Transient thermal analysis of a cryogenic hydrogen vessel Christian Laa a, Christian Neugebauer b, Johannes Stipsitz c a Austrian Aerospace GmbH, Vienna, Austria, christian.laa@space.at b Austrian Aerospace GmbH, Vienna, Austria, christian.neugebauer@space.at c Austrian Aerospace GmbH, Vienna, Austria, johannes.stipsitz@space.at ABSTRACT: The thermal performance of an automotive liquid hydrogen tank has been characterized under transient thermal conditions such as the cool-down and warming up of vapor cooled shields and other massive parts. These transient thermal load cases were considered in a simplified finite element analysis including superinsulation. This model includes volume elements for the super-insulation and shell elements for the inner and outer wall as well as for the heat shields. The links and suspensions are represented by beam elements. Transient analyses for time periods of about one month have been performed. For each time step the temperature distribution at the heat shields and the heat flow through the insulation have been calculated. The amount of boil-off has been calculated for different designs and for different operation cycles. This thermal model has been used to compare different design options, in order to optimize the tank. KEYWORDS : analysis, thermal, hydrogen, liquid, transportation INTRODUCTION : Austrian Aerospace engineers and produces thermal hardware products and is a manufacturer of multi layer insulation (MLI) for space applications and for cryogenic storage vessels. These insulation foils are also called super insulation (SI) at cryogenic applications. A new development is the optimized insulation for liquid hydrogen vessels in close cooperation with car manufacturers (see Ref.[1]). During operation of the car liquid hydrogen from the storage vessel is used to run the engine. This leads to a pressure reduction in the vessel. If the pressure drops below the allowed limits during engine operation it is necessary to heat the liquid hydrogen. This is done with heat exchange tubes and with warm gas inside the tubes. During parking periods the heat flow through the insulation and via the suspensions of the inner vessel could lead to liquid hydrogen evaporation. The pressure of the hydrogen gas above the liquid increases until the allowed maximum is reached. After that hydrogen gas has to be blown off to keep the pressure inside the vessel within the allowed limits. The performance of the insulation has to be optimized to avoid fuel loss during such periods. One possibility is to use the enthalpy difference of the cold hydrogen gas which is used to run the engine to cool a heat sink during operation periods. This heat sink is connected with a shield in the isolation of the vessel. During parking periods the heat from outside is conducted from the shield to the heat sink. This reduces the amount of heat which reaches the stored liquid hydrogen. Therefore the pressure increase will be reduced and the fuel loss due to boil-off can be avoided. To find an optimum design of the cryogenic storage vessel and its isolation transient simulations of the thermal behaviour are needed. A quantitative evaluation of the design can be performed. These calculations are needed for the dimensioning of the isolation and the suspension of the cryogenic storage vessel. 1/8
MODEL DESCRIPTION : To investigate the performance of the insulation a finite element model has been developed. This model describes the thermal behaviour of the cryogenic vessel (see Fig.1). It allows calculating the heat flow and the temperature distribution during typical drive cycles of the car. RT RT RT RT H 2 Outer Vacuum Vessel Suspension Suspension MLI MLI Shield MLI MLI Contact Spreader Suspension Heat sink Contact Pipe wall H2 in pipe Inner Vessel MLI MLI Liquid H 2 Fig.1: Heat Flow into a Crogenic Storage Vessel A simple model with only few elements and nodes is needed in order to perform the required transient nonlinear thermal analyses for operation and parking periods of the cars within a reasonable amount of time (see Fig.3). Nevertheless this model has to describe the main features of the hardware correctly with respect to the temperature distribution and the heat flow. The temperature of the stored cold mass is at the boiling point of H 2 of about 28 K and the temperature of the outer vacuum vessel is at about room temperature RT. Fig.2: Cryogenic Storage Vessel for a Passenger Car, from Ref.[1] Fig.3: Simple Finite Elemente Model of Cryogenic Storage Vessel The geometry of the choosen finite element model has the same volume and surface area as the real vessel. The dimensions are similar and therefore the distances at the vessel for the heat flow are representative. 2/8
To reduce the heat transfer by infrared radiation in the vacuum gap between the outer and the inner vessel, highly reflective isolation foils are used. For optimization the material parameters of this isolation have been varied. One possible design would be the following: MLI between outer vessel and shield: 20 Layers of aluminium Al1050, 100 µm thick, interleaved with glass fibre spacer Shield: MLI between shield and inner vessel: aluminium Al1050, 125 μm thick 20 Layers of aluminium Al1050, 100 µm thick, interleaved with glass fibre spacer The heat transfer through the MLI isolation foils which are located in the vacuum gap between the inner and outer vessel is a mixture of linear heat transfer by conduction and non-linear heat transfer by infrared radiation. The conductive part of the heat transfer is dominated by the conductance of the spacer between the reflective layers. The infrared radiation between the reflective layers is limited by the low emissivity of the highly reflective foils and may be influenced by shadowing of the spacer. Therefore it is not possible to calculate the heat transfer through the MLI by common radiation heat exchange as provided by the available software tools. One way to describe this behaviour in a finite elemente model is by volume elements of a fixed thickness and with temperature dependant conductivity (see Fig.4 and Fig.5). The validity of this methode of heat transfer calculations is limited by the lack of measurement data. Ongoing work at Austrian Aerospace and partner institutes will help to get better accuracy of heat transfer calculations through MLI in the future (see Ref.[2]). Fig.4: Volume Elements for MLI and Beam Elements for Pipes An important point for the heat flow during parking and engine operation is the heat conduction in the pipes and between the cold gas or liquid and the pipe walls. The beam elements which describe the pipes are situated outside the model of the vessel for better visualization of the results. There are two ascending pipes for refill and fuel supply to the engine and three ascending pipes for the heat exchanger and the cabling. Additional loops of the pipes are located inside the heat sink. All pipes are of stainless steel. The pipe dimensions are taken into account in the model. Temperature dependant material parameters for cryogenic temperatures have been taken from data sheets and from the software Cryocomp V3.06. The material parameters for hydrogen have been taken from the software Gaspak V3.31. The size of the final model was 1363 elements and 763 nodes. 3/8
100% Outer MLI 20 Layers 80% Inner MLI 20 Layers Outer MLI 10 Layers Conductivity 60% 40% Inner MLI 10 Layers 20% 0% 0 50 100 150 200 250 300 Temperature in K Fig.5: Temperature dependant conductivity for MLI volume elements The heat conductance between the cold gas or liquid and the pipe walls is calculated between iterations according to the actual state of the vessel. According to the speed of the medium different formula are applied according to common theories: Reynolds number: Re ( Tm, mp ) d pipe 4mp π η (Tm ) Nusselt number: for turbulent flow (Re > 10 4 ): NuTur ( Tm, mp ) := 0.024 Re ( Tm, mp ) 0.786 Pr ( Tm ) 0.45 1 + d pipe l ges 2 3 for laminar flow (Re < 10 4 ): with NuLam ( Tm, mp ) := 3.66 + Tm...mean temperature of pipe cross section mp...mass flow d pipe...inner pipe diameter η...dynamic viscosity Pr...Prandtl number l ges...length of pipe d pipe 0.0677 Pr ( Tm ) Re ( Tm, mp ) l ges 1 + 0.1 Pr ( Tm ) k ( Tm, mp ) := Nu ( Tm, mp ) λ ( Tm ) π l seg Re ( Tm, mp ) d pipe l ges 1.33 0.83 4/8
RESULTS : With the model described transient analysis runs have been performed. The model parameters and design details have been varied to find the optimum within the given boundaries. One trade-off was for instance the comparison of the design with and without a heat sink at the fuel line to the engine which is connected to the shield inside the isolation foils. The benefit of such a heat sink could be demonstrated by calculation of the time for pressure increase and the fuel loss due to boil-off with and without heat sink. The time to reach the maximum allowed pressure could be extended for a typical drive cycle with heat sink by +94 %. The reduction of fuel loss due to boil-off with heat sink for this cycle was calculated to be -73 %. The calculated profile of mass and pressure for such a typical drive cycle is given in Fig.6. The temperature distribution at the shield inside the isolation and at the pipes is given in Fig.7 for a driving period and in Fig.8 for a parking period with pressure increase. For a parking period with boil-off it is shown in Fig.9. In Fig.10 the temperature profile for a typical drive cycle is given for heat sink temperature, shield temperature, temperature of heat exchanger and suspension temperature. The calculated profile of heat conducted through the insulation to the liquid hydrogen for such a typical drive cycle is shown in Fig.11. With the visualization of the resulting temperature distribution it is possible to see how the heat sink and the shield work. The effect may be explained by the enthalpy difference of the fuel which is not needed if it is used for running the engine and which can be stored in the heat sink. During parking periods the heat coming from the surrounding environment goes then first to the shield and to the heat sink and the pressure build-up and the following boil-off is reduced. 100% 90% 80% 70% Mass and Pressure 60% 50% 40% 30% 20% 10% H2-mass H2-pressure 0% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Time in days Fig.6: Hydrogen Pressure and Stored Mass in the Vessel for typical Usage 5/8
Shield: 31...42 K Heat sink: 29 K Fig.7: Temperature Distribution at the Cryogenic Storage Vessel during Driving Shield: 136...157 K Heat sink: 136 K Fig.8: Temperature Distribution at the Cryogenic Storage Vessel during Parking pressure increase Shield: 80...106 K Heat sink: 79 K Fig.9: Temperature Distribution at the Cryogenic Storage Vessel during Parking boil-off 6/8
300 250 T-heat-sink T-exhaust-shield 200 T-heat-exchanger T-Suspension Temperature in K 150 100 50 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Time in Days Fig.10: Temperature Profile of Storage Vessel Elements for typical Usage 3 2,5 Q_Pressure-increase Q_Boiloff 2 Heat load to H2 in W 1,5 1 0,5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Time in days Fig.11: Heat Load to Liquid Hydrogen for typical Usage 7/8
CONCLUSION : The isolation of a liquid hydrogen storage vessel for passenger cars has been investigated. For performance evaluation a simplified finite element model has been developed. With this model transient analysis runs have been performed. The model parameters and design details have been varied to find the optimum within the given boundaries. A design trade-off with and without a heat sink connected to the fuel line to the engine and with the shield inside the isolation foils demonstrated the benefit of the heat sink Extension of time for pressure increase with heat sink +94 % Reduction of fuel loss due to boil-off with heat sink -73 % A further performance increase of the isolation is limited by the heat conduction through the suspension of the inner vessel and the pipes. Improvements of these parts can be evaluated using the described model. References: [1] T.Brunner, On the way to a new generation of production passenger car integrated LH2 storage systems, BMW Group, GERMANY, paper number 196 of this conference [2] Ch.Forster, T.Králik, Ch.Laa, V.Musilova, T.Schmid, J.Stipsitz, Heat transfer through super insulation from ambient to cryogenic temperatures, CryoPraque2006, to be published 8/8