Two-dimensional thermal analysis of liquid hydrogen tank insulation

international journal of hydrogen energy 34 (2009) 6357–6363

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Two-dimensional thermal analysis of liquid hydrogen tank insulation Gulru Babaca, Altug Sismana,*, Tolga Cimenb a

Istanbul Technical University, Energy Institute, Ayazaga campus, 34469 Maslak, Istanbul, Turkey Jaguar and Landrover, Banbury Road, Gaydon, Warwick CV35 0RR, UK

b

article info

abstract

Article history:

Liquid hydrogen (LH2) storage has the advantage of high volumetric energy density, while

Received 5 May 2009

boil-off losses constitute a major disadvantage. To minimize the losses, complicated

Accepted 12 May 2009

insulation techniques are necessary. In general, Multi Layer Insulation (MLI) and a Vapor-

Available online 16 June 2009

Cooled Shield (VCS) are used together in LH2 tanks. In the design of an LH2 tank with VCS, the main goal is to find the optimum location for the VCS in order to minimize heat

Keywords:

leakage. In this study, a 2D thermal model is developed by considering the temperature

Liquid hydrogen storage

dependencies of the thermal conductivity and heat capacity of hydrogen gas. The devel-

Thermal analysis

oped model is used to analyze the effects of model considerations on heat leakage

Optimum design

predictions. Furthermore, heat leakage in insulation of LH2 tanks with single and double VCS is analyzed for an automobile application, and the optimum locations of the VCS for minimization of heat leakage are determined for both cases. ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

There is currently an increasing frequency of the use of hydrogen energy because hydrogen can be produced from renewable energy resources such as hydro, biomass, wind, and solar energy instead of fossil fuels. Hydrogen has a higher gravimetric energy density than fossil fuels and contains no elements with potential to produce pollutants such as SO2, CO, CO2, or volatile organic chemicals. These advantages have led to increased interest in the development of hydrogen economies and related research [1–3]. One of the main problems in hydrogen technology is that of storage. Hydrogen can be stored in the gas and liquid phases, and in materials with high surface-to-volume ratios such as metal hydrides and carbon nanostructures [3,4]. Among these methods, the most promising is liquid hydrogen (LH2) storage because it has the highest volumetric energy density of all of

the methods. Because of this advantage, LH2 storage is especially preferred for mobile applications such as cars, vehicles, and spacecraft [5–10]. In large-scale marine and highway transportations of hydrogen, liquid storage is preferred for the same reason [11]. Super-insulated cryogenic tanks are used to store the hydrogen as a liquid at 101 kPa and 20 K. The main disadvantage of LH2 storage is the vaporization of hydrogen due to heat leakage to the tank [4,12–14]. Different insulation techniques have been used to minimize this heat leakage [5,9–11]. One of the most promising insulation methods is the combined use of Multi Layer Insulation (MLI) and a Vapor-Cooled Shield (VCS) [15]. In a cryogenic tank with VCS, the evaporated hydrogen flows in a spiral pipe embedded in the MLI structure of the tank. The evaporated cold hydrogen gas in the spiral pipe absorbs some part of the heat leakage to the tank. In other words, the spiral pipe acts as a VCS since it decreases heat leakage and boil-off

* Corresponding author. Tel.: þ90 212 2853898; fax: þ90 212 285 3884. E-mail address: [email protected] (A. Sisman). 0360-3199/$ – see front matter ª 2009 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2009.05.052

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international journal of hydrogen energy 34 (2009) 6357–6363

losses significantly. To design a cryogenic tank with VCS, the main goal is to find an optimum location for the VCS that minimizes the heat leakage. To address this aim, a thermal model has been developed in the literature by considering 1D (radial) conductive heat transfer and a constant heat capacity of hydrogen [15]. In this study, the 1D model is improved by considering 2D (radial and axial) conductive and convective heat transfers, as well as the temperature dependencies of heat capacity and the thermal conductivity of hydrogen (cH p and kH ). The improved model is used to analyze the effects of model considerations on heat leakage predictions. The improved model is also applied to find the optimum locations for the VCS in an LH2 tank for an automobile application. Axial and radial temperature distributions and heat leakages are examined for different thicknesses and locations of the VCS. The optimum locations of the VCS are determined for the cases of single and double VCSs, and it is shown that the temperature dependencies of the heat capacity and thermal conductivity of hydrogen lead to considerable decreases in predictions of the model for standing time. Additionally, the base areas of the tank are important to consider for the total heat leakage. Furthermore, it is observed that there is no appreciable difference between the heat leakages of tanks with single and double VCS. The results can be used to understand the effects of model considerations on predictions for boil-off losses and to provide a basis for the industrial design of an LH2 tank with VCS.

2.

Mathematical model

An LH2 tank insulated by MLI with a serial-type double VCS under high vacuum has been proposed as the best configuration for reducing heat leakage effectively [15]. This proposal was based on a thermal model constructed with the assumptions of 1D (radial) conductive heat transfer and a constant heat capacity of hydrogen gas. The same tank configuration has been chosen in this study to allow for comparison of the results. For simplicity, a constant has been assumed for the heat capacity of hydrogen gas in the model given in the literature. However, both the heat capacity and thermal conductivity of H2 gas strongly depend on temperature. For example, heat capacity is 12 kJ/kg K at 21 K, while it is 16.5 kJ/kg K at 170 K. Similarly, thermal conductivity is 0.016 W/mK at 21 K, while it is 0.2 W/mK at 300 K [16]. The temperature dependencies of the heat capacity and thermal conductivity of hydrogen gas are shown in Fig. 1a and b, respectively [16]. The improved model developed in this study considers both of these temperature dependencies as well as 2D (radial and axial) conductive and convective heat transfer. In addition, the heat leakage due to the base areas of the tank is considered. A schematic configuration of the considered LH2 tank is given in _ indicates the mass flow rate of the Fig. 2. In this figure, m evaporated hydrogen due to heat leakage to the tank from the environment, and Ri and Ro are the radial positions of the inner and outer walls with temperatures of 21 K and 300 K, respectively. The evaporated hydrogen is released to the atmosphere after it is swirled in a spiral pipe (VCS) surrounding the inner part of the tank insulation instead of

Fig. 1 – (a) Specific heat capacity of hydrogen versus temperature at a pressure of 101 kPa. (b) Thermal conductivity of hydrogen versus temperature at a pressure of 101 kPa.

releasing it directly to the atmosphere. Therefore, the evaporated cold hydrogen gas in the spiral pipe absorbs some part of the heat leakage to the tank. In general, the spiral pipe acts as a VCS since it decreases the heat leakage and boil-off losses significantly. The actual geometry of the spiral pipe (VCS) is shown in detail in Figs. 3 and 4. In these figures, d and d represent the diameter and the wall thickness of the pipe, respectively. In the steady state, the mass flow rate of the vaporized hydrogen is: _ ¼ m

Q_ ¼ rðTÞAU hfv

(1)

where A is the pipe cross-section given by A ¼ pd2 =4, hfv is the enthalpy difference between liquid and vapor phases (hfv ¼ 443 kJ/kg at 101 kPa), r and Q_ are the gas density and the total heat leakage rate, respectively and U is the flow velocity of the gas. Consequently, the flow velocity of the gas can easily be expressed as:

international journal of hydrogen energy 34 (2009) 6357–6363

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Fig. 2 – LH2 tank with double VCS.

Fig. 3 – Enlarged cross-sectional view of a spiral pipe (left) and schematic view of LH2 tank and VCS (right).

U¼

Q_ 4 ¼ hfv rðTÞ pd2

(2)

Because of the spiral shape of the pipe, gas flows in a spiral geometry, and the axial velocity component of the gas can be determined by considering Figs. 2 and 3 as follows: Uz ¼

Dz d þ 2d d þ 2d : ¼ ¼ Dt Dt 2pR2 =U

(3)

By using Eqs. (2) and (3), Uz is determined as: Uz ¼

2ðd þ 2dÞQ_ : p2 R2 d2 hfv rðTÞ

Fig. 4 – Front view of spiral pipe (VCS).

(4)

and r(T ) is calculated by using the ideal gas equation of state, rðTÞ ¼ p=RT. The temperature change in each cycle of the gas through the spiral pipe is comparatively smaller than the total temperature change throughout the entire pipe. Therefore, instead of the complicated 3D spiral flow geometry of the gas in the VCS, it is possible to assume that the gas flows axially in a radial jacket with velocity Uz, as seen in Fig. 5. The axial projection of the spiral movement of the gas is considered by velocity Uz. Pressure is taken as a constant quantity, p ¼ 101 kPa, since a pressure increment is not allowed by releasing the vaporized hydrogen. Steady-state energy balance equations are written for insulation and gas flow regions (VCS) as follows: Insulation region : kins V2 T ¼ 0

(5)

vT ! ! ¼0 Gas flow region :  V $kH ðTÞ V T þ rðTÞcH p ðTÞUz ðTÞ vz

(6)

The symmetry boundary condition, vT/vr ¼ 0, is used on the symmetry axes of the tank (r ¼ 0), and other boundary condi_ is tions are shown in Fig. 6. The total heat leakage rate, Q, calculated by boundary integration of the heat flux over the inner surface of the tank. To solve the coupled Eqs. (5) and (6), the finite element method (FEM) is used in a MATLAB environment. The domain considered is represented by nearly 50,000 mesh elements and the relative error tolerance is chosen as 106.

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Fig. 5 – LH2 tank with simplified VCS geometry.

3. Effects of model assumptions on the predictions The model developed in this study is applied to different cases to show the effects of different assumptions on predictions for heat leakage rate and stand time. To compare the results and check model reliability, geometry, size, material, and other working parameters of the tank are chosen as the same as those of the model given in the literature [15]. Therefore, the tank volume is 0.002 m3, which corresponds to 0.141 kg LH2. Sizes and material properties are as follows: L ¼ 0.13 m, Ri ¼ 0.07 m, R1 ¼ 0.09 m, R2 ¼ 0.112 m, R0 ¼ 0.140 m, and kins ¼ 40 mW/mK. Heat leakage rate, boil-off flow rate, and the stand time are calculated for different cases and the results are summarized in Table 1. For cases with the VCS, the optimum VCS position is always determined and the results are given for this optimum, which minimizes the heat leakage

~_ rate. The dimensionless heat leakage rate, Q, is defined as ~ _ Q_ MLI , where Q_ MLI is the heat leakage rate when MLI is Q_ ¼ Q= used alone for the insulation (without VCS). Constant values of heat capacity and thermal conductivity of hydrogen gas are considered as cH p ¼ 12:14 kJ=kg K and kH ¼ 0:0157 W=mK, respectively. The results of Case I are based on the assumptions of 1D heat transfer and zero heat leakage from the base areas of the tank. It can be seen that the boil-off flow rate for a constant heat capacity is obtained at 1.073 g/day, which can be recalculated as 1.08 g/day by considering the results given in Ref. [15]. The relative difference is less than 0.65%, which shows agreement between the model developed here and that of the literature. Comparison of the heat leakage rates for the cases of MLI þ double VCS and MLI alone shows that the heat leakage rate can be decreased by 60% by using a double VCS. Therefore, the stand time prediction increases from 55 days to 134 days. Furthermore, it is shown that the temperature dependence of heat capacity does not affect the predictions considerably. In Case II, 2D heat transfer is considered while the assumption of zero heat leakage from the base areas of the tank is still used. The results show that the stand time prediction for MLI insulation is 20% shorter than that of the 1D model, and particularly, the temperature dependency of thermal conductivity of hydrogen has a considerable effect on the predictions. Stand time prediction decreases from 172 days to 145 days (15.7% decrease) due to the temperature dependency of thermal conductivity, while it decreases to 164 days (4.6% decrease) due to the temperature dependency of hydrogen heat capacity. Both of the temperature dependencies cause nearly a 20% decrease in stand time predictions, which is noticeable. Furthermore, it appears that the stand time can be three times (139/44 z 3) longer when the double VCS option is used. In Case III, both 2D heat transfer and the heat leakage from the base areas of the tank are considered. It can be clearly seen that consideration of heat leakage from the base areas is very important. When the base areas are considered, stand time becomes 59 days instead of 139 days. The use of VCS also seems to be necessary for the base areas.

4. Model results for an automobile application

Fig. 6 – Boundary conditions for the considered LH2 tank.

To analyze the effect of single and double VCS on the boil-off losses from a liquid hydrogen tank used in practical applications, a tank for an automobile application was considered and the heat leakage rate, boil-off flow rate, and the stand time were examined for single and double VCS cases. For small-scale applications such as automobiles, insulation must be thicker to ensure that the stand time is long enough because of a high surface-to-volume ratio. In this case, tank volume is a small portion of the total volume (tank and insulation volume). Therefore, the advantage of the high volumetric energy density of liquid hydrogen storage is lost for this small-scale application. On the other hand, the high gravimetric energy density, which is also important for mobile applications, is still an advantage since the thermal insulator

international journal of hydrogen energy 34 (2009) 6357–6363

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Table 1 – Heat loss rate, boil-off mass flow rate and the stand time for a liquid hydrogen tank having 2 l volume and 0.141 kg LH2. VCS diameter is chosen as 0.014 m. ~ _ _ Cases and assumptions Q(W) Q_ m(g/day) tD (day) Case I: 1D (radial conductive) heat transfer and zero heat leakages from the base areas a-MLI 0.0132 0.0055 b-MLI þ Double VCS b1. Cp: constant 0.0054 b2. Cp: T dependent Case II: 2D (radial and axial, conductive and convective) heat transfer and zero a-MLI b-MLI þ Double VCS b1. Cp: constant k: constant b2. k: T dependent Cp: constant b3. Cp: T dependent k: constant b4. Cp: T dependent k: T dependent Case III: 2D (radial and axial, conductive and convective) heat transfer a-MLI b-MLI þ Double VCS b1. Cp: constant k: constant b2. k: T dependent Cp: constant b3. Cp: T dependent k: constant b4. Cp: T dependent k: T dependent

is a light material. For an automobile powered by a hydrogen fuel cell, nearly 5 kg of H2 is necessary for a range of 480 km [17]. Therefore, the tank volume was chosen at 0.063 m3. Length and inner/outer radii are considered as L ¼ 0.7 m, Ri ¼ 0.175 m, and Ro ¼ 0.35 m, respectively. The thermal conductivity of MLI is kins ¼ 40 mW/mK [18]. Temperature dependencies of heat capacity, thermal conductivity of hydrogen gas, and the heat leakage from the base areas of the tank are considered for all cases. For the single VCS case, calculations were done for different locations and diameters of the VCS. A schematic view of the tank is given in Fig. 7. Dimensionless quantities are used for the heat leakage rate and the radial positions of the ~ ¼ R=Ro , VCS. Dimensionless radial position is described as R

1 0.417 0.409

heat leakages from the base areas 0.0166 1 0.0042 0.253

2.574 1.073 1.053

55 131 134

3.237 0.819

44 172

0.0050

0.301

0.975

145

0.0044

0.265

0.858

164

0.0052

0.313

1.014

139

0.0252 0.0112

1 0.444

4.915 2.184

29 65

0.0120

0.476

2.340

60

0.0114

0.452

2.223

63

0.0122

0.484

2.379

59

while the dimensionless heat leakage rate was already defined in Section 3. Heat leakage rate versus radial position of a single VCS is shown in Fig. 8a for different diameters of VCS. It can be observed that there is an optimum location for the radial ~1 y0:7, which minimizes the heat leakage. position of VCS, R ~_ _ Q MLI and Q min are calculated as 0.1003 W and 0.4, respectively. It is possible to say that the heat leakage rate can be decreased by 60% using a single VCS. The existence of the VCS causes a decrease in the temperature of the location where it is positioned and increases the temperature gradient in the outer region (the region between the VCS and the external surface of the tank). Naturally, the situation is opposite for the inner region or the region between VCS and the internal surface of the tank. Therefore, heat transfer increases in the

Fig. 7 – Schematic view of LH2 tank for an automobile application.

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~ Fig. 8 – (a) Dimensionless heat leakage rate Q_ versus dimensionless location of VCS for different VCS diameters. (b) Temperature distribution for optimum location of VCS with a diameter of 0.014 m.

outer region while it decreases in the inner region. However, this functionality of the VCS depends on its heat capacity. If a VCS is positioned near the external surface of the tank, it cannot absorb enough heat energy to balance the increase of heat transfer in the outer region. Consequently, the heat leakage to the tank increases. Alternatively, if a VCS is positioned near the internal surface of the tank, it cannot decrease the heat transfer in the inner region and the heat leakage to the tank again increases. These situations can be seen in Fig. 8a. Furthermore, the total heat capacity of the gas inside the VCS increases with the total volume of the VCS as Cp ¼ Vrcp , and the larger VCS absorbs more heat energy. Therefore, it is expected that the increase in VCS diameter decreases the heat leakage to the tank as well as the output temperature of the gas, as shown in Fig. 8a. It is clear that this may be true up to a critical diameter of the VCS. The heat leakage can increase for VCS diameters larger than this critical value since the heat conductivity of hydrogen is higher than

that of MLI. In this study, the considered diameters seem to be smaller than this critical value and the value of d ¼ 0.014 m gives the best result. The temperature distribution is given in Fig. 8b for d ¼ 0.014 m. Also, an interesting behavior appears for the VCS positioned around 0.8 for very small VCS diameters such as d ¼ 0.004, 0.006, and 0.008 m. Heat leakage rate increases with decreasing diameter of VCS. For very small VCS diameters, the increment becomes larger than that for the larger ones. This behavior shows that the VCS cannot absorb enough heat energy to balance the increment of heat transfer in the outer region for very small diameters, as seen in Fig. 8a. For the case of a double VCS, heat leakage rate is shown in Fig. 9a as a function of location of the VCSs for a diameter of 0.014 m. In this contour graph, the x- and y-axes correspond to the dimensionless radial positions of the first and the second VCS, respectively, and the contour values show the dimensionless heat leakage rates. The minimum value of Q_eis obtained at 0.41. Therefore, the mass flow rate due to boil-off

Fig. 9 – (a) Contour graph for dimensionless heat leakage rate versus different VCS locations for VCS diameter of 0.014 m. (b) Temperature distribution for the optimum location of VCSs with diameter of 0.014 m.

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Table 2 – Heat loss rate, boil-off mass flow rate and the stand time for a liquid hydrogen tank having 63 lt volume and 4.46 kg LH2. VCS diameter is chosen as 0.014 m. ~ _ _ Cases and assumptions 2D (radial and axial, conductive and convective) heat transfer Q(W) Q_ m(g/day) tD (day) Case IV

a-MLI b-MLI þ Single VCS c-MLI þ Double VCS

b1. Cp: T dependent b2. k: T dependent c1. Cp: T dependent c2. k: T dependent

losses can be reduced up to 59%. In contrast, it seems that there is no difference between the single and double VCS options; this is due to the high thermal conductivity of hydrogen gas inside the VCS. Too much hydrogen replaces the MLI material in the case of the double VCS option. The values of heat leakage rate, boil-off flow rate, and stand time are summarized in Table 2 for the different insulation options.

5.

Conclusion

In this study, a 2D model is developed for thermal analysis of liquid hydrogen tank insulation with VCS. In this model, the temperature dependencies of the thermal conductivity and heat capacity of hydrogen are considered, as well as heat leakage from the base areas of the tank. For a cylindrical tank, the model predictions for heat leakage rate show that the considerations of 2D heat transfer and the temperature dependency cause noticeable differences in the predictions, particularly for the thermal conductivity of hydrogen gas. Therefore, the improved model gives more realistic predictions for the stand time and properly optimizes the VCS positions. For a cylindrical tank, length and diameter must be equal or close to each other in value to minimize the surfaceto-volume ratio. For this reason, the base areas of the tank are important for heat leakage in addition to the lateral surfaces. Model results show that the use of a VCS for the base areas is also important for decreasing the total heat leakage. Furthermore, the effects of location and thickness of the VCS on heat leakage are examined, and the location is optimized to minimize the heat leakage, and a better VCS performance is achieved for larger VCS diameters. On the other hand, the heat leakage can increase with VCS diameters above a critical value due to the reduction of MLI thickness. For an automobile application, insulation of liquid hydrogen tanks with single and double VCS was analyzed. It was found that the heat leakage can be reduced up to 60% and 59% by using single and double VCS, respectively. Therefore, a single VCS option seems to be the best option for reducing the heat leakage effectively.

Acknowledgement The authors thank the referee and editor for their constructive comments, criticisms, and suggestions, which improved the quality of the manuscript.

0.1003 0.0401

1 0.400

19.562 7.821

228 570

0.0415

0.414

8.099

551

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