Experimental study of a straight channel printed circuit heat exchanger on supercritical CO2 near the critical point with water cooling

International Journal of Heat and Mass Transfer 150 (2020) 119364

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Experimental study of a straight channel printed circuit heat exchanger on supercritical CO2 near the critical point with water cooling Joo Hyun Park a,c, Jin Gyu Kwon a, Tae Ho Kim b, Moo Hwan Kim a,b, Jae-Eun Cha c, HangJin Jo a,b,∗ a

Division of Advanced Nuclear Engineering, POSTECH, Pohang 790-784, South Korea Mechanical Engineering, POSTECH, Pohang 790-784, South Korea c Korea Atomic Energy Research Institute, Daejeon 34057, South Korea b

a r t i c l e

i n f o

Article history: Received 25 November 2019 Revised 10 January 2020 Accepted 10 January 2020

Keywords: Carbon dioxide (CO2 ) Brayton cycle Heat transfer Supercritical

a b s t r a c t The study presents an experimental examination of heat transfer of straight printed circuit heat exchanger (PCHE) for a precooler of supercritical carbon dioxide (sCO2 ) Brayton cycle. To perform heat transfer experiment, experimental loop for thermal hydraulic of CO2 in supercritical (ETHICS) was constructed at POSTECH. The straight PCHE was independently manufactured by photochemical etching and diffusion bonding process. An experiment for CO2 cooling with water was conducted via the ETHICS. We focused on heat transfer and flow characteristics of CO2 in the printed circuit heat exchanger. The experiments were conducted at three operating conditions for CO2 cooling, namely the trans-critical case (cooling from supercritical state to subcooled liquid), near the critical case (cooling from gas-like supercritical state to liquid-like supercritical state), and far critical case (cooling just in gas-like supercritical state). Nusselt numbers for different pressure and different operating conditions were compared by following typical analysis used in previous which is using averaged enthalpy based on inlet and outlet data but we conclude that the method of average value using inlet and outlet data is not appropriate for data reduction due to significant changes in the properties of CO2 near the critical point. Instead of that, we propose to use discretization method in data reduction of experimental data of CO2 near the critical point. It is difficult to predict heat transfer performance near the critical point of CO2 in PCHE. Hence, the data from this experiments and discretization method for data reduction are useful in designing a precooler for the sCO2 Brayton cycle. © 2020 Elsevier Ltd. All rights reserved.

1. Introduction The supercritical carbon dioxide Brayton cycle (sCO2 BC) is a promising power conversion system with advantages of high thermal efficiency, simple cycle layout, compactness of components, and wide operation range [1]. The aforementioned advantages are the result of high density and low compressibility of sCO2 near the critical point of CO2 (30.98 °C, 7.38 MPa) due to wide and rapid variation in the thermodynamic properties of sCO2 near the point [1,2]. Given the advantages, the sCO2 BC is evaluated as a power-conversion system for numerous applications including nuclear, geo-thermal, solar, and thermal power plants.

∗ Corresponding author at: Division of Advanced Nuclear Engineering, POSTECH, Pohang 790-784, South Korea. E-mail address: [email protected] (H. Jo).

https://doi.org/10.1016/j.ijheatmasstransfer.2020.119364 0017-9310/© 2020 Elsevier Ltd. All rights reserved.

Due to low compressibility, the size of turbomachinery of sCO2 BC can be compact. However, conventional heat exchangers such as shall and tube type are large. Therefore, to attain compactness of whole system in sCO2 BC, compactness of heat exchanger should be attained. Among the compact heat exchanger, a printed circuit heat exchanger (PCHE) take an attention for heat exchanger of sCO2 BC. Specifically, PCHE exhibit the advantages of small size and structural rigidity. They are widely chosen as a heat source and sink for a compact sCO2 power conversion system [3,4]. The PCHE typically exploits a diffusion-bonded array of plates on which semicircular channels are engraved via etching [5]. The denselystacked structure allows high compactness, and the diffusionbonded junctions enables high rigidity. The PCHE is suitable for supplying heat to the sCO2 BC, which requires intensive heat transfer and durability for harsh conditions of high temperature and

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Nomenclature A Ac Dh P T h k Kform P p Q r rw rs T U u V LMTD PCHE sCO2 Re

area (m2 ) cross-sectional area (m2 ) hydraulic diameter (m) differential pressure (Pa) log mean temperature difference (K) convective heat transfer coefficient (W/m2 -K) thermal conductivity (W/m-K) form loss coefficient (-) pressure (Pa) perimeter (m) heat transfer rate (kW) resistance thermal conduction resistance fouling resistance temperature (K) overall heat transfer coefficient (W/m2 -K) uncertainty (%) velocity (m/s) log mean temperature difference printed circuit heat exchanger supercritical carbon dioxide Reynolds number

pressure. The optimal geometry of the PCHE constitutes a tradeoff between thermal efficiency and structural reliability. To take advantages of PCHE, many researcher actively conducted investigation of PCHE. Hydraulic and thermal characteristics of PCHEs are experimentally and numerically investigated [6–26]. The PCHEs exhibit different flow channel geometries, and many researchers examined the thermal-hydraulic efficiency of the PCHEs. As a basic design of PCHE, straight channels have been investigated via numerical simulations and experiments [6,7]. To increase heat transfer performance of PCHE, some researchers have investigated thermal-hydraulic characteristics of zigzag PCHE via experimental data and computational fluid dynamic (CFD) [8–12]. Other researchers focused on PCHEs by comparing different channel types [13–25]. Tsuzuki et al. developed a new PCHE with S-shaped fins via numerical simulations [13]. The S-shape fin PCHE included a one-fifth pressure drop, which was comparable to zigzag PCHE with the same heat transfer performance. Kim et al. suggested airfoil fin PCHE and investigated heat transfer performance [14]. Pressure drop of airfoil fin PCHE is 1/20 when compared to that of a zigzag PCHE with same heat transfer performance. The sensitivity analysis of airfoil fin with parameters of airfoil fin was suggested by Kim et al. [15]. Kwon et al. suggested correlations for airfoil fin PCHE for recuperator of sCO2 operating conditions [16]. The correlations take a form of the Dittus–Boelter term with nondimensional parameters of the airfoil fin array. The heat transfer and pressure drop characteristics of the PCHE was investigated by Seo et al. [17] in an experimental water–water loop. They suggested heat transfer correlations for water–water heat transfer at laminar flow in the Reynolds number range of 100–850. The thermal characteristics of PCHE with S-shape and zigzag were experimentally investigated by Ngo et al. [18]. The thermal-hydraulic efficiency of PCHE in the cryogenic region was investigated and focused on the effects of flow maldistribution and axial conduction [26]. Among these various studies, some PCHE research were performed to apply on a precooler of sCO2 BC [27,28]. The precooler is commonly operated to cool CO2 using water. The precooler sets

Nu Pr

Nusselt number Prandtl number

Greek symbols μ viscosity (kg/(m-s)) ρ density (kg/m3 ) Subscripts Ave CO2 Core Entrance Exit exp H2 O i in InletTube InletHeader n IO out OutletHeader OutletTube total

average carbon dioxide core in PCHE entrance of channel in PCHE exit of PCHE experiment water ith node in inlet tube of PCHE inlet header of PCHE number of node inlet and outlet out outlet header of PCHE outlet tube of PCHE total

the operating conditions of compressor. The compressor of sCO2 BC is operated near the critical point to use in the high-density region. Therefore, outlet conditions of precooler is at high density region near the critical point. This indicates that CO2 experiences a significant change in thermo-physical properties in the precooler. Thus, experiments and analysis for precooler are more complex due to changes in properties and different working fluids on the two sides of heat exchanger. In a previous study, research focused on estimating the precooler operating condition and suggesting correlations for the precooler. An experimental and numerical study was performed by using zigzag PCHE and suggesting correlations for precooler operating conditions by Baik et al. [27]. Chu et al. [28] examined experimental heat transfer characteristics of straight PCHE in a sCO2 -water loop and analyzed the phenomena with average value based on inlet and outlet measured data. In the previous PCHE works, the analysis method of thermal resistance theory with average properties of inlet and outlet data was used to analyze experimental results of PCHE. The method is a convenient and effective methodology as a data reduction for heat exchanger that exhibits constant properties or slight change of properties. However, heat transfer process involving significant change in properties, e.g. precooler operating near the critical point of fluid, is not suitable for the method based on average values of the inlet and outlet point. In other words, it is not proper to use the method for estimating significant changes in properties near the critical point of CO2 in PCHE. To attain realistic analyze results of experiments, the change of properties in the PCHE channel along the flow direction should be considered even though measuring the internal distributed state of a PCHE in experiments is difficult instead of using inlet and outlet data. In the present study, a discretization method is proposed to estimate significant changes in properties near the critical point of CO2 in PCHE. The local Nusselt number of sCO2 along the channel of PCHE was obtained via the discretization method, and the results of PCHE experiment were compared according to different data reduction method. To perform the experiment of PCHE, a 3 kW PCHE with straight channel was designed and fabricated

J.H. Park, J.G. Kwon and T.H. Kim et al. / International Journal of Heat and Mass Transfer 150 (2020) 119364

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Fig. 1. Picture of experimental loop for thermal hydraulic of CO2 in supercritical (ETHICS) at POSTECH.

Table 1 Main design parameters of ETHICS. System maximum conditions Max PCHE inlet pressure (MPa) Max PCHE inlet temperature ( °C) Max total pressure loss (kPa)

Target conditions of PCHE experiment 10.8 100 500

via chemical etching and diffusion bonding process. Experiments were conducted to investigate the operating condition of precooler; CO2 cooling process by using water. The heat transfer of sCO2 in the PCHE were tested in three operating conditions for CO2 cooling, namely the trans-critical case (cooling from supercritical state to subcooled liquid), near-critical case (cooling from gas-like supercritical state to liquid-like supercritical state), and far-critical case (cooling just in gas-like supercritical state). The effects of inlet pressure and mass flow rate on the heat transfer and flow characteristics were analyzed.

2. Experimental facility and PCHE 2.1. sCO2 test loop To develop the heat transfer model for precooler and investigate the performance of PCHE, the experimental loop for thermal hydraulic of CO2 in supercritical (ETHICS) is constructed at POSTECH (Fig. 1). The data from ETHICS experiments is important as it constitutes basic data of heat transfer between CO2 and water to increase the understanding of thermo-physical behavior of CO2 near its critical point. The experimental loop (Fig. 2 and Table 1) consists of three parts: a CO2 -supplying part, a CO2 -circulation part including heat transfer test section and PCHE test section (red arrow in Fig. 2), and a water-supplying part (blue arrow in Fig. 2). The tube material corresponds to SUS316. The tube inner diameters are 3/8 , 1/2 , and 3/4 in ETHICS. In the CO2 -supplying part, a CO2 pressure tank fed CO2 into the circulation part. An air-driven pump (Maximator, G35) with an electric regulator pressurized the circulation loop in the experimental condition.

Target PCHE inlet pressure (MPa) Target PCHE inlet temperature ( °C) Maximum pressure loss of PCHE (kPa)

8.0 70 100

In the CO2 circulation part (PCHE hot side), CO2 was cooled through a shell and tube heat exchanger (cooler-2) that used water as a coolant, which is supplied by a circulation bath (Jeiotech, RW-2040 G). In front of cooler-2, additional cooling of CO2 was performed via the PCHE type heat exchanger (Cooler-1) that used water as a coolant, which is supplied by a circulation bath (Polyscience, AP45R series). A magnetic driven pump (Phosentech Inc., MD series) circulated CO2 at a constant motor speed to maintain a constant mass flow rate which was measured via a Coriolis flow meter (RHEONIK, RHM04) with a rated accuracy of 0.20%. The mass flow rate was measured at the pump outlet. Needle valves were used to control the mass flow rate via a bypass line. After passing through the flow meter, CO2 was heated by a gas circulation heater (WATLOW, Cast-X 20 0 0) with a maximum capacity of 6 kW to increase the inlet temperature of the test section up to the experimental condition. The heater was controlled by a power controller (HANYOUNG NUX, TPR-2 N) and a temperature controller (Autonics, TZ4ST). The inlet and outlet temperatures of PCHE test section of CO2 were measured via resistance temperature detectors (RTDs, Omega engineering) of 1/10 DIN class with an accuracy of ±0.045 °C at 30 °C. The CO2 outlet absolute pressure was measured via an absolute pressure transducer (Setra, Model 204) that exhibits an accuracy of ±0.073% in full span. The differential pressure of CO2 between inlet and outlet of PCHE was measured via a differential pressure transmitter (Yokogawa, EJA110E, range 0–100 kPa) that exhibits an accuracy of ±0.055% in full span. The filter was located in front of the cooler-2 inlet. In the water-supplying part (PCHE cold side), a chiller (Jeiotech, HS-45H) with a maximum cooling capacity of 6.5 kW maintained the water temperature with ±0.2 °C stability and water supplied by the embedded pump of the chiller that provided a maximum flow rate of 70 L/min. Water mass flow rate was controlled by by-

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Fig. 2. Schematic diagram of the experimental loop for thermal hydraulic of CO2 in supercritical (ETHICS) at POSTECH.

Table 2 Measurement accuracy. Sensor type

Span

Accuracy

RTD ( °C,%) Abs. pressure transducer (MPa,%) Diff. pressure transmitter (kPa,%) Mass flow rate (kg/min,%)

0–100 0–20 0–100 0–5

± ± ± ±

0.03 – 0.08 0.073 0.055 0.2

pass line with valves. The suppling water to the PCHE was measured via a Coriolis flow meter (RHEONIK, RHM04) with a rated accuracy of 0.20%. The inlet and outlet temperatures of PCHE test section of water were measured via resistance temperature detectors (RTDs, Omega engineering) of 1/10 DIN class with an accuracy of ±0.045 °C at 30 °C. The water inlet absolute pressure was measured via an absolute pressure transducer (Setra, Model 206) with an accuracy of ±0.98% in full span. The differential pressure of water between the inlet and outlet of PCHE was measured via a differential pressure transmitter (Yokogawa, EJA110E range 0100 kPa) with an accuracy of ±0.055% in full span. The filter was located in front of the inlet of Coriolis flow meter. The accuracy of main measurement device was tabulated (Table 2). The experimental data were logged via a data acquisition system (Agilent, 34980A) when the experimental condition was in the steady state for 10 min. The experiments were conducted sequentially while the heat flux was increased although other variables were held constant until the cooling capacity was suitable. The local temperature of each component was measured via a thermocouple (TC, Omega engineering, K-type) to control the loop; cooler-2 inlet and outlet, pump inlet and, heater inlet and outlet.

Additionally, to measure the pump head, differential pressure between pump inlet and outlet was measured via a differential pressure transmitter (Yokogawa, EJA110E range 0–500 kPa). The differential pressure represents entire differential pressure of CO2 circulation loop. To use high purity CO2 in the experiment, vacuum condition was set by a vacuum pump (ULVAC KIKO, INC., GLD-051). Additionally, to use high purity water at experiment, deionized water was used as a cooling water in the PCHE cold channel.

2.2. PCHE specification The printed circuit heat exchanger (PCHE) is manufactured by Energyn in Korea. The physical size of the designed PCHE core corresponded to 640 mm x 40 mm x 32 mm (Fig. 3) and was independently fabricated via photochemical etching and diffusion bonding process. The plate was fabricated using a 1.2-mm-thick SS316L plate used on each side, i.e., hot and cold. The internal flow channel dimensions (Figs. 3(b) and 4) are composed of straight channels (Table 3), and the etching depth corresponded to 0.6 mm. The PCHE core included a hot side (CO2 ) and cold side (water) in which channels were straight. Single banking was adopted. The hot side has 7 plates and the cold side included 7 plates. The channel width is 1.2 mm. The wall thickness between channels corresponded to 0.6 mm. The hot and cold side plate included 11 chemically-etched channels; and minimum wall thickness of internal pressure boundary corresponded to 0.6 mm to endure 20 MPa, which corresponds to the ASME pressure vessel standard [29]. In the hot and cold side, 77 rows were stacked.

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Fig. 3. PCHE for experiments; (a) Whole appearance of PCHE, (b) Actual plate of straight channel.

Fig. 6. Schematic for the measuring point of differential pressure.

3. Data reduction Fig. 4. Schematic of PCHE cross-section with parameters.

3.1. Data reduction 3.1.1. Data reduction and average method The average heat transfer rate is defined as follows:

Table 3 Main design parameters of PCHE. Parameter

Hot channel

Cold channel

Channel type Channel length (mm) Number of channels in plate (EA) Number of plates Plate thickness (mm) Channel width (mm) Etching depth (mm) Wall thickness (mm)

Straight 640 11 7 1.2 1.2 0.6 0.6

Straight 640 11 7 1.2 1.2 0.6 0.6

Qave =

(QCO2 + QH2 O ) 2

,

(1)

where QC O2 denotes the heat release rate on the CO2 side, and QH2 O denotes the heat absorption rate on the water side. The total heat transfer coefficient is defined as follows:

U=

Qave , A c o 2 T

(2)

where AC O2 denotes total heat transfer area on CO2 side.



T =





TC O2 ,out − TH2 O,in − TC O2 ,in − TH2 O,out



ln

TC O2 ,out −TH2 O,in TC O2 ,in −TH2 O,out





(3)

where Eq. (3) denotes logarithmic mean temperature difference. The thermal resistance analysis method is described as follows:

1 1 1 = + rW + rs + , UA hC O2 AC O2 hH2 O AH2 O Fig. 5. Schematic diagram of discretization along the flow direction.

(4)

where rw is the thermal conduction resistance, and rs denotes the fouling resistance that corresponds to zero if the heat exchanger

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Fig. 7. Experimental conditions with properties; temperature vs. density and Cp.

Where,

Dh =

4Ac P

(10)

Nu correlation proposed by Seo et al. [17] is more appropriate to analyze the data of water side than constant Nu because it reflects the change in heat transfer with the change in flow rate. Therefore, Nu correlation by proposed Seo et al. [17] should be used to analyze the data of water side in this study. The Nu of CO2 is obtained by the definition like the Eq. (7) as

hDh , k

N uC O2 =

(11)

The average Nu (Nuave ) was obtained from the enthalpy-based average using inlet and outlet data. These data reduction method typically used to analyze the results of experiments of heat exchanger.

Fig. 8. Heat balance between CO2 and water.

is clean. Subsequently, the heat transfer coefficient is calculated as follows:



hC O2 =

AC O2 AC O2 − AC O2 rW − UA hH2 O AH2 O

−1

,

(5)

since the heat transfer areas for CO2 and H2 O are equivalent, the Eq. (5) could be simplified as



hC O2 =

1 1 − AC O2 rW − U hH2 O

−1

,

(6)

Where

hH2 O

N uH2 O k = , Dh

3.1.2. Discretization method for data reduction Nu had been attained using the enthalpy based average value in the case of constant thermo-physical properties, but as pointed out in previous section, when properties significantly change along the flow direction in the channel, then the average value cannot represent actual phenomena. To investigate proper data reduction method, we propose a discretization method, and Nu from the discretization method (NuDis ) is compared with the results of typical data reduction method obtained from the enthalpy-based average using inlet and outlet data (Nuave ). The PCHE core length corresponds to 640 mm, and we discretize the domain (Fig. 5). The unit section length is selected as an enthalpy difference lower than 0.3 kJ/kg to avoid significant changes in the thermo-physical properties in the unit section.

Q˙ = m˙ (hin − hout )

(11)

hi − hi−1 < 0.3 kJ/kg

(12)

(7)

In this study, flow of water is laminar with a Reynolds number from 100 to 900. The Nu correlations for laminar flow in previous research have been studied [17,30–33]. Base on intensive review, two selections would be reasonable; the one is using constant Nu for laminar flow, [30]

Nu = 4.089,

(8)

And the other one is that correlation was proposed by Seo et al. [17]. They suggested heat transfer correlations for water–water heat transfer at laminar flow in the Reynolds number range of 100–850. 1

N uH2 O = 0.7203Re0.178 P r 3 (μ/μw )0.14 , 100 < Re < 850, 3.5 < Pr < 5.2

(9)

Based on above criteria, the length of the unit section is determined. Flow direction length divided by proper length. n is a number of node according to unit length;

n ≥ 640

(13)

Heat transfer rate of unit section is defined as;

Q˙ /n = Q˙ i

(14)

The Nu for each node is obtained as follows:

N uDis =

hDh , k

(15)

J.H. Park, J.G. Kwon and T.H. Kim et al. / International Journal of Heat and Mass Transfer 150 (2020) 119364 Table 6 Experimental conditions.

Table 4 Form loss factor to estimate the pressure drop [34]. Form factor Tees Elbows Inlet Header Outlet header

Line flow, flanged Regular 90°, flanged Entrance expansion Sudden contraction Sudden expansion Exit contraction

0.2 0.3 0.72 0.42 1 0.05

Table 5 Uncertainty of the experiments. Parameter

Uncertainty

Unit

QC O2 QH2 O Uexp hC O2 hH2 O

1.2 – 2.3 1.2 – 2.3 7.5 7.5 7.2

% % % % %

3.1.3. Estimation of pressure drop The pressure drop of PCHE in the experiment includes additional form loss at the inlet and outlet; header of PCHE (Fig. 6). The pressure drop of core is estimated by eliminating additional form loss from the total pressure drop of experimental data as follows:

Ptotal = PInletT ube + PInletHeader + PEntrance + PCore +PExit + POuletHeader + POut let T ube

(16)

Form loss equation was used to estimate additional pressure loss and header pressure loss as follows:

P = K f orm ×

1 × ρ × V2 2

(17)

The form loss factor is tabulated in Table 4 from extant literature [34]. 3.2. Uncertainty analysis An uncertainty analysis is performed to estimate uncertainties of the experimental results as follows:



uy =

N i=1



∂f ∂ Xi

2 u2xi

7

(18)

Where, y = f(X1 , X2 , X3 , · · · XN ) In the experiment, independent variables, Xi , denote the temperature (T), pressure (P), and mass flow rate (m˙ ). The dependent variables, y, denote the heat transfer rate (Q), overall heat transfer coefficient (U), heat transfer coefficient of CO2 (hC O2 ), and heat transfer coefficient of water (hH2 O ). The detailed analysis method is presented using the ISO uncertainty guideline [35]. The results of the analysis are listed in Table 5. 4. Results and discussion 4.1. Experimental conditions The thermal properties of CO2 exhibits a drastic change near the critical point. Fig. 7 shows properties of CO2 based on temperature variation. The specific heat exhibits a peak value after temperature of critical point above critical pressure, where the peak point of specific heat is a pseudo critical point. The density of CO2 exhibits a high value at the subcooled liquid state. However, the density exhibits a rapid variation near the critical point above the critical point.

Re 40 0 0 – 20,0 0 0 (16 Temperature ( °C) point) Inlet Outlet

Pressure (MPa) Inlet

Far critical (A to B)

7.5 7.8 8.0 8.5 7.5 7.8 8.0 8.5 7.5 7.8 8.0 8.5

70

40

Near-critical (A to C) 65

31.5

Trans-critical (B to D) 44

28

The distinction of phase, between gas and liquid, disappears above the critical point. At the pressure above the critical point, subcooled liquid having temperature lower than the critical point would be turned to supercritical fluid if the fluid is heated. In this process, properties undergo drastic change even in small temperature increase. Between critical point (start of supercritical state) and pseudocritical point, the properties of material shows a characteristics of liquid. Therefore this region is called as liquid-like supercritical state. When material located far above from the critical and pseudocritical point, material is called as gas-like supercritical state. If the compressor is operated at the near-critical point, the sCO2 BC exhibits high efficiency due to decreases in compression work. Therefore, the liquid-like supercritical state is preferred as outlet conditions of the precooler. The experiments were conducted at three operating conditions for CO2 cooling; far critical case (cooling just in gas-like supercritical state; A to B at Fig. 7), near the critical case (cooling from gaslike supercritical state to liquid-like supercritical state; A to C at Fig. 7), and trans-critical case (cooling from supercritical state to subcooled liquid; B to D at Fig. 7). The experimental conditions are listed in Table 6. Fig. 8 shows the heat balance of the experiment which is well matched between CO2 and water. The results indicate that the error of heat balance is lower than 6%. Heat transfer is procedure from CO2 to water. Results of the experiments are reasonable and reliable with respect to the thermal-physics law. 4.2. Average Nusselt number with inlet and outlet data Fig. 9 shows Nu as a function of Re for various operating conditions. The results indicate that Nu increases with increases in Re. In other words the heat transfer performance of CO2 increases with increases in the mass flow rate. Far-critical case exhibits a similar Nu and similar gradient of Nu at different pressures. Near critical case exhibits slight variation of Nu depending on pressure condition. Trans-critical case exhibits significant difference between each pressure condition. Furthermore, the growth tendency of Nu of trans-critical case is not linear, and it has local maximum and higher pressure case exhibits an early maximum point when compared to that of the lower pressure case. The gradient of Nu growth of trans-critical case increases also as CO2 pressure increases. It was expected that Nu of near critical case is higher than Nu of far critical case, however Nu of near critical case lower than Nu of far critical case. We believe that the difference is attributed to the data reduction methodology using average value based on inlet and outlet. In other words, the average value between inlet and outlet data is not proper to represent actual phenomena happened near the supercritical condition. So, we conclude that data reduction method with average value using inlet and outlet data is not suitable to analyze experimental results near the critical point, and

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Fig. 9. Nu vs. Re for different cooling cases.

we propose a new reduction procedure for analyzing heat transfer phenomena near the critical condition. 4.3. Nusselt number with discretization method Nu had been attained by using the averaged enthalpy value in the case of constant thermo-physical properties, however, as pointed out in previous section, when properties significantly change along the flow direction in the channel, then the average value cannot be representative of actual phenomena. To investigate proper data reduction method, we propose the discretization method, and the method is evaluated by comparing the results obtained Nu from the enthalpy-based average using inlet and outlet data (NuIO,ave ) and Nu from discretization method (NuDis ). 4.3.1. Far-critical case Far critical case (A to B, 7.5 MPa, Reave = 14,400) is shown in Fig. 10(a) and (b). Temperature of CO2 linearly decreases along the flow direction length and temperature of water linearly increases along the flow direction length Fig. 10(a)). Point ((1) shows a minimum point of LMTD, and it implies a minimum temperature difference point between CO2 and water. As a result of the discretization method, NuDis shows differences compared with the average reduction method and the trend of NuDis exhibits a similar tendency with specific heat of CO2 along the flow direction (Fig. 10(b)). In the figures, the average reduction methods like the typical reduction method but with different inlet and outlet conditions are compared. The average value of the discretization method (NuDis,ave ), averaged value but with inlet and outlet calculated with the discretization method, exhibits different with NuIO,ave (Fig. 10(b)) using the typical inlet and outlet condition. Just for the clarification, although the averaged value is plotted for all length range for the comparison purpose with the local Nu calculated via NuDIS , NuDis,ave and NuIO,ave does not represent local values. It means that average value of CO2 properties is inadequate to represent the heat transfer performance although PCHE outlet temperature of far-critical case exceeds that of the pseudo-critical point and CO2 does not experience a significant change in properties. 4.3.2. Near-critical case Results of near critical case (A to C, 7.5 MPa, Reave = 10,0 0 0) are shown in Fig. 11(a) and (b). Temperature of CO2 decreases as a non-linear parabolic curve along the flow direction length. The CO2 approaches the pseudo-critical point during the cooling process, and specific heat significantly increases in Fig. 11(b) and it

Fig. 10. Far-critical case (A to B), value distribution along the flow direction; (a) temperature variation based on flow direction, (b) Nu and specific heat variation based on flow direction.

affects the change in temperature near the pseudo-critical point in Fig. 11(a). Temperature of water linearly increases along the flow direction length in Fig. 11(a). Point (1) shows a minimum point of LMTD, and it implies a minimum temperature difference point between CO2 and water. Point (2) is a pseudo-critical point in Fig. 11(a). Point (2) is the same as the peak point of specific heat in Fig. 11(b). NuDis exhibits a peak point at the pseudo-critical point (Fig. 11(b)). Drastic change of thermos-physical properties affects the heat transfer between CO2 and water. NuDis,ave does not coincide with NuIO,ave in Fig. 11(b), and the difference is much larger than the far-critical case. Therefore, the change in thermo-physical properties along the flow direction in channel should be considered for data reduction. 4.3.3. Trans-critical case The results of trans-critical case (B to D, 7.5 MPa, Reave = 12,500) are shown in Fig. 12(a) and (b). Temperature of CO2 decreases as an S-curve along the flow direction. This case also suffers significant thermal properties change during the cooling process. Point (2) in Fig. 12(a) is the same as the peak point of specific heat in Fig. 12(b). Point (3) indicates an inflection point of LMTD. LMTD increases until CO2 temperature is far from the pseudo-critical temperature at point (3) in Fig. 12(a). After

J.H. Park, J.G. Kwon and T.H. Kim et al. / International Journal of Heat and Mass Transfer 150 (2020) 119364

Fig. 11. Near-critical case (A to C), value distribution along the flow direction; (a) temperature variation based on flow direction, (b) Nu and specific heat variation based on flow direction.

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Fig. 12. Trans-critical case (B to D), value distribution along the flow direction; (a) temperature variation based on flow direction, (b) Nu and specific heat variation based on flow direction.

point (3), LMTD decreases. The peak point of NuDis exists at the pseudo-critical point (Fig. 12(b)). NuDis,ave also shows significant difference compared with NuIO,ave . The CO2 outlet conditions of PCHE exhibits a low NuDis value because the CO2 temperature fully decreases from the pseudo-critical temperature. To compare the results of experiments with different operating conditions, i.e., far-critical case (A to B), near-critical case (A to C), and trans-critical case (B to D), NuDis of each case is plotted in Fig. 13. NuDis exhibits increasing tendency along the flow direction with the cooling process but details are depending on the conditions. At the far-critical case, the CO2 temperature of inlet and outlet is far from the pseudo-critical point. Therefore, CO2 does not experience significant change in properties. Near-critical and trans-critical have a peak point of NuDis due to the effect of drastic change of properties of CO2 . The CO2 in these two cases passes through the pseudo-critical point during the cooling process. 4.4. Comparison of Nuaccording to data reduction method Fig. 14 shows the comparison between NuIO,ave and NuDis,ave . The slope of the Nu is similar between NuIO,ave and NuDis,ave at far-critical case (Fig. 14(a)) but there was a difference between the two. From near-critical case, the slope of Nu is different be-

Fig. 13. Nu variation based on flow direction with three cases; Far-critical case (A to B), Near-critical case (A to C), Trans-critical case (B to D).

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J.H. Park, J.G. Kwon and T.H. Kim et al. / International Journal of Heat and Mass Transfer 150 (2020) 119364

tween NuIO,ave and NuDis,ave (Fig. 14(b)). Also, the difference of the NuIO,ave and NuDis,ave at far-critical case is larger than that at nearcritical case. The difference between NuIO,ave and NuDis,ave increases as Re increases. NuIO,ave shows a variation between CO2 pressures at trans-critical case, but NuDis,ave does not shows a significant difference (Fig. 14(c)). Therefore, the data reduction by using the enthalpy based average value using inlet and outlet data can be used in data reduction of experiments that exhibits constant properties or slight change of properties. The method is a convenient and effective methodology. However, the heat transfer process that attains significant change in properties such as that in the near-critical and transcritical case is not suitable for the method based on average values of the inlet and outlet point. The discretization method is an effective method for data reduction that reflects the change in properties in the PCHE channel. Therefore we conclude that heat transfer correlations should be developed that include local heat transfer coefficient and the design of PCHE for the precooler should be considered for the change in thermo-physical properties. 5. Conclusion

Fig. 14. Comparison of Nu according to data reduction method ((a) Far-critical case, (b) Near-critical case, and (c) Trans-critical case).

In the study, the PCHE experiments with straight channel are performed at supercritical state of CO2 using experimental loop for thermal hydraulic of CO2 in supercritical (ETHICS). ETHICS is used to accumulate experience while operating a 3-kW precooler of supercritical CO2 Brayton cycle (sCO2 BC) and to develop a designing method of PCHE to design a precooler. Hence, experiments were performed to test the straight PCHE of ETHICS, and the characteristics of the experiments are analyzed. We focused on the heat transfer and flow characteristics of CO2 in a printed circuit heat exchanger. The experiments were conducted at three operating conditions for CO2 cooling, namely the trans-critical case (cooling from supercritical state to subcooled liquid), near critical case (cooling from gas-like supercritical state to liquid-like supercritical state), and far critical case (cooling just in gas-like supercritical state). Typical data reduction by using the enthalpy based average value using inlet and outlet data can be used in data reduction of experiments that exhibits constant properties. However, when properties significantly change along the flow direction in the channel, then the average value cannot represent actual phenomena. To investigate proper data reduction method, we propose a discretization method, and Nu from the discretization method (NuIO,Dis ) is compared with the results of typical data reduction method obtained from the enthalpy-based average using inlet and outlet data (NuIO,ave ). Typical data reduction method was used to analyze the result of experiments. The effects of sCO2 pressure and different operating conditions on the heat transfer performance of PCHE were investigated. The results of analysis exhibits a significant difference in the dependency of Nu with Re according to operating condition. And, before the data reduction, it was expected that Nu of nearcritical case is higher than Nu of far-critical case due to peak of specific heat near the critical point. However the results of analysis was shown that Nu of near critical case lower than Nu of far critical case. Therefore, the typical method is not proper to include the effect of significant changes in thermo-physical properties and is not proper to represent actual phenomena happened near the supercritical condition. The discretization method was used to properly include the effect of significant changes in thermo-physical properties for PCHE channel. As a results of comparison between NuIO,ave and NuDIS,ave , far-critical case shows a difference between the NuIO,ave and NuDIS,ave but the difference was small compared with the other cases. Near-critical and trans-critical cases show a signifi-

J.H. Park, J.G. Kwon and T.H. Kim et al. / International Journal of Heat and Mass Transfer 150 (2020) 119364

cant difference between the NuIO,ave and NuDIS,ave due to significant changes in thermo-physical properties and especially specific heat, and it affects the change in Nu based on flow direction. Therefore, the heat transfer process that attains significant change in properties is not suitable for the typical data reduction method based on average values of the inlet and outlet point. Thus, the discretization method is an effective method for data reduction that reflects the change in properties in the PCHE channel. Additionally, changes in thermo-physical properties should be considered in the design of PCHE for the precooler. 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. Acknowledgments This research was supported by civil-military technology cooperation program (No. 17-CM-EN-04) and by global PhD fellowship from NRF (National Research Foundation of Korea) by the Ministry of Science, ICT and Future Planning (NRF-2018H1A2A1062673). References [1] V. Dostal, M.J. Driscoll, Hejzlar P, A supercritical carbon dioxide cycle for next generation nuclear reactors, MIT-ANP-TR-10 0 (20 04). [2] J.H. Park, S.W. Bae, H.S. Park, M.H. Kim, J.E. Cha, Transient analysis and validation with experimental data of supercritical CO2 integral experimental loop by using MARS, Energy 147 (2017) 1030–1043. [3] J.H. Park, H.S. Park, J.G. Kwon, T.H. Kim, M.H. Kim, Optimization and thermodynamic analysis of supercritical CO2 Brayton recompression cycle for various small modular reactors, Energy 160 (2018) 520–535. [4] F. Xin, T. Ma, Y. Chen, Wang Q, Study on chemical spray etching of stainless steel for printed circuit heat exchanger channels, Nucl. Eng. Des. 341 (2019) 91–99. [5] C. Huang, W. Cai, Y. Wang, Y. Liu, Q. Li, B. Li, Review on the characteristics of flow and heat transfer in printed circuit heat exchangers, Appl. Therm. Eng. 153 (2019) 190–205. [6] M. Chen, Sun X, R.N. Christensen, S. Shi, I. Skavdahl, V. Utgikar, P. Sabharawall, Experimental and numerical study of a printed circuit heat exchanger, Ann. Nucl. Energy 97 (2016) 221–231. [7] Z. Zhao, X. Zhang, K. Zhao, P. Jiang, Y. Chen, Numerical investigation on heat transfer and flow characteristics of supercritical nitrogen in a straight channel of printed circuit heat exchanger, Appl. Therm. Eng 126 (2017) 717–729. [8] S.M. Lee, K.Y. Kim, S.W. Kim, Multi-objective optimization of a double-faced type printed circuit heat exchanger, Appl. Therm. Eng. 60 (2013) 44e. [9] I.H. Kim, H.C. No, Thermal–hydraulic physical models for a printed circuit heat exchanger covering He, He–CO2 mixture, and water fluids using experimental data and CFD, Exp. Therm. Fluid Sci. 48 (2013) 213–221. [10] S.M. Lee, K.Y. Kim, Multi-objective optimization of arc-shaped ribs in the channels of a printed circuit heat exchanger, Int. J. Therm. Sci. 94 (2015) 1–8. [11] H.H. Khan, A.M. Aneesh, A. Sharma, A. Srivastava, P. Chaudhuri, Thermal-hydraulic characteristics and performance of 3D wavy channel based printed circuit heat exchanger, Appl. Therm. Eng. 87 (2015) 519–528. [12] H. Zhang, J. Guo, X. Huai, K. Cheng, C. X, Studies on the thermal-hydraulic performance of zigzag channel with supercritical pressure CO2, J. Supercrit. Fluids 148 (2019) 104–115.

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