Modeling the Effective Thermal Conductivity of Polyurethane Foams
Chung-jen TSENG1, Masahiro NAKAJIMA2, Masahito YAMAGUCHI2, Takao OHMORI2
1 New Energy & Ind. Tech. Development Org., 29F, 3-1-1, Higashi Ikebukuro,Toshima-ku Tokyo 170
2 Adv. Tech. Dept., Research Institute, IHI Co., Ltd., 1 Shin-nakahara, Isogo, Yokohama 235
The thermal conductivity of the polyurethane (PU) foam in the temperature range between 300 K and 20 K is investigated for the development of liquid hydrogen storage tanks. An analytical model, including the contributions from radiative heat transfer, is used to predict the thermal conductivity of the PU foams. The theoretical results are found to be in very good agreements with measured thermal conductivity of the PU foams under normal and reduced pressures. Radiative heat transfer is found to accounts for about 10 to 20 % at room temperatures. The thermal conductivity of the PU foam can be reduced by as much as 70% by evacuating the gases in the foam cells. Effects of pressure on the thermal performance of the foams are discussed. In case of hydrogen leak, to maintain the effective thermal conductivity of PU foams below 8 mW/mK, the pressure of hydrogen gas must be kept under 10-3 kPa.
Hydrogen is a promising energy source which does not produce any pollutants when it burns. We would like to see it to become one of the primary energy sources in the twenty first century. WE-NET(World Energy NETwork) project was launched in 1993 to promote the use of hydrogen as a clean energy source. In the WE-NET project, the whole system including the technology of hydrogen production, storage, transportation, and utilization is investigated. The authors has been participating in designing large scale liquid hydrogen storage tanks [1,2]. IHI has proposed a combined polyurethane foam(PUF) and vacuum insulation system. PUF is selected because it offers high strength-to-weight ratio for structure material and has reliable insulation performance for a wide range of vacuum pressure.
There are two important subjects to be studied about this type of insulation system. One is to obtain thermal conductivity data of PUF. Prior to the work undertaken at IHI, the thermal conductivity data of PUF was available only for temperatures above 95[K]. In our investigations, data from 320[K] to 20[K] are obtained under two pressure conditions [3,4]. The difference between the two cases which is caused by evacuating the gases in PUF pores is realized. Theoretical analysis is also performed to study the details of the heat transfer mechanisms of PUF. Obtained theoretical expression explains the experimental results very well. The characteristics of the thermal conductivity of PUF are also explained.
Another subject is the analysis of the thermal performance of insulation systems. Liquid hydrogen storage needs ten times higher insulation performance than the case for LNG. The high performance insulation system can be constructed with the obtained thermal conductivity of PUF. Insulation systems based on the PUF data will be proposed and discussed. The boil-off gas rate under hydrogen leak condition will also be discussed.
Keywords: Thermal Conductivity; Polyurethane Foam; Insulation; Liquid Hydrogen
As a promising clean energy source in the twenty first century, hydrogen offers a non-polluting, inexhaustible, efficient, and potentially cost-effective energy system. However, large scale liquid hydrogen transportation and storage post a new challenge to engineers due to its extremely low temperature (20K). High performance thermal insulation systems are required. In this work, we examine one of the potential candidates, polyurethane (PU) foam. PU foam offers a high strength-to-weight ratio, low thermal conductivity, and low cost. More importantly, in case of leak occurrence, the closed-cell structure provides some protection to prevent the insulation performance from deteriorating rapidly as opposed to open-pore insulations such as powder and multilayer insulations. Recently, the thermal conductivity of PU foams from room temperature to 20K were measured using a steady-state cylindrical method. In the present study, effects of pressure on the effective thermal conductivity of PU foam will be studied. The takeoff pressure of the insulation system will also be compared with other insulation systems.
2. Effective Thermal Conductivity Model
The PU foam used in this study has a closed-cell porous structure and a density of 32 kg/m3. The average diameter of the cells is approximately 400 mm. Heat is transferred through the PU foam via four mechanisms: (1) gas conduction, (2) solid conduction, (3) radiation, and (4) convection. The total heat flow is a result of the interactions between the four modes. Natural convection within the pores is negligible since the pore size is very small. The effective thermal conductivity,keff , of PU foam can be estimated by the following equation with good accuracy
where k is the thermal conductivity of the pure solid material,F the porosity,F'=F2/3 , n the refractive index, B the extinction coefficient, s the Stefan-Boltzmann constant, and the gas mixture thermal conductivity, kg', can be evaluated by
where a is the accommodation coefficient, d the pore diameter, l the mean free path, X the mole fraction. The effect of pressure on keff is accounted for by the factor fp in the above equations which takes into account both the molecule-to-molecule and molecule-to-wall collisions. The coefficient Aij are defined as
where M is molecular weight, is the monatomic value of the thermal conductivity, and is an empirical constant. The detail can be found in Reid et al.
3. Results and discussion
Figure 1 shows the analytical results along with the measurement data. (Details of the experimental setup and procedure can be found in .) For both the atmospheric pressure and evacuated cases, good agreements were obtained. The inversions at 240-280K in the former case and 155-175K in the latter case are caused by the condensation of lower-conducting R141b gas. Further decrease in the effective thermal conductivity, keff, at 40K are caused by the condensation of air. It is shown that thermal conductivity of PU foams can be reduced by as much as 70% by evacuating the foams. Radiative transfer contribution is negligibly small at low temperatures, but accounts for about 10 to 20% at room temperatures.
The proposed insulation system for liquid hydrogen storage tank will be operated in vacuum condition (cryopumped at 20K). But in case of hydrogen leak from the inner vessel, the insulation performance will decrease because the saturation vapor pressure of hydrogen is 1 atm at 20K. Moreover, the thermal conductivity of hydrogen gas is very high. It is thus very important to study the performance of the insulation system for hydrogen leak case.
Figure 2 shows the effective thermal conductivity of PU foams filled with hydrogen gas at various pressure. The average keff increases from 3.9 mW/mK at 10-4 kPa, to 6.5 mW/mK at 10-3 kPa, to 21 mW/mK at 10-2 kPa, to 71 mW/mK at 10-1 kPa, to 105 mW/mK at 1 kPa, and to 110 mW/mK at 10 kPa. To achieve the design goal of less than 8 mW/mK, it is necessary to keep the pressure below 10-3 kPa.
Figure 3 compares the take-off pressure and pressure dependency of the effective thermal conductivity for several types of insulation systems commonly used in cryogenic applications. The take-off pressure is the pressure that the thermal conductivity of an insulation system starts to increase rapidly. For the results shown in Fig. 3, the boundaries are kept at 90K and 293K, respectively. The data for fibrous insulation, powder (perlite) insulation, and multilayer insulation (MLI) are measurement data from Kaganer. The curve for PU foam is obtained from the present analytical model. The MLI has the lowest thermal conductivity, but it requires high degree of vacuum. The take-off pressure is about 10-6 kPa. The perlite system also has very low thermal conductivity at high vacuum, but relatively high keff when pressure is higher 10 kPa. The take-off pressure is about 10-2 kPa. The fibrous insulation has relatively high keff and a take-off pressure of approximately 10-4 kPa. The take-off pressure of the PU foam is about 10-3 kPa, so it is not very difficult to operate. The PU foam system also has the lowest thermal conductivity among the four for pressures higher than 10 kPa.
The thermal conductivity of the polyurethane (PU) foam in the temperature range between 300 K and 20 K is investigated. An analytical model, including the contributions from radiative heat transfer, is used to predict the thermal conductivity of the PU foams. The theoretical results are found to be in very good agreements with measured thermal conductivity of the PU foams under normal and reduced pressures. The thermal conductivity of the PU foam can be reduced by as much as 70% by evacuating the gases in the foam cells. Effects of pressure on the thermal performance of the foams are discussed. In case of hydrogen leak, the pressure of hydrogen gas needs to be kept under 10-3 kPa in order to maintain the effective thermal conductivity of below 8 mW/mK.
C.J.Tseng et al., Cryogenics, in press, (1997).
C.L. Tien and G.R. Cunnington, Cryogenic Insulation Heat Transfer, in Advances in Heat Transfer, 9 (1976) 349.
R.C. Reid et al., The Properties of Gases and Liquids, 4th ed, McGraw-Hill, Inc., New York (1987).
M.G. Kaganer, Thermal Insulation in Cryogenic Engineering, IPST Press, Israel (1969).
This study was performed as a part of the WE-NET (International clean energy network using hydrogen conversion) project which is launched by NEDO (the New Energy and Industrial Technology Development Organization) under the support of the Agency of Industrial Science and Technology.