# Experimental investigation on tetra-n-butyl-ammonium bromide clathrate hydrate slurry flows in a horizontal tube: flow behavior and its rheological model.

In the area of air conditioning, the tetra-n-butyl-ammonium bromide (TBAB) clathrate hydrate slurry (CHS) is a promising high-density
latent-heat carrying medium. In this article, flow properties of two
types of TBAB CHS were experimentally investigated in a horizontal tube
with parameters of pressure drop [DELTA]P, flow velocity of CHS V, and
solid mass fraction X. First, the Bingham rheological characteristics of
TBAB CHS were confirmed in the range of solid mass fraction of [chi]
[less than or equal to] 22% for type A and [chi] [less than or equal to]
25% for

type B, respectively. Then, the re-laminarization phenomenon and region of weakened flow resistance were found according to the variation of pressure drop [DELTA]P affected by the velocity and solid mass fraction X throughout the flow regions, including laminar, intermediate, and turbulent flows. The deduction of the critical flow velocity and region of entire laminar flow velocity were useful for latent-heat transportation applications. Finally, the criterial relations between Fanning friction factor f and Metzner-Reed Reynolds number [Re.sub.M] were obtained for laminar-flow and turbulent-flow regions, respectively.

Introduction

To date, many kinds of solid--liquid two-phase slurries have been used in the areas of thermal storage and latent-heat transportation, such as ice slurries, micro-emulsion slurries, micro-capsule slurries, and hydrate slurries. Those slurry-like mediums have some common advantages that satisfy the requirements defining a modern heat-transfer fluid, which means high heat capacity, ease of production, the possibility of thermal storage in the carrier itself, good fluidity, and lack of environmental adverse effects. Hereinto, the tetran-butyl-ammonium bromide (TBAB) clathrate hydrate slurry (CHS) was believed to be a promising high-density latent-heat carrying medium (Ogoshi et al. 2001; Takao et al. 2002; Tanasawa 2002; Hao et al. 2003; Obata et al. 2003; Ogoshi and Takao 2004).

The TBAB CHS is comprised of fine solid particles (TBAB clathrate hydrate crystal) and its aqueous solution. Its phase change could take place under the conditions of normal atmospheric pressure and a temperature range of 278-285 K (41-53.6[degrees]F), depending on the initial concentration of aqueous solution, which is much easier than some other slurries. Two types of TBAB hydrate crystal exist: type A with a prism shape and 193 kJ/kg (101.65 cal/lb) latent heat and type B with an unfixed shape and 205 kJ/kg (107.97 cal/lb) latent heat (Oyama et al. 2005; Shimada et al. 2005). Moreover, the diameters of crystal particles distribute in the range of [10.sup.-5] - [10.sup.-6] m (3.28 x [10.sup.-5] - [10.sup.-6] ft) (Darbouret et al. 2005b), and the particles hardly conglomerate with each other. Thus, it is easy to produce a TBAB CHS and keep its good fluidity. Many advantages make a TBAB CHS possibly applicable to thermal storage or latent-heat transportation systems to achieve energy savings.

[FIGURE 1 OMITTED]

For industrial applications, it is also necessary to further investigate other features, such as the flow mechanism and pressure drop properties. The TBAB CHS has been only studied for about 10 years in air-conditioning and latent-heat transportation areas. An analysis of the existing literature shows that the research on flow properties and heat transfer characteristics of TBAB CHSs is very limited. J FE Engineering Corporation (Japan) has been doing research works (Ogoshi and Takao 2004; Hayashi et al. 2000) that mainly focused on the applied technologies in the air-conditioning area but less on the basic flow properties. And the relationship between the friction coefficient and Metzner-Reed Reynolds number [Re.sub.M] was obtained experimentally. Darbouret et al. (2005a, 2005b) did more detailed research on pressure drop in pipe flow, and they drew the conclusion that TBAB CHSs satisfied the Bingham non-Newtonian model, but their works are limited in the laminar flow regime and lack the data of transition and turbulent regimes.

In this article, the TBAB CHS flow in horizontal tubes was experimentally researched. The rheological properties were determined for type A and type B clathrate hydrate slurries, corresponding to the initial aqueous solution concentration of 30.0 wt% and 17.3 wt%, respectively. It was analyzed systematically to clarify the regularity of how solid particles affect the flow regime and resistance. Some conclusions were compared to that of ice slurries (Metzner and Reed 1955; Knodel et al. 2000; Ayel et al. 2003; Lee et al. 2006).

Experimental studies

Experiment stand

The measurements were performed using the test stand shown in Figure 1. The whole system was composed of two main modules--the CHS production module and the circulation and test module. A flat-plate heat exchanger was used to produce the CHS by chilling the TBAB solution. The CHS was stored in a storage tank and circulated via a variable-volume pump. An electric heater was introduced to adjust the solid mass fraction X of the CHS, and a gear agitator could ensure the mixture to be homogeneous. The whole circulation pipeline was set up using PVC pipes. An exchangeable segment, with length 4 m (13.12 ft) and inside diameter D = 0.027 m (0.0886 ft), allowed the flow parameters to be measured and ensured the flow to be fully formed. The test segment was 2.8 m (9.186 ft) long. A transparent plexiglass tube was installed at the upstream section in order to observe flow state of the TBAB CHS.

The fundamental parameters, including pressure drop ([DELTA]P), flow velocity (V), and solid mass fraction ([chi]), could be measured accurately using the equipment listed in Table 1. The measured data were recorded by a data acquisition system.

Differential pressure measurements, used for determining flow resistance, were carried out by means of differential pressure meters with a proper measuring scale to actual pressure drop. The position for pressure acquisition was set at the side of the horizontal tube in order to facilitate automatic venting of impulse conduits, which were not insulated. The two differential pressure transducers were calibrated by the static-pressure water column method. The main measuring devices are listed in Table 1.

The determination of [chi] of the CHS is worth noting. Because the solid phase hardly conglomerates and stratifies lentamente, the CHS can be treated as a homogeneous fluid. In this work, the calculation of [chi] is based on the phase equilibrium temperature of the CHS, which was measured by a high-accuracy temperature sensor Pt 100 placed at the inlet and outlet of the test segment (Shimada et al. 2005; Song et al. 2009). The accuracy of this method was calibrated via calorimeter off-line measurement. In the meantime, density measurement of the CHS via a Coriolis mass flow meter could be supplementary to determine [chi] by the weighted average method. The mass flow of the Coriolis meter was calibrated by the timing and weighting method for the entire expected velocity range.

Procedures

There are two types of clathrate hydrate crystal, type A and type 13, produced from the TBAB aqueous solution of the initial concentration equal to 30.0 wt% and 17.3 wt%, respectively. First, the TBA13 CHS was produced through cooling the aqueous solution by the generation apparatus and accumulated in the storage tank. Second, the CHS was circulated through the arranged pipeline. The flow velocities and solid mass fraction of the CHS were controlled under the pre-arranged conditions in order to obtain the flow-related parameters. Last, the CHS was reproduced several times to fulfill the variation of measured parameters. In the whole process, type A and type B CHSs were kept under the same procedure.

Measurements were taken under controlled conditions to ensure the repeatability and coherence of the obtained results.

Measurement ranges of flow parameters

The measurement parameters were limited as follows.

(1) Test tube with inside diameter D = 0.027 m (0.0886 it).

(2) Mean flow velocities 0.2 < V < 1.7 [ms.sup.-1] (0.4474 < V < 3.803 mph), with the corresponding Reynolds number values in the range of 100 < [Re.sub.M] < 4000.

(3) Solid mass fraction 0 [less than or equal to] [chi] [less than or equal to] 22.2% for type A and 0 [less than or equal to] [chi] [less than or equal to] 25.0% for type B.

Results and discussion

The results are presented in details for type A CHSs. The general results include measurements for type A and type B in this work.

Effects of flow velocity

Figure 2 shows the values of the pressure drops as a function of mean velocity. By and large, the flow resistance increases monotonically with the mean velocity of the CHS. For each curve of constant [chi], there exists an obvious kneepoint, which is deemed as the transition point from laminar to turbulent because of the pressure drop rapidly increasing. With the increasing of [chi], the knee point moves toward higher velocity. It can be explained that the existing of solid particles is helpful to keep the laminar flow of the CHS. This trend is confirmed for both type A and type B CHSs.

Another phenomenon is that for each given solid mass fraction [chi], there exists one velocity region in which the pressure drops of the CHS are lower than that of the carrying fluid flow ([chi] = 0), referred to here as the region of weakened flow resistance. It was observed that those velocity regions do not stay immovable, but they tend to move toward higher velocities with the increasing of mass fraction [chi]. The reason is that the higher [chi] makes the CHS flow tend to keep a laminar state, even at higher velocities. In other words, the existence of solid particles induces the transition region move to the higher flow velocity region, which could be considered as re-laminarization phenomenon.

[FIGURE 2 OMITTED]

Effects of solid mass fraction

The values of the pressure drops as a function of solid mass fraction [chi] can represent those phenomenons mentioned above from another aspect, as shown in Figure 3. At a constant flow velocity of each curve, there exists a solid fraction region in which the pressure drop presents a common trend of valley to peak, meaning that the flow behavior returns to a laminar flow from turbulence with the increasing of solid mass fraction X. The existence of solids results in the re-laminarization phenomenon.

[FIGURE 3 OMITTED]

According to the region of weakened flow resistance and the re-laminarization phenomenon, one region of entire laminar flow velocity can be deduced. That is to say, if the carrying fluid ([chi] = 0) flows in the laminar region at one velocity, the CHS would definitely be in the laminar region under the same condition. The critical velocity could be calculated from the definition of critical Re of the TBAB solution. The region of entire laminar flow velocity is useful for its latent-heat transportation applications.

Linking all knee points at different flow velocities to a curve can obtain a transition flow curve, as shown in Figure 3. Above the transition curve, the CHS flows in the transition and turbulent states, and under the transition curve, it is in the laminar state.

Rheological model

The rheological properties of the TBAB CHS are studied by analyzing the relationship between the shear stress on tube wall [[tau].sub.w], in laminar region, where

[[tau].sub.w] = D[DELTA]P/(4L). (1)

Based on the functions, the flow curves [[tau].sub.w],(8V/D) are shown in Figure 4. Experimental data of different [chi] in laminar regions are fitted into line with slope and interception.

According to the description of the Bingham rheological model, the TBAB CHS, including types A and B, is verified as Bingham fluid in the range of 0 [less than or equal to] [chi] [less than or equal to] 22.2% and 0 [less than or equal to] [chi] [less than or equal to] 25.0%, respectively. That agrees with Darbouret et al. (2005b) and disagrees with Hayashi et al. (2000), who thought the CHS would meet the Ostwald de Waele rheologieal model in which [[tau].sub.0] = 0 and [[tau].sub.w] (8 V/D) shows non-linearity.

Flow transition

Like any other fluids, the flow type of the CHS is judged by the dimensionless Reynolds number. The general Reynolds number [Re.sub.M], which stands by the Metzner-Reed definition, is usually adopted for non-Newtonian fluids (Metzner and Reed 1955). That avails the comparison between Bingham non-Newtonian fluids and Newtonian fluids. [Re.sub.M] is de fined as

[Re.sub.M] = ([[rho].sub.s] D V)/[[mu].sub.e]. (2)

[FIGURE 4 OMITTED]

For the Bingham fluids, the effective viscosity [[mu].sub.e] can be defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

Based on the Buckingham equation, by ignoring its higher-order terms, it can be simplified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

Equations 3 and 4 can be derived as [[mu].sub.e] = D[[tau].sub.0]/6V + [mu], where [mu] and [[tau].sub.0] have been determined by the CHS flow experiment data.

Figure 5 shows the regularity of flow type transition from laminar to turbulent. Unlike Newtonian fluids, the critical [Re.sub.M] of the CHS flow is no longer a constant, but it is monotonously increasing with the increase of solid mass fraction [chi]. The experiments proved that the critical [Re.sub.M] is in the range of 2000-2300 for type A CHSs and 1800-2200 for type B CHSs. The criterion can be used to judge the flow type for the TBAB CHS in the range of 0 [less than or equal to] [chi] [less than or equal to] 22% for type A CHSs and 0 [less than or equal to] [chi] [less than or equal to] 25% for type B CHSs.

Correlations of flow resistance

The pressure drop of per unit length was transformed into Fanning friction factor f, which is based on the definition as

f = D[DELTA]P/4L/[rho][V.sup.2]/2 (5)

Figure 6 shows the logarithmic plot between f and [Re.sub.M]. It is obvious that they have the same correlations for type A and type B CHSs. In the laminar-flow region, the relationship off = 16/[Re.sub.M] is confirmed, which is same as the classical Newtonian fluids (f = 16/Re). In the turbulent-flow region, the experiment data are fitted into the following relation as

f = 0.1021[Re.sup.-0.2708.sub.M] (3,000 [less than or equal to] [Re.sub.M] [less than or equal to] 20, 000). (6)

One attraction is that the lower limit of [Re.sub.M] is higher than [Re.sub.Mc] for type A and type B CHSs because it is not a constant at different [chi], as mentioned in "Flow Transition" section. Based on the experimental data, the CHS flow basically goes into the turbulent region when [Re.sub.M] [greater than or equal to] 3000.

Conclusions

An analysis of the experimental results leads to the following conclusions.

(1) The first systematized investigation found the re-laminarization phenomenon and deduced the region of weakened flow resistance for CHS tube flows.

(2) For transport purposes, it is recommended to use CHSs with a certain range of solid mass fractions and to keep the flow in the region of entire laminar flow velocity.

(3) The rheological characteristics of the TBAB CHS flow obey the Bingham model for type A within 0 [less than or equal to] [chi] [less than or equal to] 22% and for type B within 0 [less than or equal to] [chi] [less than or equal to] 25%.

(4) The criteria for judgment of flow type transition and the correlations of f - [Re.sub.M] in laminar-flow and turbulent-flows regions bring conveniences to engineering applications.

DOI: 10.1080/10789669.2012.652796

Acknowledgment

This work has been financially supported by National Natural Science Foundation of China (No. U0634005).

Received July 12, 2011; accepted December 4, 2011

References

Ayel, V., O. Lottin, and H. Peergosszini. 2003. Rheology, flow behaviour and heat transfer of ice slurries: A review of the state of the art. International Journal of Refrigeration 26(1):95-107.

Darbouret, M., M. Cournil, and J.-M. Herri. 2005a. Rheological study of a hydrate slurry for air conditioning application. Fifth International Conference on Gas Hydrates, June 13-16, Trondheim, Norway.

Darbouret, M., M. Cournil, and J.-M Herri. 2005b. Rheological study of TBAB hydrate slurries as secondary two-phase refrigerants. International Journal of Refrigeration 28(5):663-71.

Hao, Y., C.Y. Zhou, D.Q. Liang, S.S. Fan, and Z.P. Feng. 2003. Recent research advances on hydrate slurry and ice slurry fur high density latent-heat transportation. Journal of Chemical Industry and Engineering (China) 54(suppl.):57-61.

Hayashi, K., S. Takao, H. Ogoshi, and S. Matsumoto. 2000. Research and development on high-density cold latent-heat medium transportation technology. IEA Annex 10, Phase Change Materials and Chemical Reactions for Thermal Energy Storage, Tsu, Japan.

Knodel, B.D., D.M. France, U. Choi, and M. Wamsganss. 2000. Heat transfer and pressure drop in ice-water slurries. Applied Thermal Engineering 20(7):671-85.

Lee, D.W., E.S. Yoon, M.C. Joo, and A. Sharma. 2006. Heat transfer characteristics of the ice slurry at melting process in a tube flow. International Journal of Refrigeration 29(3):451-5.

Metzner, A.B., and J.C. Reed. 1955. Flow of non-Newtonian fluids--correlation of the laminar, transition, and turbulent-flow regions. A.I.Ch.E. Journal 4(1):434-40.

Obata, Y., N. Masuda, K. Joo, and A. Katoh. 2003. Hydrate slurry air conditioning system, advanced technologies towards new era of energy industries. NKK Technical Review 109-13.

Ogoshi, H., and S. Takao. 2004. Air-conditioning system using clathrate hydrate slurry. JFE Technical Report, pp. 1-5.

Ogoshi, H., S. Takao, and S. Fukushima. 2001. Method for transporting cold latent heat and system. US Patent 6,237, 346.

Oyama, It., W. Shimada, T. Ebinuma, Y. Kamata, S. Takeya, T. Uchida, J. Nagano, and H. Narita. 2005. Phase diagram, latant heat, and specific heat of TBAB semiclathrate hydrate crystals. Fluid Phase Equilibia 234: 131-35.

Shimada, W., T. Ebinuma, H. Oyama, Y. Kamata, and H. Narita. 2005. Free-growth forms and growth kinetics of tetra-nbutyl-ammonium bromide semi-clathrate hydrate crystals. Journal o.f Crystal Growth 274:246-50.

Song, W.J., R. Xiao, C. Huang, S.H. He, K. J. Dong, and Z.P. Zeng. 2009. Experimental investigation on TBAB clathrate hydrate slurry flows in a horizontal tube: Forced convective heat transfer behaviors. International Journal of Refrigeration 32(7):1801-7.

Takao, S., H. Ogoshi, and S. Matsumoto. 2002. Air conditioning and thermal storage system using clathrate hydrate slurry. US Patent 0,083,720 A1.

Tanasawa, I., and S. Takao. 2002. Clathrate hydrate slurry of tetra-n-butylammonium bromide as a cold-storage material. Proceedings of the 4th International Conference on Gas Hydrate, Yokohama, Japan, May 19-23.

* Corresponding author e-mail: fengzp@ms.giec.ac.cn

Wenji Song, Rui Xiao, and Zi-ping Feng *

Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Key Laboratory of Renewable Energy and Gas Hydrate, Guangzhou 510640, China

Wenji Song, PhO, is Associate Professor. Rui Xiao, PhD, is Associate Professor. Zi-ping Feng, PhD, is Professor.

type B, respectively. Then, the re-laminarization phenomenon and region of weakened flow resistance were found according to the variation of pressure drop [DELTA]P affected by the velocity and solid mass fraction X throughout the flow regions, including laminar, intermediate, and turbulent flows. The deduction of the critical flow velocity and region of entire laminar flow velocity were useful for latent-heat transportation applications. Finally, the criterial relations between Fanning friction factor f and Metzner-Reed Reynolds number [Re.sub.M] were obtained for laminar-flow and turbulent-flow regions, respectively.

Introduction

To date, many kinds of solid--liquid two-phase slurries have been used in the areas of thermal storage and latent-heat transportation, such as ice slurries, micro-emulsion slurries, micro-capsule slurries, and hydrate slurries. Those slurry-like mediums have some common advantages that satisfy the requirements defining a modern heat-transfer fluid, which means high heat capacity, ease of production, the possibility of thermal storage in the carrier itself, good fluidity, and lack of environmental adverse effects. Hereinto, the tetran-butyl-ammonium bromide (TBAB) clathrate hydrate slurry (CHS) was believed to be a promising high-density latent-heat carrying medium (Ogoshi et al. 2001; Takao et al. 2002; Tanasawa 2002; Hao et al. 2003; Obata et al. 2003; Ogoshi and Takao 2004).

The TBAB CHS is comprised of fine solid particles (TBAB clathrate hydrate crystal) and its aqueous solution. Its phase change could take place under the conditions of normal atmospheric pressure and a temperature range of 278-285 K (41-53.6[degrees]F), depending on the initial concentration of aqueous solution, which is much easier than some other slurries. Two types of TBAB hydrate crystal exist: type A with a prism shape and 193 kJ/kg (101.65 cal/lb) latent heat and type B with an unfixed shape and 205 kJ/kg (107.97 cal/lb) latent heat (Oyama et al. 2005; Shimada et al. 2005). Moreover, the diameters of crystal particles distribute in the range of [10.sup.-5] - [10.sup.-6] m (3.28 x [10.sup.-5] - [10.sup.-6] ft) (Darbouret et al. 2005b), and the particles hardly conglomerate with each other. Thus, it is easy to produce a TBAB CHS and keep its good fluidity. Many advantages make a TBAB CHS possibly applicable to thermal storage or latent-heat transportation systems to achieve energy savings.

[FIGURE 1 OMITTED]

For industrial applications, it is also necessary to further investigate other features, such as the flow mechanism and pressure drop properties. The TBAB CHS has been only studied for about 10 years in air-conditioning and latent-heat transportation areas. An analysis of the existing literature shows that the research on flow properties and heat transfer characteristics of TBAB CHSs is very limited. J FE Engineering Corporation (Japan) has been doing research works (Ogoshi and Takao 2004; Hayashi et al. 2000) that mainly focused on the applied technologies in the air-conditioning area but less on the basic flow properties. And the relationship between the friction coefficient and Metzner-Reed Reynolds number [Re.sub.M] was obtained experimentally. Darbouret et al. (2005a, 2005b) did more detailed research on pressure drop in pipe flow, and they drew the conclusion that TBAB CHSs satisfied the Bingham non-Newtonian model, but their works are limited in the laminar flow regime and lack the data of transition and turbulent regimes.

In this article, the TBAB CHS flow in horizontal tubes was experimentally researched. The rheological properties were determined for type A and type B clathrate hydrate slurries, corresponding to the initial aqueous solution concentration of 30.0 wt% and 17.3 wt%, respectively. It was analyzed systematically to clarify the regularity of how solid particles affect the flow regime and resistance. Some conclusions were compared to that of ice slurries (Metzner and Reed 1955; Knodel et al. 2000; Ayel et al. 2003; Lee et al. 2006).

Experimental studies

Experiment stand

The measurements were performed using the test stand shown in Figure 1. The whole system was composed of two main modules--the CHS production module and the circulation and test module. A flat-plate heat exchanger was used to produce the CHS by chilling the TBAB solution. The CHS was stored in a storage tank and circulated via a variable-volume pump. An electric heater was introduced to adjust the solid mass fraction X of the CHS, and a gear agitator could ensure the mixture to be homogeneous. The whole circulation pipeline was set up using PVC pipes. An exchangeable segment, with length 4 m (13.12 ft) and inside diameter D = 0.027 m (0.0886 ft), allowed the flow parameters to be measured and ensured the flow to be fully formed. The test segment was 2.8 m (9.186 ft) long. A transparent plexiglass tube was installed at the upstream section in order to observe flow state of the TBAB CHS.

The fundamental parameters, including pressure drop ([DELTA]P), flow velocity (V), and solid mass fraction ([chi]), could be measured accurately using the equipment listed in Table 1. The measured data were recorded by a data acquisition system.

Differential pressure measurements, used for determining flow resistance, were carried out by means of differential pressure meters with a proper measuring scale to actual pressure drop. The position for pressure acquisition was set at the side of the horizontal tube in order to facilitate automatic venting of impulse conduits, which were not insulated. The two differential pressure transducers were calibrated by the static-pressure water column method. The main measuring devices are listed in Table 1.

The determination of [chi] of the CHS is worth noting. Because the solid phase hardly conglomerates and stratifies lentamente, the CHS can be treated as a homogeneous fluid. In this work, the calculation of [chi] is based on the phase equilibrium temperature of the CHS, which was measured by a high-accuracy temperature sensor Pt 100 placed at the inlet and outlet of the test segment (Shimada et al. 2005; Song et al. 2009). The accuracy of this method was calibrated via calorimeter off-line measurement. In the meantime, density measurement of the CHS via a Coriolis mass flow meter could be supplementary to determine [chi] by the weighted average method. The mass flow of the Coriolis meter was calibrated by the timing and weighting method for the entire expected velocity range.

Procedures

There are two types of clathrate hydrate crystal, type A and type 13, produced from the TBAB aqueous solution of the initial concentration equal to 30.0 wt% and 17.3 wt%, respectively. First, the TBA13 CHS was produced through cooling the aqueous solution by the generation apparatus and accumulated in the storage tank. Second, the CHS was circulated through the arranged pipeline. The flow velocities and solid mass fraction of the CHS were controlled under the pre-arranged conditions in order to obtain the flow-related parameters. Last, the CHS was reproduced several times to fulfill the variation of measured parameters. In the whole process, type A and type B CHSs were kept under the same procedure.

Measurements were taken under controlled conditions to ensure the repeatability and coherence of the obtained results.

Measurement ranges of flow parameters

The measurement parameters were limited as follows.

(1) Test tube with inside diameter D = 0.027 m (0.0886 it).

(2) Mean flow velocities 0.2 < V < 1.7 [ms.sup.-1] (0.4474 < V < 3.803 mph), with the corresponding Reynolds number values in the range of 100 < [Re.sub.M] < 4000.

(3) Solid mass fraction 0 [less than or equal to] [chi] [less than or equal to] 22.2% for type A and 0 [less than or equal to] [chi] [less than or equal to] 25.0% for type B.

Results and discussion

The results are presented in details for type A CHSs. The general results include measurements for type A and type B in this work.

Effects of flow velocity

Figure 2 shows the values of the pressure drops as a function of mean velocity. By and large, the flow resistance increases monotonically with the mean velocity of the CHS. For each curve of constant [chi], there exists an obvious kneepoint, which is deemed as the transition point from laminar to turbulent because of the pressure drop rapidly increasing. With the increasing of [chi], the knee point moves toward higher velocity. It can be explained that the existing of solid particles is helpful to keep the laminar flow of the CHS. This trend is confirmed for both type A and type B CHSs.

Another phenomenon is that for each given solid mass fraction [chi], there exists one velocity region in which the pressure drops of the CHS are lower than that of the carrying fluid flow ([chi] = 0), referred to here as the region of weakened flow resistance. It was observed that those velocity regions do not stay immovable, but they tend to move toward higher velocities with the increasing of mass fraction [chi]. The reason is that the higher [chi] makes the CHS flow tend to keep a laminar state, even at higher velocities. In other words, the existence of solid particles induces the transition region move to the higher flow velocity region, which could be considered as re-laminarization phenomenon.

[FIGURE 2 OMITTED]

Effects of solid mass fraction

The values of the pressure drops as a function of solid mass fraction [chi] can represent those phenomenons mentioned above from another aspect, as shown in Figure 3. At a constant flow velocity of each curve, there exists a solid fraction region in which the pressure drop presents a common trend of valley to peak, meaning that the flow behavior returns to a laminar flow from turbulence with the increasing of solid mass fraction X. The existence of solids results in the re-laminarization phenomenon.

[FIGURE 3 OMITTED]

According to the region of weakened flow resistance and the re-laminarization phenomenon, one region of entire laminar flow velocity can be deduced. That is to say, if the carrying fluid ([chi] = 0) flows in the laminar region at one velocity, the CHS would definitely be in the laminar region under the same condition. The critical velocity could be calculated from the definition of critical Re of the TBAB solution. The region of entire laminar flow velocity is useful for its latent-heat transportation applications.

Linking all knee points at different flow velocities to a curve can obtain a transition flow curve, as shown in Figure 3. Above the transition curve, the CHS flows in the transition and turbulent states, and under the transition curve, it is in the laminar state.

Rheological model

The rheological properties of the TBAB CHS are studied by analyzing the relationship between the shear stress on tube wall [[tau].sub.w], in laminar region, where

[[tau].sub.w] = D[DELTA]P/(4L). (1)

Based on the functions, the flow curves [[tau].sub.w],(8V/D) are shown in Figure 4. Experimental data of different [chi] in laminar regions are fitted into line with slope and interception.

According to the description of the Bingham rheological model, the TBAB CHS, including types A and B, is verified as Bingham fluid in the range of 0 [less than or equal to] [chi] [less than or equal to] 22.2% and 0 [less than or equal to] [chi] [less than or equal to] 25.0%, respectively. That agrees with Darbouret et al. (2005b) and disagrees with Hayashi et al. (2000), who thought the CHS would meet the Ostwald de Waele rheologieal model in which [[tau].sub.0] = 0 and [[tau].sub.w] (8 V/D) shows non-linearity.

Flow transition

Like any other fluids, the flow type of the CHS is judged by the dimensionless Reynolds number. The general Reynolds number [Re.sub.M], which stands by the Metzner-Reed definition, is usually adopted for non-Newtonian fluids (Metzner and Reed 1955). That avails the comparison between Bingham non-Newtonian fluids and Newtonian fluids. [Re.sub.M] is de fined as

[Re.sub.M] = ([[rho].sub.s] D V)/[[mu].sub.e]. (2)

[FIGURE 4 OMITTED]

For the Bingham fluids, the effective viscosity [[mu].sub.e] can be defined as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

Based on the Buckingham equation, by ignoring its higher-order terms, it can be simplified as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

Equations 3 and 4 can be derived as [[mu].sub.e] = D[[tau].sub.0]/6V + [mu], where [mu] and [[tau].sub.0] have been determined by the CHS flow experiment data.

Figure 5 shows the regularity of flow type transition from laminar to turbulent. Unlike Newtonian fluids, the critical [Re.sub.M] of the CHS flow is no longer a constant, but it is monotonously increasing with the increase of solid mass fraction [chi]. The experiments proved that the critical [Re.sub.M] is in the range of 2000-2300 for type A CHSs and 1800-2200 for type B CHSs. The criterion can be used to judge the flow type for the TBAB CHS in the range of 0 [less than or equal to] [chi] [less than or equal to] 22% for type A CHSs and 0 [less than or equal to] [chi] [less than or equal to] 25% for type B CHSs.

Correlations of flow resistance

The pressure drop of per unit length was transformed into Fanning friction factor f, which is based on the definition as

f = D[DELTA]P/4L/[rho][V.sup.2]/2 (5)

Figure 6 shows the logarithmic plot between f and [Re.sub.M]. It is obvious that they have the same correlations for type A and type B CHSs. In the laminar-flow region, the relationship off = 16/[Re.sub.M] is confirmed, which is same as the classical Newtonian fluids (f = 16/Re). In the turbulent-flow region, the experiment data are fitted into the following relation as

f = 0.1021[Re.sup.-0.2708.sub.M] (3,000 [less than or equal to] [Re.sub.M] [less than or equal to] 20, 000). (6)

One attraction is that the lower limit of [Re.sub.M] is higher than [Re.sub.Mc] for type A and type B CHSs because it is not a constant at different [chi], as mentioned in "Flow Transition" section. Based on the experimental data, the CHS flow basically goes into the turbulent region when [Re.sub.M] [greater than or equal to] 3000.

Conclusions

An analysis of the experimental results leads to the following conclusions.

(1) The first systematized investigation found the re-laminarization phenomenon and deduced the region of weakened flow resistance for CHS tube flows.

(2) For transport purposes, it is recommended to use CHSs with a certain range of solid mass fractions and to keep the flow in the region of entire laminar flow velocity.

(3) The rheological characteristics of the TBAB CHS flow obey the Bingham model for type A within 0 [less than or equal to] [chi] [less than or equal to] 22% and for type B within 0 [less than or equal to] [chi] [less than or equal to] 25%.

(4) The criteria for judgment of flow type transition and the correlations of f - [Re.sub.M] in laminar-flow and turbulent-flows regions bring conveniences to engineering applications.

Nomenclature D = inside diameter of tube f = Fanning friction factor L = length of tube [Re.sub.M] = Metzner-Reed Reynolds Number V = flow velocity Greek symbols [Y.sub.w] = shear rate on tube wall [DELTA]P = pressure drop [eta] = plastic viscosity of clathrate hydrate slurry [[mu].sub.e] = effective viscosity of clathrate hydrate slurry [[rho].sub.s] = density of clathrate hydrate slurry [[tau].sub.0] = yield shear stress of clathrate hydrate slurry [[tau].sub.w] = shear stress on tube wall [chi] = solid mass fraction

DOI: 10.1080/10789669.2012.652796

Acknowledgment

This work has been financially supported by National Natural Science Foundation of China (No. U0634005).

Received July 12, 2011; accepted December 4, 2011

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* Corresponding author e-mail: fengzp@ms.giec.ac.cn

Wenji Song, Rui Xiao, and Zi-ping Feng *

Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Key Laboratory of Renewable Energy and Gas Hydrate, Guangzhou 510640, China

Wenji Song, PhO, is Associate Professor. Rui Xiao, PhD, is Associate Professor. Zi-ping Feng, PhD, is Professor.

Table 1. The most important measuring devices. Device Type Coriolis mass flow DFJD ZLJC7 meter Differential pressure SYSTEM-3351 transducers SYSTEM-3351 Temperature sensors Mantled Pt100 [PHI]5 mm Data acquisition Agilent 34970A system Device Measuring range Coriolis mass flow 0-7000 kg * [h.sup.-1] (0-15,432.34 lb/hr) meter 0-1.6 g * [cm.sup.-3] (0-0.0578 Win.) Differential pressure 0-2 kPa (0-41.76 bf/[ft.sup.2]) transducers 0-60 kPa (0-1252.8 bf/[ft.sup.2]) Temperature sensors -200-+500[degrees]C (-328-+932[degrees]F) Data acquisition / system Device Accuracy Coriolis mass flow [+ or -]0.25% meter Differential pressure 0.2 FS transducers 0.2 FS Temperature sensors [+ or -]0.15[degrees]C (32.3[degrees]F) Data acquisition / system

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Author: | Song, Wenji; Xiao, Rui; Feng, Zi-ping |
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Publication: | HVAC & R Research |

Date: | Jun 1, 2012 |

Words: | 3367 |

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