Coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressures: An experimental research

Coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressures: An experimental research

Applied Thermal Engineering 159 (2019) 113962 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.c...

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Applied Thermal Engineering 159 (2019) 113962

Contents lists available at ScienceDirect

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

Research Paper

Coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressures: An experimental research

T



Qingqing Wanga, Zichen Songa, Yulong Zhenga, Yongguang Yina, Lang Liub, Haijun Wanga, , Jianan Yaoa a b

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China China Ship Development and Design Center, Shanghai 201108, China

H I GH L IG H T S

about coupled heat transfer of supercritical water was conducted. • Experiment of three experimental variables on heat transfer were investigated. • Effects effect on the heat transfer was analyzed emphatically. • Buoyancy • A new heat transfer empirical correlation was proposed.

A R T I C LE I N FO

A B S T R A C T

Keywords: Supercritical pressure water Coupled convection heat transfer Double pipe heat exchanger Buoyancy effect New correlation

An experiment about coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressure was conducted. The effects of experimental variables on the heat transfer were investigated, and the buoyancy effect on the heat transfer of the outer pipe was analyzed emphatically. There is a difference between the peak heat transfer coefficient temperature and the pseudo-critical temperature, and the difference increases with the increase of pressure. This phenomenon is caused by the temperature gradient and the variations of thermal-physical properties in the heat transfer section. The mass flow rates of the inner pipe side and outer pipe side were always equal, and one side will offset the effect of the other side on the heat transfer. The heat transfer coefficient of the outer pipe increases with the increase of water temperature at the inlet of the inner pipe when the mean bulk temperature is lower than the pseudo-critical temperature, due to the buoyancy effect decreases at the same time. While, the buoyancy effect is almost independent of the water temperature at the inlet of the inner pipe when the mean bulk temperature is higher than the pseudo-critical temperature, due to the buoyancy effect is non-significant. A new heat transfer empirical correlation was proposed, which includes 94.01% of experimental data are within ± 25% error bars.

1. Introduction At present, the generation IV nuclear power plants are highly concerned. The main focuses of new nuclear power plants are reducing the power costs and improving the system safety effectively. Hence, the selection of the working medium is significant. Since the supercritical fluids have the high convective heat transfer efficiency and simpler design, they are widely used in many advanced thermal conversion systems as a working medium [1]. Particularly in the generation IV nuclear power plants, the supercritical fluid is used as a working medium for supercritical water reactor [2,3] and high-temperature gas cooled reactor [4]. Therefore, the study of supercritical convection heat



transfer has engineering significance. Hall et al. [5] reviewed the experimental and theoretical research of the supercritical convection heat transfer. They discussed the effects of thermal-physical properties change on the heat transfer of supercritical fluids. Yoshida and Mori [6] evaluated the experimental study and theoretical analysis of the flow and heat transfer characteristics of supercritical water and supercritical CO2. They believe that the rapid variations of thermal-physical properties of the supercritical fluids near the pseudo-critical point are the main reasons for the peak of heat transfer coefficient under the condition of low heat flux. Pioro et al. [7,8] systematically studied the heat transfer experiments of supercritical water and supercritical CO2, and pointed out that the particular

Corresponding author at: Xi'an Jiaotong University, Xi'an, Shanxi 710049, China. E-mail address: [email protected] (H. Wang).

https://doi.org/10.1016/j.applthermaleng.2019.113962 Received 1 December 2018; Received in revised form 2 May 2019; Accepted 15 June 2019 Available online 15 June 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A Bu Cp d D DH g Gr h L Nu p Pr Qm Re T U v

Greek symbols ΔT λ μ ρ Φ

heat transfer area [m2] buoyancy criterion number specific heat capacity [J⋅kg−1⋅K−1] diameter of inner pipe [m] inner diameter of outer pipe [m] hydraulic diameter of outer pipe [m] gravitational acceleration [m⋅s−2] Grashof number enthalpy [J] length [m] Nusselt number pressure [MPa] Prandtl number mass flow rate [kg⋅s−1] Reynolds number temperature [°C] total heat transfer coefficient [W⋅m−2⋅K−1] velocity [m⋅s−1]

arithmetic mean temperature difference [°C] thermal conductivity [W⋅m−1⋅K−1] dynamic viscosity [Pa⋅s] density [kg⋅m−3] heat transfer rate [W]

Subscripts ave b i in o out pc w

average bulk inner pipe side inlet outer pipe side outlet pseudo-critical wall

pipes with different inner diameters at constant wall temperature. They pointed out that the buoyancy has a significant effect on heat transfer of the horizontal pipe when the criteria Gr/Reb2 > 10−3, and the buoyancy effect is significant although the Reynolds numbers reach up to 105. Bae et al. [13] experimentally studied the vertical upward and downward convection heat transfer of supercritical CO2 in a circular pipe. It was found that when the buoyancy parameter is in the range of 10−6 < Grb/Reb2.7 < 2 × 10−5, there is a significant decrease in Nusselt number, and the heat transfer deteriorated as Grb/ Reb2.7 > 2.0 × 10−5. Once the heat transfer deteriorated, it entered a new heat transfer regime and did not return to normal although Grb/ Reb2.7 < 2.0 × 10−5. Yu et al. [14] studied the effect of buoyancy on heat transfer characteristics of supercritical pressure water in horizontal pipes by experiment. They found that buoyancy makes a noticeable difference of heat transfer characteristics between the top and bottom

experimental phenomena, such as heat transfer enhancement, heat transfer deterioration, and normal heat transfer exist in the heat transfer of supercritical fluids. These studies have shown that the heat transfer of supercritical fluids is different from the traditional singlephase fluids, and now there is no unified theory for supercritical convection heat transfer mechanism. However, it is known that there are sharp variations of the thermal-physical properties of the fluid in the pseudo-critical region, which make the heat transfer of the supercritical fluid complex [9]. Buoyancy has an important influence on the distribution of shear stress and velocity profile in the near-wall boundary layer [10]. Some scholars believe that the empirical correlation of supercritical heat transfer is inconsistent with the experimental data, which is mainly due to improper handling of the buoyancy [11]. Zhao and Liao [12] experimentally studied the convection heat transfer of supercritical CO2 in

Fig. 1. Experimental system. 2

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other part flows through the main valve and mass flowmeter to the heat exchanger, and absorbs the heat of the high-temperature water from the test section. After entering the preheater and being heated up, the deionized water flows into the test section as the low-temperature fluid. Then it enters the heat section and is heated up as a high-temperature fluid of the test section to realize the heat transfer with the low-temperature fluid. Afterward, the high-temperature fluid from the test section flows through the heat exchanger and then returns to the water tank after being cooled by the condenser. The cooling water in the condenser is pumped by the condensing pump and cooled in the cooling tower after coming out of the condenser. The mass flow rates on both sides of the test section are always equal. The inlet temperature of the low-temperature fluid would be fixed in the experiment. By adjusting the power of the heat section, the high-temperature fluid of the test section could realize different heat transfer states with the low-temperature fluid. All heating methods in the experiment are direct electric heating. The preheater and heat section separately supply heating power with maximum capacities of 640 kW and 500 kW. The test section is a horizontal double pipe heat exchanger and the geometry of the test section is shown in Fig. 2. All materials of the double pipe heat exchanger are 316L stainless steel. The diameters of the inner pipe are di = 15 mm and do = 20 mm, and the inner diameter of the outer pipe is D = 35 mm. The thickness of both heads of the double pipe heat exchanger is 12 mm. The length of the heat transfer zone is L = 1500 mm, and the centers of two branch pipes both are located 30 mm inside the ends of the heat transfer zone. Thermocouple measuring points are uniformly distributed at the top and bottom of the outer wall of the inner pipe to measuring the wall temperature. There are both ten measuring points on the top and bottom of the outer wall of the inner pipe, and all the axial distances between two adjacent measuring points are 120 mm, so the temperature measuring length of the heat transfer zone is 1080 mm. The 20 thermocouples are all the Ktype thermocouples with a diameter of 0.3 mm. K-type armored thermocouples with a diameter of 3 mm are arranged at the inlet and outlet of the inner and outer pipe to measure the fluid temperature. The inner pipe side of the test section is the low-temperature water at supercritical pressure, and the outer pipe side of the test section is the high-temperature water at supercritical pressure. Silicate insulation cotton is laid on the outer wall of the outer pipe to reduce the environmental heat loss. Pressure sensors with model Rosemont 3051 are arranged at the inlets on both sides of the double pipe heat exchanger.

surfaces of the horizontal pipe, and the single buoyancy criterion of buoyancy cannot be completely universal under different heat transfer conditions. Many researchers [15–23] have proposed different criteria for studying buoyancy effect. Huang and Li [11] made evaluation and analysis on most current buoyancy criteria for supercritical fluids heat transfer. It is necessary to discuss and determine the applicable buoyancy criteria according to the actual experimental conditions. It should be noted that most of the studies on supercritical heat transfer are based on the condition of constant wall temperature or constant heat flux. In practical engineering, especially in heat exchanger, there are some coupled heat transfer between supercritical fluid and other fluid, such as the heat transfer between two supercritical CO2 in the regenerator of the high-temperature gas-cooled reactor using supercritical CO2 Brayton cycle system [24] and the heat transfer between the high temperature molten salt and supercritical CO2 in the molten salt cooling reactor [25,26]. Zhao and Che [27] numerically studied the conjugate heat transfer of supercritical CO2 in a vertical double pipe heat exchanger. It is found that mixed convection is the primary heat transfer mechanism for the supercritical CO2 conjugate heat transfer and the high viscosity can prevent the distortion of the flow field and reduce the heat transfer deterioration. Ma et al. [28] experimentally studied on the heat transfer between supercritical CO2 and water in a double pipe heat exchanger. They found that the mass flux of water side has a more significant effect on the heat transfer than that of the supercritical CO2 side, and the buoyancy effect on the heat transfer is large at the small mass flux of supercritical CO2 side, while the pressure of supercritical CO2 side and mass flux of waterside have little influence on the buoyancy. It can be concluded that the influence of thermal boundary on the heat transfer between the supercritical fluid and other fluid is significant. However, there are fewer studies about the coupled heat transfer of supercritical fluids. Therefore, an experimental work on the coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressure is conducted. 2. Experimental apparatus and data reduction 2.1. Experimental apparatus The experiment is carried out in the high-temperature and highpressure steam-water test loop in Xi’an Jiaotong University, and the experimental system and procedure are shown as Fig. 1. The deionized water in the water tank flows through the filter and is pressurized by the piston pump with a maximum pressure of 40 MPa, and then it is divided into two parts. One part of the deionized water is served as the bypass system to meet the needs of pressure and flow regulation. The

2.2. Data reduction All data in the experiment were collected and recorded by IMP 3595

Fig. 2. Test section. 3

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inlet pressure on both sides of the double pipe and ignoring the impact of pressure drop. The operating pressure p is calculated by:

Table 1 Experimental uncertainty analysis. Variables

Uncertainty

Fluid temperature/°C Wall temperature/°C Pressure/MPa Mass flow rate/kg⋅h−1 U/W⋅m−2⋅K−1 Uo/W⋅m−2⋅K−1 Re Nu Gr Bu

± 0.06% ± 0.16% ± 0.34% ± 0.74% ± 2.90% ± 2.60% ± 1.00% ± 2.68% ± 2.23% ± 3.50%

p=

pi,in + po,in 2

(10)

where the pi,in and po,in are the pressures measured at the inlet of the inner pipe and outer pipe separately.

4(πD 2 /4 − πdo2/4) = D − do π (D + d o )

DH =

(11)

The hydraulic diameter DH of the outer pipe is defined in Eq. (11).

Nub =

Uo DH λb

(12)

data acquisition system. The calculated parameters are obtained from the original measured data using the following equations.

The Nusselt number of the outer pipe is defined as Eq. (12), and the λb is the thermal conductivity of water at Tb and p.

Φi = Qm (h i,out − h i,in )

(1)

Re b =

Φo = Qm (ho,in − h o,out )

(2)

Φave AΔT

vb =

(3)

Φi + Φo 2

ΔT =

(To,in − Ti,out ) + (To,out − Ti,in ) 2

An experiment about coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressure is carried out, and the major parameters had the following ranges: the operating pressure p: 23–25 MPa, the mass flow rate Qm: 541–604 kg·h−1, the water temperature at inlet of inner pipe Ti,in: 290–350 °C. In the experiment, the mass flow rates on both sides of the double pipe exchanger are always equal. The effects of operating pressure, mass flow rate and water temperature at the inlet of the inner pipe on the heat transfer coefficient are discussed in the following, and the buoyancy effect on the outer pipe is analyzed emphatically.

(4)

(6)

where Ti,in, Ti,out, To,in, and To,out are water temperature at the inlet and outlet of the inner pipe and the outer pipe separately. The arithmetic mean temperature difference ΔT is adopted because always the 1 < (To,in − Ti,out)/(To,out − Ti,in) < 1.7 in the experiment.

Uo =

Φave A (Tb − Tw )

3.1. Effect of operating pressure Fig. 3 and Fig. 4 show the effect of the operating pressure on the heat transfer coefficient under the condition of the mass flow rate Qm = 573 kg·h−1 and the water temperature at the inlet of inner pipe Ti,in = 320 °C. The variation trend of the total heat transfer coefficient with the mean bulk temperature is similar at different pressures according to Fig. 3. With the increase of the mean bulk temperature, the total heat transfer coefficient first increases and reaches the peak near the pseudo-critical temperature, and then decreases, which generally presents a parabolic change. The total heat transfer coefficient is less affected by pressure when the temperature is below and away from the pseudo-critical temperature. When in the pseudo-critical region, the peak value of the total heat transfer coefficient decreases with the increase of the operating pressure, and the temperature corresponding to the peak of the total heat transfer coefficient moves toward the hightemperature side with the increase of the operating pressure. This variation is similar to that of the specific heat capacity of the fluid under different supercritical pressures as shown as Fig. 5. It can be inferred that the influence of the operating pressure mainly affects the

(7)

The heat transfer coefficient of the outer pipe side Uo is defined as the ratio of heat flux and temperature difference between the fluid of the outer pipe and the outer wall of the inner pipe as shown in Eq. (7). The Tb is the mean bulk temperature of the outer pipe, the Tw is the average outer wall temperature of the inner pipe, which are calculated by:

Tb =

Tw =

To,in + To,out 2 20 ∑j=1

(8)

Tw,j

20

(14)

3. Results and discussion

(5)

A = πd o L

Qm 4Qm = ρ b (πD 2 /4 − πdo2/4) πρ b (D 2 − do2 )

The vb is the velocity of the water at Tb and p, and calculated as Eq. (14). All properties of the fluid used in the experimental data processing are calculated using the NIST REFPROP [29]. According to the method proposed by the reference [30], the uncertainties in measured and calculated parameters of the experiment were summarized in Table 1.

In the double pipe heat exchanger, the total heat transfer coefficient U based on the outer pipe side heat transfer area is calculated by Eq. (3). The Φave is the average heat transfer rate, A is the heat transfer area of the outer pipe side, and ΔT is the arithmetic mean temperature difference of between the inner pipe side and outer pipe side, which are calculated by:

Φave =

(13)

The Reynolds number of the outer pipe is calculated as Eq. (13). The ρb is the density of the water and μb is the dynamic viscosity of the water, which are evaluated at Tb and p.

The heat transfer rate of the inner pipe side Φi is calculated as Eq. (1), and the heat transfer rate of the outer pipe side Φo is calculated as Eq. (2). The Qm is the mass flow rate of the water in the test section. hi,in, hi,out, ho,in and ho,out are enthalpies of the water at the inlet and the outlet of the inner pipe and outer pipe which are evaluated at the pressure and with the water temperatures respectively. The experimental data are considered to be valid when the relative error calculated as |Φi − Φo|/Φi is less than 10%.

U=

ρ b v b DH μb

(9)

where the Tw,j is the local outer wall temperature of the inner pipe. The operating pressure p is the average fluid pressure in the total double pipe heat exchanger, which is taken from the average value of 4

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interesting phenomenon is that the difference between the temperature corresponding to the peak of the heat transfer coefficient and the pseudo-critical temperature decreases with the decreasing operating pressure. The reasons for this phenomenon may be that the specific heat capacity Cp of the supercritical fluid reaches its peak at the pseudocritical temperature, and the peak value decreases with the decreasing operating pressure. When the heat exchange rate is the same under different supercritical pressures, the fluid pressure is lower, and the change of the fluid temperature will be the smaller. Therefore, the temperature gradient of the cross-section can be decreased with the decreasing operating pressure, and the difference between the temperature corresponding to the peak of the heat transfer coefficient and the pseudo-critical temperature will be decreasing as the operating pressure decreases. As shown in Fig. 4, the effect of operating pressure on the heat transfer coefficient of the outer pipe is similar to that of the total heat transfer coefficient. The heat transfer coefficient of the outer pipe is much higher than the total heat transfer coefficient under the same conditions. The heat transfer coefficient of the outer pipe changes more dramatically with the variation of pressure in the pseudo-critical region comparing with the total heat transfer coefficient.

Fig. 3. Effect of operating pressure on the total heat transfer coefficient.

3.2. Effect of mass flow rate Fig. 6 and Fig. 7 show the effect of the mass flow rate on the heat transfer coefficient under the condition of the water temperature at the inlet of inner pipe Ti,in = 320 °C and the operating pressure p = 25 MPa. As shown in Fig. 6, the total heat transfer coefficients at different flow rates change as the parabolically distribution with the increase of the mean bulk temperature, and reach the peak value near the pseudo-critical temperature. The increase of the mass flow rate can increase the total heat transfer coefficient in general. It should be noted that the mass flow rate close to the pseudo-critical temperature has a relatively insignificant effect on the total heat transfer coefficient when the mean bulk temperature is lower than the pseudo-critical temperature. The heat transfer coefficient of the outer pipe is almost unaffected by the mass flow rate according to Fig. 6. It can be found that the heat transfer coefficient of the outer pipe changes slightly with the increase of the mass flow rate only near the pseudo-critical region. The possible reason is that the mass flow rates in the inner and outer pipes were in the same in the experiments, and one side will offset the effect of the other side on the heat transfer coefficient of the outer pipe.

Fig. 4. Effect of operating pressure on heat transfer coefficient of outer pipe.

3.3. Effect of water temperature at the inlet of inner pipe Fig. 8 and Fig. 9 show the effect of the water temperature at the inlet of inner pipe Ti,in on the heat transfer coefficient under the condition of

Fig. 5. Thermal-physical properties vary with temperature at different pressures.

heat transfer by changing the thermal-physical properties. The temperature at which the total heat transfer coefficient reaches the peak is always slightly higher than the pseudo-critical temperature. Ma et al. [28] also found this phenomenon. In this regard, they explained that there is a temperature gradient in the cross section of the heat transfer channel, and the temperature near the wall is always lower than the temperature at the center of the cross-section. The temperature near the wall is first lowered to the pseudo-critical temperature than the average temperature in the cross-section, so the temperature corresponding to the peak of the heat transfer coefficient is slightly higher than the pseudo-critical temperature. Another

Fig. 6. Effect of mass flow rate on total heat transfer coefficient. 5

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be the cause of this phenomenon. The effect of Ti,in on the heat transfer coefficient of the outer pipe is similar to that on the total heat transfer coefficient according to Fig. 9. 3.4. Effect of buoyancy on the outer pipe The radial density gradient on the cross section caused by a sharp variation in the thermal-physical properties of the supercritical fluid in the pseudo-critical region results in the buoyancy effect [23]. When the flow rate of the supercritical fluid decreases or the heat load increases, the buoyancy effect will gradually increase, and the forced convection heat transfer will gradually change into the mixed convection heat transfer. In order to study the effect of buoyancy on the heat transfer coefficient of the outer pipe, a buoyancy criterion proposed by Jackson and Hall [19] was adopted, which is widely used at present [11,31] and shown as the following:

Fig. 7. Effect of mass flow rate on heat transfer coefficient of outer pipe.

Bu =

Gr =

Gr b Reb2.7

(15)

(ρ b − ρw ) ρ b gDH3 μ b2

(16)

where the ρw is the density of the water in the outer pipe at the wall average temperature Tw, and the g is the gravitational acceleration which is equal to 9.8 m⋅s−2. When the Bu > 10−5, the buoyancy effect on the heat transfer coefficient of the outer pipe cannot be neglected. Fig. 10 compares the buoyancy effect on the heat transfer coefficient of the outer pipe at different pressures. The buoyancy effect is significant in the pseudo-critical region at different pressures. In particular, the value of Bu drops suddenly near 380 °C at 23 MPa. The possible reason for this phenomenon is that the variations of the supercritical water thermal-physical properties are more dramatic than those at other pressures near the pseudo-critical point as shown as Fig. 5. The increase of pressure makes the thermal-physical properties smooth with the increase of temperature, so the change of buoyancy parameter Bu becomes smoothly. Fig. 11 shows the buoyancy effect on the heat transfer of the outer pipe under the condition of different mass flow rates. All the buoyancy effects are significant in the pseudo-critical region. The Bu value decreases slightly with the increase of the mass flow rate, and the influence of the mass flow rate can be almost ignored in general, which is consistent with the variation trend of the heat transfer coefficient of the outer pipe affected by the mass flow rate. The possible reason is that the mass flow rates in the inner and outer pipes were in the same in the experiments, and one side will offset the effect of the other side on the heat transfer coefficient of the outer pipe. Fig. 12 shows the buoyancy effect on the heat transfer of the outer pipe under the condition of different water temperatures at the inlet of

Fig. 8. Effect of water temperature at the inlet of inner pipe on the total heat transfer coefficient.

Fig. 9. Effect of water temperature at the inlet of inner pipe on the heat transfer coefficient of outer pipe.

the mass flow rate Qm = 604 kg·h−1 and the operating pressure p = 25 MPa. As shown as in Fig. 8, the total heat transfer coefficient increases first and then decreases with the increase of the mean bulk temperature, and reaches the peak in the pseudo-critical region. When the mean bulk temperature is lower than the pseudo-critical temperature, it can be found that the total heat transfer coefficient increases with the increase of Ti,in. However, when the mean bulk temperature is higher than the pseudo-critical temperature, the total heat transfer coefficient is not significantly affected by Ti,in. The buoyancy effect may

Fig. 10. Buoyancy effect under different pressure conditions. 6

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Fig. 11. Buoyancy effect under different mass flow rate conditions.

Fig. 13. A comparison between four typical empirical correlations and experimental data. Table 3 Mean error and RMS error for selected correlations. Author

Mean error

RMS error

Ma et al [28] Bringer and Smith [32] Bishop et al. [33] Jackson and Hall [34] Mokry et al. [35] New correlation

−52.717 −81.199 −75.366 −76.978 −77.035 0.820

54.486 81.411 75.623 77.290 77.249 13.006

Fig. 12. Buoyancy effect under different water temperature at the inlet of inner pipe.

Table 2 Classic heat transfer correlations of supercritical fluids. Author

Correlations

Ma et al [28]

ρ

−0.3

ρ

0.43

ρ

−0.3

Nub = 0.0183Re b0.82 Pr b0.5 ⎛ b ⎞ ⎝ ρw ⎠ Bringer and Smith [32] Bishop et al. [33] Jackson and Hall [34] Mokry et al. [35]

⎡ ⎛ Gr ⎞ ⎢2.61 − 86.965 ⎜ Re 2.7 ⎟ ⎝ b ⎠ ⎣

0.458

⎤ ⎥ ⎦

Nub = 0.0266Re b0.77 Pr b0.55 Nub = 0.0069Re b0.9 Pr b0.66 ⎛ w ⎞ ⎝ ρb ⎠

(1 + 2.4 ) DH L

Fig. 14. Comparison between experimental values and calculated values.

Nub = 0.0183Re b0.82 Pr b0.5 ⎛ b ⎞ ⎝ ρw ⎠ ρ

Nub = 0.0061Re b0.904 Pr b0.684 ⎛ w ⎞ ⎝ ρb ⎠

0.564

the inner pipe Ti,in. The buoyancy effect decreases with the increase of the Ti,in. When the Ti,in is 290 °C and 320 °C, the buoyancy effect is significant in the pseudo-critical region. When the Ti,in is 350 °C, the buoyancy effect on the heat transfer of the outer pipe is always not significant. Combined with Fig. 8 and Fig. 9, when the mean bulk temperature is lower than the pseudo-critical temperature, the mass flow rate is low due to the larger water density of the outer pipe, so the buoyancy effect is relatively large. The water temperature at the inlet of the inner pipe Ti,in will affect the outer wall temperature of the inner pipe Tw. The outer wall temperature of the inner pipe increases as the Ti,in increases, so the temperature gradient in the cross section of the outer pipe decreases and the buoyancy effect also decreases. The buoyancy effect on the heat transfer is adverse. Therefore, when the mean bulk temperature is lower than the pseudo-critical temperature,

Fig. 15. Comparison between experimental heat transfer coefficients and calculated values.

7

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the heat transfer coefficient of the outer pipe increases with the increase of Ti,in. When the mean bulk temperature is higher than the pseudocritical temperature, the buoyancy effect is not significant, so the heat transfer coefficient of the outer pipe is almost independent of the Ti,in.

i=n

RMS error =

Dittus-Boelter formula is the most common correlation of the forced convection heat transfer in pipe. Most empirical correlations of heat transfer are based on the Dittus-Boelter formula. Bringer and Smith [32] studied the forced convection heat transfer of supercritical water and supercritical CO2 in the pipe and proposed an empirical correlation without modification term of thermal-physical properties. This correlation predicts accurately the convective heat transfer coefficient only far away from the pseudo-critical region. Bishop et al. [33] studied the heat transfer characteristics of the upward flows in the vertical circular and annular pipes and obtained the empirical correlation with the correction terms of density and inlet attenuation effect. Jackson and Hall [34] compared different empirical correlations and experimental data, and proposed a new modified Krasnoshchekov’s correlation, which ignores buoyancy effect and is in good agreement with the experiment. Ma et al. [28] proposed a new empirical correlation with buoyancy correction referring to Bruch's correlation [35], which is in good agreement with 90% of experimental data within ± 30% error. Mokry et al. [36] used the Buckingham П-theorem for dimensional analysis to produce a new empirical correlation with the density correction term, which has an uncertainty about ± 25% for calculated. The above typical empirical correlations are shown in Table 2. As shown in Fig. 13, a typical set of experimental heat transfer coefficients of the outer pipe is selected and compared with that predicted by four empirical correlations in Table 2. It is found that the heat transfer coefficients calculated by different empirical correlations are similar, and all of them are consistent with the variation trend of experimental values, but there is a sizeable numerical deviation between the calculated results and experimental data. Therefore, it is necessary to summarize a new empirical correlation. After referring to the form of Jackson’s correlation [37], a new empirical correlation about the heat transfer coefficients of the outer pipe with the density correction and specific heat capacity correction was proposed. The new empirical correlation has the form as: z

(18)

where the coefficients (c, x, y, z, w) are calculated by multiple linear regression using the software Excel 2016.The new empirical correlation is shown as: −3.201

⎛ Cp w ⎞ ⎜ ⎟ ⎝ Cp b ⎠

0.76015

(19)

where the Cpb and Cpw are the specific heat capacity of the water, which are evaluated at Tb and Tw separately.

error =

Nu calculated − Nub Nub i=n

Mean error =

∑i

errori

n

(20)

× 100%

(22)

(1) The heat transfer coefficient presents a parabolic change with the increase of the mean bulk temperature and reaches the peak in the pseudo-critical region. The peak heat transfer coefficient decreases and moves towards to the side of high temperature with the increase of operating pressure. There is a difference between the peak heat transfer coefficient temperature and the pseudo-critical temperature, and the difference increases with the increase of pressure. The temperature gradient on heat transfer section and the variations of thermal-physical properties especially the density mainly cause this phenomenon. (2) The total heat transfer coefficient increases slightly with the increase of the mass flow rate. The heat transfer coefficient of the outer tube is almost independent of the mass flow rate. The possible reason is that the mass flow rates of inner pipe side and outer pipe side are always equal, and one side will offset the effect of the other side on the heat transfer. (3) The heat transfer coefficient of the outer pipe increases with the increase of water temperature at the inlet of the inner pipe when the mean bulk temperature is lower than the pseudo-critical temperature due to the buoyancy effect decreases at the same time, while which is almost independent of the water temperature at the inlet of the inner pipe when the mean bulk temperature is higher than the pseudo-critical temperature due to the buoyancy effect is non-significant. (4) The buoyancy effect is significant in the pseudo-critical region at different pressures. The value of Bu drops suddenly near 380 °C at 23 MPa when the mass flow rate Qm = 573 kg·h−1 and the water temperature at inlet of inner pipe Ti,in = 320 °C. The possible reason for this phenomenon is that the variations of the supercritical water thermal-physical properties are more dramatic than those at other pressures near the pseudo-critical point. The Bu value decreases slightly with the increase of the mass flow rate, and the influence of the mass flow rate can be almost ignored in general, which is consistent with the variation trend of the heat transfer coefficient of the outer pipe affected by the mass flow rate. (5) A new heat transfer empirical correlation with the density correction and specific heat capacity correction was proposed, which includes 94.01% of experimental data are within ± 25% error bars.

In order to calculate the coefficients (c, x, y, z, w), the equation is linearized. It is shown as:

ρ Nub = 0.00816Reb1.01586 Prb1.20196 ⎛⎜ w ⎞⎟ ⎝ ρb ⎠

× 100%

An experiment about coupled convection heat transfer of water in a double pipe heat exchanger at supercritical pressure is conducted. The effect of the operating pressure, the mass flow rate, the water temperature at the inlet of the inner pipe and the buoyancy on heat transfer are studied. The main conclusions are summarized as follows:

(17)

Cp ρw ) + w lg( w ) ρb Cp b

n

4. Conclusions

w

lg(Nub) = lgc + x lg(Reb) + ylg(Prb) + z lg(

errori 2

The prediction performance of these correlations was evaluated by Eqs. (20)–(22) [38], and results were shown in Table 3. Compared with the new correlation, all these correlations mentioned in Table 2 are not applicable to the coupled supercritical heat transfer. The strong coupling heat transfer between two fluids of equal mass flow rate at the supercritical pressure is different from traditional heat transfer conditions in previous studies. It can be seen that the new empirical correlation have 94.01% of experimental data are within ± 25% error bars according to Fig. 14. Fig. 15 shows the comparison between the experimental values of the heat transfer coefficient of the outer pipe and the calculated values of the new empirical correlation under two different working conditions. It can be found that the new empirical correlation can predict the experiment well.

3.5. Heat transfer correlation of outer pipe

Cp ρ Nub = cRebx Prby ⎜⎛ w ⎟⎞ ⎜⎛ w ⎟⎞ ρ ⎝ b ⎠ ⎝ Cp b ⎠

∑i

(21) 8

Applied Thermal Engineering 159 (2019) 113962

Q. Wang, et al.

Declaration of Competing Interest

heated circular tube, Teplofizika Vysokikh Temp. 15 (1977) 815–821. [19] J.D. Jackson, W.B. Hall, Influence of buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions, Turbulent Forced Convection in Channels and Bundles, Hemisphere, New York, 1979, pp. 613–640. [20] S. Kakac, R.K. Shah, W. Aung, Handbook of Single-phase Convective Heat transfer, Wiley, 1987 (Chapter 18). [21] J.D. Jackson, M.A. Cotton, B.P. Axcell, Studies of mixed convection in vertical pipes, Int. J. Heat Fluid Flow 10 (1989) 2–15. [22] D.M. McEligot, J.D. Jackson, “Deterioration” criteria for convective heat transfer in gas flow through non-circular ducts, Nucl. Eng. Des. 232 (2004) 327–333. [23] S.H. Liu, Y.P. Huang, G.X. Liu, J.F. Wang, L.K.H. Leung, Improvement of buoyancy and acceleration parameters for forced and mixed convective heat transfer to supercritical fluids flowing in vertical tubes, Int. J. Heat Mass Transf. 106 (2017) 1144–1156. [24] S.G. Kim, Y. Lee, Y. Ahn, J. Lee, CFD aided approach to design printed circuit heat exchangers for supercritical CO2 Brayton cycle application, Ann. Nucl. Energy 92 (2016) 175–185. [25] Y. Lee, J. Lee, Structural assessment of intermediate printed circuit heat exchanger for sodium-cooled fast reactor with supercritical CO2 cycle, Ann. Nucl. Energy 73 (2014) 84–95. [26] I.H. Kim, X. Zhang, R. Christensen, X. Sun, Design study and cost assessment of straight, zigzag, S-shape, and OSF PCHEs for a FLiNaK-SCO2 Secondary Heat Exchanger in FHRs, Ann. Nucl. Energy 94 (2016) 129–137. [27] Z. Zhao, D. Che, Numerical investigation of conjugate heat transfer to supercritical CO2 in a vertical tube-in-tube heat exchanger, Numer. Heat Tranf. A-Appl. 67 (2015) 857–882. [28] T. Ma, W.X. Chu, X.Y. Xu, Y.T. Chen, Q.W. Wang, An experimental study on heat transfer between supercritical carbon dioxide and water near the pseudo-critical temperature in a double pipe heat exchanger, Int. J. Heat Mass Transf. 93 (2016) 379–387. [29] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2013. [30] S.J. Kline, F. McClintock, Describing uncertainties in single-sample experiments, Mech. Eng. 75 (1953) 3–8. [31] Z. Li, Y. Wu, J. Lu, D. Zhang, H. Zhang, Heat transfer to supercritical water in circular tubes with circumferentially non-uniform heating, Appl. Therm. Eng. 70 (2014) 190–200. [32] P.R. Bringer, J.M. Smith, Heat transfer in the critical region, AIChE J. 3 (1957) 49–55. [33] A.A. Bishop, R.O. Sandberg, L.S. Tong, High Temperature Supercritical Pressure Water Loop: Part IV. Forced Convection Heat Transfer to Water at Near-Critical Temperatures and Super-Critical Pressures, Westinghouse Electric Corporation, Pittsburgh, 1964. [34] J.D. Jackson, W.B. Hall, Forced convection heat transfer to fluids at supercritical pressure, in: S. Kakac, D.B. Spalding (Eds.), Turbulent Forced Convection in Channels and Bundles, Hemisphere, New York, 1979, pp. 563–611. [35] A. Bruch, A. Bontemps, S. Colasson, Experimental investigation of heat transfer of supercritical carbon dioxide flowing in a cooled vertical tube, Int. J. Heat Mass Transf. 52 (2009) 2589–2598. [36] S. Mokry, I. Pioro, A. Farah, K. King, S. Gupta, W. Peiman, P. Kirillov, Development of supercritical water heat-transfer correlation for vertical bare tubes, Nuc. Eng. Des. 241 (2011) 1126–1136. [37] J.D. Jackson, Consideration of the heat transfer properties of supercritical pressure water in connection with the cooling of advanced nuclear reactors, Procdings of 13th Pacific Basin Nuclear Conference, Shenzhen, (2002). [38] G. Liu, Y. Huang, J. Wang, F. Lv, Effect of buoyancy and flow acceleration on heat transfer of supercritical CO2 in natural circulation loop, Int. J. Heat Mass Transf. 91 (2015) 640–646.

The authors declare no competing financial interest. Acknowledgements This project was supported by the National Natural Science Foundation of China (Grant No. 11675128). The authors thanks to experimentalists Xu Zhang for helping in the production of test section and Zefu Hu for helping in the experimental apparatus operation. References [1] X. Lei, H. Li, N. Dinh, W. Zhang, A study of heat transfer scaling of supercritical pressure water in horizontal tubes, Int. J. Heat Mass Transf. 114 (2017) 923–933. [2] X. Cheng, X.J. Liu, Y.H. Yang, A mixed core for supercritical water-cooled reactors, Nucl. Eng. Technol. 40 (2008) 117–126. [3] T. Schulenberg, J. Starflinger, P. Marsault, D. Bittermann, C. Maraczy, European supercritical water cooled reactor, Nuc. Eng. Des. 241 (2011) 3505–3513. [4] V. Dostal, P. Hejzlar, M.J. Driscoll, High-performance supercritical carbon dioxide cycle for next-generation nuclear reactors, Nucl. Technol. 154 (2006) 265–282. [5] W. Hall, J. Jackson, A. Watson, A review of forced convection heat transfer to fluids at supercritical pressures, Proc. Inst. Mech. Eng. 39 (1967) 10–22. [6] S. Yoshida, H. Mori, Heat transfer to supercritical pressure fluids flowing in tubes, Proceedings of the 1st International Symposium on Supercritical Water-Cooled Reactor Design and Technology, (2000). [7] I.L. Pioro, H.F. Khartabil, R.B. Duffey, Heat transfer to supercritical fluids flowing in channels—empirical correlations (survey), Nucl. Eng. Des. 230 (2004) 69–91. [8] I.L. Pioro, R.B. Duffey, T.J. Dumouchel, Hydraulic resistance of fluids flowing in channels at supercritical pressures (survey), Nucl. Eng. Des. 231 (2004) 187–197. [9] X. Lei, H. Li, W. Zhang, N. Dinh, Y. Guo, S. Yu, Experimental study on the difference of heat transfer characteristics between vertical and horizontal flows of supercritical pressure water, Appl. Therm. Eng. 113 (2017) 609–620. [10] S. Zhang, X. Xu, C. Liu, Y. Zhang, C. Dang, The buoyancy force and flow acceleration effects of supercritical CO2 on the turbulent heat transfer characteristics in heated vertical helically coiled tube, Int. J. Heat Mass Transf. 125 (2018) 274–289. [11] D. Huang, W. Li, A brief review on the buoyancy criteria for supercritical fluids, Appl. Therm. Eng. 131 (2018) 977–987. [12] S.M. Liao, T.S. Zhao, Measurements of heat transfer coefficients from supercritical carbon dioxide flowing in horizontal mini/micro channels, J. Heat Transf.-Trans. ASME 124 (2002) 413–420. [13] Y.Y. Bae, H.Y. Kim, D.J. Kang, Forced and mixed convection heat transfer to supercritical CO2 vertically flowing in a uniformly-heated circular tube, Exp. Therm. Fluid Sci. 34 (2010) 1295–1308. [14] S. Yu, H. Li, X. Lei, Y. Feng, Y. Zhang, H. He, T. Wang, Influence of buoyancy on heat transfer to water flowing in horizontal tubes under supercritical pressure, Appl. Therm. Eng. 59 (2013) 380–388. [15] B.S. Petukhov, A.F. Polyakov, V.A. Kuleshov, Y.L. Sheckter, Turbulent flow and heat transfer in horizontal tubes with substantial influence of thermogravitational forces, ASME Paper NO. NC 4:8, 1974. [16] J.D. Jackson, W.B. Hall, J. Fewster, A. Watson, M.J. Watts, Heat transfer to supercritical pressure fluids, UKAEA, AERER 8158, 1975, Design Report 34. [17] G.A. Adebiyi, W.B. Hall, Experimental investigation of heat transfer to supercritical pressure carbon dioxide in a horizontal pipe, Int. J. Heat Mass Transf. 19 (1976) 715–720. [18] V.S. Protopopov, Generalized correlations for the local heat-transfer coefficients turbulent flows of water and carbon dioxide at supercritical pressure in a uniform

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