Pressure-drop reduction and heat-transfer deterioration of slush nitrogen in horizontal pipe flow

Cryogenics 51 (2011) 563–574

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Pressure-drop reduction and heat-transfer deterioration of slush nitrogen in horizontal pipe flow q Katsuhide Ohira a,⇑, Kei Nakagomi a, Norifumi Takahashi b a b

Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan Tomari Power Station, Hokkaido Electric Power Co. Inc., 219-1 Yamanoue, Horikappu-mura, Tomari-mura, Fruu-gun, Hokkaido 045-0201, Japan

a r t i c l e

i n f o

Article history: Received 28 May 2011 Accepted 30 July 2011 Available online 5 August 2011 Keywords: Slush nitrogen Pressure-drop reduction Heat-transfer deterioration Two-phase flow Hydrogen energy

a b s t r a c t Cryogenic slush fluids such as slush hydrogen and slush nitrogen are two-phase, single-component fluids containing solid particles in a liquid. Since their density and refrigerant capacity are greater than those of liquid-state fluid alone, there are high expectations for the use of slush fluids in various applications such as clean-energy fuels, spacecraft fuels for improved efficiency in transportation and storage, and as refrigerants for high-temperature superconducting equipment. Experimental tests were performed using slush nitrogen to obtain the flow and heat-transfer characteristics in two different types of horizontal circular pipes with inner diameters of 10 and 15 mm. One of the primary objectives for the study was to investigate the effect of pipe diameter on the pressure-drop reduction and heat-transfer deterioration of slush nitrogen according to changes in the pipe flow velocity, solid fraction and heat flux. In the case of an inner diameter of 15 mm, pressure drop was reduced and heat-transfer characteristics deteriorated when the pipe flow velocity was higher than 3.6 m/s. On the other hand, in the case of an inner diameter of 10 mm, pressure drop was reduced and heat-transfer characteristics deteriorated when the pipe flow velocity was higher than 2.0 m/s. From these results, it can be seen that a larger pipe diameter produces a higher onset velocity for reducing pressure drop and deteriorating heat-transfer characteristics. Furthermore, based on observations using a high-speed video camera, it was confirmed that pressure drop was reduced and heat-transfer characteristics deteriorated when the solid particles migrated to the center of the pipe and the flow pattern of the solid particles inside the pipe was pseudo-homogeneous. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Single-component fluids containing solid particles in a liquid, known as cryogenic solid–liquid, two-phase slush fluids possess superior characteristics in terms of high density and refrigerant capacity (i.e., enthalpy). There are high expectations for the use of slush fluids in various applications such as clean-energy fuels, spacecraft fuels for improved efficiency in transportation and storage, and as refrigerants for high-temperature superconducting equipment. Representative slush fluids are slush hydrogen (14 K) and slush nitrogen (63 K). Compared to normal boiling liquid hydrogen (20 K), slush hydrogen with a solid weight fraction of 50 wt.% exhibits a 16% greater density, and an 18% increase in refrigerant capacity. In the case of slush nitrogen, also at a solid weight fraction of 50 wt.%, the respective increases are 16% and 22%. These properties would allow, for instance, size reductions in the fuel tanks currently used to hold liquid hydrogen for spacecraft, thus contributing to larger satellite payloads. In another q

This article is an English translation of Teion Kogaku 2011;46(3):149–161.

⇑ Corresponding author. Tel.: +81 22 217 5227.

E-mail address: [email protected] (K. Ohira). 0011-2275/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2011.07.008

practical example, when heat enters slush hydrogen during pipeline transportation due to heat in-leak, a portion of the heat is absorbed by the heat of fusion, and, thus, the rise in the liquid temperature is reduced and the phase change from liquid to vapor–liquid, two-phase flow is suppressed while the solid fraction decreases, given the superior characteristics of slush hydrogen as a functionally thermal fluid. Based on the transport and storage advantages of slush fluids, the present authors have proposed a liquid hydrogen energy system [1,2] that can be expected to deliver synergetic effects, as indicated in Fig. 1. For example, when using slush hydrogen as a refrigerant in MgB2 superconducting electrical power transmission, the further utilization of slush or liquid hydrogen as a refrigerant for superconducting magnetic energy storage (SMES) at the destination end would simultaneously enable the long-distance transmission and transportation of electrical power and hydrogen fuel, as well as simultaneous storage. The technology items required for slush fluid applications are presented in Fig. 2. As shown at the upper left of Fig. 1, the technologies developed thus far by the present authors encompass slush hydrogen production methods including the world’s first hydrogen liquefaction by means of magnetic refrigeration [3–5], heat-transfer

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the required power for pumps and to prevent quench propagation. Currently, however, these phenomena remain insufficiently understood, at least in the context of pipeline transport of slush fluids and the use of slush fluids as refrigerants for superconducting power equipment. In the present study, flow and heat-transfer characteristics were experimentally elucidated with respect to slush nitrogen flow in a horizontal heat transfer pipe. Two different types of circular pipe having inner diameters of 10 mm and 15 mm were used to investigate pressure-drop and treat-transfer characteristics in slush nitrogen flow, and the differences between the two pipe sizes were compared and discussed. A high-speed video camera was also employed to record flow patterns, enabling consideration of the respective relationships with pressure-drop and heat-transfer characteristics, and thus promoting enhanced understanding of pressure drop reduction and heat transfer deterioration phenomena. 2. Experimental apparatus and conditions Fig. 1. Synergetic effect of a combination of slush hydrogen and superconducting equipment.

2.1. Experimental apparatus

characteristics of slush hydrogen and slush nitrogen for SMES [6], as well as high-precision density meters and mass flow rate meters [7–11]. The present authors have reported on research into the flow and heat-transfer characteristics of slush nitrogen, indicating the pressure-drop reduction when the flow velocity of slush nitrogen exceeds 3.6 m/s in a 15 mm inner-diameter pipe [2], and the heat-transfer deterioration of forced-convection heat transfer [12]. Sindt et al. have investigated pressure drop reduction in a 16.6 mm inner diameter pipe in experimental research on slush hydrogen, but have not reported on heat-transfer characteristics [13]. Another report has considered flow and heat-transfer characteristics of slush nitrogen in a 14 mm inner diameter pipe in the flow velocity region of within 3.0 m/s, but has not obtained those characteristics in the higher flow velocity region where pressuredrop reduction and heat-transfer deterioration phenomena become apparent [14]. In a scenario where a slush fluid is subjected to pumped transport over a long distance in combination with superconducting electrical power transmission, pressure-drop reduction and heat-transfer deterioration phenomena are extremely important from the standpoint of design data required in order to reduce

An overview of the experimental apparatus is presented in Fig. 3, including the slush nitrogen production and run tank (with a capacity of 0.05 m3), the test section for measuring flow and heat-transfer characteristics, the visualization section equipped with a high-speed video camera for observing and recording flow patterns, and the catch tank for storing slush nitrogen subsequent to the flow test (also with a capacity of 0.05 m3). As the details of the experimental apparatus and measurement systems have been reported previously [2], the description below focuses on those points that are different. The absolute maximum value of the solid nitrogen particle diameter of slush nitrogen produced using the freeze–thaw method is in the range of 0.5–2.0 mm, with an average particle diameter of 1.36 mm [2]. A capacitance-type density meter, consisting of a flat-plate and two cylindrical rods, [7] is placed in the run tank. A capacitance level meter, consisting of a flat-plate and a cylindrical rod, is also installed to measure the change in the fluid level during the flow test for evaluating the mean flow velocity in the test section [2]. The capacitance values of the density and level meters were measured using an LCR meter. Following slush nitrogen production, the inside of the run tank is pressurized by means of

Gas Pressurization

Spray Method

Production Technology

Freeze-Thaw Method Auger Method

Transfer Method Transfer Technology

Magnetic Refrigeration Method

Pump

Flow Characteristics (Pressure Drop, Flow Pattern)

Capacitance Method

Aging Effect Storage Technology

Density

Stratification Pool Boiling

Heat Transfer Technology

Forced Convection

Displacement (Piston, Piston, Bladder Bladder)

β or

γ Ray Method

Microwave Method

Measurement Technology

Capacitance Method Mass Flow Rate

Microwave Method

Fig. 2. Technology items for slush fluid applications.

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Slush N2 Production and Run Tank 50 L

Heater GHe Stirrer

Vacuum Pump

550

130

1025

206

Test Section Visualization Section ID: 10 or 15mm ID: 10 or 15mm

Catch Tank 50 L Fig. 3. Experimental apparatus for the slush nitrogen flow test.

helium gas at 0.11–0.20 MPa, and slush nitrogen then flows into the test section. For each instance of flow, after reaching a steady-state flow, the unheated pressure drop was first measured, followed by measurement of pressure drop and heat transfer characteristics during heating. Flow patterns were imaged for both unheated and heated flows using a high-speed video camera. The test section consists of two types of heat-transfer circular pipe, either 10 or 15 mm in inner diameter. A schematic view of the 10 mm diameter test section is presented in Fig. 4. The pipe is made of oxygen-free copper, and measures 1025 mm in total length, 10 mm in inner diameter, and 12 mm in outer diameter. The pressure-drop measurement length is 550 mm, and the heated length (by means of heater wire) is 800 mm. The heater wire consists of Nichrome wire, wound non-inductively around the pipe outer wall, and affixed using Stycast. Pressure drop is measured by means of a diaphragm-type differential-pressure gauge (rated capacity of 20 kPa, with accuracy of ±60 Pa). The local heat transfer coefficient is calculated using measured temperatures at four locations on the bottom of the pipe outer wall, positioned at 150 (T1), 350 (T2), 475 (T3), and 600 (T4) mm from the initial heating point, as well as measured bulk temperatures at upstream and downstream locations of the heating section (Tup and Tdown) inside the pipe. The sensors used for these wall and bulk temperature measurements are silicon diode temperature sensors (accuracy of ±22 mK at a temperature of 77 K), and these sensors are pre-calibrated using liquid and slush nitrogen. Also,

200

550

50

ΔP

P φ 10

P

Tup 125

150

T2

T1

T3

T4

Tdown

50

350 475 600 800 1025 Fig. 4. Schematic illustration of the test section (D = 10 mm).

the hydrodynamic entry length and thermal entry length upstream from the heated section are deemed sufficient. The 15 mm inner diameter heat transfer pipe has an outer diameter of 17 mm and a heated length of 810 mm. The local heat transfer coefficient is measured at three locations (155, 355 and 705 mm), with overall length and pressure drop measurement length being the same as for the 10 mm pipe [12]. As noted below in Section 3.2, consideration in the present context is centered on the location at 600 mm (T4) from the initial point of heating in the case of the 10 mm inner diameter pipe, and on that at 705 mm in the case of the 15 mm pipe. Scattering of the particles in the slush nitrogen is anticipated, as well as time-wise and spatial variation in the particle distributions, and efforts are made to minimize any measurement error from the measurement systems [2]. The visualization section consists of an acrylic external pipe with a length of 206 mm for high-vacuum thermal insulation, and an internal circular pipe made of quartz glass matching the respective test sections (i.e., either 10 mm in inner diameter, 12 mm in outer diameter and 130 mm in length, or 15 mm in inner diameter, 18 mm in outer diameter and 130 mm in length). The high-speed video camera used to observe the flow patterns was a FASTCAM SA5 manufactured by Photron, and white light was employed as the backlight source. A maximum of 7000 fps is possible at the highest resolution of 1024  1024 pixels, but the frame rate actually used was 4000 fps with exposure time of 1/8000–1/ 20000 s. 2.2. Experimental conditions The respective sets of experimental conditions are indicated below. (Note that the Reynolds number Re is calculated using the slush density and liquid nitrogen viscosity.) (1) 10 mm inner diameter pipe Mean flow velocity umean Reynolds number Re Solid weight fraction Heat flux q

0.16–5.2 m/s 1.0  104–1.5  105 2.3–31.8 wt.% 0, 10, 30 kW/m2

(2) 15 mm inner diameter pipe Mean flow velocity umean Reynolds number Re Solid weight fraction Heat flux q

1.3–4.6 m/s 6.1  104–2.1  105 11.0–38.3 wt.% 0, 10, 30 kW/m2

3. Experimental results and discussion 3.1. Pressure drop characteristics in unheated flow In a previous report [2], we compared the pressure drop characteristics for slush nitrogen (63 K, triple point temperature) during unheated flow through a 15 mm inner diameter pipe on the one hand, with the Prandtl–Karman Eq. (1) (referred to hereafter as the P–K equation) obtained by means of calculation from the physical properties of subcooled liquid nitrogen on the other. In the present study, the pressure drop and heat transfer characteristics of slush nitrogen are compared directly with the characteristics as experimentally obtained for subcooled liquid nitrogen. The pressure drop characteristics considered below in this section are for slush and subcooled liquid nitrogen in the unheated 10 mm inner diameter pipe, and these results are compared with those previously reported [2] (i.e., for the 15 mm pipe). Fig. 5 shows, for unheated flow of subcooled liquid nitrogen in the 10 mm inner diameter pipe, the measurement results (open circles, s) corresponding to mean flow velocity and pressure drop per unit length. The thinner solid line in the figure represents the

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10 Prandtl-Karman Eq. Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

20

15

Pressure Drop Ratio rdP [-]

Pressure Drop per Unit Length ΔP/L [kPa/m]

25

Fitted Curve (Subcooled LN 2)

10

Prandtl-Karman Eq.

5

0

Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%] 1

0.1

0

1

2

3

4

5

6

0

1

2

3

4

5

6

Mean Velocity u mean [m /s]

Mean Velocity u mean [m/s] Fig. 5. Mean velocity and pressure drop of the subcooled liquid nitrogen and slush nitrogen (D = 10 mm, q = 0 kW/m2).

Fig. 6. Mean velocity and pressure drop ratio of the slush nitrogen (D = 10 mm, q = 0 kW/m2).

P–K Eq. (1). Substituting the pipe friction factor k obtained from the mean flow velocity umean using Eq. (1) for the Darcy–Weisbach Eq. (2), thus obtaining pressure drop DPl, the mean flow velocity and pressure drop per unit length DP/L are expressed.

reproduced in Fig. 7. The images in Fig. 7 are further enlarged in Fig. 8 to show the vicinity of the bottom of the pipe in greater detail. Pressure drop ratio is defined by,

pffiffiffi 1 pffiffiffi ¼ 2:0  log10 ðRe kÞ  0:8 k

ð1Þ

rdP ¼

1 L DPl ¼ k  ql u2mean  2 D

ð2Þ

Here, Re is the Reynolds number, DPl is the pressure drop, D is the pipe inner diameter of 10 mm, L is the pressure drop measurement length of 550 mm, and ql and umean are the density and mean flow velocity, respectively, for subcooled liquid nitrogen at 63 K. The thicker solid line in Fig. 5 represents the approximation curve by the least squares method as applied to the experimental results for subcooled liquid nitrogen. The results obtained for the 15 mm inner diameter pipe were the same as for the 10 mm pipe. Fig. 5 also shows the measurement results for mean flow velocity and pressure drop per unit length for the unheated flow of slush nitrogen in the 10 mm inner diameter pipe. A comparison of the results for slush and subcooled liquid nitrogen is presented below. At a flow velocity in the range of 2.0–3.5 m/s, and with a solid fraction of within 14 wt.%, pressure drop reduction can be confirmed, in that the pressure drop for slush nitrogen is less than that for subcooled liquid nitrogen. In high- and low-velocity flow regions of within 2.0 m/s or above 3.5 m/s, pressure drop reduction cannot be clearly confirmed. Furthermore, even in the region where pressure-drop reduction does occur (2.0–3.5 m/s), it cannot be confirmed when the solid fraction is above 14 wt.%. Thus, the pressure drop characteristics of slush nitrogen tend to differ depending on differences in flow velocity and solid fraction. In tests using a 15 mm inner diameter stainless steel circular pipe (with a pressure drop measurement length of 400 mm), in comparison with the P–K equation, pressure-drop reduction is confirmed at flow velocity of 3.6–5.9 m/s and solid fraction of 4.8–17 wt.% [2]. With a larger diameter pipe, the threshold levels of velocity and solid fraction for the onset of pressure drop reduction become greater. Apart from slush fluids, experiments with limestone slurry also confirm that differing pipe diameter leads to differing pressure drop reduction onset values in terms of velocity and solid fraction [15]. The relationship between the mean flow velocity and the pressure drop ratio for the 10 mm inner diameter pipe is presented in Fig. 6. The dashed line in the figure shows the general trend of the pressure drop ratio, while the circled numbers 1–4 indicate the flow patterns observed using the high-speed video camera and

DPsl DPsub

ð3Þ

where DPsl is the pressure drop for slush nitrogen, and DPsub is the pressure drop obtained from the approximation curve by the least squares method for subcooled liquid nitrogen as shown in Fig. 5. It can be seen that, in the case of rdP < 1, the pressure drop for slush nitrogen decreases, and in the case of rdP > 1, it becomes greater than that for subcooled liquid nitrogen. From Fig. 6, in the flow velocity region of within 1.0 m/s, the pressure drop ratio is extremely high compared to other flow regions. The pressure drop ratio

(1) 0.35 m/s, 23.8 wt%.

(2) 1.28 m/s, 7.05 wt%.

(3) 2.62 m/s, 11.7 wt%.

(4) 4.18 m/s, 15.6 wt%. Fig. 7. Flow patterns under the experimental conditions shown in Fig. 6 (D = 10 mm, q = 0 kW/m2).

K. Ohira et al. / Cryogenics 51 (2011) 563–574

(1) 0.35 m/s, 23.8 wt%.

(2) 1.28 m/s, 7.05 wt%.

(3) 2.62 m/s, 11.7 wt%.

(4) 4.18 m/s, 15.6 wt%. Fig. 8. Visualizations of solid particles at the bottom of the pipe for the slush nitrogen shown in Fig. 7 (D = 10 mm, q = 0 kW/m2).

decreases as flow velocity increases, and, in the vicinity of 1.9 m/s, rdP = 1, meaning that the pressure drop for slush nitrogen reaches a value equivalent to that for subcooled liquid nitrogen. In the case of solid fraction within 14 wt.%, it is seen that the pressure drop ratio begins to become less than 1 (rdP < 1) in the vicinity of flow velocity of 2.0 m/s, and pressure drop reduction becomes apparent. The pressure drop ratio declines with increasing flow velocity, until the flow velocity vicinity of 2.8 m/s, until the maximum rdP = 0.75. These results are in general agreement with those for the 15 mm inner diameter pipe, where the pressure drop ratio is 0.77 times in comparison with the P–K equation [2]. With further increases in flow velocity, the pressure drop ratio begins to increase, until rdP = 1 in the flow velocity vicinity of 3.5 m/s. At flow velocities higher than 3.5 m/s, unlike the low-velocity region of within 2.0 m/s, the pressure drop ratio approaches a value of around 1.1, and does not exhibit any major change. This phenomenon is also confirmed for 15 mm inner diameter pipe, with the pressure drop ratio approaching approximately 1.15 in comparison with the P–K equation [2]. Because the pressure drop ratio is compared with the P–K equation in Ref. [2], comparison with the results from the present study leads to a slightly larger pressure drop ratio. On the other hand, at a solid fraction of over 14 wt.%, while there is a tendency for rdP > 1 in all flow velocity regions, such that the pressure drop ratio decreases with increasing flow velocity; as in the case of a solid fraction of within 14 wt.% in the high-velocity flow region, the pressure drop ratio then approaches a constant value, with no major change thereafter. The fact that pressure drop reduction does not appear with a solid fraction of over 14 wt.% is considered to be due to greater interference at a higher solid fraction among the solid particles themselves, between the particles and the pipe walls, and between the solid particles and the liquid. The flow velocity and solid fraction corresponding to the circled numbers 1–4 shown in Fig. 6 are as follows: (1) 0.35 m/s, 23.8 wt.%; (2) 1.28 m/s, 7.05 wt.%; (3) 2.62 m/s, 11.7 wt.%; and (4) 4.18 m/s, 15.6 wt.%. From the visualization results revealed by the high-speed video camera in Figs. 7 and 8, flow pattern (1) is

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seen to be sliding bed flow. Because the flow velocity is extremely low, the solid particles concentrate at the pipe bottom, with liquid flowing in the upper part of the pipe. Accordingly, the higher the location within the pipe, the larger the flow velocity is. The mass of the solid particles is at the bottom, and flows as if being pulled along by the liquid above. This makes extremely high interference among the particles themselves, between the particles and the pipe bottom wall, and between the particles and the liquid. It is the sum of these interferences that causes a greater pressure drop ratio compared to other flow velocity regions. Flow pattern (2) is characterized as heterogeneous flow. Here, there is a high distribution of solid particles at the pipe bottom, and interference between the particles and the liquid is thought to be considerable. Consequently, as in the case of sliding bed flow, the pressure drop ratio is higher than 1. However, since the concentration of solid particles at the pipe bottom is not as great, interference among the particles is lower, and the pressure drop ratio is less than for sliding bed flow. Flow pattern (3) can be described as pseudo-homogeneous flow. In the flow velocity region under consideration, pressure drop reduction becomes apparent. Image (3) in Fig. 7 is not clear, but the corresponding image in Fig. 8 exhibits a liquid layer containing few solid particles in the vicinity of the pipe wall. That is, in pseudohomogeneous flow, the solid particles move towards the center of the pipe, leaving a liquid layer with few solid particles near the wall. This movement results in reduced interference between the particles and the wall, in contrast to the cases of the sliding bed flow and heterogeneous flow patterns. At the same time, the group of particles at the center of the pipe is observed to behave in a manner similar to an elastic body. This appears to suppress the diffusion of turbulence generated within the liquid layer near the wall to the center of the pipe, as well as suppressing the further growth of turbulence. As a result, it is considered that slush nitrogen is subject to reduced pressure drop in comparison with subcooled liquid nitrogen. Similar to pattern (3), pattern (4) is also pseudo-homogeneous flow, although the collisions between the solid particles and the pipe wall are more clearly seen. Because the flow velocity is greater than in the case of (3), greater turbulence grows in the liquid, and, since the turbulence-induced interference (between particles and liquid, among particles, and between particles and the pipe wall) dominates the pressure drop reduction effect, the pressure drop ratio is thought to rise above 1. However, as noted previously, even when the flow velocity continues to increase, the pressure drop ratio approaches a constant value. This is considered to be due to the competing effects of, on the one hand, increased turbulence near the pipe wall and particle interference, and on the other, the suppression of turbulence by the group of solid particles at the center. With respect to the flow patterns observed in the 15 mm inner diameter pipe, the particle image velocimetry (PIV) results have been previously reported, and are available for reference [2]. Next, in order to use the Froude number to estimate the flow velocity at which pressure drop reduction becomes apparent, even with differing pipe diameters, Eq. (4) was employed to calculate the Froude number.

umean Fr ¼ pffiffiffiffiffiffi gD

ð4Þ

The Froude number at the flow velocity marking the onset of pressure drop reduction is Fr = 6.4 in the case of the 10 mm inner diameter pipe, and Fr = 9.1 in the case of the 15 mm pipe, indicating the lack of good agreement. It is thus considered necessary to introduce a dimensionless parameter, taking into account factors such as the solid fraction, in order to employ the Froude number for prediction in the current context.

K. Ohira et al. / Cryogenics 51 (2011) 563–574

As discussed above, the behavior of solid particles has an important relationship with pressure drop reduction. Also, while interference-induced pressure drop by solid particles is dominant in low-velocity flow regions, liquid turbulence-induced pressure drop is dominant in high-velocity flow regions. 3.2. Pressure drop and heat transfer characteristics in heated flow In evaluating heat transfer characteristics, the local heat transfer coefficient was employed, as calculated according to

h¼

q T wall  T bulk

ð5Þ

Here, q is the heat flux, Twall is the temperature of the pipe inner wall, and Tbulk is the bulk temperature. As the differential between the inner and outer wall temperatures is small according to the heat transfer calculation in the experimental conditions (D = 10 mm, and q = 30 kW/m2, such that the temperature differential is 0.029 K), the temperature measured at the outer wall Twall is taken to represent the inner wall temperature as well. With respect to local bulk temperature, so as not to affect the flow and heat transfer conditions within the heat transfer measurement section, the linear interpolation method, which is generally used in heat transfer experiments, was applied using the temperatures measured at upstream and downstream points inside the pipe. Prior to measuring the pressure drop and heat transfer coefficient of slush nitrogen under heated conditions, subcooled liquid nitrogen (63 K, triple point temperature) was used in order to confirm the experimental apparatus, measurement systems, and the above-noted measurement method. Fig. 9 presents the heat transfer characteristics for subcooled liquid nitrogen in the 10 mm inner diameter pipe, together with comparative results for the Sieder– Tate equation



lbulk Nu ¼ 0:027  Re0:8  Pr0:14=3  lwall

0:14 ð6Þ

Here, Nu is the Nusselt number, Re is the Reynolds number, Pr is the Prandtl number, and lwall and lbulk are the viscosities of subcooled liquid nitrogen at the wall temperature and bulk temperature, respectively. From Fig. 9, it can be seen that the experimental results for subcooled liquid nitrogen are within about ±10% with respect to the Sieder–Tate equation. This indicates good agreement, even in the case of the 15 mm inner diameter pipe.

The solid fraction of slush nitrogen changes with heating. Assuming that all of the applied heat is used as heat of fusion for the solid particles, and in the case of a 10 mm inner diameter pipe with q = 10 kW/m2, and at a flow velocity of 3.0 m/s, the solid fraction would decrease by 3.59 wt.%. In actuality, however, the applied heat is also used to raise the temperature of the liquid (i.e., sensible heat). Also, the time required for passing through the heated section of 800 mm at a flow velocity of 3.0 m/s is extremely short, at 0.27 s. Considering that most of the heat from the pipe wall would be directly transferred to the liquid, and subsequently transferred from the liquid to the solid particles, the change in solid fraction due to melting of the solid would be small. It is thus considered for the purpose of the present discussion that the effect on the solid fraction is generally slight. Fig. 10a and b shows the relationship between the mean flow velocity and the local heat transfer coefficient at points located 150 mm (T1) and 475 mm (T3), respectively, as measured from the start point of heating, along the 10 mm inner diameter pipe, with heat flux q = 30 kW/m2. Fig. 11b shows this relationship at the 600 mm (T4) location, simultaneously obtained. The thicker solid line represents the approximation curve by the least squares method with respect to the local heat-transfer coefficient for subcooled liquid nitrogen. The local heat-transfer coefficient at the location 150 mm from the heating start point (Fig. 10a) exhib-

14

Local Heat Transfer Coefficient 2 h [kW/m K]

568

Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

12 10

Fitted Curve (Subcooled LN 2)

8 6 4 2 0

0

1

2

3

4

5

6

Mean Velocity u mean [m /s]

(a) l = 150 mm, q = 30 kW/m2.

Local Heat Transfer Coefficient h [kW/m2K]

10

103 Sieder-Tate Eq.

Nu /(Pr 1/3 ( µbulk /µwall )0.14 ) [-]

Subcooled, 10 [kW/m2] Subcooled, 30 [kW/m2]

+10 % -10 %

Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

9 8 7 6

Fitted Curve (Subcooled LN 2)

5 4 3 2 1 0

2

10

104

105

106

Reynolds Number Re [-] Fig. 9. Heat-transfer characteristics of the subcooled liquid nitrogen (D = 10 mm, q = 10, 30 kW/m2).

0

1

2

3

4

5

6

Mean Velocity u mean [m /s]

(b) l = 475 mm, q = 30 kW/m2. Fig. 10. Local heat-transfer coefficient and mean velocity of the slush nitrogen (D = 10 mm, q = 30 kW/m2).

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8 7

35 30 25

Fitted Curve (Subcooled LN 2)

6 5

20

4

15

3 10

2

5

1 0

0

1

2

3

4

5

6

0

Mean Velocity u mean [m /s]

(a) q = 10 kW/m2.

9 8 7

40

Fitted Curve (Subcooled LN 2)

Prandtl-Karman Eq. Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

35 30

6

25

5

20

4

15

3 10 2 5

1 0

0

1

2

3

4

5

6

Pressure Drop per Unit Lengthhhh ΔP/L [kPa/m]

Local Heat Transfer Coefficientutt 2 h [kW/m K]

10

0

Mean Velocity u mean [m /s]

(b) q = 30 kW/m2. Fig. 11. Local heat-transfer coefficient and pressure drop according to changes in the mean velocity (D = 10 mm, q = 10, 30 kW/m2).

14

28 Prandtl-Karman Eq. Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

12 10

Fitted Curve (Subcooled LN2)

24 20

8

16

6

12

4

8

2

4

0

0

1

2

3

4

5

6

Pressure Drop per Unit Length ΔP /L [kPa/m]

9

from the vicinity of 2.0 m/s in flow velocity. Furthermore, in the region higher than 2.0 m/s, reduced heat-transfer coefficients can be confirmed for all solid fractions. Because both pressure drop reduction and heat-transfer coefficient deterioration become apparent from the vicinity of 2.0 m/s in flow velocity, it is considered that both are induced by the same causative phenomenon. That is, the flow pattern becomes pseudo-homogeneous at a flow velocity of around 2.0 m/s, and pressure drop is reduced according to the same mechanism as in the unheated flow. The group of solid particles at the center of the pipe suppresses the diffusion of turbulence generated in the liquid layer near the wall to the pipe center, while the wall turbulence itself is also inhibited to grow. It is thought that, as a result, thermal convection due to turbulent mixing from the pipe wall to the pipe center is suppressed, and that the heat transfer coefficient declines. The behavior of the solid particles can thus be seen to have an important influence on heat transfer characteristics as well. Fig. 12 shows the local heat-transfer coefficient and the pressure drop per unit length according to changes in the mean flow velocity for the 15 mm inner diameter pipe. For Fig. 12a and b, q = 10 and 30 kW/m2, respectively. The meaning of the solid lines is the same as for Fig. 11. From Fig. 12, regardless of heat flux, at a flow velocity of over 3.6 m/s and in the solid fraction range of 10–30 wt.%, the pressure drop for slush nitrogen declines relative to that of sub-

Local Heat Ttansfer Coefficienttt h [kW/m2K]

Local Heat Transfer Coefficient 2 h [kW/m K]

Prandtl-Karman Eq. Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%]

Pressure Drop per Unit Length h ΔP/L [kPa/m]

40

10

0

Mean Velocity u mean [m/s]

(a) q = 10 kW/m2. 28 Prandtl-Karman Eq. Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

12 10

24 20

Fitted Curve (Subcooled LN2)

8

16

6

12

4

8

2

4

0

0

1

2

3

4

5

6

Pressure Drop per Unit Length ΔP /L [kPa/m]

14

Local Heat Ttansfer Coefficienttt 2 h [kW/m K]

its higher values for both subcooled liquid and slush nitrogen than those at the 475 mm or 600 mm locations, suggesting that the heat transfer condition has not reached steady state. Comparing the local heat-transfer coefficients at the 475 mm and 600 mm locations (Figs. 10b and 11b), it can be seen that there is almost no difference caused by location for either subcooled liquid or slush nitrogen. For the purpose of discussion, then, the local heat-transfer coefficients considered are those at 600 (T4) mm from the heating start point for the 10 mm inner diameter pipe, and at 705 mm for the 15 mm pipe. Fig. 11 presents the local heat-transfer coefficient and the pressure drop per unit length according to changes in the mean flow velocity for the 10 mm inner diameter pipe. For Fig. 11a and b, q = 10 and 30 kW/m2, respectively. The thinner solid lines in the figure represent the P–K equation, while the thicker solid lines represent the least squares approximations for pressure drop per unit length and the local heat-transfer coefficient with respect to subcooled liquid nitrogen (q = 10, 30 kW/m2). Regardless of heat flux, the pressure drop for slush nitrogen begins to decline relative to that for subcooled liquid nitrogen from the vicinity of 2.0 m/s in flow velocity, just as in the unheated flow. On the other hand, with respect to the local heat-transfer coefficient as well, a decline is noted for slush nitrogen as compared to subcooled liquid nitrogen

0

Mean Velocity u mean [m /s]

(b) q = 30 kW/m2. Fig. 12. Local heat-transfer coefficient and pressure drop according to changes in the mean velocity (D = 15 mm, q = 10, 30 kW/m2).

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cooled liquid nitrogen. In the case of the 15 mm inner diameter pipe, both pressure drop reduction and heat-transfer coefficient deterioration begin to occur from the vicinity of 3.6 m/s in flow velocity. The mechanism with respect to this phenomenon is considered to be the same as for the 10 mm inner diameter pipe. In the case of the 15 mm pipe, pseudo-homogeneous flow is thought to initiate from the vicinity of 3.6 m/s, which corresponds to the previously reported result (i.e., unheated flow) [2]. As in the unheated condition, the onset flow velocity for pressure drop reduction and heat transfer deterioration differs with the pipe inner diameter. The 15 mm inner diameter pipe is characterized by the onset of these phenomena at a higher flow velocity than for the 10 mm inner diameter pipe. Also, the solid fraction at which pressure drop reduction becomes apparent is 14 wt.% in the case of the 10 mm inner diameter pipe, the corresponding figure for the 15 mm pipe is 10–30 wt.%; as in the unheated flow, the smaller the pipe diameter, the lower the solid fraction at which pressure drop reduction initiates. Since interference between solid particles and the pipe wall becomes greater at a higher solid fraction in a smaller diameter pipe, pressure drop reduction does not occur as easily, and is thus seen to initiate at a comparatively low solid fraction. Fig. 13 indicates the relationship between the mean flow velocity and the pressure drop ratio for the heated 10 mm inner

2.2 Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%]

Pressure Drop Ratio rdP [-]

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4

0

1

2

3

4

5

6

Mean Velocity u mean [m /s]

(a) q = 10 kW/m2. 2.2 Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

Pressure Drop Ratio rdP [-]

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4

0

1

2

3

4

5

6

Mean Velocity u mean [m /s]

(b) q = 30 kW/m2. Fig. 13. Pressure drop ratio and mean velocity of the slush nitrogen (D = 10 mm, q = 10, 30 kW/m2).

diameter pipe. The dashed line in the figure indicates the approximate trend of the pressure drop ratio. For Fig. 13a and b, q = 10 and 30 kW/m2, respectively. The pressure drop ratio in the heated flow, as is the case in Eq. (3), is the ratio of the pressure drop for slush nitrogen (heated) to the pressure drop for subcooled liquid nitrogen (heated) obtained by the least squares method. From Fig. 13, it can be seen that in the low-velocity region of within 2.0 m/s, the pressure drop ratio presents a large value as compared to other regions. This tendency is the same as in the unheated flow (see Fig. 6). However, especially in the region of within 1.5 m/s, as opposed to the unheated flow where rdP = 1.67–7.35, the pressure drop ratio becomes smaller in the heated flow (q = 10 kW/m2), where rdP = 1.53–2.16. In this lower-velocity region, particularly for sliding bed flow, the solid particles slide along the bottom of the pipe, resulting in a longer residence time within the pipe, meaning that more of the solid particles are subject to melting due to heating than under higher-velocity conditions. This serves to prevent the rise of the liquid temperature at the bottom of the pipe, and tends to maintain liquid viscosity at a higher level. On the other hand, as in the case of subcooled liquid nitrogen, liquid viscosity is decreased by heating for most of the liquid near the pipe wall, excepting the pipe bottom. To a greater extent than the inhibiting effect on viscosity decrease of the liquid at the pipe bottom, the melting of the solid particles serves to reduce interference among the particles, between particles and the wall, and between the particles and the liquid nitrogen (as compared to the unheated flow), and it is thought that, as a result, the pressure drop ratio becomes smaller than for the unheated flow. Nevertheless, in flow velocity region above 2.0 m/s, where rdP < 1, the minimum value for the pressure drop ratio is rdP = 0.77 regardless of heat flux, which is about the same as the minimum value of rdP = 0.75 for the unheated flow. Accordingly, the rate of pressure drop reduction is nearly equivalent in both the unheated and heated flows. Also, in the high-velocity region higher than 3.5 m/s, similarly to the unheated flow, the pressure drop ratio does not change appreciably with increased flow velocity, and can be confirmed to approach a constant value. The reason for this is the same as in the unheated flow. It should be noted that, although there is considerable scattering in the overall data, this is considered to represent the influence of heating. Fig. 14 presents the relationship between the mean flow velocity and the pressure drop ratio for the 15 mm inner diameter pipe. The dashed line in the figure indicates the approximate trend of the pressure drop ratio. For Fig. 14a and b, q = 10 and 30 kW/m2, respectively. In the low-velocity region of within 3.6 m/s, high solid fractions (30–40 wt.%) exhibit comparatively large values for pressure drop ratio as compared to other velocity regions. At low solid fractions (10–20 wt.%), however, the pressure drop ratio is approximately rdP = 1 and remains constant. On the other hand, in the case of the 10 mm inner diameter pipe, even at low solid fractions, the pressure drop ratio displays a large value in the low-velocity region (see Fig. 13). In the case of the 15 mm inner diameter pipe, the flow becomes heterogeneous in flow velocity regions of within 3.6 m/s; it is thus considered that, while solid particle interference increases at higher solid fractions, interference is less at lower solid fractions when the pipe diameter is larger. Also, in the case of solid fraction of 10–30 wt.%, while pressure drop reduction initiates in the flow velocity region of over 3.6 m/s, the minimum values of the pressure-drop ratio are rdP = 0.83 at q = 10 kW/m2, and rdP = 0.61 at q = 30 kW/m2. In contrast to the 10 mm inner diameter pipe, a difference in the minimum value of the pressure drop ratio is seen according to heat flux, and the cause of this phenomenon is not clear. At a solid fraction of 30–40 wt.%, rdP can be confirmed to approach 1.05–1.1 with increased flow velocity. This trend is the same as for the 10 mm inner diameter pipe (see Fig. 13). Also, while the tendency for the

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2.2

2.2

Pressure Drop Ratio rdp [-]

2 1.8

Local Heat Transfer Coefficient Ratio rh [-]

Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

1.6 1.4 1.2 1 0.8 0.6 0.4

0

1

2

3

4

5

1.6 1.4 1.2 1 0.8 0.6 0

1

2

3

4

5

Mean Velocity u mean [m/s]

Mean Velocity u mean [m/s]

(a) q = 10 kW/m2.

(a) q = 10 kW/m2.

6

2.2

Local Heat Transfer Coefficient Ratio rh [-]

2.2 Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

2

Pressure Drop Ratio rdp [-]

1.8

0.4

6

Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%]

2

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0

1

2

3

4

5

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4

6

Subcooled 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

2

0

1

2

3

4

5

Mean Velocity u mean [m /s]

Mean Velocity u mean [m/s]

(b) q = 30 kW/m2.

(b) q = 30 kW/m2.

6

Fig. 14. Pressure drop ratio and mean velocity of the slush nitrogen (D = 15 mm, q = 10, 30 kW/m2).

Fig. 15. Local heat-transfer coefficient ratio and mean velocity of the slush nitrogen (D = 10 mm, q = 10, 30 kW/m2).

pressure drop ratio to approach rdP = 1.05–1.1 cannot be confirmed with respect to solid fractions of 10–30 wt.%, it is thought that the pressure drop ratio does approach a constant value in the highvelocity region of over 5.0 m/s. Fig. 15 presents the relationship between the mean flow velocity and the local heat-transfer coefficient ratio for the 10 mm inner diameter pipe, while Fig. 16 indicates this relationship for the 15 mm inner diameter pipe. The dashed lines in the figures show the approximate tendency of the local heat-transfer coefficient ratio. For (a) and (b), q = 10 and 30 kW/m2, respectively. The local heat-transfer coefficient ratio is defined according to Eq. (7) below.

(in contrast to the pressure drop ratio), with rh = 1 (approximately). That is, heat transfer is not promoted. At a flow velocity of over 2.0 m/s, the minimum values of the heat-transfer coefficient ratio are rh = 0.73 at q = 10 kW/m2, and rh = 0.82 at q = 30 kW/m2, such that a difference can be seen depending on heat flux. Also, regardless of heat flux, the heat transfer coefficient remains at a reduced level at flow velocities of over 3.5 m/s, where pressure drop reduction does not appear. At velocities of over 3.5 m/s, yet further increases in velocity lead to greater liquid turbulence and greater solid-particle interference; pressure drop increases relative to subcooled liquid nitrogen, but the major portion of solid particle interference (among particles, and between particles and the liquid) develops in the central part of the pipe. In the liquid layer near the pipe wall, there are fewer solid particles, and the heat transfer between the pipe wall and the liquid occurs directly. Since turbulence and heat convections to the pipe center are suppressed by the group of solid particles, it is considered that the promotion of heat transfer hardly occurs at all, meaning that the heat transfer coefficient remains at a reduced level. In the case of the 15 mm inner diameter pipe, rh = 1 (approximately) at flow velocities of within 3.6 m/s, and heat transfer is not promoted. At flow velocities of over 3.6 m/s, the heat transfer coefficient decreases to rh < 1, but the minimum value of the heat-transfer coefficient ratio is rh = 0.80 at q = 10 kW/m2, and

rh ¼

hsl hsub

ð7Þ

Here, hsl is the local heat-transfer coefficient of slush nitrogen, and hsub is the local heat-transfer coefficient of subcooled liquid nitrogen as obtained by the least squares method. For the 10 mm inner diameter pipe, where q = 10 kW/m2, it becomes the case that rh < 1 at flow velocities of within 1.0 m/s. In this flow velocity region, solid particles are sliding very slowly along the bottom of the pipe, and this is considered to be a cause of heat transfer deterioration. At a flow velocity of 1.0–2.0 m/s, the heat-transfer coefficient ratio does not display a large value

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10 Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

2 1.8

Wall Temperature Increase ΔTwall [K]

Local Heat Transfer Coefficient Ratio rh [-]

2.2

1.6 1.4 1.2 1 0.8 0.6 0.4

0

1

2

3

4

5

6

Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

9 8 7 6

q = 30 kW/m2

5 4 3

q = 10 kW/m2

2 1 0

Mean Velocity u mean [m /s]

0

1

2

3

4

5

6

Mean Velocity u mean [m/s]

(a) q = 10 kW/m2.

(a) Wall temperature increase Twall. Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

2 1.8

2.5

1.6 1.4 1.2 1 0.8 0.6 0.4

0

1

2

3

4

5

6

Mean Velocity u mean [m /s] 2

(b) q = 30 kW/m . Fig. 16. Local heat-transfer coefficient ratio and mean velocity of the slush nitrogen (D = 15 mm, q = 10, 30 kW/m2).

Bulk Temperature Increase ΔTbulk [K]

Local Heat Transfer Coefficient Ratio rh [-]

2.2 Subcooled 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

2.0

1.5 q = 30 kW/m2

1.0

q = 10 kW/m2

0.5

0.0

0

1

2

3

4

5

6

Mean Velocity u mean [m/s]

(b) Bulk temperature increase ΔTbulk. Fig. 17. Wall and bulk temperatures increase at the heat-transfer measurement point, and mean velocity (D = 15 mm, q = 10, 30 kW/m2).

rh = 0.72 at q = 30 kW/m2, such that differences due to heat flux become apparent, as in the case of the 10 mm inner diameter pipe. The minimum value for the heat-transfer coefficient ratio is smaller when the heat flux is greater, which is the opposite of the trend in the case of the 10 mm pipe. Fig. 17 presents the relationship between the mean flow velocity and the temperature increases (DTwall for wall and DTbulk for bulk) for the 15 mm inner diameter pipe. DTwall represents the difference between the wall temperature at the 705 mm location and the bulk temperature at the inlet of the heating section, while DTbulk represents the difference between the bulk temperatures at the 705 mm location and at the inlet of the heating section. The bulk temperature at the inlet of the heating section is the value measured by the temperature sensor at the upstream location. With respect to the increase in the wall temperature, although the DTwall figure for slush nitrogen in low-velocity flow is small compared with that for subcooled liquid nitrogen, both values become about the same for high-velocity flow. Given that the wall temperature sensor is placed at the bottom of the pipe, it is supposed that the influence of the melting of solid particles moving along the pipe bottom at low velocity results in a smaller temperature increase, but this is not clear. In high-velocity, pseudo -homogeneous flows, solid nitrogen particles move to the center of the pipe, with considerable liquid in the vicinity of the pipe wall,

and it is thought that the increase in the wall temperature DTwall is about the same as, or slightly greater than that of subcooled liquid nitrogen. On the other hand, with respect to the increase in bulk temperature, the DTbulk figure for slush nitrogen is smaller than for subcooled liquid nitrogen in all flow velocity regions. It can thus be understood that, relative to subcooled liquid nitrogen, thermal convection in the case of slush nitrogen does not extend to the pipe center. Also, as indicated by the arrows in Fig. 17 indicating lowvelocity flow at a low solid fraction, DTbulk rises more than in the case of a high solid fraction. That is, in the case of low velocity and low solid fraction, thermal convection extends to the center of the pipe, relative to the case of a high solid fraction. For a low solid fraction, since the turbulence suppression effect caused by the group of solid particles is less than for a high solid fraction, it is considered that thermal convection is promoted by turbulent mixing. Next, let us examine the correlation between the pressure-drop reduction ratio and the local heat-transfer coefficient reduction ratio. Fig. 18 illustrates the relationship between the pressure drop ratio (Eq. (3)) and the local heat-transfer coefficient ratio (Eq. (7)) for the 10 mm inner diameter pipe. For Fig. 18a and b, q = 10 and 30 kW/m2, respectively. The solid lines in the figure represent

573

2 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%]

r h = r dP

1.5 Pressure Drop Reduction

Increase in u mean (Decrease in r dP ) Increase in solid fraction

1

0.5 0.5

Increase in u mean (Increase in r dP )

1

Heat Transfer Coefficient Reduction

1.5

2

Pressure Drop Ratio r dP [-]

2 0-7 [wt%] 7-14 [wt%] 14-21 [wt%] 21-28 [wt%] 28-35 [wt%]

r h = r dP

1.5 Pressure Drop Reduction

Increase in u mean (Decrease in r dP ) Increase in solid fraction

1

Increase in u mean (Increase in r dP)

0.5 0.5

1

Heat Transfer Coefficient Reduction

1.5

2

Pressure Drop Ratio r dP [-]

(b) q = 30 kW/m2. Fig. 18. Correlation between the local heat-transfer coefficient and pressure drop ratios (D = 10 mm, q = 10, 30 kW/m2).

rh = rdP, that is, where the pressure drop ratio and heat-transfer coefficient ratio are equivalent, and in the case where rdP = 1 and rh = 1, the pressure drop and heat transfer coefficient for slush nitrogen are the same as those for subcooled liquid nitrogen. Regardless of heat flux, almost all of the data points lie on the lower side of the line representing rh = rdP, positioned in the region where rh < rdP, and it can be seen as a general trend that the heat-transfer coefficient ratio is smaller than the pressure drop ratio. In particular, it is often the case that even when rdP > 1, it still holds that rh < 1. In other words, even in the high-velocity flow region or in the case of a high solid fraction, where pressure drop reduction does not appear, the heat transfer coefficient of slush nitrogen is lower than that of subcooled liquid nitrogen. Turning our attention to the solid fraction, it can be seen that, regardless of heat flux, the greater the solid fraction, the greater the deviation from the solid line expressing rh = rdP. That is, the difference between the pressure drop ratio and the heat-transfer coefficient ratio becomes greater. The influence of solid particle interference becomes larger at higher solid fractions, but, as discussed previously, heat transfer takes place in the liquid layer near the pipe wall where there are few solid particles, and it is considered that there is almost no effect caused by the solid fraction. As a result, the pressure drop ratio tends to be higher at a high solid fraction as compared to a low solid fraction.

Local Heat Transfer Coefficient Ratio rh [-]

Local Heat Transfer Coefficient Ratio rh [-]

(a) q = 10 kW/m2.

At q = 30 kW/m2, compared to q = 10 kW/m2, particularly with solid fractions of 7–14 wt.%, the approach of the data points to the line expressing rh = rdP can be confirmed. That is, due to the large heat flux, it is thought that the heat transfer state of slush nitrogen with a low solid fraction approaches that of liquid nitrogen because of solid particle melting. Fig. 19 shows the relationship between the pressure drop ratio and the local heat-transfer coefficient ratio for the 15 mm inner diameter pipe. For Fig. 19a and b, q = 10 and 30 kW/m2, respectively. In the case of q = 10 kW/m2, the overall trend is basically the same as for the 10 mm pipe. Almost all of the data points are positioned in the region where rh < rdP, and it can be confirmed that the heat-transfer coefficient ratio is smaller than the pressure drop ratio. Also, although at solid fractions of 10–20 wt.%, the pressure drop ratio and the heat-transfer coefficient ratio are nearly the same values (near the line expressing rh = rdP), it can be seen that the difference between these ratios becomes greater for solid fractions of 30–40 wt.%. This trend is the same as for the 10 mm inner diameter pipe. On the other hand, at q = 30 kW/m2, the trend is somewhat different compared to the 10 mm pipe. In the region where pressure drop reduction does not occur (rdP > 1), the trend is the same as for the 10 mm pipe, but in the region where pressure drop reduction does occur (rdP < 1), the data points are generally above the line expressing rh = rdP (therefore rh > rdP), such that the 2 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

1.5

r h = r dP

Pressure Drop Reduction

Increase in u mean (Decrease in r dP )

1 Increase in solid fraction Increase in u mean (Increase in r dP )

0.5 0.5

1

Heat Transfer Coefficient Reduction

1.5

2

Pressure Drop Ratio r dP [-]

(a) q = 10 kW/m2. Local Heat Transfer Coefficient Ratio rh [-]

Local Heat Transfer Coefficient Ratio rh [-]

K. Ohira et al. / Cryogenics 51 (2011) 563–574

2 10-20 [wt%] 20-30 [wt%] 30-40 [wt%]

1.5

r h = r dP

Pressure Drop Reduction

Increase in u mean (Decrease in r dP )

1 Increase in solid fraction

0.5 0.5

Increase in u mean (Increase in r dP )

1

Heat Transfer Coefficient Reduction

1.5

2

Pressure Drop Ratio r dP [-]

(b) q = 30 kW/m2. Fig. 19. Correlation between the local heat-transfer coefficient and pressure drop ratios (D = 15 mm, q = 10, 30 kW/m2).

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pressure drop reduction ratio is greater than the local heat-transfer coefficient reduction ratio. From Figs. 18 and 19, irrespective of the pipe inner diameter, the degree of change in the pressure drop ratio is greater than that of the heat-transfer coefficient ratio. This indicates that the pressure drop ratio is more sensitive than the local heat-transfer coefficient ratio to changes in flow velocity and solid fraction. 4. Conclusions The pressure drop and heat transfer characteristics of slush nitrogen flows in horizontal, circular pipes with inner diameters of 10 mm and 15 mm were experimentally elucidated. In the case of the 10 mm inner diameter pipe, at flow velocities of 2.0–3.5 m/s and a solid fraction of within 14 wt.%, it was confirmed that pressure drop reduction occurs, in which the pressure drop for slush nitrogen becomes smaller than that for subcooled liquid nitrogen. In the case of the 15 mm pipe, at flow velocities of over 3.6 m/s and solid fractions of 10–30 wt.%, pressure drop reduction has also been confirmed [2]. That is, the flow velocity and solid fraction ranges where pressure drop reduction becomes apparent differ depending on the diameter of the pipe. Pressure drop reduction is an important phenomenon in the current context because it contributes to the reduction of required power for the pumped transport of slush fluids. The mechanism involved in pressure drop reduction, as previously reported [2], has to do with the movement of solid particles to the pipe center at flow velocities where pseudo-homogeneous flow is formed, thus creating a liquid layer near the pipe wall that contains few solid particles. The group of solid particles at the pipe center is thought to suppress the diffusion of turbulence generated within the liquid layer near the wall to the pipe center, as well as suppressing any further growth of turbulence. Also, in the flow velocity region where pressure drop reduction does not appear (over 3.5 m/s in the case of a pipe with an inner diameter of 10 mm), even when the flow velocity rises and pseudo-homogeneous flow occurs, the pressure drop of slush nitrogen tends to approach a level equivalent to approximately 1.1 times the pressure drop of subcooled liquid nitrogen. Consequently, even in a highvelocity flow region where pressure drop reduction would not become apparent in pump-driven pipeline transport, the required power for the transfer pump would not be substantially different from that associated with subcooled liquid nitrogen. With respect to heat transfer characteristics, it was found that, at flow velocity of over 2.0 m/s in the case of the 10 mm inner diameter pipe or at over 3.6 m/s in the case of the 15 mm inner diameter pipe, the local heat-transfer coefficient of slush nitrogen became lower than that of subcooled liquid nitrogen. The reason for this decrease is considered to be the same as the pressure drop reduction mechanism. That is, the group of solid particles having moved to the center of the pipe suppresses the diffusion of turbulence generated within the liquid layer near the wall to the pipe center, as well as suppressing any further growth of turbulence, and as a result, thermal convection towards the center of the pipe due to turbulent mixing is thought to be prevented.

There remain many aspects of the pressure drop reduction and heat-transfer deterioration phenomena that are insufficiently understood, and more detailed experimental work is required in the future. In particular, depending on the pipe diameter, the ranges of flow velocity and solid fraction where pressure drop reduction occurs are different, and it is anticipated that the introduction of a dimensionless parameter would enable the prediction of the flow velocity and solid fraction at which the reduction phenomenon would become apparent, even with differing pipe diameters. Acknowledgment This study was financially supported by JSPS under Grant-inAid for Scientific Research (B) No. 21360091. References [1] Ohira K. Liquid and slush hydrogen: its application and technology development. TEION KOGAKU 2006;41:61–72 [in Japanese]. [2] Ohira K. Pressure drop reduction phenomenon of slush nitrogen flow in a horizontal pipe. Cryogenics 2011;51:389–96; Ohira K. Pressure drop reduction phenomenon of slush nitrogen flow in a horizontal pipe. TEION KOGAKU 2010;45:484–92 [in Japanese]. [3] Ohira K, Nakamichi K, Furumoto H. Experimental study on magnetic refrigeration for the liquefaction of hydrogen. Adv Cryog Eng 2000;45: 1747–54. [4] Ohira K. Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube. Heat Transfer Asian Res 2001;30:542–60; Ohira K. Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube. Trans JSME Ser B 2000;66:174–81 [in Japanese]. [5] Ohira K. Study of production technology for slush hydrogen. Adv Cryog Eng 2004;49:56–63. [6] Ohira K. Study of nucleate boiling heat transfer to slush hydrogen and slush nitrogen. Heat Transfer Asian Res 2003;32:13–28; Ohira K. Study of nucleate boiling heat transfer to slush hydrogen and slush nitrogen. Trans JSME Ser B 1999;65:4055–62 [in Japanese]. [7] Ohira K, Nakamichi K. Development of a high-accuracy capacitance-type densimeter for slush hydrogen. JSME Int J Ser B 2000;43:162–70; Ohira K, Nakamichi K. Development of a high-accuracy capacitance-type densimeter for slush hydrogen. Trans JSME Ser B 1999;65:1438–45 [in Japanese]. [8] Ohira K, Nakamichi K, Kihara Y. Study on the development of a capacitancetype flowmeter for slush hydrogen. Cryogenics 2003;43:607–13. [9] Ohira K, Nakamichi K, Kihara Y. Development of a microwave-type densimeter for slush hydrogen. Cryogenics 2003;43:615–20. [10] Ohira K, Nakamichi K, Kihara Y. Development of a waveguide-type flowmeter using microwave method for slush hydrogen. JSME Int J Ser B 2005;69: 114–21; Ohira K, Nakamichi K, Kihara Y. Development of a waveguide-type flowmeter using microwave method for slush hydrogen. Trans JSME Ser B 2003;69: 1928–34 [in Japanese]. [11] Ohira K. Development of density and mass flow rate measurement technologies for slush hydrogen. Cryogenics 2004;44:59–68; Ohira K. Development of density and mass flow rate measurement technologies for slush hydrogen. TEION KOGAKU 2005;40:396–403 [in Japanese]. [12] Ohira K, Takahashi N, Nozawa M, Ishimoto J. Heat transfer and pressure drop reduction of slush nitrogen in a turbulent pipe flow. Proc 22nd ICEC 2008:353–8. [13] Sindt CF, Ludtke PR. Slush hydrogen flow characteristics and solid fraction upgrading. Adv Cryog Eng 1970;15:382–90. [14] Ikeuchi M, Machida A, Ono R, Matsuo K. Fundamental study of heat transfer characteristics of flowing slush nitrogen. TEION KOGAKU 2007;42:96–101 [in Japanese]. [15] Terada S. Pipeline transportation of solid–liquid mixture. Tokyo: Rikou Tosho; 1973. p. 75–77 [in Japanese].