversion efficiency and diminish negative environmental and economic impacts [2]. Over the past few decades, as a typical simple passive device with high thermal conductivity, heat pipe has been widely used as a high-efficiency heattransfer element to enhance the performance of waste heat recovery systems [3]. It should be noted that in terrestrial waste heat recovery applications, it is common for high-temperature waste heat sources to be positioned above the heat sink [4]. However, it is acknowledged that when the hot end (i.e., evaporator) is located above the cold end (i.e., condenser) for the conventional heat pipes with a wick structures inside

⁎

(namely, so-called anti-gravity orientation), the heat-transfer performance and operation stability of the heat pipe are drastically deteriorated, and may be even lost [5]. Therefore, in recent years, many attempts have been made to improve the anti-gravity performance of traditional heat pipes, such as modifying wick structures [6] and proposing new overall designs [7]. However, limited by the closed evaporation–condensation cycle mainly under the capillary pumping mechanism [8], the anti-gravity performance of traditional heat pipes with an interior wick structure remains unsatisfactory [5]. Compared with traditional heat pipes, oscillating heat pipes (OHPs), the new members of the heat pipe family [9], possess unique wickless structures and operational mechanisms [10], which may possibly achieve high-efficiency anti-gravity operations [11]. Generally, OHP exist as an open-looped/closed-looped meandering capillary tube with no interior wick structure [12], which is first evacuated and then partially filled by the working fluid. Because of the significant role of interface tension in the capillary tube, the working fluid is naturally

Corresponding author at: College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, PR China. E-mail address: [email protected] (Y. Chen).

https://doi.org/10.1016/j.enconman.2019.112404 Received 16 September 2019; Received in revised form 10 December 2019; Accepted 11 December 2019 0196-8904/ © 2019 Published by Elsevier Ltd.

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Nomenclature A a Bo cp D er es Fo g H K L m n P Q R T t x, y, z

η θ ρ σ τ

area (mm2) thermal diffusivity (m2 s−1) Bond number specific heat (J/(kg·°C)) hydraulic diameter (mm) random uncertainty system uncertainty Fourier number gravity acceleration (m/s2) height (mm) thermal conductivity (W/(m·°C)) length (mm) mass (kg) number pressure (Pa) heating power (W) thermal resistance (°C/W) temperature (°C) time (h) axial coordinate

Subscripts a c d e g H i o s V w af hre qht max pt tot 0

Greek symbols δ Δ

efficiency of heat recovery (%) inclination angle (°) density (kg m−3) interface tension (N/m) typical duration of sampling (s)

thickness (mm) difference

distributed in the form of random interconnected vapor–liquid slugs in the OHP [13]. When heated in one part (namely, the evaporator) and cooled in another (namely, the condenser), OHP could realize the efficient heat transfer between the evaporator and condenser via an internal characteristic self-sustained fluid oscillations [14], which are propelled by a non-equilibrium saturation pressure difference between the evaporator and the condenser [15]. Because of their special structure and operating principle, OHPs have several distinct advantages, such as their low cost [16], simple construction [17], high flexibility [13], and especially their attainable good anti-gravity performance under specific conditions [18]. In this context, a number of studies, particularly experimental ones, have been conducted to investigate the gravity adaptability of OHPs by testing their thermal performance under different orientations (i.e., a different gravity component in the direction of heat transfer) [19]. From these previous works, it should be noted that even though OHPs work based on the internal thermally driven oscillatory fluid flow when the interface tension plays a stronger role than gravity [14], gravity still has an important positive function in the self-sustained fluid flow and heat transfer of the OHP [20]. As an example, gravity contributes to the uneven pressure distribution in the OHP, which could enhance the fluid oscillation and the accompanying mass and heat transfer [21]. Moreover, gravity promotes the backflow of the liquid phase into the evaporator of the OHP, which is helpful for the liquid supplement to the continuous boiling/evaporation there, and helps to avoid the “dryingout” of the evaporator [22]. Therefore, in these previous studies, the thermal performance of the OHP is improved with the increasing orientation from 0° (horizontal-heated) to 90° (bottom-heated and topcooled), while it is not satisfactory and even lost in horizontal orientation [19]. However, many other available works have verified that OHPs may be efficient at horizontal [18] and even anti-gravity orientation (top-heated and bottom-cooled) [16]. These works showed that strengthening the anti-gravity factors in the OHP could effectively weaken the effects of orientation (i.e., gravity) on the thermal performance of OHP [23], such as enhancing the effect of the interface tension on the self-sustained fluid flow by decreasing the inner diameter of

adiabatic section condenser diesel evaporator grating horizontal/height index/inner outer steady vertical wall air flue heat recovery experiment quartz glass heaters maximum pilot test total initial

the OHP [24], enlarging the unbalanced driving pressure difference in the OHP via applying the non-uniform heating on the evaporator [25]. In particular, several investigations have shown that drastically increasing the number of “U-turns” in the OHP [26] produced a cumulative driving pressure difference in each “U-turn,” which could realize the effective anti-gravity operation of the OHP. In addition, some novel designs have been further proposed to improve the gravity adaptability of the OHP by enhancing the counter-gravity factors, e.g., introducing the nonuniform geometry designs (such as dual-diameter channel/tube [27] and uneven-turn [28]) to enhance the imbalanced driving pressure difference in the OHP, modifying the inner wall properties or structures (such as the hydrophilic/hydrophobic inner tube wall [29] and inner wall wick structures [30]) to provide additional power to drive the backflow of the liquid phase into the evaporator in addition to the gravity. Based on these previous studies, several attempts have been made to apply the anti-gravity OHP to efficient electrical cooling [26] and thermal energy storage [17] at all orientations. In summary, the use of OHPs is a possible approach to realize the anti-gravity high-efficiency heat transfer that is required to achieve real waste heat recovery from an upper heat source to a lower heat sink. In addition, many studies have been performed to clarify the role of orientation (i.e., gravity) on the thermal performance of OHPs, and several efforts were carried out to improve the gravity adaptability of OHPs. However, these previous works mainly concentrated on the conditions with the orientation of the OHPs from 0° (horizontal-heated) to 90° (bottom-heated and top-cooled). The operating characteristics of the anti-gravity OHPs (i.e., at the orientation of −90° (top-heated and bottom-cooled)) are still not fully understood. In particular, investigations into the real application of anti-gravity OHPs to the long-distance efficient waste heat recovery remain limited. Therefore, in the current work, a thermal experimental study is performed to clarify the operating characteristics of an anti-gravity OHP and to verify its effective performance. Accordingly, this anti-gravity OHP is introduced as a core part of the heat conductor to recover waste heat from the upper hightemperature “exhaust” to preheat the lower diesel, and a corresponding conceptual facility is set up and experimentally tested based on four 2

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Fig. 1. Experimental setup for pilot thermal test of the OHP used in waste heat recovery: (a) schematic diagram of experiment setup; (b) illustrative locations of thermocouples; (c) photograph of the OHP and its cross-section.

3

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heat conductor designs to verify the practicability of anti-gravity OHPs in real waste heat recovery applications.

positions of the thermocouples are marked in Fig. 1(b) and listed in Table 1. In the current experiment, owing to the high thermal conductivity and small thickness (0.5 mm) of the capillary tube wall, the Fourier number of the capillary tube wall, Fo = (awτd)/δw2, has a range of 501.5–551.6, where aw is the thermal diffusivity of tube wall, τd is the typical duration of sampling (here τd = 1.0 s), δw is the thickness of the tube wall. It can be concluded from the value of Fo that the inner and outer wall temperatures oscillate in phase [20]. Therefore, the outer wall temperature variation of the capillary tube can give a reasonable reflection of thermo-hydrodynamic characteristics in the OHP.

2. Pilot thermal test of oscillating heat pipe used in waste heat recovery In the current study, before applying an anti-gravity OHP to enhance waste heat recovery, a pilot thermal test is conducted to confirm whether the anti-gravity OHP is able to operate effectively. 2.1. Experimental setup for pilot thermal test of oscillating heat pipe

2.2. Data reduction and uncertainty analysis for pilot thermal test of oscillating heat pipe

Fig. 1 displays a detailed schematic diagram of the experimental setup for the pilot thermal test of the OHP used in waste heat recovery. As illustrated in Fig. 1(a), the experimental setup mainly comprises four units, i.e., an electric heating unit, an air-cooling unit, a temperature measurement and data acquisition unit, and the tested OHP. The OHP is fabricated by bending a copper capillary tube (outer diameter: Do = 3.0 mm; inner diameter: Di = 2.0 mm) into a serpentine configuration with 35 turns. The OHP is composed of three sections, namely the condenser, adiabatic, and evaporator sections, with respective lengths of 360 mm, 240 mm, and 230 mm. Herein, the detailed geometric parameters of the OHP are shown in Fig. 1(b) and Table 1. In addition, as depicted in Fig. 1(a), the inclination angle θ is defined to characterize the orientation of the OHP, and it is set as 90° (gravityassisted mode), 45°, 0° (horizontal mode), −45°, and −90° (antigravity mode) in the pilot thermal test. Before the test, the inner volume of the OHP is first evacuated to less than 10-2 Pa via a vacuum unit by the combination of a rotary pump (Rankuum® 2X-8) and a diffusion pump (Rankuum® K-150), and it is then partially filled with the degassed working fluid via a precise charging system. According to our previous studies on OHPs filled with different working fluids [20], methanol is used as the working fluid in the current experiment owing to its low viscosity and large saturation pressure gradient (dP/dT)sat, which are beneficial to the thermal performance of the OHP. Moreover, the filling ratio (ratio of the working fluid volume to the total inner volume of OHP) is set to be 70% [18] in order to guarantee that sufficient liquid remains in the evaporator to sustain the effective nucleation and evaporation, which are required for oscillatory fluid flow in the anti-gravity OHP. Accordingly, the Bond number Bo = D(g(ρlρv)/σ)0.5 (a common dimensionless number that characterizes the ratio of gravitational force to surface tension force) of the pilot thermal test is 0.842–0.986, which is well within the Bo range for the definition of the OHP [11]. During the pilot thermal test, the OHP is heated at the evaporator by a constant power via the electric heating unit, and it is cooled at the condenser via the air-cooling unit. In the electric heating unit, the constant heating power to the OHP is generated by a Ni-Cr electric heating wire tightly wrapped around the evaporator, which is supplied and regulated by a DC power supply (Seadilly® HCP220-13) as well as measured by a digital power meter (NAPUI® PM9804). For the aircooling unit, a standard axial fan (LVYI® 300-4P) is used to provide the forced air convection cooling for the condenser, where the ambient temperature is kept at 20 ± 1.5℃. In order to reduce the heat loss from the OHP, the evaporator and adiabatic sections are well thermally insulated via a layer of aluminum silicate glass fiber. Accordingly to the previous experiments on the OHPs with multiturn [28], to obtain the reliable temperature variation, distribution and level for the operating OHP and ensure these measured temperature data are independent of the number of temperature measuring points, 36 thermocouples (OMEGA®, T-type, ± 0.5℃ accuracy) are tightly attached to the corresponding temperature measuring points on the outer wall of the OHP, i.e., e1–e12 at evaporator, a1–a12 at the adiabatic section and c1–c12 at the condenser, as shown in Fig. 1(b). The measured temperature data are monitored and collected by a data acquisition instrument (Agilent 34972) connected to a computer. The detailed

To quantitatively evaluate the thermal performance of the OHP under different operating conditions, the total thermal resistance (Rpt) and effective thermal conductivity (Kpt) of the OHP are respectively defined as follows:

• Overall thermal resistance of the OHP: Rpt =

T¯e

T¯c

(1)

Q pt

where Qpt is the total heating power imposed on the OHP, and T¯e and T¯c are the average temperature value of the evaporator and condenser, respectively, 12 i=1

T¯e =

Tei

T¯c =

12

12 i=1

Tci

(2)

12

Here, Tei and Tci are the measured temperature values at the evaporator and condenser by each thermal thermocouple shown in Fig. 1(b). Note that for the waste heat recovery applications, it is the overall thermal resistance of two parallel thermal resistances (i.e., the thermal resistance of solid material and the thermal resistance of the oscillating vapor–liquid flow in the OHP [11]) that determines the heat recovery performance. Therefore, herein, the temperature values are the outer wall temperature values of the OHP in the current work.

• Effective thermal conductivity of the OHP: Kpt =

A=

L tot 1 A Rpt

n Do2 4

L tot =

(3)

(Le + Lc ) + La 2

(4)

where A is the total cross-sectional area of the OHP, n is the number of parallel tubes of the OHP, Ltot is the effective heat-transfer length of the OHP, and La, Le, Lc are the lengths of the adiabatic section, evaporator, and condenser, respectively. Accordingly, the maximum uncertainties of measurement parameters in the pilot thermal test of the OHP are listed in Table 2. In this table, the uncertainties of the direct measurement parameters, including Tei, Tai, Tci, are determined by the system uncertainty es from the precision of instruments (thermocouples) and the random uncertainty er from the repeatability of data as:

e=

es2 + e2r

(5)

Table 1 Detailed geometric parameters of the OHP.

4

Physical parameter

Dimension

Physical parameter

Dimension

Le (mm) La (mm) Lc (mm) L1 (mm)

200 240 360 140

L2 (mm) L3 (mm) Lh (mm) Lw (mm)

90 30 830 250

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condenser is reduced by increasing θ at the same heating power, which indicates an improvement of the heat transfer from the hot end to the cold one.

Table 2 Maximum uncertainties of measurement parameters in the pilot thermal test of OHP. Parameters

Tei

Tai

Tci

Qpt

Rpt

Kpt

Maximum uncertainties (%)

0.7

0.6

0.8

5.6

6.4

7.3

2.3.2. Thermal performance According to Eqs. (1)–(4), the variations of the total thermal resistance and effective thermal conductivity of the OHP with an increasing heating power under different orientations are calculated and displayed in Fig. 3, which are also compared with those of a pure copper possessing the same geometry as the OHP. As shown in Fig. 3, the OHP processes the smaller Rpt and larger Kpt (i.e., the better heattransfer performance) than the pure copper under different θ, which indicates that an effective sensible and latent heat transfer is achieved via the self-sustained fluid flow in the OHP at any orientation. It is also recognized that, owing to the enhancement of the thermal driving force in the OHP, the thermal performance of the OHP is improved with the increasing heating power, especially from Qpt = 50 W to Qpt = 200 W, because the inner fluid motion pattern transits from the “stop-start” motion to the pseudo-steady circulation. In addition, for the same heating power, the OHP has a better thermal performance under a larger θ. The above-mentioned phenomena all indicate that the self-sustained fluid oscillatory motions can be attained in the OHP, even under antigravity condition; however, gravity still plays a non-negligible positive role in the fluid movement and thermal performance of the OHP. Moreover, it should be noted that the current OHP (including the weight of filled working fluid) only has about 58% of the weight of the pure copper with the same geometry owing to its unique partially hollow tubular configuration.

i: index of thermocouple.

The uncertainty of Q is derived from both the precision of the digital power meter and the total heat loss from the OHP to the ambience. In addition, the uncertainties of the indirect measurement parameters, such as R and K, are calculated by using the error propagation method according to their definitions [31]. 2.3. Results and discussion for pilot thermal test of oscillating heat pipe In order to clarify the influence of gravity on the thermal performance of the OHP and to confirm the effective operation of the antigravity OHP, the wall temperature oscillations of the OHP are tested at inclination angles of −90°, −45°, 0°, −45°, and 90° under different heating powers ranging from 50 W to 500 W in the pilot thermal test. Furthermore, the total thermal resistance and effective thermal conductivity of the OHP are compared. For each tested condition, the OHP wall temperature is guaranteed to maintain the quasi-steady oscillations for more than 1800 s. 2.3.1. Temperature oscillation characteristics The wall temperature level and oscillation characteristics could provide an indication of the possible fluid behaviors in the OHP [14]. Therefore, Fig. 2 indicates the representative wall temperature oscillations at the evaporator (Te3), condenser (Tc3), and adiabatic sections (Ta3 and Ta4) under various operating conditions. It can be seen that the overall wall temperature increases with an increasing heat input to the OHP. However, the detailed temperature oscillation characteristics vary with the operating conditions, clearly indicating the changes in the inner fluid behaviors of the OHP. At the low heating power of 50 W, the evaporator wall temperature intermittently increases with no fluctuations, in conjunction with a smooth decrease in the condenser wall temperature (see Fig. 2(b)), which indicates the complete stop of fluid movement and the consequent deterioration of heat transfer from the evaporator to the condenser. Then, it decreases sharply with a sudden wall temperature rise in the condenser, indicating that the fluid movement is initiated soon after the stoppage. Under this state, such a “stop-start” motion of fluid repeats irregularly with time (see Fig. 2(b)), which can be reflected by the uneven intermittent wall temperature oscillations. When the heating power increases, the thermal driving force in the OHP is strengthened, resulting in a more continuous fluid movement and a change in the fluid motion pattern, as inferred from Fig. 2(c) and (d). It is seen that there is a clear difference in the wall temperature profiles between the adjacent tubes at the adiabatic section (see Ta3 and Ta4 in Fig. 2(c) and (d), respectively), implying that the cold fluid flowing from the condenser is heated at the evaporator U-turn and flows back through the adjacent tube, i.e., the inner fluid takes up a circulatory motion in the OHP. It can also be seen from the oscillatory temperature profiles that (see Fig. 2(j) and (l)) the circulatory flow is pseudo-steady, with flow oscillations and direction reversals taking place intermittently [32]. From Fig. 2(d), (f), (h), (j) and (l), it is also seen that, the quasisteady temperature difference between the evaporator and the hotter adiabatic tube in the same U-turn (i.e., Te3 and Ta3), and that between the condenser and the adjacent colder adiabatic tube (i.e., Tc3 and Ta4), both decrease with the inclination angle θ ranging from −90° to 90° at the same heating power under the state of bulk fluid circulation, implying a faster inner fluid circulation by increasing θ. In addition, the quasi-steady temperature difference between the evaporator and

3. Application of anti-gravity oscillating heat pipe to enhancement of waste heat recovery As indicated by the above pilot thermal test, the anti-gravity OHP is able to realize effective self-sustained work without the aid of a pump, and it has a particularly improved thermal performance compared with traditional pure copper heat conductors, which indicates that there is good potential for the heat-transfer enhancement from the upper heat source to the bottom object in real applications. Note that for the application of internal-combustion-engine driven power supply units (e.g., diesel-generator-based power supply unit) in the alpine area [33], it is necessary to provide the complementary heat to maintain the flowability of the fuel oil, so as to improve the efficiency and stability of the engine in low-temperature environments. Obviously, local waste heat recovery and utilization of the high-temperature exhaust from the engine is an effective way to supply the complementary heat to the fuel oil. It should be noted that in order to facilitate the transportation, installation, and maintenance of the internal-combustion-engine driven power supply unit, a fuel oil tank is usually installed at the bottom of the unit, which is under the engine-generator module, including the high-temperature exhaust pipe [34]. Therefore, the anti-gravity OHP is introduced to enhance the waste heat recovery from the upper hightemperature “exhaust” to preheat the diesel in the lower fuel tank. Moreover, to verify this idea, a corresponding conceptual facility is set up and experimentally tested, as shown in Fig. 4. 3.1. Experimental setup for waste heat recovery From Figs. 4 and 5, it can be seen that the anti-gravity waste heat recovery conceptual facility consists of a high-temperature exhaust simulation unit, a heat conductor, an ambient temperature maintenance unit, as well as a temperature measurement and data acquisition unit. In the high-temperature exhaust simulation unit, the high-temperature exhaust is simulated by the electrically heated air flowing through a flue, as shown in Fig. 4(a). In this unit, the fresh air with an ambient temperature of 20 ± 1.5℃ is supplied by a centrifugal blower 5

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Fig. 2. Wall temperature variations of the OHP under different operating conditions in pilot thermal test: (a) anti-gravity condition (θ = −90°); (b) ~ (d) partial enlargement of (a); (e) θ = −45°; (f) partial enlargement of (e); (g) horizontal condition (θ = 0°); (h) partial enlargement of (g); (i) θ = 45°; (j) partial enlargement of (i); (k) gravity-assisted condition (θ = 90°); (l) partial enlargement of (k).

(DAERTUO® XGB-250) and heated by eight quartz glass heaters installed at the inlet of the air flue, whose locations are shown in part (ii) of Fig. 4(a). The flow rate of the air is maintained at 10 m3/h, and the electric-heating power of each quartz glass heater remains the same and is maintained at a constant value in the experiment. However, as depicted in part (i) of Fig. 4(a), a cylinder fuel tank that is 80% filled with diesel (density ρd = 840 kg/m3, thermal conductivity coefficient

Kd = 0.12 W/m·°C, and specific heat cpd = 2100 J/kg·°C at 20℃) is set below the high-temperature “exhaust” flue. Here, the diesel tank is well thermally insulated by the outside polyethylene layer, and placed into a closed thermotank to ensure a stable ambient temperature condition. The temperature inside the closed thermotank is maintained at about 20 ± 1℃ by a forced convection heat exchanger of a constant-temperature water circulating cooling unit. 6

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1.0

0.2

0.5

0.0

50

150

250 350 Qpt (W)

450

0.0

18

15 10

12

5

6

0

50

150

In order to reclaim the heat from the upper high-temperature “exhaust” to preheat the lower diesel, an OHP is introduced as the key heat conductor between the hot and cold ends, as illustrated in part (i) of Fig. 4(a). In particular, considering the large volume and low thermal conductivity of the diesel, a copper grating is fabricated and inserted into the tank to improve the effective thermal conductivity of the diesel (see Fig. 4(b) and (c)), with the aim of further enhancing the heat recovery. In addition, to demonstrate the enhancement of heat recovery by the OHP, the heat recovery performance of a pure copper serpentine bar having the same geometry as the OHP is tested and compared with that of the OHP. That is, as shown in Fig. 4(b), four heat conductor designs (i.e., OHP, OHP + G, CB, and CB + G, for short) are proposed for the conceptual facility, and their corresponding heat recovery performances are tested and compared in the current study. Furthermore, in order to test the heat recovery performance, several thermocouples (OMEGA®, T-type, ± 0.5℃ accuracy) were set in different parts of the experimental apparatus to measure the temperature variations during the heat recovery process (see parts (i) and (iii) in Fig. 4(a)), including A1 and A2 fixed along the axis of the high-temperature “exhaust” flue,

250 350 Qpt (W)

450

0 550

-1

24

⋅m )

/W)

0.4

20

30

-90° -45° Copper

−3

1.5

90° 45° 0°

25

Κpt⋅10 (W/

0.6

Rpt (

-1

2.0

/W)

-90° -45° Copper

Rpt (

90° 45° 0°

(b)

−3

0.8

2.5

Κpt⋅10 (W/

(a) 1.0

⋅m )

Fig. 2. (continued) Fig. 3. (a) Total thermal resistance and (b) effective thermal conductivity of the OHP under different operating conditions in pilot thermal test. (i) 1DC stabilized power supply; 2-Digital power meter; 3-Heat conductor; 4Quartz glass heaters; 5-Hot air flue; 6Ventilating duct; 7-Rotameter; 8Centrifugal blower; 9-Flow regulating valve; 10-Closed thermotank; 11Finned heat exchanger; 12-Cooling fan; 13-Liquid flowmeter; 14-Constanttemperature water bath; 15-Diesel tank; 16-Computer; 17-Data acquisition instrument; (ii) Layout of quartz glass heaters; (iii) Layout of temperature measurement points in the diesel storage tank.

H1-H3 attached in the middle of hot, adiabatic, and cold sections of the heat conductor, respectively, and 1–14 installed in the diesel. In this experiment, the lengths of condenser, adiabatic, and evaporator sections are fixed according to the previous experimental studies [11]. Details of the size and location dimensions of the above-mentioned experimental setup have been marked in Fig. 4 and listed in Table 3. 3.2. Data reduction and uncertainty analysis for waste heat recovery experiment In order to quantitatively evaluate and clarify the heat recovery performance for four heat conductor designs, the heat recovery efficiency is used to characterize the effective ratio of reclaimed heat to the total waste heat of the high-temperature “exhaust”

=

Q hre × 100% Qqht t

(6)

where Qqht is the total heating power of the quartz glass heaters, t is the time needed to warm the diesel from T0 to Ts, and Qhre is the total heat 7

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Fig. 4. (a) Schematic diagram of experimental setup for the anti-gravity waste heat recovery conceptual facility; (b) four designs of heat conductor for the waste heat recovery; (c) detailed geometry and image of copper grating used in the heat conductor.

8

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Table 4 Maximum uncertainties of measurement parameters in the waste heat recovery experiment.

Hot air flue

Heat conductor

Closed thermotank Finned heat exchanger

Computer Diesel tank

Constanttemperature water bath

Centrifugal blower Flow regulating valve

Power regulator

Ventilating duct

Power meter

Fig. 5. Image of experimental setup for the anti-gravity waste heat recovery conceptual facility.

ΔTH,

Maximum uncertainties (%)

0.9

0.8

1.5

max

ΔTV, 1.6

max

Qht

Rhre

Khre

η

6.1

6.8

7.6

8.1

3.3. Results and discussion for waste heat recovery experiment In the current waste heat recovery experiment, three constant heating powers are imposed on the “exhaust”, i.e., Qht = 500 W, 700 W, and 900 W (i.e., 62.5 W, 87.5 W, and 112.5 W, respectively, for each quartz glass heater). Here, the Bond number of the anti-gravity OHP in the waste heat recovery experiment is 0.814–0.923, which is smaller than that in the pilot test, and ensures the effective operation of the anti-gravity OHP. The heat recovery performance of different heat conductor designs under these heating powers were compared and analyzed in order to verify the enhancement of waste heat recovery via the application of the anti-gravity OHP.

Table 3 Detailed dimension parameters of experimental setup for the anti-gravity waste heat recovery conceptual facility shown in Fig. 4. Physical parameter

Dimension

Physical parameter

Dimension

L1′ (mm) L2′ (mm) L3′ (mm) Le (mm) La (mm) Lc (mm) Laf (mm) Lw (mm) Daf (mm) Dt (mm)

80 140 110 230 240 360 1000 100 200 500

H (mm) h (mm) Lg1 (mm) Lg2 (mm) Lg3 (mm) Lg4 (mm) Lg5 (mm) Lg6 (mm) Lg7 (mm) Lg8 (mm)

500 400 400 400 200 125 120 90 70 50

3.3.1. Characteristic temperature evolution and distribution of heat conductor Generally, the thermal performance of the heat conductor during the heat recovery process could be directly reflected by its own temperature evolution and distribution. Therefore, Fig. 6 compares the temperature evolution at characteristic locations (H1, H2, and H3 marked in Fig. 4(a)) on the heat conductors with four designs. As shown, at the initial stage of the heat recovery process, the heat conductor is significantly heated owing to the large temperature difference between it and the high-temperature “exhaust”. Therefore, the temperature of the heat conductor increases rapidly. With time, the increase in the heat conductor temperature decreases as this temperature difference decreases gradually. Finally, the heat conductor temperature reaches steady as the heat absorption and loss of the heat conductor become equal. Note that at the initial stage of the heat recovery process, the temperature of the OHP heat conductor exhibits no oscillation, indicating that the working fluid in the OHP is not initiated and the heat transfer via the heat conductor depends primarily on the heat conduction. Consequently, the temperature of the OHP heat conductor has a similarly increasing profile compared with that of the pure copper heat conductor. Afterwards, when the OHP starts up by the sufficient accumulation of heat at the hot end, an irregular temperature oscillation appears on the heat conductor. In particular, compared with the pure copper heat conductor, there is an obvious drop in the evaporator temperature and an apparent rise in the condenser temperature, for the OHP heat conductor, which reduces the temperature difference between the cold and hot ends of the OHP heat conductor. This shows that the thermal performance of the OHP heat conductor is significantly improved by its interior sensible and latent heat transfer via the oscillatory fluid flow. In addition, at the same location, the temperature evolutions on the heat conductor without the copper grating are quite similar with those with the copper grating, implying that the copper grating has little

absorbed by the diesel, which is defined as the sensible heat change of the diesel during the whole heat recovery process

T0)

Ti

serpentine bar with or without the copper grating are also quantitatively evaluated based on Eqs. (1) and (3) in order to analyze the effects of the heat conductor design on the heat recovery performance, where the total heating power imposed on the OHP is regarded as Qhre, as defined in Eq. (7). According to the error analysis method mentioned above, the maximum uncertainties of these characteristic measurement parameters in the waste heat recovery experiment are also listed in Table 4.

Rotameter

Q hre = md cpd T = md cpd (Ts

THi

i: index of thermocouple. Cooling fan

Data acquisition instrument

Parameters

(7)

In Eq. (7), md is the total mass of the diesel, T0 is the initial temperature of the diesel, which is calculated as the average initial temperature of points 1–14 in the diesel (see part (iii) in Fig. 4 (a)), and Ts is the final steady temperature of the diesel during the heat recovery process, which is also calculated as the average final steady temperature of points 1–14 in the diesel (see part (iii) in Fig. 4 (a)). On the other hand, in real applications, the temperature stability of the inlet fuel also affects the operation stability and reliability of the internal combustion engine [35], which could be influenced by the temperature uniformity of fuel. Therefore, to examine the effect of four heat conductor designs on the temperature uniformity in the diesel during the heat recovery process, two characteristic maximum temperature differences in the diesel are defined, namely the maximum horizontal temperature difference (ΔTH, max) and the maximum vertical temperature difference (ΔTV, max). As shown in part (iii) of Fig. 4(a), on every marked cyan horizontal sectorial plane, there is a maximum temperature difference among the measured temperature values at four measuring points (e.g., points 3, 8, 11, and 14 on the top cyan horizontal sectorial plane). Therefore, there are three maximum temperature differences on three marked cyan horizontal sectorial planes marked by the part (iii) of Fig. 4(a), and ΔTH, max is defined as the highest value among these three maximum temperature differences. Similarly, ΔTV, max is defined as the highest value among four maximum temperature differences on four red vertical solid lines marked in part (iii) of Fig. 4(a). In addition, the overall thermal resistance (Rhre) and effective thermal conductivity (Khre) of the OHP and pure copper 9

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Fig. 6. Variations of temperature on the core part (OHP/pure copper bar) of heat conductor during the waste heat recovery process obtained using four designs of heat conductor.

influence on the temperature evolution of the core part (OHP/pure copper bar) of the heat conductor.

height is very small (less than 0.8℃), which indicates a weak heattransfer strength along the horizontal direction in the diesel. Compared with the diesel temperature evolution and distribution in the horizontal direction at the same height, diesel temperature experiences distinct evolution and distribution in the vertical direction at the same horizontal position, as shown in Fig. 8. It can be seen that during the heat recovery process, the diesel temperature experiences an obvious decrease with the growing depth in the tank, implying a dominant heat transfer in the vertical direction relative to the horizontal direction. This phenomenon also indicates that the total heat recovered by the heat conductor is transferred mainly downwards, and warms the on-way diesel, with decreasing heat absorbed by the deeper diesel. Furthermore, it is shown that using the OHP heat conductor, the final stable diesel temperature is higher than that obtained using the pure copper heat conductor, especially at a high heating power imposed on the “exhaust.” According to the above pilot thermal test and the subsequent Fig. 10, this can be attributed to the better heat-transfer performance of the anti-gravity OHP than the pure copper, particularly when the heating power is high. In addition, because the OHP heat conductor has a better thermal conductivity along the vertical

3.3.2. Characteristic temperature evolution and distribution of diesel The heat recovery performance is intuitively characterized by the temperature distribution and evolution of diesel. Therefore, Figs. 7 and 8 represent the diesel temperature evolution during the heat recovery process at the same height with different horizontal position (points 3, 8, 11, and 14 shown in Fig. 4(a)) and at the same horizontal position with different heights in the tank (points 4, 5, 6, 7, and 8 shown in Fig. 4(a)), respectively. As shown in Fig. 7, during the heat recovery process, the diesel temperature at the same height increases sharply initially, and then gradually climbs to a stable value using different heat conductors. In particular, the diesel temperature at the same height decreases with increasing distance to the core part of the heat conductor. Moreover, the maximum diesel temperature difference in the horizontal direction at the same height is reduced by adding copper grating, implying an enhancement of the heat conduction in the horizontal direction via the copper grating. However, the diesel temperature difference at the same 10

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Fig. 7. Variations of diesel temperature in the horizontal direction during the waste heat recovery process obtained using four heat conductor designs.

direction, the recovered heat can be more easily transferred downwards, resulting in a higher stable diesel temperature at the bottom of the tank. However, as depicted in Fig. 8, when the copper grating is added to the diesel, the final stable diesel temperature in the upper part of the tank is lower (see T7 and T8), while that at the bottom of the tank is higher (see T4 and T5), indicating that the heat conduction from the top diesel to the bottom one is effectively improved by the copper grating. In order to further characterize the effects of the heat conductor design on the variation of the diesel temperature uniformity during the heat recovery process, Fig. 9 shows the evolutions of the maximum

horizontal temperature difference (ΔTH, max) and maximum vertical temperature difference (ΔTV, max) defined in Section 2.2. As displayed, ΔTH, max and ΔTV, max exhibit distinct evolutions because of the distinct heat-transfer performance along the horizontal and vertical directions in the diesel, as stated above. Specifically, for different heat conductors under various heating powers imposed on the “exhaust,” ΔTH, max first increases rapidly and then gradually decreases to a stable value (see inset (i) in Fig. 9). This is because at the initial stage of heat recovery, the heat diffusion is slow and weak along the horizontal direction owing to the low thermal conductivity of the diesel. Consequently, heat accumulation occurs near the core part of the heat conductor, and 11

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Fig. 8. Variations of diesel temperature in the vertical direction during the waste heat recovery process by using four designs of heat conductor.

thus ΔTV, max keeps rising until it reaches a stable value. Moreover, owing to a much better thermal conductivity compared with the pure copper conductor, the OHP heat conductor is able to significantly improve the diesel temperature uniformity along the vertical direction, i.e., ΔTV, max is much smaller by using the OHP heat conductor (see inset (ii) in Fig. 9). In addition, by adding the copper grating, the effective thermal conductivities of the diesel along the horizontal and vertical directions are both increased, which also enhances the diesel temperature uniformity (see insets (i) and (ii) in Fig. 9), especially in the vertical direction with a large temperature difference (see inset (ii) in Fig. 9).

induces a rapid temperature rise of the diesel there, while the diesel far from the heat conductor at the same height remains at the initial temperature, leading to the initial rapid increase of ΔTH, max. Over time, the heat accumulated near the core part of the heat conductor is gradually diffuses in the horizontal direction, which slowly reduces ΔTH, max. Compared with the evolution of ΔTH, max, ΔTV, max also first increases quickly but then climbs slowly to a stable value without any “overshoot” (see inset (ii) in Fig. 9). As discussed above, this could be attributed to the decreasing heat absorbed by the deeper diesel when the recovered heat transfers downwards via the heat conductor. As a result, the top diesel always obtains more heat than the bottom one, and 12

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Fig. 9. Variations of maximum diesel temperature difference in the horizontal and vertical direction during the waste heat recovery process obtained using four designs of heat conductor.

3.3.3. Waste heat recovery performance The above-mentioned characteristic temperature evolution and distribution during the heat recovery process indicate that the antigravity heat recovery performance of the conceptual facility mainly depends on the heat-transfer performance of the heat conductors. Therefore, Fig. 10 presents the total thermal resistance and effective thermal conductivity of the core part (OHP/pure copper bar) of different heat conductors when the heat recovery process reaches steady state. As shown, similar to the results of the pilot thermal test, the working anti-gravity OHP possesses much better heat-transfer performance than the pure copper bar, especially under the large heating power imposed on the “exhaust.” Specifically, the average total thermal resistance of the OHP is 56.2%, 30.5%, and 25.9% of that of the pure copper bar under heating powers of 500 W, 700 W, and 900 W,

(a) 3

CB OHP

(b) 2400 -1

CB+G OHP+G

CB OHP

1800

Khre (W/m⋅

2

1200

Rhre (

/W)

)

CB+G OHP+G

respectively. Correspondingly, the average equivalent thermal conductivity of the OHP is 1.8 times, 3.2 times, and 3.9 times that of the pure copper bar. Moreover, it can been seen that the addition of the pure copper grating helps to slightly improve the heat-transfer performance of the core part of the heat conductor. To further compare the heat recovery performance under different operating conditions, Fig. 11 presents the heat recovery efficiency obtained using different heat conductors at various heating powers imposed on the “exhaust” at different times (t = 5 h, 10 h, 15 h, and 20 h). As shown, the heat recovery efficiency decreases slightly from 5 h to 20 h owing to the decrease in the temperature difference between the “exhaust” and the diesel (seen from Fig. 6), which reduces the heat reclaimed with respect to that imposed on the “exhaust.” In addition, owing to the improving heat-transfer performance of OHP with

1

0

500

700 Qht (W)

600 0

900

500

700 Qht (W)

900

Fig. 10. (a) Total thermal resistance and (b) effective thermal conductivity of the core part (OHP/pure copper bar) of heat conductor under different heating power imposed on the “exhaust” when the heat recovery process reaches steady state. 13

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(a) 15

Qr=500W

CB+G OHP+G

(b) 15

9 6

CB+G OHP+G

CB OHP

9 6 3

3 0

Qr=700W

12 η (%)

η (%)

12

CB OHP

5

10

t (h)

15

0

20

(c)15 Q =900W r

η (%)

12

5

10

CB+G OHP+G

CB OHP

t (h)

15

20

9 6 3 0

5

10

t (h)

15

20

Fig. 11. Comparisons among the absorbed heat by the diesel using four designs of heat conductor in the waste heat recovery experiment.

increasing heating power (see Fig. 10), the heat recovery efficiency obtained using the heat conductors with OHP is larger under the higher heating power (see Fig. 11). In particular, it can be seen from Fig. 11 that depending on the better heat-transfer performance, the anti-gravity OHP heat conductor possesses a better heat recovery performance than the pure copper conductor. As an example, when the heat recovery process reaches steady state at t = 20 h, under the heating power of 500 W, 700 W, and 900 W, the average heat recovery efficiency of the heat conductors using OHP is respectively 1.62 times, 1.69 times, and 1.71 times that obtained via the heat conductors using the pure copper bar. Furthermore, because the addition of copper grating enhances the heat transfer from the core part of the heat conductor to the diesel in three-dimensional (3D) space, it also increases the heat recovery performance of the conceptual facility. For instance, for the OHP heat conductor, the heat recovery efficiency achieves improvements of 2.5%, 3.0%, and 5.2% under heating powers of 500 W, 700 W, and 900 W, respectively, by using the copper grating. Furthermore, weight and material costs of four heat conductor designs are calculated and listed in Table 5. It can be seen that heat conductors using the anti-gravity OHP has a cost advantage compared to the pure copper conductor, which further indicates a good potential of the anti-gravity OHP for the waste heat recovery. On the other hand, adding copper grating induces higher material costs. However, owing to more efficient heat recovery performance by using the copper grating, the heat conductors including the copper grating will gradually show their advantage with increasing service time. Note that the lengths of condenser, adiabatic, and evaporator sections are fixed in this experiment. However, the length of adiabatic section plays an important role in the thermal performance of the OHP because it can affects the oscillation of vapor and liquid slugs as well as fluid flow friction in the OHP [36]. Therefore, it is worth conducting a further study on clarifying the influence of the length of adiabatic section on the heat recovery performance of the anti-gravity OHP.

waste heat recovery from the upper heat source to a lower object. Based on a pilot thermal test carried out to confirm the effective operation of the anti-gravity OHP and to understand the influence of gravity on its thermal performance, a conceptual facility using the anti-gravity OHP as a core part of the heat conductor is set up to recover waste heat from the upper high-temperature “exhaust” in order to preheat the lower diesel. To demonstrate this idea, a thermal experiment is conducted to investigate and compare the heat recovery performance of the conceptual facility based on four designs of heat conductor. The major conclusions are as follows: (1) The current anti-gravity OHP with 35 turns and filling ratio of 70% is able to effectively work under Bo = 0.814–0.986, which can realize a much better heat-transfer performance along a distance of 0.83 m, and only has a 58% weight relative to conventional pure copper with the same geometry. However, gravity still has a nonnegligible positive function on the interior fluid dynamics and thermal performance of the OHP. (2) Compared with the traditional pure copper heat conductor used in the heat recovery, the current anti-gravity OHP exhibits a greater ability to recover heat from the upper high-temperature exhaust to preheat the diesel in the lower fuel tank. When the heat recovery process reaches steady state, the heat recovery efficiency of the conceptual facility using the anti-gravity OHP as the heat conductor is higher (about 1.66 times on average) than that obtained using the pure copper heat conductor, especially under large heat load. (3) During the heat recovery process, the temperature uniformity of Table 5 Weight and material costs of four heat conductor designs (evaluated according to Nov. 30, 2019 CNH and wholesale market price in P.R. China).

4. Conclusions In this study, an anti-gravity OHP is introduced to enhance the 14

Heat conductor design

Weight (kg)

Material costs ($)

OHP (including working fluid) CB OHP + G (including working fluid) CB + G

2.15 3.68 22.03 23.46

25.74 45.42 139.18 157.89

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diesel can be improved by increasing its effective thermal conductivity via filling a pure copper grating inside, particularly when there is a significant temperature difference in the diesel. This also enhances the heat recovery efficiency of the anti-gravity OHP conceptual facility by an average of around 3.6% under the current experimental conditions.

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CRediT authorship contribution statement Xiangdong Liu: Methodology, Investigation, Conceptualization, Writing - original draft. Xiaotian Han: Formal analysis. Zhaoyu Wang: Validation, Investigation. Guanqiu Hao: Data curation. Ziwen Zhang: Investigation. Yongping Chen: Supervision, Project administration, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 51876184 and 51725602), Natural Science Foundation of Jiangsu Province (No. BK20180102), Six-talent Peak Project of Jiangsu Province (No. JNHB-074), the China Postdoctoral Science Foundation (Nos. 2017M621835 and 2019T120469) and Jiangsu Planned Projects for Postdoctoral Research Funds (No. 1701188B). References [1] Saghafifar M, Omar A, Mohammadi K, Alashkar A, Gadalla M. A review of unconventional bottoming cycles for waste heat recovery: Part I - analysis, design, and optimization. Energ Convers Manage 2019;198:110905. [2] Omar A, Saghafifar M, Mohammadi K, Alashkar A, Gadalla M. A review of unconventional bottoming cycles for waste heat recovery: Part II - applications. Energ Convers Manage 2019;180:559–83. [3] Chaudhry HN, Hughes BR, Ghani SA. A review of heat pipe systems for heat recovery and renewable energy applications. Renew Sust Energ Rev 2012;16:2249–59. [4] Dobriansky Y, Wojcik R. State of the art review of conventional and anti-gravity thermosyphons: Focus on two working fluids. Int J Therm Sci 2019;136:491–508. [5] Shafieian A, Khiadani M, Nosrati A. Strategies to improve the thermal performance of heat pipe solar collectors in solar systems: a review. Energ Convers Manage 2019;183:307–31. [6] Li H, Wang XG, Liu ZS, Tang Y, Yuan W, Zhou R, et al. Experimental investigation on the sintered wick of the anti-gravity loop-shaped heat pipe. Exp Therm Fluid Sci 2015;68:689–96. [7] Zhao J, Yuan DZ, Tang DW, Jiang YY. Heat transfer characteristics of a concentric annular high temperature heat pipe under anti-gravity conditions. Appl Therm Eng 2019;148:817–24. [8] Jiang L, Ling J, Jiang L, Tang Y, Li Y, Zhou W, et al. Thermal performance of a novel porous crack composite wick heat pipe. Energ Convers Manage 2014;81:10–8. [9] Akachi H, Štulc P. Pulsating heat pipes. In: Proceedings of the fifth international heat pipe symposium, Melbourne, Australia; 1996. p. 208–17.

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