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Performance of the cold transport system utilizing evaporation-freezing phenomena with a cold trap
International Journal of Refrigeration 27 (2004) 255–263 www.elsevier.com/locate/ijrefrig
Performance of the cold transport system utilizing evaporation-freezing phenomena with a cold trap Isao Satoh*, Takushi Saito, Kazumoto Shima Department of Mechanical and Control Engineering, Tokyo Institute of Technology, 12-1, O-okayama 2, Meguro-ku, Tokyo 152-8552, Japan Received 25 August 2003; received in revised form 30 September 2003; accepted 30 September 2003
Abstract This paper dealt with the performance of a novel cold transport system for the waste cold from the gasification process of Liquefied Natural Gas (LNG), which has been proposed by one of the authors. The system consists of an evaporator, a cold trap, and a pipeline between them, and the LNG cold poured into the cold trap is transported to the evaporator as a flow of low-pressure water vapor. In this study, cold transport rate of a small-scale system was experimentally examined under various conditions, and the efficiency of cold transport was discussed. The results clearly showed that, as suggested by a theoretical relation based on the pressure drop due to vapor flow in the pipeline, cold transport rate is affected both by the pressure difference between the evaporator and cold trap, and by the length, diameter and friction factor of the pipeline. However it was also shown that the transport rate is hardly influenced by the temperature of pipeline wall. Based on the theoretical relation and the experimental results obtained herein, a guideline for designing the cold transport system was derived. # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Air conditioning; Process; LNG; Mass transfer; Evaporation
Performance d’un syste`me de transport de froid faisant appel a` des phe´nome`nes d’e´vaporation/conge´lation et un pie`ge a` basse tempe´rature Mots cle´s : Conditionnement d’air ; Proce´de´ ; GNL ; Transfert de masse ; E´vaporateur
1. Introduction Most energy-consuming countries including Japan use Liquefied Natural Gas (LNG) as a kind of fossil fuel, and the consumption of LNG tends to increase because influence on the environment due to the combustion of natural gas, which mainly consists of methane,
* Corresponding author. Tel.: +81-3-5734-3238; fax: +813-5734-3917. E-mail addresses: [email protected]. 0140-7007/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2003.09.007
is smaller than other fossil fuels. As the consumption of LNG increases, it is required to utilize the waste cold, which is exhausted in the gasification process, of LNG effectively. For example, 54.1 million metric ton of LNG has been imported into Japan in 2000 [1], and gasification of this LNG produces 2.761016 J of waste cold at quite low temperature (about 160 C), but only a part of this cold has been utilized effectively so far. For the present, the most typical use of the waste cold of LNG gasification is power augmentation of gas/ steam combined-cycle power plants due to inlet-air cooling. For example, Yoshida et al. [2] demonstrated
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Nomenclature A ci D kf L Le Lf mv pe pw p Qc t Te Tf Tg Ti
area of heat transfer surface in the cold trap (m2) specific heat of frost (J kg1K1) inner diameter of the pipeline (see Fig. 1) (m) thermal conductivity of frost (W m1 K1) length of the pipeline (see Fig. 1) (m) latent heat due to evaporation of PCM (J kg1) latent heat due to freezing of PCM, (J kg1) mass flow rate of PCM vapor (kg s1) pressure in the evaporator (see Fig. 1) (Pa) pressure in the cold trap (see Fig. 1) (Pa) pressure drop in the pipeline (see Fig. 1) (Pa) the maximum transportation rate of cold (see Fig. 1) (W) time of cold transport (s) temperature of PCM in the evaporator ( C) surface temperature of frost in the cold trap ( C) gasification temperature of LNG ( C) freezing temperature of PCM ( C)
Greek letters thickness of frost layer (m) l friction coefficient of the pipeline, dimensionless average density of the vapor in the pipeline (kg m3) f density of frost layer (kg m3)
the downtown area for air-conditioning during the summer season. However LNG cold has not been utilized for this purpose so far. This is because the method for transporting the LNG cold has not been well developed. Generally, it is often utilized the sensible/latent heat of heat transfer media for transporting the thermal energy. But the temperature of cold produced in the LNG gasification is much too low to store it in an ordinary heat transfer medium, such as water or fluorocarbons, as it is, and thus the transport of LNG cold by using an ordinary heat transfer medium results in waste of exergy in part. Moreover, conventional cold transport systems require additional power input for pumping the heat transfer media, and this pumping power increases evidently with elongation of transport distance. In order to overcome the weak points of conventional cold transport systems, and to utilize the LNG cold for air-conditioning in the downtown area as well, one of the authors has proposed a novel cold transport system for the waste cold from the gasification process of LNG [6]. Construction of this system and principle of cold transport with this system are summarized in the next section, but it should be noted that this system transports the cold from the gasification process of LNG to the downtown area as ‘‘vapor’’ of a phase change material (PCM), and thus exergy of the cold from LNG is utilized as a driving force for the vapor flow; no additional power is required for transporting the cold. The authors [7] have examined the feasibility of this system, and it was shown that the cold can actually be transported with this system. After that, the evaporation-freezing of water occurring in an evaporator (cold generator) of this system have been examined [8]. Following up these studies, cold transport rate and efficiency of this system were experimentally examined under various conditions, and a guideline for designing the cold transport system was derived in this paper.
2. Cold transport system utilizing evaporation-freeizng with a cold trap that the relative increase in output power of a LNGfueled gas turbine power plant having an output of 243 MW7 units amounts to 7.1% by adopting the inlet-air cooling system using the LNG cold during the summer season in Japan. Similar studies have been reported by Song et al. [3] and Kim et al. [4], and feasibility of the inlet-air cooling was demonstrated under various operation conditions. Other applications, e.g. cold warehouses, freeze-drying of foods, and dry ice making, of cold from LNG gasification are also examined from the practical point of view [5]. In addition to these, there is a great demand for cold in the downtown area far from the LNG gasification plants; a large amount of cold is consumed in
The novel transport system for the waste cold from the LNG gasification process is schematically shown in Fig. 1. This system consists of an evaporator, a cold trap, and a pipeline between them. In the evaporator placed in the downtown area, a PCM is cooled by its evaporation and finally freezes. The frozen PCM contains the cold at its freezing temperature, which can be used for air conditioning etc. after the evaporationfreezing process. The vapor from the evaporator flows through the pipeline, and is trapped on a heat transfer surface in the cold trap cooled by the evaporating LNG, the temperature of which is lower than the freezing temperature of the PCM.
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3. Experimental apparatus and procedure
Fig. 1. A novel transport system for waste cold from LNG gasification process.
Performance of this system would be dominated by the pressure difference between the evaporator and cold trap. In other words, transportation rate of the cold with this system is limited by the condition under which the pressure drop p in the pipeline due to the vapor flow is balanced against the pressure difference (pepw) between the evaporator and cold trap. Namely, if the pressure drop in the pipeline is evaluated by using an ordinary friction coefficient l, the maximum transportation rate Qc of cold could be estimated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðpe pw Þ2 D 5 ; ð1Þ Qc ¼ L e 8lL where Le the latent heat due to evaporation of the PCM, D and L the diameter and length of the pipeline, and the average density of the vapor in the pipeline. Ideally the pressure pe in the evaporator is the saturate pressure of PCM at its freezing temperature, and the pressure pw in the cold trap is that at the surface temperature of frost generated on the heat transfer surface in the cold trap. This suggests that the cold transport rate of this system is influenced by the temperatures of PCM in the evaporator and cold trap, and by the conditions, e.g. length, diameter, and/or friction factor, of the pipeline between them. On the other hand, neglecting the cold release from the surface of system components, and neglecting the cold consumed for cooling the frost grown on a heat transfer surface in the cold trap, efficiency of cold transport, that is the ratio of cold transferred to the evaporator to that consumed at the cold trap, could be estimated as
: Le mv Le ; : ¼ ðLe þ Lf Þmv Le þ Lf
A small scale cold transport system was constructed and the transport rate of cold was measured with this system. Water was used as the PCM for this system. The schematic diagram of this system was shown in Fig. 2. As shown in this figure, the system consists of an evaporator, which is a thermally insulated glass flask containing pure water, a cold trap, a pipeline between them, a vacuum pump for evacuating the system, and a data acquisition system. Initial weight of water in the evaporator was set at 500 1 g. A heat transfer surface in the cold trap was cooled by evaporating liquefied nitrogen (LN2) instead of LNG, for safety reasons. In order to examine the effects of the pipeline condition on the cold transport rate, tubes shown in Table 1 were used as the pipeline between the evaporator and cold trap. On the copper tube, an electric heater is installed so as to heat up the pipeline wall. By using the heated pipeline, cold transport with cold release at the pipeline wall was examined. The amount of cold transferred to the evaporator was evaluated from the change of water temperature in the evaporator, and the cold consumed in the cold trap was estimated from the flow rate of LN2 poured into the heat transfer surface in the cold trap. In order to evaluate the amount of cold transferred to the evaporator by using the change of water temperature, water in the evaporator was maintained at a temperature higher than the freezing temperature (=0 C) throughout the experiment. Near the heat transfer surface in the cold trap, thermocouples were installed in order to measure the temperature profile within the frost layer generated on the heat transfer surface. Before the experiment, air/vapor in the system was evacuated by using a vacuum pump, and thus the system was filled with water vapor from the evaporator. After that, a valve between the cold trap and the vacuum pump and that between the cold trap and the evaporator were closed, and the heat transfer surface was cooled by LN2 so as to lower the pressure in the cold trap. And then the valve between the cold trap and the evaporator was opened, and data acquisition was started.
ð2Þ
where Lf the latent heat due to freezing of the PCM, and mv the mass flow rate of PCM vapor from the evaporator to the cold trap. This relation suggests that the efficiency is hardly affected by the system conditions, and that the efficiency for the ideal condition is about 88% if water was used as the PCM.
Fig. 2. Experimental apparatus.
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Table 1 Pipelines used in the experiment and the efficiency of cold transport Pipeline length L (m)
Pipeline diameter D (mm)
Material
Pipeline wall temp.
Efficiency (%)
0.5 1.0 0.5 1.0 1.0 1.0
6 6 12 6 6 6
Rubber Rubber Rubber Copper Copper Copper
Room temp. Room temp. Room temp. Room temp. Heated at 40–50 C Heated at 80–90 C
56 65 53 66 71 60
Fig. 3. Typical change of water temperature in the evaporator during the cold transport.
4. Results and discussion 4.1. Cold transport rate and effect of frost generation in the cold trap
Fig. 4. Temperature in the frost layer growing on a heat transfer surface in the cold trap.
First of all, characteristics of the cold transport of this system were examined. Fig. 3 shows the typical change of water temperature in the evaporator as a function of time elapsed. As shown in this figure, the water in the evaporator is cooled due to its evaporation, but the cooling rate dTe/dt, i.e. rate of cold transport Qc from the cold trap to the evaporator, decreases with time. This is because the pressure difference between the evaporator and cold trap decreases with time elapsed. Namely, saturate pressure of water in the evaporator tends to decrease with time because of lowering temperature of water. On the contrary, pressure in the cold trap tends to increase with time, since surface temperature of frost grown on a heat transfer surface in the cold trap rises due to thermal resistance of the frost layer. Under our experimental conditions, however, the latter effect is negligible, and the cold transport rate is mainly dominated by the water temperature in the evaporator. Fig. 4 shows the temperature profile in the frost layer growing on a heat transfer surface in the cold trap. As shown in this figure, temperature measured with a thermocouple installed 0.5 mm apart from the heat transfer surface in the cold trap decreases suddenly at about 15 min after the operation. This means that the frost
layer growing on the heat transfer surface reaches the thermocouple. At that time, i.e. when the thickness of the frost layer became 0.5 mm, temperature difference Tf between inner- and outer-surface of the frost layer was about 10 K, and cold transport rate Qc was about 10 W. From these results, one can estimate the apparent thermal conductivity kf of the frost layer as kf
Qc 10 0:0005 ¼ ¼ 0:083 Wm1 K1 DTf A 10 6 103
Where A is the area of heat transfer surface in the cold trap, and is about 6103 m2 (O.D=6 mm, length=320 mm). Namely, the apparent thermal conductivity kf of the frost is the value in the order of 0.1 W m1 K1, and therefore the surface temperature rise of frost layer would not be neglected. However temperature rise due to the thermal resistance of frost layer affects little the pressure in the cold trap, because, as shown in Fig. 5, saturate pressure of ice in low temperature range is quite low (order of 103 Pa at 100 C) compared to the pressure (several 100 Pa) in the evaporator where evaporation-freezing of water occurs at around 0 C. Fig. 5 suggests that the effect of thermal resistance of frost
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Fig. 5. Saturate pressure of ice.
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Fig. 7. Cold transport rate against the pipeline diameter.
Fig. 8. Effect of pipeline materials, i.e. friction factor, on the cold transport rate. Fig. 6. Cold transport rate against the pipeline length.
layer on the pressure difference, i.e. cold transport rate, between the evaporator and cold trap would be actualized only when the surface temperature of frost exceeds about 30 C. 4.2. Effect of pipeline conditions on the cold transport rate Then, the effect of pipeline conditions on the cold transport rate of this system was examined. Fig. 6 shows the cold transport rate Qc measured with pipelines of different length. In this figure, the cold transport rates were plotted against the pipeline length L. One can easily observe from this figure that the cold transport rate of this system is inversely in proportion to the square root of the pipeline length (Qc/L0.5), as suggested by the theoretical estimation Eq. (1). The cold transport rate for different pipeline diameters are shown in Fig. 7. The cold transport rate increases with increasing the pipeline diameter, and is affected more sensitively by the pipeline diameter than
by the length. Fig. 7 shows that Qc is in proportion with D1.9, while the theoretical estimation, Eq. (1) suggests Qc/D2.5. This discrepancy could be explained by the fact that the experimental setup used in this study has a valve on the pipeline, and that pressure drop due to the valve would not be negligibly small in comparison with that due to the pipeline. The effect of pipeline material on the cold transport rate is shown in Fig. 8. In this study, tubes made of rubber and copper were used as the pipeline, and these tubes are considered to have different friction factors, because of the difference of roughness on the inner surface. As shown in this figure, cold transport rate of the system with copper tube pipeline is about 40% higher than that with a rubber tube pipeline. This result suggests that, under the experimental condition, the friction factor of copper tube is half of that of rubber tube. From these results, it can be concluded that the effect of pipeline conditions on the cold transport rate of this system can be well estimated by the theoretical relation Eq. (1).
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4.3. Effect of cold release at the pipeline wall on the cold transport rate As mentioned in the previous section, the cold transport rate of this system can be basically estimated by Eq. (1). However cold release at the pipeline wall is not taken into account in the theoretical estimation; if the pipeline wall of a practical system was heated by the surrounding air and/or sunshine, cold release occurs at the pipeline, and the cold transport rate would decrease from that estimated by Eq. (1). In this study, therefore, cold transport rate was measured using an intentionally heated pipeline, and the effect of cold release at the pipeline wall was discussed. Fig. 9 shows the cold transport rate for different pipeline wall temperatures. As shown in this figure, cold transport rate from the cold trap to the evaporator decreases with rising the temperature of pipeline wall as the matter of course, but the decrease is about 30% or less even if the pipeline wall is heated at unrealistic high temperature, 80–90 C. This is because the medium flowing through the pipeline is water vapor at low pressure, and thus heat transfer between the medium and pipeline wall is limited. This result suggests that, in the practical transport system, there is no need to install heavy thermal insulation around the pipeline. This would be one of the most valuable features of this system. 4.4. Efficiency of the cold transport With this cold transport system, whole cold poured into the cold trap cannot be transported to the evaporator, even if no cold release occurred at the pipeline wall. This is because, in this system, PCM vapor is trapped onto the heat transfer surface in the cold trap, and a part of cold is consumed to condense/solidify the vapor. As mentioned in Section 2, the efficiency of cold transport of this system is basically estimated by the ratio of latent heat due to freezing of the PCM to that due to evaporation as Eq. (2). But in the practical system, the efficiency might be reduced by the cold release.
In this study, the efficiency of cold transport was evaluated directly from LN2 consumption at the cold trap, which corresponds to the amount of cold poured into the cold trap, and the change of water temperature in the evaporator, i.e. the cold transported to the evaporator. The efficiencies of the cold transport obtained for various pipeline conditions are summarized in Table 1. The efficiencies obtained here are somewhat scattered because of the difficulty on measurement of LN2 consumption at the cold trap, but the values of efficiency are about 50–70% and are not definitely affected by the pipeline conditions nor by the heat release at the pipeline wall. The value of efficiency, 50– 70%, obtained for the experimental setup used in this study is about 70% of the theoretical value estimated by Eq. (2). This might be due to transient operation of the experimental system. Namely, in this study, the efficiency was evaluated for a short operation period, 20–25 min, including start-up operation, and a part of cold poured into the cold trap may be consumed for cooling the components of the system. For the practical cold transport system having longer operation period, therefore, it is expected that the efficiency of this system becomes higher than the one obtained in this study.
5. A guideline for designing the system By summing up the results obtained in this study, a guideline for designing the cold transport system can be derived. As shown in the previous section, the cold transport rate of this system would be estimated by using Eq. (1). In this relation, pressure pe in the evaporator is determined by saturate pressure at the freezing temperature of PCM in the evaporator, and the pressure pw in the cold trap equals to the saturated pressure of frozen PCM at the surface temperature Tf of frost formed on the heat transfer surface in the cold trap. Namely, the mass flow rate mv of the vapor of PCM can be estimated as; sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðpe pw ðTf ÞÞv 2 D 5 : ð3Þ mv ¼ 8lL On the other hand, the frost surface temperature can be estimated by the thickness and thermal conductivity kf of frost layer as well as the heat flow through the frost as follows; mv ðLe þ Lf þ ci ðTi Tf ÞÞ ¼ kf
Fig. 9. Effect of pipeline wall temperature, i.e. cold release at the pipeline wall, on the cold transport rate.
Tf Tg A;
ð4Þ
where Le and Lf the latent heat due to condensation and freezing of PCM, ci the specific heat of the frost, Ti the freezing temperature of PCM, Tg the surface temperature of the heat transfer surface, which equals to the gasification temperature of LNG, and A the heat transfer area in
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Fig. 10. A diagram showing the operation condition of the system.
Table 2 Assumptions used for obtaining Figs. 10 and 11 Conditions
Assumed
PCM Latent heat due to evaporation, Le Latent heat due to freezing, Lf Average density of vapor in the pipeline, v Freezing temperature at the frost surface, Ti Thermal conductivity of the frost, kf Average density of the frost, f Specific heat of the frost, ci Pressure in the evaporator, e Gasification temperature of LNG, Tg Friction coefficient of the pipeline, l
Water 2.44106 J kg1 3.34105 J kg1 0.00485 kg m3 0 C 0.1 W m1 K1 500 kg m3 2103 J kg1 K1 300 Paa 160 C 1
a This pressure corresponds to the freezing temperature Te=8 C.
the cold trap. The left hand side of this equation shows the heat generation due to condensation/sublimation of PCM vapor and cooling down of the frost formed on the heat transfer surface. Moreover, the thickness of frost layer can be evaluated from the total amount of cold transported to the evaporator, i.e. total amount of the PCM vapor transported to the cold trap, as follows; ðt f A ¼ mv dt; ð5Þ 0
where f shows the apparent density of frost layer. The mass flow rate mv of the PCM vapor would be affected
by the frost layer thickness, and thus be a function of time. But, as mentioned in the following, change in the mass flow rate of PCM vapor is quite small under the practical operation condition. Therefore Eq. (5) would be simplified as; f A mv; max t:
ð6Þ
The cold transport rate Qc, i.e. the product of latent heat due to evaporation Le of PCM and the mass flow rate mv of PCM vapor, obtained from the relations (3) and (4) are shown in Fig. 10 as functions of the surface temperature Tf of frost layer; the relation between the diameter and length of pipeline D5/L and the ratio of frost layer thickness to the heat transfer area /A are used as the parameters for Eqs. (3) and (4), respectively. In order to obtain this figure, the values shown in Table 2 were assumed. As shown in Fig. 10, the cold transport rate is mainly dominated by the diameterlength relation D5/L, and for a fixed pipeline condition, the cold transport rate slightly decreases with increasing in the frost surface temperature Tf. The relation between the frost thickness and the cold transport rate Qc can be evaluated from the cross point of the curve for relation (3) with fixed D5/L value and the curves for relation (4). However, as mentioned in Section 4.1, the effect of frost surface temperature Tf on the cold transport rate Qc is not so evident, except for the case where the frost surface temperature is higher than about 30 C. From the results, one can easily guess that this system can be continuously operated until the frost surface temperature reaches about 30 C without defrosting.
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Fig. 11. A diagram for estimating the defrost timing.
In order to estimate the defrost timing, relation (5) or (6) should be used. Fig. 11 shows the relation between the operation time t/A2 and frost thickness /A deduced from the relation (6); the pipeline condition D5/L was used as the parameter. By reading the frost thickness / A at the end of continuous operation for a prescribed pipeline condition D5/L from Fig. 10, one can estimate the time t/A2 with Fig. 11. For example, when the diameter and length of the pipeline are 1 m and 10 km, i.e. D5/L=1104 m4, cold transport rate, frost thickness and frost surface temperature at the end of continuous operation would be evaluated from Fig. 10 as Qc=3104 W, /A=3104 m1, and Tf=30 C, respectively. Under the circumstance, the period for continuous operation can be estimated from Fig. 11 as t/A2=10 s m4. If the continuous operation period, i.e. defrost interval, t is set as 3104 s (about 8 h), the area A of the heat transfer surface in the cold trap would be 54 m2, and the frost thickness at the end of continuous operation would be 0.164 m. In Fig. 10, the cold transport efficiency of this system was shown as a function of frost surface temperature Tf as well. For evaluation of the efficiency shown in this figure, as shown in Eq. (4), sensible heat generation due to temperature change of frost is taken into account, and thus the value of efficiency is slightly different from the one estimated by Eq. (2). But the value of efficiency shown in Fig. 10 is in the range from 80 to 88%. This efficiency is for the ideal condition without cold release from the system, but as mentioned in the Section 4.4, the efficiency of this system is little affected by operation conditions, including the cold release at the pipeline wall. It can be concluded that, therefore, practical cold transport system of high efficiency would be achieved by
this concept. Moreover, note that the cold corresponding to the residue of the efficiency shown in Fig. 10 is stored in the cold trap as the frost, and total effectiveness of this system would be improved if the cold stored in the cold trap is utilized during the defrost operation.
6. Conclusions In this paper, cold transport rate and efficiency of a novel transport system for waste cold from the LNG gasification process were experimentally examined. Cold transport rate was measured under various pipeline conditions, and it was shown that, as suggested by a theoretical relation Eq. (1), cold transport rate is affected both by the water/frost temperature, i.e. saturate pressure, in the evaporator and the cold trap, and by the length, diameter and friction factor of the pipeline between them. However it was also shown that the transport rate is hardly influenced by the temperature of pipeline wall; cold release at the pipeline wall results in decrease in the cold transport rate as the matter of course, but the decrease is less than 30% even if the pipeline wall is heated up to unrealistic temperature. This suggests that, in the practical system, there is no need to install heavy thermal insulation onto the pipeline. From the experimental results, efficiency of cold transport was evaluated, and the efficiency of the experimental system was 50–70%, that is about 70% of theoretical value. The efficiency of the experimental system may have been lowered by the transient operation of the setup, and therefore that for the practical system in longer operation period is expected to be higher than the value obtained in this study.
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Summing up the obtained results, a guideline for designing the cold transport system was derived. Diagrams showing the operation condition and defrost timing of this system were obtained from the theoretical relations Eqs. (3)–(5), and the performance of a cold transport system in realistic scale was discussed from the practical viewpoint. Acknowledgements This study was financially supported in part by the Japan Society of the Promotion of Science under the ‘‘Research for the Future Program [Fundamental Research on Thermal Energy Storage to Preserve Environment (JSPS-RFTF97P01003)].’’ References [1] Website of the Agency for Natural Resources and Energy of Japan, http://www.enecho.meti.go.jp/english/energy/ lng/trends.html.
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[2] Yoshida K, Matsubara W, Yajima H, Makihara H, Tokuda M, Onoda S. Development of gas turbine suctionair cooling system using LNG cold heat. MitsubishiHeavy Industries Technical Review 1998;35(6):402–5 (in Japanese). [3] Song CH, Ro ST. Performance enhancement of a gas turbine with humid air and utilization of LNG cold energy. ASME paper; 1998. 98-GT-58. [4] Kim TS, Ro ST. Power augmentation of combined cycle power plants using cold energy of liquefied natural gas. Energy 2000;25(9):841–56. [5] For example, http://www.chiyoda-corp.com/biz/j/ enechem/naturalgas/lng_rei.shtml. [in Japanese]. [6] Japan Patent, No. 3062756. [7] Sonobe M, Saito T, Satoh I. A transport/storage system for the waste cold of the LNG gasification process utilizing an evaporation freezing phenomenon. Proc 38th National Heat Transfer Symp of Japan 2001;1:231–2 (in Japanese). [8] Satoh I, Fushinobu K, Hashimoto Y. Freezing of a water droplet due to evaporation- heat transfer dominating the evaporation—freezing phenomenon and the effect of boiling on freezing characteristics. Int J Refrigeration 2002;25: 226–34.
Performance of the cold transport system utilizing evaporation-freezing phenomena with a cold trap Isao Satoh*, Takushi Saito, Kazumoto Shima Department of Mechanical and Control Engineering, Tokyo Institute of Technology, 12-1, O-okayama 2, Meguro-ku, Tokyo 152-8552, Japan Received 25 August 2003; received in revised form 30 September 2003; accepted 30 September 2003
Abstract This paper dealt with the performance of a novel cold transport system for the waste cold from the gasification process of Liquefied Natural Gas (LNG), which has been proposed by one of the authors. The system consists of an evaporator, a cold trap, and a pipeline between them, and the LNG cold poured into the cold trap is transported to the evaporator as a flow of low-pressure water vapor. In this study, cold transport rate of a small-scale system was experimentally examined under various conditions, and the efficiency of cold transport was discussed. The results clearly showed that, as suggested by a theoretical relation based on the pressure drop due to vapor flow in the pipeline, cold transport rate is affected both by the pressure difference between the evaporator and cold trap, and by the length, diameter and friction factor of the pipeline. However it was also shown that the transport rate is hardly influenced by the temperature of pipeline wall. Based on the theoretical relation and the experimental results obtained herein, a guideline for designing the cold transport system was derived. # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Air conditioning; Process; LNG; Mass transfer; Evaporation
Performance d’un syste`me de transport de froid faisant appel a` des phe´nome`nes d’e´vaporation/conge´lation et un pie`ge a` basse tempe´rature Mots cle´s : Conditionnement d’air ; Proce´de´ ; GNL ; Transfert de masse ; E´vaporateur
1. Introduction Most energy-consuming countries including Japan use Liquefied Natural Gas (LNG) as a kind of fossil fuel, and the consumption of LNG tends to increase because influence on the environment due to the combustion of natural gas, which mainly consists of methane,
* Corresponding author. Tel.: +81-3-5734-3238; fax: +813-5734-3917. E-mail addresses: [email protected]. 0140-7007/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2003.09.007
is smaller than other fossil fuels. As the consumption of LNG increases, it is required to utilize the waste cold, which is exhausted in the gasification process, of LNG effectively. For example, 54.1 million metric ton of LNG has been imported into Japan in 2000 [1], and gasification of this LNG produces 2.761016 J of waste cold at quite low temperature (about 160 C), but only a part of this cold has been utilized effectively so far. For the present, the most typical use of the waste cold of LNG gasification is power augmentation of gas/ steam combined-cycle power plants due to inlet-air cooling. For example, Yoshida et al. [2] demonstrated
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Nomenclature A ci D kf L Le Lf mv pe pw p Qc t Te Tf Tg Ti
area of heat transfer surface in the cold trap (m2) specific heat of frost (J kg1K1) inner diameter of the pipeline (see Fig. 1) (m) thermal conductivity of frost (W m1 K1) length of the pipeline (see Fig. 1) (m) latent heat due to evaporation of PCM (J kg1) latent heat due to freezing of PCM, (J kg1) mass flow rate of PCM vapor (kg s1) pressure in the evaporator (see Fig. 1) (Pa) pressure in the cold trap (see Fig. 1) (Pa) pressure drop in the pipeline (see Fig. 1) (Pa) the maximum transportation rate of cold (see Fig. 1) (W) time of cold transport (s) temperature of PCM in the evaporator ( C) surface temperature of frost in the cold trap ( C) gasification temperature of LNG ( C) freezing temperature of PCM ( C)
Greek letters thickness of frost layer (m) l friction coefficient of the pipeline, dimensionless average density of the vapor in the pipeline (kg m3) f density of frost layer (kg m3)
the downtown area for air-conditioning during the summer season. However LNG cold has not been utilized for this purpose so far. This is because the method for transporting the LNG cold has not been well developed. Generally, it is often utilized the sensible/latent heat of heat transfer media for transporting the thermal energy. But the temperature of cold produced in the LNG gasification is much too low to store it in an ordinary heat transfer medium, such as water or fluorocarbons, as it is, and thus the transport of LNG cold by using an ordinary heat transfer medium results in waste of exergy in part. Moreover, conventional cold transport systems require additional power input for pumping the heat transfer media, and this pumping power increases evidently with elongation of transport distance. In order to overcome the weak points of conventional cold transport systems, and to utilize the LNG cold for air-conditioning in the downtown area as well, one of the authors has proposed a novel cold transport system for the waste cold from the gasification process of LNG [6]. Construction of this system and principle of cold transport with this system are summarized in the next section, but it should be noted that this system transports the cold from the gasification process of LNG to the downtown area as ‘‘vapor’’ of a phase change material (PCM), and thus exergy of the cold from LNG is utilized as a driving force for the vapor flow; no additional power is required for transporting the cold. The authors [7] have examined the feasibility of this system, and it was shown that the cold can actually be transported with this system. After that, the evaporation-freezing of water occurring in an evaporator (cold generator) of this system have been examined [8]. Following up these studies, cold transport rate and efficiency of this system were experimentally examined under various conditions, and a guideline for designing the cold transport system was derived in this paper.
2. Cold transport system utilizing evaporation-freeizng with a cold trap that the relative increase in output power of a LNGfueled gas turbine power plant having an output of 243 MW7 units amounts to 7.1% by adopting the inlet-air cooling system using the LNG cold during the summer season in Japan. Similar studies have been reported by Song et al. [3] and Kim et al. [4], and feasibility of the inlet-air cooling was demonstrated under various operation conditions. Other applications, e.g. cold warehouses, freeze-drying of foods, and dry ice making, of cold from LNG gasification are also examined from the practical point of view [5]. In addition to these, there is a great demand for cold in the downtown area far from the LNG gasification plants; a large amount of cold is consumed in
The novel transport system for the waste cold from the LNG gasification process is schematically shown in Fig. 1. This system consists of an evaporator, a cold trap, and a pipeline between them. In the evaporator placed in the downtown area, a PCM is cooled by its evaporation and finally freezes. The frozen PCM contains the cold at its freezing temperature, which can be used for air conditioning etc. after the evaporationfreezing process. The vapor from the evaporator flows through the pipeline, and is trapped on a heat transfer surface in the cold trap cooled by the evaporating LNG, the temperature of which is lower than the freezing temperature of the PCM.
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3. Experimental apparatus and procedure
Fig. 1. A novel transport system for waste cold from LNG gasification process.
Performance of this system would be dominated by the pressure difference between the evaporator and cold trap. In other words, transportation rate of the cold with this system is limited by the condition under which the pressure drop p in the pipeline due to the vapor flow is balanced against the pressure difference (pepw) between the evaporator and cold trap. Namely, if the pressure drop in the pipeline is evaluated by using an ordinary friction coefficient l, the maximum transportation rate Qc of cold could be estimated as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðpe pw Þ2 D 5 ; ð1Þ Qc ¼ L e 8lL where Le the latent heat due to evaporation of the PCM, D and L the diameter and length of the pipeline, and the average density of the vapor in the pipeline. Ideally the pressure pe in the evaporator is the saturate pressure of PCM at its freezing temperature, and the pressure pw in the cold trap is that at the surface temperature of frost generated on the heat transfer surface in the cold trap. This suggests that the cold transport rate of this system is influenced by the temperatures of PCM in the evaporator and cold trap, and by the conditions, e.g. length, diameter, and/or friction factor, of the pipeline between them. On the other hand, neglecting the cold release from the surface of system components, and neglecting the cold consumed for cooling the frost grown on a heat transfer surface in the cold trap, efficiency of cold transport, that is the ratio of cold transferred to the evaporator to that consumed at the cold trap, could be estimated as
: Le mv Le ; : ¼ ðLe þ Lf Þmv Le þ Lf
A small scale cold transport system was constructed and the transport rate of cold was measured with this system. Water was used as the PCM for this system. The schematic diagram of this system was shown in Fig. 2. As shown in this figure, the system consists of an evaporator, which is a thermally insulated glass flask containing pure water, a cold trap, a pipeline between them, a vacuum pump for evacuating the system, and a data acquisition system. Initial weight of water in the evaporator was set at 500 1 g. A heat transfer surface in the cold trap was cooled by evaporating liquefied nitrogen (LN2) instead of LNG, for safety reasons. In order to examine the effects of the pipeline condition on the cold transport rate, tubes shown in Table 1 were used as the pipeline between the evaporator and cold trap. On the copper tube, an electric heater is installed so as to heat up the pipeline wall. By using the heated pipeline, cold transport with cold release at the pipeline wall was examined. The amount of cold transferred to the evaporator was evaluated from the change of water temperature in the evaporator, and the cold consumed in the cold trap was estimated from the flow rate of LN2 poured into the heat transfer surface in the cold trap. In order to evaluate the amount of cold transferred to the evaporator by using the change of water temperature, water in the evaporator was maintained at a temperature higher than the freezing temperature (=0 C) throughout the experiment. Near the heat transfer surface in the cold trap, thermocouples were installed in order to measure the temperature profile within the frost layer generated on the heat transfer surface. Before the experiment, air/vapor in the system was evacuated by using a vacuum pump, and thus the system was filled with water vapor from the evaporator. After that, a valve between the cold trap and the vacuum pump and that between the cold trap and the evaporator were closed, and the heat transfer surface was cooled by LN2 so as to lower the pressure in the cold trap. And then the valve between the cold trap and the evaporator was opened, and data acquisition was started.
ð2Þ
where Lf the latent heat due to freezing of the PCM, and mv the mass flow rate of PCM vapor from the evaporator to the cold trap. This relation suggests that the efficiency is hardly affected by the system conditions, and that the efficiency for the ideal condition is about 88% if water was used as the PCM.
Fig. 2. Experimental apparatus.
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Table 1 Pipelines used in the experiment and the efficiency of cold transport Pipeline length L (m)
Pipeline diameter D (mm)
Material
Pipeline wall temp.
Efficiency (%)
0.5 1.0 0.5 1.0 1.0 1.0
6 6 12 6 6 6
Rubber Rubber Rubber Copper Copper Copper
Room temp. Room temp. Room temp. Room temp. Heated at 40–50 C Heated at 80–90 C
56 65 53 66 71 60
Fig. 3. Typical change of water temperature in the evaporator during the cold transport.
4. Results and discussion 4.1. Cold transport rate and effect of frost generation in the cold trap
Fig. 4. Temperature in the frost layer growing on a heat transfer surface in the cold trap.
First of all, characteristics of the cold transport of this system were examined. Fig. 3 shows the typical change of water temperature in the evaporator as a function of time elapsed. As shown in this figure, the water in the evaporator is cooled due to its evaporation, but the cooling rate dTe/dt, i.e. rate of cold transport Qc from the cold trap to the evaporator, decreases with time. This is because the pressure difference between the evaporator and cold trap decreases with time elapsed. Namely, saturate pressure of water in the evaporator tends to decrease with time because of lowering temperature of water. On the contrary, pressure in the cold trap tends to increase with time, since surface temperature of frost grown on a heat transfer surface in the cold trap rises due to thermal resistance of the frost layer. Under our experimental conditions, however, the latter effect is negligible, and the cold transport rate is mainly dominated by the water temperature in the evaporator. Fig. 4 shows the temperature profile in the frost layer growing on a heat transfer surface in the cold trap. As shown in this figure, temperature measured with a thermocouple installed 0.5 mm apart from the heat transfer surface in the cold trap decreases suddenly at about 15 min after the operation. This means that the frost
layer growing on the heat transfer surface reaches the thermocouple. At that time, i.e. when the thickness of the frost layer became 0.5 mm, temperature difference Tf between inner- and outer-surface of the frost layer was about 10 K, and cold transport rate Qc was about 10 W. From these results, one can estimate the apparent thermal conductivity kf of the frost layer as kf
Qc 10 0:0005 ¼ ¼ 0:083 Wm1 K1 DTf A 10 6 103
Where A is the area of heat transfer surface in the cold trap, and is about 6103 m2 (O.D=6 mm, length=320 mm). Namely, the apparent thermal conductivity kf of the frost is the value in the order of 0.1 W m1 K1, and therefore the surface temperature rise of frost layer would not be neglected. However temperature rise due to the thermal resistance of frost layer affects little the pressure in the cold trap, because, as shown in Fig. 5, saturate pressure of ice in low temperature range is quite low (order of 103 Pa at 100 C) compared to the pressure (several 100 Pa) in the evaporator where evaporation-freezing of water occurs at around 0 C. Fig. 5 suggests that the effect of thermal resistance of frost
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Fig. 5. Saturate pressure of ice.
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Fig. 7. Cold transport rate against the pipeline diameter.
Fig. 8. Effect of pipeline materials, i.e. friction factor, on the cold transport rate. Fig. 6. Cold transport rate against the pipeline length.
layer on the pressure difference, i.e. cold transport rate, between the evaporator and cold trap would be actualized only when the surface temperature of frost exceeds about 30 C. 4.2. Effect of pipeline conditions on the cold transport rate Then, the effect of pipeline conditions on the cold transport rate of this system was examined. Fig. 6 shows the cold transport rate Qc measured with pipelines of different length. In this figure, the cold transport rates were plotted against the pipeline length L. One can easily observe from this figure that the cold transport rate of this system is inversely in proportion to the square root of the pipeline length (Qc/L0.5), as suggested by the theoretical estimation Eq. (1). The cold transport rate for different pipeline diameters are shown in Fig. 7. The cold transport rate increases with increasing the pipeline diameter, and is affected more sensitively by the pipeline diameter than
by the length. Fig. 7 shows that Qc is in proportion with D1.9, while the theoretical estimation, Eq. (1) suggests Qc/D2.5. This discrepancy could be explained by the fact that the experimental setup used in this study has a valve on the pipeline, and that pressure drop due to the valve would not be negligibly small in comparison with that due to the pipeline. The effect of pipeline material on the cold transport rate is shown in Fig. 8. In this study, tubes made of rubber and copper were used as the pipeline, and these tubes are considered to have different friction factors, because of the difference of roughness on the inner surface. As shown in this figure, cold transport rate of the system with copper tube pipeline is about 40% higher than that with a rubber tube pipeline. This result suggests that, under the experimental condition, the friction factor of copper tube is half of that of rubber tube. From these results, it can be concluded that the effect of pipeline conditions on the cold transport rate of this system can be well estimated by the theoretical relation Eq. (1).
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4.3. Effect of cold release at the pipeline wall on the cold transport rate As mentioned in the previous section, the cold transport rate of this system can be basically estimated by Eq. (1). However cold release at the pipeline wall is not taken into account in the theoretical estimation; if the pipeline wall of a practical system was heated by the surrounding air and/or sunshine, cold release occurs at the pipeline, and the cold transport rate would decrease from that estimated by Eq. (1). In this study, therefore, cold transport rate was measured using an intentionally heated pipeline, and the effect of cold release at the pipeline wall was discussed. Fig. 9 shows the cold transport rate for different pipeline wall temperatures. As shown in this figure, cold transport rate from the cold trap to the evaporator decreases with rising the temperature of pipeline wall as the matter of course, but the decrease is about 30% or less even if the pipeline wall is heated at unrealistic high temperature, 80–90 C. This is because the medium flowing through the pipeline is water vapor at low pressure, and thus heat transfer between the medium and pipeline wall is limited. This result suggests that, in the practical transport system, there is no need to install heavy thermal insulation around the pipeline. This would be one of the most valuable features of this system. 4.4. Efficiency of the cold transport With this cold transport system, whole cold poured into the cold trap cannot be transported to the evaporator, even if no cold release occurred at the pipeline wall. This is because, in this system, PCM vapor is trapped onto the heat transfer surface in the cold trap, and a part of cold is consumed to condense/solidify the vapor. As mentioned in Section 2, the efficiency of cold transport of this system is basically estimated by the ratio of latent heat due to freezing of the PCM to that due to evaporation as Eq. (2). But in the practical system, the efficiency might be reduced by the cold release.
In this study, the efficiency of cold transport was evaluated directly from LN2 consumption at the cold trap, which corresponds to the amount of cold poured into the cold trap, and the change of water temperature in the evaporator, i.e. the cold transported to the evaporator. The efficiencies of the cold transport obtained for various pipeline conditions are summarized in Table 1. The efficiencies obtained here are somewhat scattered because of the difficulty on measurement of LN2 consumption at the cold trap, but the values of efficiency are about 50–70% and are not definitely affected by the pipeline conditions nor by the heat release at the pipeline wall. The value of efficiency, 50– 70%, obtained for the experimental setup used in this study is about 70% of the theoretical value estimated by Eq. (2). This might be due to transient operation of the experimental system. Namely, in this study, the efficiency was evaluated for a short operation period, 20–25 min, including start-up operation, and a part of cold poured into the cold trap may be consumed for cooling the components of the system. For the practical cold transport system having longer operation period, therefore, it is expected that the efficiency of this system becomes higher than the one obtained in this study.
5. A guideline for designing the system By summing up the results obtained in this study, a guideline for designing the cold transport system can be derived. As shown in the previous section, the cold transport rate of this system would be estimated by using Eq. (1). In this relation, pressure pe in the evaporator is determined by saturate pressure at the freezing temperature of PCM in the evaporator, and the pressure pw in the cold trap equals to the saturated pressure of frozen PCM at the surface temperature Tf of frost formed on the heat transfer surface in the cold trap. Namely, the mass flow rate mv of the vapor of PCM can be estimated as; sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðpe pw ðTf ÞÞv 2 D 5 : ð3Þ mv ¼ 8lL On the other hand, the frost surface temperature can be estimated by the thickness and thermal conductivity kf of frost layer as well as the heat flow through the frost as follows; mv ðLe þ Lf þ ci ðTi Tf ÞÞ ¼ kf
Fig. 9. Effect of pipeline wall temperature, i.e. cold release at the pipeline wall, on the cold transport rate.
Tf Tg A;
ð4Þ
where Le and Lf the latent heat due to condensation and freezing of PCM, ci the specific heat of the frost, Ti the freezing temperature of PCM, Tg the surface temperature of the heat transfer surface, which equals to the gasification temperature of LNG, and A the heat transfer area in
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Fig. 10. A diagram showing the operation condition of the system.
Table 2 Assumptions used for obtaining Figs. 10 and 11 Conditions
Assumed
PCM Latent heat due to evaporation, Le Latent heat due to freezing, Lf Average density of vapor in the pipeline, v Freezing temperature at the frost surface, Ti Thermal conductivity of the frost, kf Average density of the frost, f Specific heat of the frost, ci Pressure in the evaporator, e Gasification temperature of LNG, Tg Friction coefficient of the pipeline, l
Water 2.44106 J kg1 3.34105 J kg1 0.00485 kg m3 0 C 0.1 W m1 K1 500 kg m3 2103 J kg1 K1 300 Paa 160 C 1
a This pressure corresponds to the freezing temperature Te=8 C.
the cold trap. The left hand side of this equation shows the heat generation due to condensation/sublimation of PCM vapor and cooling down of the frost formed on the heat transfer surface. Moreover, the thickness of frost layer can be evaluated from the total amount of cold transported to the evaporator, i.e. total amount of the PCM vapor transported to the cold trap, as follows; ðt f A ¼ mv dt; ð5Þ 0
where f shows the apparent density of frost layer. The mass flow rate mv of the PCM vapor would be affected
by the frost layer thickness, and thus be a function of time. But, as mentioned in the following, change in the mass flow rate of PCM vapor is quite small under the practical operation condition. Therefore Eq. (5) would be simplified as; f A mv; max t:
ð6Þ
The cold transport rate Qc, i.e. the product of latent heat due to evaporation Le of PCM and the mass flow rate mv of PCM vapor, obtained from the relations (3) and (4) are shown in Fig. 10 as functions of the surface temperature Tf of frost layer; the relation between the diameter and length of pipeline D5/L and the ratio of frost layer thickness to the heat transfer area /A are used as the parameters for Eqs. (3) and (4), respectively. In order to obtain this figure, the values shown in Table 2 were assumed. As shown in Fig. 10, the cold transport rate is mainly dominated by the diameterlength relation D5/L, and for a fixed pipeline condition, the cold transport rate slightly decreases with increasing in the frost surface temperature Tf. The relation between the frost thickness and the cold transport rate Qc can be evaluated from the cross point of the curve for relation (3) with fixed D5/L value and the curves for relation (4). However, as mentioned in Section 4.1, the effect of frost surface temperature Tf on the cold transport rate Qc is not so evident, except for the case where the frost surface temperature is higher than about 30 C. From the results, one can easily guess that this system can be continuously operated until the frost surface temperature reaches about 30 C without defrosting.
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Fig. 11. A diagram for estimating the defrost timing.
In order to estimate the defrost timing, relation (5) or (6) should be used. Fig. 11 shows the relation between the operation time t/A2 and frost thickness /A deduced from the relation (6); the pipeline condition D5/L was used as the parameter. By reading the frost thickness / A at the end of continuous operation for a prescribed pipeline condition D5/L from Fig. 10, one can estimate the time t/A2 with Fig. 11. For example, when the diameter and length of the pipeline are 1 m and 10 km, i.e. D5/L=1104 m4, cold transport rate, frost thickness and frost surface temperature at the end of continuous operation would be evaluated from Fig. 10 as Qc=3104 W, /A=3104 m1, and Tf=30 C, respectively. Under the circumstance, the period for continuous operation can be estimated from Fig. 11 as t/A2=10 s m4. If the continuous operation period, i.e. defrost interval, t is set as 3104 s (about 8 h), the area A of the heat transfer surface in the cold trap would be 54 m2, and the frost thickness at the end of continuous operation would be 0.164 m. In Fig. 10, the cold transport efficiency of this system was shown as a function of frost surface temperature Tf as well. For evaluation of the efficiency shown in this figure, as shown in Eq. (4), sensible heat generation due to temperature change of frost is taken into account, and thus the value of efficiency is slightly different from the one estimated by Eq. (2). But the value of efficiency shown in Fig. 10 is in the range from 80 to 88%. This efficiency is for the ideal condition without cold release from the system, but as mentioned in the Section 4.4, the efficiency of this system is little affected by operation conditions, including the cold release at the pipeline wall. It can be concluded that, therefore, practical cold transport system of high efficiency would be achieved by
this concept. Moreover, note that the cold corresponding to the residue of the efficiency shown in Fig. 10 is stored in the cold trap as the frost, and total effectiveness of this system would be improved if the cold stored in the cold trap is utilized during the defrost operation.
6. Conclusions In this paper, cold transport rate and efficiency of a novel transport system for waste cold from the LNG gasification process were experimentally examined. Cold transport rate was measured under various pipeline conditions, and it was shown that, as suggested by a theoretical relation Eq. (1), cold transport rate is affected both by the water/frost temperature, i.e. saturate pressure, in the evaporator and the cold trap, and by the length, diameter and friction factor of the pipeline between them. However it was also shown that the transport rate is hardly influenced by the temperature of pipeline wall; cold release at the pipeline wall results in decrease in the cold transport rate as the matter of course, but the decrease is less than 30% even if the pipeline wall is heated up to unrealistic temperature. This suggests that, in the practical system, there is no need to install heavy thermal insulation onto the pipeline. From the experimental results, efficiency of cold transport was evaluated, and the efficiency of the experimental system was 50–70%, that is about 70% of theoretical value. The efficiency of the experimental system may have been lowered by the transient operation of the setup, and therefore that for the practical system in longer operation period is expected to be higher than the value obtained in this study.
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Summing up the obtained results, a guideline for designing the cold transport system was derived. Diagrams showing the operation condition and defrost timing of this system were obtained from the theoretical relations Eqs. (3)–(5), and the performance of a cold transport system in realistic scale was discussed from the practical viewpoint. Acknowledgements This study was financially supported in part by the Japan Society of the Promotion of Science under the ‘‘Research for the Future Program [Fundamental Research on Thermal Energy Storage to Preserve Environment (JSPS-RFTF97P01003)].’’ References [1] Website of the Agency for Natural Resources and Energy of Japan, http://www.enecho.meti.go.jp/english/energy/ lng/trends.html.
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[2] Yoshida K, Matsubara W, Yajima H, Makihara H, Tokuda M, Onoda S. Development of gas turbine suctionair cooling system using LNG cold heat. MitsubishiHeavy Industries Technical Review 1998;35(6):402–5 (in Japanese). [3] Song CH, Ro ST. Performance enhancement of a gas turbine with humid air and utilization of LNG cold energy. ASME paper; 1998. 98-GT-58. [4] Kim TS, Ro ST. Power augmentation of combined cycle power plants using cold energy of liquefied natural gas. Energy 2000;25(9):841–56. [5] For example, http://www.chiyoda-corp.com/biz/j/ enechem/naturalgas/lng_rei.shtml. [in Japanese]. [6] Japan Patent, No. 3062756. [7] Sonobe M, Saito T, Satoh I. A transport/storage system for the waste cold of the LNG gasification process utilizing an evaporation freezing phenomenon. Proc 38th National Heat Transfer Symp of Japan 2001;1:231–2 (in Japanese). [8] Satoh I, Fushinobu K, Hashimoto Y. Freezing of a water droplet due to evaporation- heat transfer dominating the evaporation—freezing phenomenon and the effect of boiling on freezing characteristics. Int J Refrigeration 2002;25: 226–34.