Hydraulic resistance of in-tube cooling supercritical water accompanying out-tube pool boiling

Applied Thermal Engineering 141 (2018) 394–405

Contents lists available at ScienceDirect

Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Hydraulic resistance of in-tube cooling supercritical water accompanying out-tube pool boiling

T

⁎

Haicai Lv, Qincheng Bi , Zanjian Zhang, Ge Zhu, Kun Li, Hongyang Liu State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an 710049, China

H I GH L IG H T S

G R A P H I C A L A B S T R A C T

hydraulic resistance of in-tube • Studied cooling SCW with out-tube pool boiling.

a steep “pit” for friction factor • ofExisted adiabatic flow near PC region. Observed a noticeable “Λ-shaped” • profile of the cooling frictional pressure drop.

deceleration-factor into • Introduced the cooling friction factor correlation.

A R T I C LE I N FO

A B S T R A C T

Keywords: Supercritical water Hydraulic resistance Cooling Deceleration

The experiment was conducted by immersing a smooth horizontal tube in a pool tank to simulate the flow condition of Passive Residual Heat Removal System (PRHRS) in a SuperCritical Water-cooled Reactor (SCWR). Hydraulic resistance and friction factor of in-tube cooling supercritical water accompanying out-tube pool boiling were investigated in this study with test pressure ranging from 23 to 28 MPa and mass flux ranging from 600 to 1000 kg·m−2·s−1. The influence of pressure and mass flux on pressure drop in adiabatic and cooling flows was analyzed. This paper also discussed the effect of deceleration in the cooling flow and assessed various friction-factor correlations by employing the experimental data. Results showed that the friction factor of the adiabatic flow exists a steep “pit” approaching to pseudocritical region. A noticeable “Λ-shaped” profile was observed in the vicinity of the pseudocritical temperature, due to deceleration-effect of frictional pressure drop in the cooling flow. The deceleration factor of supercritical cooling flow led to the axial fluid element shrinkage and radial bulk fluid velocity parabolic distribution. Taking into account the effect of deceleration-factor, a modified correlation was proposed for in-tube cooling supercritical water accompanying out-tube pool boiling, of which the average error and root mean square error are −2.51% and 15.28% respectively.

1. Introduction

nonproliferation, which is recognized as one of the promising watercooled nuclear systems for the future [2,3]. The Fukushima Nuclear Accident [4] in March 2011 aroused security concerns of nuclear industries all over the world. How to ensure the inherent safety of nuclear reactors after extreme external events has become an issue to address. Especially, the passive residual heat removal system (PRHRS) of a

The SuperCritical Water-cooled Reactor (SCWR) is one of the six advanced nuclear-reactor concepts being developed by Generation IV [1]. A SCWR power plant presents significant advantages such as high thermal efficiency, low capital investment, simplified loop and nuclear

⁎

Corresponding author. E-mail address: [email protected] (Q. Bi).

https://doi.org/10.1016/j.applthermaleng.2018.04.136 Received 23 January 2018; Received in revised form 25 April 2018; Accepted 28 April 2018 Available online 31 May 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

Nomenclature

Cp din G H ΔH L P ΔP ΔPfr ΔPac Pr q Re T v v

μ ρ εfr

specific heat, kJ·kg−1 ·K−1 inside diameter, m mass flux, kg·m−2·s−1 enthalpy, kJ·kg−1 enthalpy increment, kJ·kg−1 cooling length, m pressure, MPa pressure drop, kPa frictional pressure drop, kPa acceleration pressure drop, kPa Prantl number heat flux, kW·m−2 Reynolds number temperature, °C specific volume, m3·kg−1 integral means specific volume, m3·kg−1

dynamic viscosity, Pa·s density, kg·m−3 friction factor

Subscripts bulk b cal calculated exp experimental inlet, inner int, i out. o outlet, outer w, wi, wo wall temperature, inner wall temperature, outer wall temperature Abbreviations

PRHRS SCWR PC

passive residual heat removal system super critical water-cooled reactor pseudocritical

Greek symbols

β

thermal expansion coefficient, K−1

tube pool boiling may expedite the cooling process and affect the hydraulic resistance, which needs to be further studied. Many experimental studies have been carried out in the hydraulic resistance of supercritical fluid [11–13]. It is found that the friction factor is related to the Reynolds number and thermal physical property ratio [14–19]. Kondrat’ev [16] conducted hydraulic resistance experiments in a horizontal heated tube within a wide range of flow condition. He found that the acceleration factor could lead to a “V-shaped” profile displayed by the friction factor of supercritical fluid within the PC region. Wang [3] conducted experiments to investigate the hydraulic resistance and friction factor of supercritical fluid in an annular channel. In his experiment, a local hump in the friction factor was observed in annular channel in the PC region, which becomes stronger with the decrease of mass flux or pressure. Zhang [20] explained the reason why concave curves and convex curves were appeared in the variation trend of the frictional coefficient along with the fluid enthalpy in the PC region. He believed that it was resulted from measurement

station blackout accident has drawn more and more attention [5]. At present, the two-phase passive cooling system has been adopted in the generation III advanced nuclear reactor to improve the safety [5–8]. As for improving inherent safety of the SCWR, the PRHRS is a good choice [9,10]. Some advanced SCWR designs incorporate a system to remove decay heat passively through the natural circulation loop. This is accomplished by submerging a heat exchanger in a tank of water to cool the supercritical water of reactor core. Supercritical fluid is taken as the working medium through the PRHRS. Beyond the pseudocritical (PC) region, the fluid does not undergo phase transition which is similar to single-phase fluid. However, near the PC region, it should be noteworthy that the thermophysical properties of supercritical fluid present steep and drastic variations (as seen in Fig. 1). These drastic variations lead to non-uniform flow features in the channel. The issue is more complicated in a PRHRS of SCWR, wherein the supercritical fluid is in-tube cooled accompanying out-tube pool boiling. The flowing condition of in-tube cooling and out-

(a) Specific volume VS bulk temperature

(b) Dynamic viscosity VS bulk temperature

Fig. 1. Thermal physical property changes with bulk temperature at the different pressure.

395

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

uncertainties of the fluid temperature. Razumoviskiy [21] detected that for a large ratio of heat flux to mass flux, the pressure drop due to flow acceleration account for a significant part of the total pressure drop. Based on an extensive literature survey about hydraulic resistance of supercritical fluid in-tube cooling, Fang [22] found that most of experimental investigations about the hydraulic resistance of supercritical fluid in past decades are supercritical CO2 cooling. Among the cooling, heating and adiabatic flows of supercritical fluid, the friction-factor distribution presents the trend: cooling > adiabatic > heating. Garimella [23] researched the pressure drop during cooling of mixed refrigerant. He proposed a friction-factor correlation with a term involving Grashof and Reynolds numbers under nature convection conditions. Petro-Popov [24] investigated the hydraulic resistance distribution of supercritical water in-tube cooling at condition of P = 23 MPa and Tb = 350–392 °C. He thought that the effect of deceleration was remarkable at supercritical water in-tube cooling and affected the magnitude of shearing stress on the wall. By comparing the convection of supercritical fluid between heating and cooling condition in vertical tubes, Jiang [25] indicated that different velocity distribution and thermal boundary layer were presented in heating and cooling tubes. Lei [26] and Krayakova [15] discussed the hydraulic resistance of supercritical water under conditions of adiabatic and heating flows. The frictional coefficient of heating flow is lower than that of the adiabatic flow, which may be ascribed to the enhancement of shearing stress in the vicinity on the heated wall. Most of the previous supercritical hydraulic resistance research have focused on water in the heated tube or CO2 in the cooled tube. The property and velocity distribution of those fluids are different from the in-tube cooling supercritical water under the circumstance of out-tube pool boiling. Moreover, flow acceleration was remarkable in a heated tube, in comparison the effect of deceleration also cannot be neglected in the cooled tube. The previous friction factor correlation for supercritical fluid seems to lose sight of the effect of deceleration or acceleration on the frictional pressure drop. Previous research indicates that long test tube can acquired the overall heat transfer coefficient and pressure drop, but the local heat transfer coefficient and pressure drop cannot be obtained [6,27]. In order to improve the experimental accuracy and control the flow condition easily, a 0.9 m long test tube with

0.5 m cooling section was chosen. Therefore, this study used a smooth horizontal tube immersing in a pool tank to simulate the flow condition of PRHRS in a SCWR. A series of experiments were performed to study the friction factor of in-tube cooling supercritical water accompanying out-tube pool boiling. The influence of pressure and mass flux on pressure drop in adiabatic and cooling flows was analyzed. It also discussed effect of deceleration in the cooling flow and assessed various friction factor correlations by employing the experimental data. Taking into account the deceleration-factor, a new predicted correlation was proposed. 2. Experimental apparatus 2.1. The experimental system The present study was carried out at the platform of HighTemperature and High-Pressure test loop operated in Xi’an Jiaotong University. Fig. 2 presents the schematic diagram of the experimental test loop. Deionized distilled water is served as the working fluid, which is pumped into the circulation pipelines by a high pressure threeplunger pump. A portion of water goes back to the water tank through the bypass valve, and the rest flows to the test section through the main valves, mass flowmeter, a regenerator and a set of pre-heaters. The preheaters are electrically heated directly by the high alternative currents with low voltages, and the maximum capability of preheater electrical power is 1.4 MW. Water from the outlet of the test section returns back to the water tank after it is cooled by a regenerator and a condenser. An number of orifices and valves are employed to reduce the pressure of fluid. The test section is consisted of a smooth tube and a pool water tank, and the smooth horizontal tube is always immersed in the pool tank to simulate the process of PRHRS in a SCWR. The mass flowmeter is used for measuring the mass flux of circulation. A series of NiCr-NiSi sheathed thermocouples are installed at different locations to monitor the fluid temperature of the system. 2.2. The test section Fig. 3 shows the structure of the test section and distribution of

Fig. 2. Schematic of high-temperature and high-pressure system. 396

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

Fig. 3. Test section and measuring points.

measure the wall temperature. Besides, the measuring points of wall temperature on the surface were covered with special fire prevention organic silicone adhesive to reduce the influence of pool boiling when measuring wall temperature [27]. These thermocouples were distributed with axial intervals of 50 mm and circumferential intervals of 90°, as shown in Fig. 3. The test section and water tank were packaged by thermal insulation material (alumina silicate fiber). The measured data was captured and transferred into an IMP 3595 data acquisition system with frequency of 1.5 Hz. In order to reduce the fluctuations of system, series of orifice and valves were installed to control the system, see the parts surrounded by red point in Fig. 2. The fluctuation in mass flux is negligible thanks to the stable test loop and the veteran technicists who controlled the values. The experiment is an ordinary steady state heat transfer and long-time (45 s) average value is used as experimental data to reduce local transient fluctuations. The uncertainties of measured and calculated parameters are given in Table 1.

Table 1 Uncertainties of measured and calculated parameters. Parameters

Unit

Uncertainty

In tube pressure Pressure difference Mass flow rate Wall temperature Fluid temperature Heat flux of pool

MPa kPa kg·h−1 °C °C kW·m−2

± 0.15% ± 0.52% ± 0.38% ± 1.40% ± 1.00% ± 4.36%

measuring points. Test section was consisted of stable section, adiabatic section and cooling section. Cooling section was made of 321 stainless steel with an inside diameter of 20 mm, a wall thickness of 2.5 mm and the length of 500 mm. Besides, two Teflon pipes were installed in both ends of the cooling section to reduce the effect of water tank wall. A pair of flange and hollow bolt were adopted to link the water tank with the test tube. A flexible graphite and a rubber gasket were squeezed between the flange and hollow bolt to ensure the circumferential sealing. Pressure drop measuring distances of cooling section and adiabatic section were 900 mm. Stable section with a length of 700 mm (L/ D > 30) was installed in the upstream of adiabatic section to ensure the fully developed flow. In order to minimize the additional measurement deviations, a pressure-measuring rings structure was designed. Inside the ring, four pressures measuring holes of 1 mm-diameter were respectively drilled on the outer surface of tube with each circumferential interval of 90°. Hence, the fluid pressure could be measured through four holes, the ring chamber and the pressure tube. Applying this ring structure, the cross-sectional average pressure of fluid was measured while reducing the pressure fluctuation. Inlet static pressure and pressure drops at both cooling section and adiabatic section were measured by 3051 capacitance-type pressure and differential pressure transducers. These measuring transducers were calibrated by a high-precision Y055 float type manometer before the experiment. Fluid temperature at the inlet and outlet of cooling section were measured by a series of 3 mm-diameter K-type sheathed thermocouples. Twenty thermocouple wires with 0.2 mm-diameter were spot-welded on the surface of the cooling section to directly

3. Data processing In general, the total pressure drop inside a smooth horizontal section can be calculated according to the following expression:

Δ P= ΔPfr + ΔPac ΔPfr

(

L G2 v in 2

ΔPfr = εfr d

)

ΔPac = G 2 (vout −vin )

(1)

where v is the average integral specific volume along the tube,

(

)

L

v = ∫L out vdL L , m3·kg−1. in It is hypothesized that the cooling test tube is cooled evenly along the tube. Hence, the fluid enthalpy presents a linear increase along the tube. Therefore, value of v could be calculated as:

v =

1 ΔH

Hout

∫H

in

vdH

(2)

For supercritical fluid, when the fluid enthalpy is beyond pseudocritical region (H = 1500–2900 kJ·kg−1) [28], the specific volume varying with enthalpy presents linear variation. The average specific volume can be calculated as follows: 397

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

v =

vout + vin 2

which is attributed to the sharp increasement of fluid specific volume with respect to temperature. At the same time, a noticeable “Λ-shaped” profile of cooling frictional pressure drop is observed in the vicinity of the pesudocritical temperature. Comparing the cooling with adiabatic frictional pressure drop, the difference is slight away from pseudocritical temperature while approaching to pseudocritical temperature, the cooling frictional pressure drop is higher than adiabatic frictional pressure drop. The most significant difference appears at 384.9 °C. It must be noted that, cooling acceleration pressure drop is negative, which runs the opposite direction of cooling frictional pressure drop. It may slow down velocity of fluid along the flowing direction, which leads to reduction of the total pressure drop near the pseudocritical temperature. This effect is called as the deceleration-factor [24]. A portion of extra frictional pressure drop is increased because of opposite accelerating flow, which is in reverse to that of the heating flow [3,20,26]. Fig. 5 presents the different influence including axial and radial directions of heating and cooling on fluid. In order to clarify the difference of heating and cooling characteristic, the idealized model was constructed as in Fig. 5 by referring to previous numerical analysis research [25,32]. Some real conditions were not taken into consideration, for example, flow direction and interaction of flow element were neglected. In the axial direction, the specific volume of inlet fluid element is higher than that of outlet in the cooling flow, which leads to shrinkage of fluid element during cooling process. Mass flux is a constant in the process of flow, and density increases as the shrinkage of fluid element, resulting in the decrease of the fluid element velocity and the deceleration effect. Whereas, in heating, on account of increasing specific volume between inlet and outlet, fluid elements will be expanded to accelerate the flow. In the radial cross section, when the bulk and wall temperature are 384.05 °C and 386.05 °C respectively, the bulk velocity presents the M-shape profile in the heating flow. However, under cooling condition, parabolic profile with a maximum velocity in the center of the tube is formed, which may be caused by the effect of deceleration-factor [25]. The different velocity distribution of bulk is formed in heating and cooling flows.

(3)

Nevertheless, when fluid enthalpy belongs to pseudocritical region, the relationship between specific volume and fluid enthalpy presents a non-linear variation. If the average specific volume is calculated by Eq. (3), the deviation reaches up to 40% [29]. Therefore, Multiple-segment Simpson’s 1/3 Rule [30] is adopted to solve the defined equation (2) of specific volume. One can subdivide the interval [Hin, Hout ] into n segments and Simpson’s 1/3 rule is repeatedly applied to calculate the specific volume over every two segments. The specific volume of segments can be acquired from a database of NIST [31], which can reduce the influence of the non-linear variation. Hence, the average integral specific volume along the tube for supercritical fluid can be calculated as follows:

v =

1 ΔH

∫HHinout vdH =

⎡ ⎢

1 h × × ⎢v Hin + 2 × Hout − Hin 3 ⎢

⎢ ⎣

h=

n−1

∑ j=1 j = odd

⎤ ⎥ v Hj + v Hout ⎥ ⎥ j=2 ⎥ j = even ⎦ n−2

v Hj + 4 ×

∑

Hout − Hin , Hj = Hj − 2 + 2 × h, j = 2, 4, ⋯, n n

(4) In this research, the total pressure drop ΔP of 900 mm cooling and adiabatic section were measured by differential pressure sensors. There exist two short adiabatic sections with length (L1, L2) of 200 mm connecting the inlet, outlet and poor tank of the cooling section, shown in Fig. 3. Due to the length of cooling section was comparatively short, the pressure drop of adiabatic section in inlet and outlet should be removed. The difference of adiabatic pressure drop between experimental inlet and outlet is merely temperature. Hence, the linear interpolation can be adopted to calculate the value, and the cooling pressure drop can be calculated as follows:

ΔPcool = ΔPmeasure cool−ΔPinlet iso−ΔPoutlet iso

(5)

where ΔPcool is the cooling pressure drop of 500 mm length, kPa. ΔPmeasure cool is the measuring pressure drop of 900 mm cooling section, kPa. ΔPinlet iso is the inlet adiabatic pressure drop, = (L1/ L) × Linear {ΔPmeasure iso (T1)} , kPa. ΔPoutlet iso is the outlet adiabatic pressure drop, = (L3 / L) × Linear {ΔPmeasure iso (T2)} , kPa. The frictional pressure drop ΔPcool fr and friction coefficient for the cooling flow are calculated as follows:

4.1.2. Effect of pressure on adiabatic and cooling flow Fig. 6 presents the variation of adiabatic frictional pressure drop and friction factor with bulk temperature at different pressure with the mass flux of 800 kg·m−2·s−1 under adiabatic flow. It is found that the pseudocritical temperature is the transformed threshold value led by the different changing tendency of frictional pressure drop and friction factor. Frictional pressure drop is not obviously affected at different

ΔPcool fr = ΔPcool−G 2 (vout −vin ) εcool fr = ΔPcool fr ×

2din LG 2v

(6)

For the adiabatic flow, the flow acceleration can be ignored as a result of unchangeable specific volume, and the measuring pressure drop is frictional pressure drop. In order to compare with the cooling flow, the same length of pressure drop is adopted. Therefore, the frictional pressure drop and friction factor of adiabatic flow are calculated as follows:

ΔPiso fr = (L2 / L) × ΔPmeasure iso εiso fr = ΔPiso fr ×

2din LG 2v

(7)

4. Results and discussion 4.1. Hydraulic resistance of the cooling and adiabatic flow 4.1.1. General behavior of the hydraulic resistance variation Fig. 4 shows the variations in the adiabatic and cooling frictional pressure drop, cooling total pressure drop, cooling acceleration pressure drop with respect to the bulk temperature. Close to pseudocritical temperature, cooling total pressure drop reduces to 0.065 kPa and then increases quickly. Cooling acceleration pressure drop rises to the maximum of -0.48 kPa with fluid temperature approaching to 384.9 °C,

Fig. 4. Variation in pressure drop with bulk temperature at P = 25 MPa, G = 800 kg·m−2·s−1. 398

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

Fig. 5. The different effect of heating and cooling on fluid.

pressure drop is proportional to friction factor and specific volume as Eq. (1), so the frictional pressure drop decreases with increase of pressure in the gas-like region. Fig. 7 shows the effect of pressure on frictional pressure drop and friction factor at different pressure with mass flux of 800 kg·m−2·s−1 under cooling flow. It is found that the frictional pressure drop of different pressure increases slowly with bulk temperature at low temperature, while at the high temperature, it increases dramatically. Close to pseudocritical temperature of different pressure, frictional pressure drop presents a “Λ-shaped” profile trend. However, this phenomenon is not observed in other supercritical cooling flow [23]. Pressure basically has no effect on frictional pressure drop except for the linking temperature points appearing the “Λ-shaped” trend. Because the test tube was immersed in a pool and thus the cooling rate of wall was quickened, causing the increasing temperature difference between bulk and wall. This has led to even more dramatic changes of thermal-physical property near pseudocritical temperature, which ultimately results in the change of friction shearing stress between the wall and bulk. Meanwhile, in the whole temperature range, the friction factor of different pressure almost shows the same changing rule, except that the minimum value of friction factor approaching to pseudocritical

pressure below the pseudo-critical temperature. But when the bulk temperature surpasses the pseudo-critical temperature, the frictional pressure drop gradually decreases with pressure increasing. The reason that the different effect of pressure on frictional pressure drop at different bulk temperature region depends on the effect of pressure on the specific volume. Fig. 1(a) shows that the specific volume is not affected by the pressure below the pesudo-critical temperature. Whereas, above the pseudocritical temperature, the specific volume decreases with the pressure increasing, and it is in accordance with the effect of pressure on the frictional pressure drop. The friction coefficient factor decreases firstly and then increases quickly with the rising bulk temperature, which exists a steep “pit”. When the bulk temperature equals to pseudocritical temperature, the experimental friction factor reduces to a minimum value. Friction factor decreases with pressure increasing at high temperature. Under the pseudocritical temperature, pressure has no effect on friction factor. While, above the pseudocritical temperature, the friction factor decreases as pressure increases. The reason is that when thermal physics of fluid approaches to gas-like region above the pseudocritical region, the compressibility of fluid increases. Meanwhile, the friction factor and specific volume decreases with increase of pressure. The frictional

(b) Friction factor

(a) Frictional pressure drop

Fig. 6. Variations of friction drop (a) and friction factor (b) with bulk enthalpy at different pressure. 399

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

(a) Frictional pressure drop

(b) Friction factor

Fig. 7. Variation of frictional pressure drop (a) and friction factor (b) for the cooling flow at different pressure with mass flux of 800 kg·m−2·s−1.

4.1.3. Effect of mass flux on adiabatic and cooling flow Fig. 8 shows frictional pressure drop and friction factor of adiabatic flow changes with bulk temperature at different mass flux. Frictional pressure drop almost basically remains the constant value under the same mass flux below the pesudo-critical temperature. Here the frictional pressure drop are approximately constant, with frictional pressure drop of 0.26 kPa at mass flux of 1000 kg·m−2·s−1 and 0.16 kPa at 800 kg·m−2·s−1. Above the pseudocritical temperature, the frictional pressure drop increases sharply, and it becomes remarkable once the bulk temperature has exceeded the pseudocritical temperature. The inlet fluid enthalpy gradually increases with increasing heat duty of pre-heating. When fluid temperature is above pseudocritical temperature, fluid status changes from liquid-like region to gas-like region. It leads to the specific volume increasing sharply. At the pesudocritical temperature, the significant increase of changing rate causes the rise of frictional pressure drop sharply. In all, frictional pressure drop rises with the mass flux increasing, which is similar to that of heated tubes [26] and annular channel [3]. However, the friction factor is almost overlapped at different mass flux.

temperature. Also note that there exists a “pit” at the pseuodo-critical temperature of different pressure. When the pressure is 23 MPa, the minimum value of friction factor is 0.007, but when the pressure increases to 27 MPa, the minimum value reaches to 0.013. It is because that thermophysical property of supercritical water changes less steeper with the pressure increasing. Friction factor is slightly higher than that of predicted result of Kondra’ev correlation [16] away from PC region. But approaching to PC region, the deviation between experimental data and the curve of Kondra’ev [16] significantly increases greatly, and the “pit” gradually departs from the calculated value. Comparing the effect of pressure on fractional pressure drop between adiabatic and cooling flow in Figs. 6 and 7. It is found that the pressure on frictional pressure drop between adiabatic and cooling flow has no difference below the pseudocritical region. While above the pseudocritical region, the pressure effect on frictional pressure drop under the adiabatic flow is more obvious than that of cooling flow. However, under the cooling flow, there exists a “Λ-shaped” profile trend on the fictional pressure drop, which does not appear under the adiabatic flow.

(a) Frictional pressure drop

(b) Friction factor

Fig. 8. Variations of frictional pressure drop (a) and friction factor (b) with bulk temperature at different mass flux, the pressure is 25 MPa. 400

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

However, the thermopysical properties of supercritical fluid change drastically when approaching to PC temperature, which may lead to the different axial acceleration effect and radial velocity distribution during the cooling flow. Therefore, the previous constant-property correlation of friction factor should be modified for predicting the supercritical fluid in-tube cooling. There already exist some summaries for modified friction factor of supercritical fluid [22,34,35]. Table 2 lists the six typical correlations and their ranges for the supercritical flow. Different corrections of thermal-physical properties were adopted by different researchers. The predicted friction factors of above six correlations have been compared with 177 experimental data acquired under the circumstance of in-tube cooling with out-tube pool boiling. Table 3 lists the predicted accuracy and calculated various error bands of different correlations. Fig. 10 shows the comparison of the above empirical friction factor correlations with experimental data. Fig. 10(a) shows that the value of Filonenoko correlation [19] gets high enough accuracy when the experimental friction factor proximates to 0.015. However, this correlation significantly underestimates the experimental data in the high friction-factor region (above 0.015). Predictions of the Mikheev correlation [18] are rather scattered with an average error of 29.95% and a root-mean-square error of 38.58%, as shown in Fig. 10(b). The predicted friction factor is smaller than the experimental value in most region. Only 11.30% and 61.02% of the experimental data are predicted within the error band of ± 10% and ± 40%, respectively. Therefore, the Prantl number correction should be adjusted in the supercritical cooling flow. Fig. 10(c) shows the predictions of TarasovaLeont’ev correlation [17] with respect to experimental friction factor. The distributed trend is similar to that of the Filonenko correlation. But the average error and root-mean-square error of Tarasova-Leont’ev correlation are 4.74% and 21.56%, which are better than those of Filonenko correlation. The improvement may be resulted in the introduction of the dynamic-viscosity correction. Fig. 10(d) shows the predicted friction factor of Kirillov correlation [14] with respect to experimental data. Comparing with Filonenko correlation, density correction is taken into account. However, the average error and rootmean-square error of the correlation reach up to −13.03% and 38.82% respectively, which did not improve the predicted accuracy. Fig. 10(e) shows the predicted friction factor of Kondrat’ev correlation [16]. The predicted value is lower than the experimental data and most of predicted error bands are focused between ± 30% and ± 40%. Although the predicted correlation is based on a horizontal tube, it may not be

A local “pit” exists at the friction factor at every different mass flux corresponding to pesudo-critical temperature. Therefore, mass flux has little influence on the friction factor of the adiabatic flow. Fig. 9 shows the effect of mass flux on frictional pressure drop and friction factor for cooling flow at the pressure of 25 MPa. Frictional pressure drop increases with rising of mass flux. There is a “Λ-shaped” profile of frictional pressure drop at different mass flux close to pseudocritical temperature, which is different with that of the adiabatic flow as shown in Fig. 8. The peak of frictional pressure drop at 384.9 °C rises with the increase of mass flux. It may be because that the higher mass flux is, the more significant decelerating effect is, which will result in the increase of friction. The friction factor decreases with the increase of mass flux, and the influence of mass flux on friction factor in the low temperature region is greater than that of the high temperature region. The reason is that the thermal property difference between the bulk and wall is higher in the low temperature region than that of high temperature. It results in improvement of fluid shear stress, which produces higher frictional pressure drop. Close to PC temperature, the friction factor presents a trend of first ascending slowly and then descending sharply. The minimum value appears at 384.9 °C with approximate number of 0.13. The cooling friction factor is similar to the Kondrat’ev correlation with the change of mass flux. Comparing the effect of mass flux on frictional pressure drop between the adiabatic and cooling flow is presented in Figs. 8 and 9. It is found that frictional pressure drop increases with mass flux increasing under the adiabatic and cooling flow, but a “Λ-shaped” profile of frictional pressure drop in the cooling flow with the increase of mass flux was more obvious than that of adiabatic flow. 4.2. Development of friction factor correlation for the cooling flow Cooling total pressure drop of the smooth horizontal tube consists of two components, which are friction and acceleration. The calculation of the acceleration pressure drop is relatively straightforward because analytical calculations can be conducted without a need for empirical correlations. However, the frictional pressure drop is highly dependent on empirical correlations. Thus, fitting of the empirical correlation, which is valid for the cooling process of PRHRS in a SCWR, is needed. An accurate prediction of the frictional pressure drop depends mainly on the friction factor. Some researchers calculated the friction factor of supercritical fluid by the constant property correlation [33].

(b) Frition factor

(a) Frictional pressure drop

Fig. 9. Variation of frictional pressure drop and friction factor at different mass flux. 401

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

Table 2 Friction factor correlations and ranges for supercritical flow. Author

Correlation

Filonenko [19]

ε fr =

Kirillov [14]

Constant property Re: 4 × 103–1012 Turbulent stabilized flow

1 (0.79lnRe − 1.64)2

Mikheev [18] Tarasova-Leont’ev [17]

Range

ε fr =

1 1 ⎛ Prw ⎞ 3 (0.79lnRe − 1.64)2 ⎝ Prb ⎠

ε fr =

μ 1 ⎛ w⎞ (0.79lnRe − 1.64)2 ⎝ μb ⎠ ρ 1 ⎛ w⎞ (0.79lnRe − 1.64)2 ⎝ ρb ⎠ 0.188 Re0.22

ε fr =

P: 22.6–26.5 MPa; G: 2000,5000 kg·m−2·s−1; q :0.58–1.32 MW·m−2 P: 22.5–27 MPa; Re: 8 × 104–1.5 × 106

0.22

0.4

Kondrat’ev [16]

ε fr =

Petro-Popov [24]

εfr / εiso, b = (μ w / μb )1/4 + 0.17(ρw / ρb )1/4|εi |/ εiso, b εi =

P: 22.6,24.5,29.4; Re = 105; q: 0.12–1.2 MW·m−2; Tb: 105–540 °C; Horizontal P = 23.5 MPa Tb = 350–392 °C Tw = 357–402 °C Reb = 2.3 × 104–2.03 × 105 q :0.16–1.28 MW·m−2

−8q ⎛ β ⎞ G ⎝ Cp ⎠b

εiso, b = (0.79lnRe−1.64)−2

Table 3 Prediction accuracy of the friction factor. Correlations

AE (%)

Filonenko [19] Mikheev [18] Tarasova-Leont’ev [17] Kirillov [14] Kondrat’ev [16] Petro-Popov [24]

AE: Average error, =

1 n

MAE (%)

18.27 29.95 4.74 -13.03 33.74 10.56 n ∑i = 1 ⎛ ⎝

MAE: Mean absolute error, =

21.32 34.60 16.21 31.79 34.10 18.87

fcal, i − fexp, i ⎞ fexp, i

⎠

1 n

RMSE: Root-mean-square error, =

1 n

% of Data Predicted within

25.06 38.58 21.56 38.82 36.57 25.83

± 10%

± 20%

± 30%

± 40%

± 50%

18.08 11.30 39.55 16.38 5.65 41.81

52.54 19.77 70.62 40.11 13.56 62.15

78.53 33.33 87.57 53.11 30.51 79.66

93.22 61.02 93.79 65.54 70.62 88.14

96.61 84.75 97.18 78.53 93.22 94.92

× 100%.

fcal, i − fexp, i fexp, i

n ∑i = 1

RMSE (%)

n ∑i = 1 ⎛ ⎝

× 100% .

fcal, i − fexp, i ⎞ fexp, i

⎠

× 100%.

factor ratio and friction-factor ratio. It can be seen that the viscosity ratio can predict the rising tendency of friction-factor, and the Prantl ratio and deceleration-factor ratio can improve the prediction near the PC region. Figs. 4 and 5 analyze the effect of deceleration-factor of supercritical cooling flow on the axial fluid element shrinkage and radial bulk velocity distribution. Therefore, the deceleration-factor should be taken into account in predicting the friction factor. Based on experimental data and taken deceleration-factor into account, a modified Pertro-Popov friction-factor correlation is proposed for predicting in-tube cooling supercritical water accompanying outtube pool boiling:

suited for supercritical water under in-tube cooling accompanying outtube pool boiling. Fig. 10(f) shows the predictions of Petro-Popov correlation [24] with respect to experimental friction factor. 41.81% and 62.15% of experimental friction factors are predicted within the error bands of ± 10% and ± 20%. However, comparing with TarasovaLeont’ev correlation [17], Petro-Popov correlation [24] performs less well within the error bands of 20%, but better within the error bands of 10%. The great improvement of Petro-Popov correlation [24] is presented comparing with Kirillov correlation [14], which may due to the reason that the introduction of deceleration factor improves the effect of density ratio correction and aggregation degree. According to above comparison and analysis, none of the six correlations can predict friction factor with enough accuracy for in-tube cooling supercritical water accompanying out-tube pool boiling. Among them, the correlations proposed by Tarasova-Leont’ev [17] and PetroPopov [24] are acceptable, but predicted accuracy needs to be further improved. The dominate thermalphysical property correction affecting the friction factor should be considered. Fig. 11 illustrates the influence parameter on friction factor at P = 25 MPa, G = 800 kg·m−2·s−1. Fig. 11(a) shows the comparison between different predicted friction factor correlations and experimental data. The Tarsova-Leont’et correlation is in agreement with experimental friction factor away from the PC region, while near the PC region, the Petro-Popov correlation can predict the “V-shape” profile of experimental data. Fig. 11(b) shows the variations of the viscosity ratio, density ratio, Prantl ratio, deceleration-

εfr / εiso, b = (μ w / μb )−0.03 + 0.829(ρw / ρb )0.32|εdec |/ εiso, b εdec =

−8q G

( ) β Cp

b

εiso, b = (0.79lnRe−1.64)−2

(8)

where εdec is the deceleration-factor, and εiso, b is the Filonenko correlation. Eq. (8) is valid for calculating the friction factor of pressure drop for supercritical water in-tube cooling with pressure of 23–27 MPa and mass flux of 600–1000 kg·m−2·s−1. Fig. 12 shows the comparison of experimental friction factor with modified Petro-Popov correlation. By the means of error analysis, the average error, mean absolute error, and root-mean-square error are −2.51%, 12.35% and 15.28% respectively. Approximately 52.41% and 96.99% of the experimental data are predicted within error bands of ± 10% and ± 30%. 402

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

Fig. 10. Friction factor predicted by empirical correlations with respect to experimental data: (a) Filonenko [19]; (b) Mikheev [18]; (c) Tarasova-Leont’ev [17]; (d) Kirillov [14]; (e) Kondrat’ev [16]; (f) Petro-Popov [24].

403

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

(a) Predicted friction factor correlation

(b) Variations of thermophysical property

Fig. 11. Analysis of influence parameter on the friction factor at P = 25 MPa, G = 800 kg·m−2·s−1.

(3) Comparing the cooling frictional pressure drop with the adiabatic one, the difference is little away from pseudocritical temperature, while approaching to pseudocritical region, the cooling frictional pressure drop is higher than the adiabatic frictional pressure drop. The most significant difference appears at pseudocritical temperature. (4) Six previous correlations were assessed with the present experimental data. The Tarasova-Leont’ev [17] and Petro-Popov [24] correlations have comparatively good predicted effect while the accuracy is not good enough. Moreover, taking into account the effect of viscosity ratio, Prantl ratio and deceleration-factor, a modified correlation from Petro-Popov correlation was proposed for in-tube cooling supercritical water accompanying out-tube pool boiling, of which the average error, and root-mean-square error are −2.51% and 15.28% respectively. References: [1] U.S. DOE, A Technology Roadmap for Generation IV Nuclear Energy Systems, Nuclear Energy Research Advisory Committee and Generation IV International Forum, 2002. [2] I.L. Pioro, R.B. Duffey, Heat Transfer and Hydraulic Resistance at Supercritical Pressures in Power-Engineering Applications, ASME Press, New York, 2007, pp. 17–80. [3] H. Wang, Q.C. Bi, G. Wu, Experimental investigation on pressure drop of supercritical water in an annular channel, J. Supercrit. Fluids 131 (2018) 47–57. [4] G. Brumfiel, D. Cyranoski, A. Abbott, Quake sparks nuclear crisis, Nature 471 (7338) (2011) 273–275. [5] W. Fu, X. Li, X. Wu, Investigation of a long term passive cooling system using twophase thermosyphon loops for the nuclear reactor spent fuel pool, Ann. Nucl. Energy 85 (2015) 346–356. [6] J.B. Wu, Q.C. Bi, C.S. Zhou, Experimental study on circulation characteristics of secondary passive heat removal system for Chinese pressurized water reactor, Appl. Therm. Eng. 77 (2015) 106–112. [7] H. Ayhan, C.N. Sökmen, Design and modeling of the passive residual heat removal system for VVERs, Ann. Nucl. Energy 95 (2016) 109–115. [8] J. Xing, D. Song, Y. Wu, HPR1000: advanced pressurized water reactor with active and passive safety, Engineering 2 (2016) (2016) 79–87. [9] L. Leung, Small and very small SCWR concept development in Canada, in: Proceedings of 8th International Symposium on Super-Critical Cooled Reactors, China (Chengdu), 2017. [10] IAEA, Passive Safety Systems and Natural Circulation in Water Cooled Nuclear Power Plants, International Atomic Energy Agency, 2009 pp. 84. [11] Z.B. Liu, Y.L. He, Y.F. Yang, Experimental study on heat transfer and pressure drop of supercritical CO2 cooled in a large tube, Appl. Therm. Eng. 70 (1) (2014) 307–315. [12] Y. Cui, H. Wang, Experimental study on convection heat transfer of R134a at supercritical pressures in a vertical tube for upward and downward flows, Appl. Therm. Eng. 129 (2018) 1414–1425. [13] Z.Q. Yang, Y.F. Shan, B. Zhang, Hydrodynamic characteristics of cyclohexane in a

Fig. 12. Comparison of experimental friction factor with modified Petro-Popov correlation.

5. Conclusions Experiments of hydraulic resistance were conducted with in-tube cooling supercritical water accompanying out-tube pool boiling to support the thermal hydraulic design of the PRHRS in a SCWR. Based on the experimental data, the following conclusions can be drawn. (1) For the adiabatic flow at supercritical pressure, the friction factor exists a steep “pit” near the pseudocritical region. Mass flux exerts weak effect on the friction factor. As pressure increasing, the friction factor presents unchanged in low temperature but a decreasing trend at high temperature, due to the influence of pressure on specific volume. (2) For the cooling flow at supercritical pressure, a noticeable “Λshaped” profile of cooling frictional pressure drop is observed in the vicinity of the pesudocritical temperature. The deceleration-effect of supercritical cooling flow leads to in the axial fluid element shrinkage and radial bulk fluid velocity parabolic distribution. Pressure basically has no effect on friction factor, while the friction factor decreases with the increase of mass flux for supercritical cooling flow. 404

Applied Thermal Engineering 141 (2018) 394–405

H. Lv et al.

[14] [15]

[16]

[17] [18] [19] [20]

[21]

[22] [23]

[24]

[25]

horizontal mini-tube at trans- and supercritical pressures, Appl. Therm. Eng. 129 (25) (2018) 62–69. P.L. Kirillov, Y.S. Yurev, V.P. Bobkov, Handbook of Thermal-Hydraulic Calculations, Energoatomizdat Publishing House, Moscow, Russia, 1990. L.Y. Krasyakova, I.I. Belyakov, N.D. Fefelova, Hydraulic resistance with isothermal and nonisothemal flow of medium at supercritical pressure, High Temp. 20 (4) (1973) 31–35. N.S. Kondrat'Ev, Heat transfer and hydraulic resistance with supercritical water flowing in tubes, Therm. Eng. (English Translation of Teploenergetika) 16 (8) (1969) 73–77. N.V. Tarasova, A.I. Leont'Ev, Hydraulic resistance during flow of water in heated pipes at supercritical pressures, High Temp. 6 (4) (1968) 721–722. M.A. Mikheev, Fundamentals of Heat Transfer, Gosenergoizdat Publishing House, Moscow, Russia, 1956. G.K. Filonenko, Hydraulic resistance of pipelines, Therm. Eng. (English Translation of Teploenergetika) 4 (1954) 40–44. Q. Zhang, H. Li, W. Zhang, Effect of fluid temperature on the frictional coefficient of supercritical pressure water flowing in adiabatic horizontal tubes, Exp. Therm Fluid Sci. 75 (2016) 189–198. V.G. Razumovskiy, A.P. Ornatskiy, E.M. Maevskiy, Hydraulic resistance and heat transfer of smooth channels with turbulent flow of water of supercritical pressure, Therm. Eng. (English Translation of Teploenergetika) 31 (2) (1984) 109–113. X.D. Fang, Y. Xu, X.H. Su, Pressure drop and friction factor correlations of supercritical flow, Nucl. Eng. Des. 242 (2012) 323–330. S. Garimella, B. Mitra, U.C. Andresen, Heat transfer and pressure drop during supercritical cooling of HFC refrigerant blends, Int. J. Heat Mass Transf. 91 (2015) (2015) 477–493. N.E. Petrov, V.E. Popov, Heat transfer and hydraulic resistance with turbulent flow in a tube of water at supercritical parameters of state, Therm. Eng. (English Translation of Teploenergetika) 35 (10) (1988) 45–48. P.X. Jiang, Z.P. Ren, B.X. Wang, Convective heat and mass transfer in water at

[26]

[27]

[28]

[29] [30] [31]

[32]

[33] [34]

[35]

405

super-critical pressures under heating or cooling conditions in vertical tubes, J. Therm. Sci. 4 (1) (1995) 15–25. X.L. Lei, H.X. Li, Y.M. Guo, Experimental study on the minimum drag coefficient of supercritical pressure water in horizontal tubes, Nucl. Eng. Des. 301 (2016) 164–174. Z.S. Nie, Q.C. Bi, S.Y. Lei, Experimental study on condensation of high-pressure steam in a horizontal tube with pool boiling outside, Int. J. Heat Mass Transf. 108 (10) (2017) 2523–2533. V.A. Kurganov, Y.A. Zeigarnik, I.V. Maslakova, Heat transfer and hydraulic resistance of supercritical-pressure coolants. Part I: Specifics of thermophysical properties of supercritical pressure fluids and turbulent heat transfer under heating conditions in round tubes (state of the art), Int. J. Heat Mass Transf. 55 (11–12) (2012) 3061–3075. Z.H. Lin, L.X. Chen, Inter-Boiler Process, Xi'an Jiaotong University, 1990, pp. 17–19. N.C. Li, L.C. Mei, Numerical Analysis, Science Press, Beijing, 2011. E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Reference Fluid Thermodynamic and Transport Properties, NIST Standard Reference Database 23, Version 9.0, U.S. Secretary of Commerce, 2010. Y. Hua, Y. Wang, H. Meng, A numerical study of supercritical forced convective heat transfer of n-heptane inside a horizontal miniature tube, J. Supercrit. Fluids 52 (1) (2010) 36–46. J. Pan, G. Wu, D. Yang, Thermal-hydraulic calculation and analysis on water wall system of 600 MW supercritical CFB boiler, Appl. Therm. Eng. 82 (2015) 225–236. I.L. Pioro, R.B. Duffey, T.J. Dumouchel, Hydraulic resistance of fluids flowing in channels at supercritical pressures (survey), Nucl. Eng. Des. 231 (2) (2004) 187–197. A. Dragunov, W. Peiman, Pressure drop analysis of a pressure-channel type supercritical water-cooled reactor, in: Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition, San Diego, California, USA, 2013.