MODELING THE TRANSIENT TEMPERATURE DISTRIBUTION WITHIN A HYDROGEN CYLINDER DURING REFUELING

3b2 Version Number : 7.51c/W (Jun 11 2001) File path : p:/santype/journals/taylor&francis/unht/v53n5/unht263284/unht263284.3d Date and Time : 9/10/07 and 18:56 Numerical Heat Transfer, Part A, 53: 1 24, 2008 Copyright # Taylor & Francis Group, LLC ISSN: 1040-7782 print=1521-0634 online DOI: 10.1080/10407780701634383 MODELING THE TRANSIENT TEMPERATURE DISTRIBUTION WITHIN A HYDROGEN CYLINDER DURING REFUELING C. J. B. Dicken 1,2 and W. Mérida 1,3 1 Institute for Fuel Cell Innovation, Vancouver, British Columbia, Canada 5 2 General Hydrogen Corporation, Richmond, British Columbia, Canada 3 Clean Energy Research Centre, University of British Columbia, Vancouver, British Columbia, Canada We report a simplified 2-dimensional axisymmetric model for predicting the gas temperature and pressure rise in a hydrogen cylinder during the fill process. The model predictions 10 were compared with in-situ measurements of the average temperature rise and temperature distribution inside a type 3, 74 L hydrogen cylinder filled to 35 MPa. 1. INTRODUCTION The current standards governing compressed gas cylinders for vehicular applications limit the gas temperature within the cylinder to a maximum of 358 K and limit 15 the gas pressure to a maximum of 1.25 times the cylinder s design pressure [1, 2]. The practical refuelling times and the dispensing accuracy for compressed hydrogen are determined by these standards. The accuracy of the fill is defined in terms of a mass ratio: the mass of gas at the completion of filling to the rated mass capacity in the cylinder. When a fill reaches the 358 K limitation the fill is stopped regardless of the mass 20 of gas dispensed, and this leads to mass rations smaller than 1 at the end of the fill. While much work has been done to measure and model the temperature rise of the gas during filling [3 17], the modeling studies to date have all assumed uniform temperature within the cylinder. The assumption is necessary in order to simplify the analysis of a cylinder s control volume. Having assumed uniform temperature, the 25 more advanced models attempt to predict the heat transfer from the gas in the cylinder to the cylinder walls and out to the surroundings. These models must determine the convective heat transfer coefficient between the gas and cylinder wall. While many empirical correlations exist for calculating the Nusselt number for the case of forced convection, these correlations depend on the geometry and require 30 Received 7 March 2007; accepted 27 July 2007. The authors would like to acknowledge General Hydrogen Corporation for their technical support and Western Economic Diversification Canada for the funding of this work and the projects associated with it. The authors would also like to thank Mark Rossetto of the National Research Council of Canada, Institute for Fuel Cell Innovation for his assistance in performing the experimental fills. Address correspondence to Mr. C. Dicken, General Hydrogen Corporation, 13120 Vanier Place, Richmond, B.C., Canada V6V 2J2. E-mail: cdicken@generalhydrogen.com 1

2 C. J. B. DICKEN AND W. MERIDA NOMENCLATURE A area [m 2 ] A constant of the Redlich Kwong equation of state B constant of the Redlich Kwong equation of state C 1e constant of the k-e model C 2e constant of the k-e model C m constant of the k-e model c p specific heat capacity, J=molK c s speed of sound in hydrogen, m=s d diameter, m Fr Froude number g gravitational acceleration 9.81, m=s 2 H total enthalpy J h specific enthalpy, J=mol h conv,avg mean convective heat transfer coefficient, inner surface, W=m 2 K h conv,in local convective heat transfer coefficient, inner surface, W=m 2 K h conv,out local convective heat transfer coefficient, outer surface, W=m 2 K i k set of 17 constants for the specific heat capacity of hydrogen k thermal conductivity, W=mK k eff effective thermal conductivity, W=mK k t turbulent kinetic energy, m 2 =s 2 L length of the cylinder, m L tube length of tube protruding from inlet, m m mass, kg _mz mass flow rate, kg=s Ma Mach number N k set of 17 constants for the specific heat capacity of hydrogen p pressure, Pa p c hydrogen critical pressure, Pa Pr t turbulent Prandlt number _Q total heat transfer rate, W q heat transfer, J R universal gas constant, J=molK Re Reynolds number r i inner radius of test cylinder, m r o outer radius of test cylinder, m T temperature, K T c hydrogen critical temperature, K T mean mean Temperature of the gas within the cylinder, K t time, s U internal energy J u velocity, m=s v specific volume m 3 =mol x distance, m e ij unit tensor e t turbulent rate of dissipation, m 2 =s 3 k lam laminate thickness, m k liner liner thickness, m k tube tube thickness, m k w total wall thickness, m m viscosity, Pas m eff effective viscosity, Pas m t turbulent viscosity, Pas q density, kg=m 3 r k constant of k-e model ¼ 1.0 r e constant of k-e model ¼ 1.3 s ij stress tensor n kinematic viscosity, m 2 =s Subscripts i j k in ref w x direction y direction z direction inlet reference state wall Superscripts e Favre average ensemble average 0 turbulent fluctuating component knowledge of the local Reynolds number inside the cylinder. The resulting models treat the cylinder as a single control volume and do not resolve the velocity profile inside the cylinder. This makes it impossible to calculate local Reynolds numbers. Furthermore, the direction of flow inside the cylinder is not uniform; there exists backflow as the incoming gas collides with the back wall of the cylinder. Hence, in most models, the Reynolds number inside the cylinder is assumed or is a parameter used for fitting data to experimental results. In order to accurately model the heat transfer from the gas to the cylinder, a model must discretize the space within the cylinder. By performing spatial discretization, 35

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 3 the model can determine the temperature and velocity profiles along with turbulence 40 parameters within the cylinder, which in turn will allow for the calculation of the convective heat transfer at the cells along the wall. This method allows for the calculation of the average temperature, but also provides the temperature at numerous locations on the grid of discrete points inside the cylinder, thus affording an appropriate comparison between the local temperature predicted by the model and the experimental measurements of local temperature. 45 Only a few of the experimental studies to date have placed more than one temperature sensor within the cylinder to measure gas temperature. The only study that has placed enough temperature sensors within the vessel to provide a temperature distribution is the study of Haque et al. [13]. This study analyzed the blowdown of a large, 50 cylinder shaped, steel pressure vessel. While this study provides insight into experimental techniques, due to the different geometry, gas and fill rates, their results are not directly useful for the analysis of the temperature distribution within a type 3 compressed gas cylinder. A study from the Gas Technology Institute found a significant spatial variability in temperature [11]. Three thermocouples located at 1 4, 1 2,and3 4 lengths of the centerline all 55 read significantly different temperatures during filling (up to 28 K difference). The study of Duncan et al. [5] found temperature differences as high as 10 K between thermocouples placed at 1=3and2=3 of the length of the cylinder centerline. From the end of filling it took 5 minutes for these thermocouples to read a uniform temperature. Our study challenges the assumption of uniform temperature by studying the 60 gas temperature distribution within the cylinder during filling. The goal of this study was to investigate the temperature field within a compressed gas cylinder during filling, in order to determine the mean temperature of the hydrogen gas and enable density calculations based on pressure and temperature. A computational fluid dynamics (CFD) model was developed to discretize the 65 cylinder spatially and to predict the distribution of gas temperature. The model considered compressible unsteady viscous flow, real gas effects, heat transfer to the cylinder walls and conduction through the cylinder walls to ambient. The model was validated by comparison with a set of experimental fast fills of a compressed gas cylinder instrumented with 63 thermocouples distributed throughout the cylinder in an 70 effort to measure the gas temperature distribution within the cylinder and provide an accurate estimate of the mean gas temperature within the cylinder. The validated model assesses the difference between the local measurements of temperature inside the cylinder and the average temperature based on the position of the local measurement. The model also helps to identify the best locations for the 75 onboard temperature sensor such that the local measurement best represents the mean gas temperature. The validated model is also used to provide insight into the heat transfer processes, which occur during filling. 2. THEORY Inherent to the fill process is a significant increase in gas temperature. The temperature rise during filling is the result of the combination of two phenomena. Hydrogen has a negative Joule-Thomson coefficient at the temperatures and pressures of filling. Hence, an isenthalpic expansion of the gas from the high-pressure tank through the dispenser throttling device into the low-pressure cylinder results 80

4 C. J. B. DICKEN AND W. MERIDA in an increase in hydrogen temperature. It is important to emphasize that the 85 isenthalpic expansion occurs within the dispenser and the result is a higher gas temperature entering the cylinder. The second phenomenon that causes a temperature rise during filling is the compression of the gas inside the cylinder. At the start of filling the gas is compressed by the introduction of the higher-pressure gas from the fuelling station. This is 90 repeated throughout the fill as the addition of gas into the cylinder compresses the gas already in the cylinder. When gas is compressed, its temperature will rise and this temperature change is called the heat of compression. For fills to 35 MPa, a comparison of the magnitudes of these two phenomenon shows that the Joule-Thomson effect has a much smaller effect on the overall temperature rise when consideration is given to the thermodynamics of the entire process [14]. 95 The temperature rise is mitigated through heat transfer from the gas to the cylinder walls. 2.1. Dimensional Analysis A dimensional analysis of the flow entering the cylinder provides insight into the nature of the flow field. In this study, a 74L, 35 MPa cylinder is used for testing. The rated mass of gas of the cylinder at 35 MPa and 15 C is 1.79 kg of hydrogen gas. The flow rate required to fill a cylinder with an initial pressure of 10 MPa to the rated mass of gas depends on the desired fill time. For this analysis we assume a lower and upper bound on fill time of 40 seconds and 5 minutes, respectively. The Reynolds number at the inlet can be determined using Eq. (1) below. 100 105 Re i ¼ _md i A i m i ð1þ Where d i is the inside diameter of the inlet tube, A i is the cross-sectional area of the inlet tube, _m is the average mass flow rate of hydrogen, and m is the viscosity of the gas. While the viscosity of the gas will vary throughout the fill depending on the density and temperature of the gas at the inlet, the average Reynolds number at the inlet 110 is on the order of 10 5. This is well within the turbulent flow regime and hence the flow at the inlet is considered turbulent. Another important dimensional parameter for this analysis is the Froude number. This dimensional parameter relates the inertial and gravitational forces acting 115 on the fluid. The Froude number is defined by Eq. (2). u i Fr i ¼ pffiffiffiffiffiffiffiffi 2gr i ð2þ Where u i is the velocity of the gas at the inlet, g is the acceleration due to gravity and 2r i is used as the vertical length scale. The velocity of the gas at the inlet will vary throughout the fill. At the onset of filling the velocity of the hydrogen gas at the inlet 120 quickly reaches its peak (within the first few seconds) and then declines slowly as the density of the gas inside the cylinder increases. It is important to note that the dispenser controls the filling rate and hence the velocity of the gas at the inlet never

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 5 Table 1 Summary of mach, reynolds, and froude numbers for a 40-second and 5-minute fill 40-second fill 5-minute fill Ma i Re i Fr i Ma i Re i Fr i Start of fill 0.140 8.2 10 5 99 0.02 1.1 10 5 13 End of fill 0.036 7.23 10 5 34 0.005 1.0 10 5 4 reaches the sonic point. The Mach number at the inlet is defined by Eq. (3). Ma i ¼ u i ¼ m c s c s q i A i ð3þ Where _m is the average mass flow rate of hydrogen gas, c s is the speed of sound of the gas, q i is the density of the gas at the inlet, and A i is the cross sectional area of the inlet. The initial and final inlet Mach numbers for the case of a 40-second and 5- minute fill are shown in Table 1. The inlet is the location of highest velocity within the cylinder and hence based on the results listed in Table 1, the flow everywhere within the cylinder can be considered subsonic. With u i determined from the Mach number, the Froude number can be calculated using Eq. (2). The resultant Reynolds and Froude numbers are summarized in Table 1. For a 40-second fill the Reynolds number indicates the flow is turbulent and that the effect of gravity on the flow is small in comparison to the inertial forces. For the 5-minute fill, the flow is also turbulent throughout filling, however, towards the end of the fill the effect of gravity on the flow field will become significant. 130 135 2.2. Model Development 140 The goal of the two dimensional model is to predict the temperature distribution within a compressed gas cylinder during filling. To this end the model utilizes the principles of computational fluid dynamics (CFD) to discretize the space within the cylinder and its walls, creating numerous control volumes over the boundaries of which, the governing equations are solved to determine the characteristics of the 145 hydrogen flow. The model assumes the flow within the cylinder to be axisymmetric with respect to the centerline of the cylinder. In essence, assuming the effect of gravity and buoyancy forces to be negligible when compared to the magnitude of the gas velocity entering the cylinder. It is important to note that this assumption is only 150 valid while the cylinder is being filled. At the completion of filling gravity and buoyancy forces will significantly affect flow within the cylinder. Further to the dimensional analysis performed above, the longer the fill time, the greater the relative effect of gravitational forces on the flow field inside the cylinder. Hence, the longer the fill time the less suitable the assumption of axisymmetric flow. For this reason the 155 model was run for the case of a 40-second fill.

6 C. J. B. DICKEN AND W. MERIDA Table 2 Cylinder dimensions Dimension=description Value Unit 4L Length of the cylinder 0.893 m r i Inner radius of the cylinder 0.179 m r o Outer radius of the cylinder 0.198 m k liner Liner thickness (assumed to be uniform throughout) 0.004 m k lam Laminate thickness (assumed to be uniform throughout) 0.015 m d inlet Inside diameter of the gas inlet tube 0.005 m k tube Wall thickness of the gas inlet tube 0.002 m L tube Length of the tube protruding into the cylinder 0.082 m For the purposes of this model, the liner and laminate that make up the cylinder walls are assumed to be isotropic. In actuality the thermal conductivity of the carbon fiber wrap is anisotropic due to the nature of the wrapping. Radiation heat transfer between the hydrogen gas and cylinder walls is assumed to be negligible due 160 to the small temperature difference between the gas and liner surface. The model is split into two computational domains. The first is the fluid domain within the cylinder, which is filled with hydrogen gas. The second domain is the cylinder wall and inlet tube. The wall is split into the liner and laminate. The dimensions used for the model are supplied in Table 2. The liner and laminate 165 thickness along the length of the cylinder is assumed to be uniform. The flow within the cylinder, and heat transfer through the walls, vary with time; hence all governing equations must be solved in their unsteady form. While the heat of compression dominates the increase in temperature during filling, viscous effects are important for accurately determining the convective heat transfer from 170 the gas to the cylinder liner. Due to the high gas velocities at the inlet and due to the fundamental problem of density varying with time, the model incorporates compressibility effects. A real gas equation of state is used instead of the ideal gas law due to the high density of the gas at the pressures of filling. As seen in the preceding section the flow at the inlet is turbulent throughout the fill and hence the model 175 solves the Reynolds averaged governing equations using a turbulence model for closure of the turbulent viscosity term. Applying the conservation of mass to the fluid region of the model and applying Reynolds averaging techniques yields the first governing equation for a finite volume. q qt q þ q ðqu Þ¼0 qx i ð4þ Where q is the ensemble average of density and v is the Favre average of velocity. The law of conservation of momentum yields the equations below. q qt ðq~u i Þþ q ðq~u i ~u j Þ¼ qp þ q s ij qu qx j qx i qx 0 iu 0 j ð5þ j s ij ¼ 2 3 me qu k ij þ m qu i þ qu j qx k qx j qx i ð6þ

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 7 The term qu 0 iu 0 j is an unclosed term and will be modeled using the k-e model 185 described below. The application of the conservation of energy principal yields q qt ðq ehþþ q qx j q eh~u j ¼ qp qt þ q qx j q j qh 0 u 0 j þ ~u i s ij þ u 0 is ij ð7þ q j ¼ k qt qx j ð8þ H ¼ h þ 1 2 u iu i The terms qh 0 u 0 j u0 i s ij are the unclosed terms, which are modeled using the k-e turbulence model. In addition to the governing equations for mass, momentum and energy, two more governing equations are required to describe the turbulence within the flow. Many turbulence models exist for obtaining closure for the governing equations. The flow field developed within the cylinder is dominated by the structure of the turbulent jet of gas protruding from the cylinder inlet. Compressible turbulent gas jets have been studied extensively as they exist in many practical fluid dynamics problems. The standard k-e model has been used in many studies of transient gas jets. Due to the assumption of isotropy inherent in the standard k-e model the results for transient gas jets tend to over-predict the spreading rate [18 20]. Adjusting the coefficients of the k-e model corrects for this over-prediction [18]. The standard k-e turbulence model [21] uses two parameters to describe the turbulence of the fluid. The turbulence kinetic energy, k, and the rate of turbulent energy dissipation, e, are defined as follows: ð9þ 190 195 200 k t 1 2 u iu i ð10þ e t ¼ n qu i qx j qu i qx j ð11þ The transport equations for the turbulent kinetic energy and its dissipation rate are as follows [22]. q qt ðqk tþþ q qx i ðqk t u i Þ ¼ q qx j m þ m t qkt qu r k qx 0 iu 0 qu j j qe 2qe k t j qx i c 2 s ð12þ q qt ðqe tþþ q qx i ðqe t u i Þ ¼ q qx j m þ m t r e qet qx j þ C 1e e t k qu0 i u0 j qu j C 2e q e2 t qx i k ð13þ The k-e model brings closure to the Reynolds averaged conservation of momentum

8 C. J. B. DICKEN AND W. MERIDA by eliminating the term qu 0 i u0 j in Eq. (5) and replacing the m in Eq. (6) by m t. Where, m t ¼ qc m k 2 t e t ð14þ The closure for the Reynolds averaged energy in Eq. (7) is gained by eliminating the term ð qh 0 u 0 j u0 i s ijþ and replacing the k in Eq. (8) with k eff, and replacing m in Eq. (6) with m eff. Where, 215 k eff ¼ k þ c pm t Pr t m eff ¼ m þ m t ð15þ ð16þ The value of the constants used in the k-e model are modified slightly as suggested by Ouellette et al. in [18] (C 1e ¼ 1.52, C 2e ¼ 1.92 and, C m ¼ 0.09). Within the domain of the cylinder walls the conservation of mass and momentum do not apply as the material is solid. The conservation of energy within the cylinder wall takes the form 220 q qt ðq wh w Þ¼k w q 2 T w qx 2 j ð17þ The heat transfer between the hydrogen gas and the cylinder liner is dominated by turbulent convection. The model employs a log law of the wall for mean temperature in the turbulent region of the thermal boundary layer and a linear conduction sub layer [22 24]. To integrate the compressibility effects of high-pressure hydrogen, the model utilizes the Redlich-Kwong real gas equation of state [25], 230 p ¼ RT ðv bþ a T 1 2ðvðv þ bþþ ð18þ Where p denotes the gas pressure, R the universal gas constant, T is the temperature of the gas, and v is the molar specific volume. The terms a and b are constants related to the critical properties of the material through the equations 235 a ¼ 0:08664 R2 Tc 2:5 p c ð19þ b ¼ 0:4275 RT c p c ð20þ The subscript c denotes the value of the property at the critical point. While many real gas equations of state exist for hydrogen, the Redlich-Kwong equation was chosen as it provides acceptable accuracy in the ranges of temperature 240 and pressure in this study, and it is less intensive computationally. Other more

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 9 accurate equations exist but require far more computation, which will severely limit the speed of the overall model. The CFD software Fluent 6.2 was used to develop the model. Since Fluent does not include a real gas library for hydrogen a significant part of this work 245 was to derive a real gas model for hydrogen based on the Redlich-Kwong equation of state. This required creating and compiling a user defined function in Fluent to calculate all of the thermodynamic property data required by the solver. The approach of [26] is followed in deriving the equations for the thermodynamic properties of hydrogen based on the Redlich-Kwong equation of state. Table 3 250 summarizes the equations derived for calculating the thermodynamic properties of hydrogen. The constants used for evaluating the specific heat at constant pressure were taken from [26]. The model uses the Fluent coupled solver with the implicit formulation, axisymmetric in space and unsteady in time. Within each time step, convergence is 255 judged by analyzing the mass flow rate of gas entering the cylinder, the rate of heat transfer to the cylinder walls and the mass averaged temperature of the gas within the cylinder. The solution for each time step is converged when these three parameters meet to a single value for each within four significant digits. 260 2.3. Boundary and Initial Conditions The model boundary conditions are assessed at the cylinder inlet, inside wall and outside wall of the cylinder. At the inlet, a pressure boundary condition is used. This boundary condition is varied with time to match the measured pressure at the inlet of the cylinder during an experimental fill. At the inlet, the flow direction is 265 assumed to be uniform in the direction of the cylinder axis. Since the energy equation is solved in the model, a total temperature boundary condition is used at the inlet. The total temperature represents the temperature of the gas at stagnation conditions. This boundary condition is also varied with time to represent experimental inlet conditions throughout the fill. 270 At the inside wall of the cylinder a non-slip boundary condition is used to solve the conservation of mass, momentum, turbulent kinetic energy and dissipation rate. There is no boundary condition for the energy equation at the inner wall. Instead the energy equation for the gas inside the cylinder, Eq. (7), is coupled to the energy equation for the cylinder walls Eq. (17). 275 At the outer wall, a constant heat transfer coefficient thermal boundary condition is used to determine the heat transfer between the cylinder wall and the environment. The temperature of the outer laminate surface of the cylinder does not change significantly during rapid filling; this supports the simplifying assumption of a constant heat transfer coefficient boundary condition. The ambient temperature is assumed to be constant throughout the fill. 280 The initial conditions for the model are defined by the initial temperature and pressure of the gas within the cylinder. The cylinder walls are assumed to be the same temperature as the gas. The pressure and temperature of the gas are assumed to be uniform within the space of the cylinder. 285

10 C. J. B. DICKEN AND W. MERIDA Table 3 Equations for thermodynamic property data based on the Redlich-Kwong equation of state Property Equation No. h h ¼ 3a n ln þ RTn 2bT 1 2 n þ b n b n 3 RT p n2 þ a pt 1 2 a T 1 2ðn þ bþ! b RT p b2 n ab ¼ 0 pt 1 2 Z T RT þ C P dt þ h ref (21) T ref q Solve cubic equation q ¼ 1 n (22) C p [24] c p ¼ p qn R 3a n 3a ln þ qt p 4bT 3 2 n þ b 2T 1 2nðn þ bþ qn qt þr X17 Nk ik (23) p k¼1 S S ¼ a n n qt ln R ln R ln 2bT 3 2 n þ b n b q ref T ref þ Z T Tref X 17 k¼1 N k T t2 1!dT þ S ref (24) C sound sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c p qn C sound ¼ n R c p qp p m m ¼ 6:3e 7 ffiffiffiffiffiffiffiffiffiffiffi p c 2:018 101325 s 2 3 ðt 0:1667 e 0 3 T 2 Tc 1 (25) B C @ T þ 0:8 A (26) Tc k k ¼ðc p þ 1:25RÞm (27) qn qp T qn qt p qq qt p qq qp T qh qt p qh qp T qn ¼ qp T 1 h i (28) a RT T 1 2 qn ¼ qt p 1 n 2 ðnþbþ þ 1 nðnþbþ 2 qq ¼ q 2 qn qt p qt p qq ¼ q 2 qn qp T qp T ðn bþ 2! R n b þ a qn 2T 3 2nðn þ bþ qp T qh ¼ c p (32) qt p " qh ¼ n T qn # qp T qt p (29) (30) (31) (33)

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 11 Figure 1. Computational grid used for modeling the compressed gas cylinder. 2.4. Computational Grid The computational grid used for the model is shown in Figure 1. The grid is a combination of structured and unstructured mesh. The inlet area, where the highest gas velocities are seen, is mapped with a high-resolution structured mesh. The walls are also discretized with a structured mesh in order to ensure enough computational 290 nodes through the cylinder wall. The bulk gas region is then meshed with an unstructured grid. The grid resolution at the wall is left coarse as the wall functions built into fluent will be used to compute the boundary layer flow parameters. The temperature rise during the first five seconds of the fill (performed using the boundary and initial conditions described in section 2.3.) is used to determine 295 the sensitivity of model solution to the number of cells within the computational grid. The model was evaluated for three grids consisting of 580, 1,170, and 4,580 cells. The corresponding temperature rise in the first five seconds was 30.75, 29.65, and 29.55 K. The grid sensitivity is greatest when the number of cells is below 1,200. As the grid is refined with greater than 1,200 cells the change in the temperature rise become minimal. The grid depicted in Figure 1 has 4,580 cells; this grid was 300 used to produce all the results provided in this study. 3. EXPERIMENTAL MATERIALS AND METHODS The model is to be validated by comparison with experimental results. A compressed gas cylinder was instrumented with 63 thermocouples to measure the temperature distribution inside the cylinder during refuelling. The thermocouples were 305 held in position by a specially designed insert with spring-loaded arms. The cylinder was filled using the Pacific Spirit Fuelling station located at the National Research Council of Canada s Institute for Fuel Cell Innovation. The fuelling station stores hydrogen at 45 MPa and transfers the hydrogen to the cylinder using a General 310 Hydrogen CH350A dispenser [27]. The compressed gas cylinder used in these experiments is a Dynetek type 3 model V074H350. The cylinder has an internal volume of 74 liters and an external diameter and length of 39.9 cm and 90 cm, respectively. The test setup of the fuelling station, dispenser, and test cylinder is detailed Figure 2. The test cylinder is instrumented with two pressure sensors for monitoring the tank pressure and inlet press- 315 ure, a thermocouple for monitoring the inlet temperature of the gas and 63 thermocouples supported inside the cylinder, which measure the hydrogen gas temperature at numerous locations within the cylinder. The thermocouples used where type T with an accuracy of þ= 1 K [27]. 320

12 C. J. B. DICKEN AND W. MERIDA Figure 2. Schematic of the test setup included ground storage, dispenser, and test cylinder. 4. RESULTS 4.1. Repeatability of Experimental Fills Many fills were performed with the experimental setup, two representative fills, here after referred to as fill 1a and 1b, were both performed at a nominal pressure ramp rate of 41.5 MPa=min. Fill 1a was initiated from an initial temperature and 325 pressure of 293.4 K and 9.36 MPa, while fill 1b was initiated from an initial temperature of 299.4 K and 9.31 MPa. The change in mean hydrogen gas temperature within the cylinder and increase in pressure during the fill are plotted in Figure 3a. The greatest increase in temperature occurs at the start of filling, where the ratio of the mass flow rate to the mass of gas within the cylinder is greatest [27]. The 330 Joule-Thomson effect is also greatest at the onset of filling where the pressure drop across the throttling device is greatest. The shape of the temperature increase is in agreement with previous studies of the filling of compressed gas cylinders [3 6, 8, 9, 11 17, 27]. Fill 1a and 1b produce virtually identical increases in mean temperature and pressure. This is due to the excellent repeatability provided by the electronically controlled CH350A dispenser. 335 In order to validate the numerical model, the initial conditions along with the temperature and pressure inlet boundary conditions measured during fill 1a where input into the model. The model was then run to produce a simulated fill. A detailed

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 13 Figure 3. (a) Measurement of the relative increase in average temperature within the cylinder during test fill 1a and 1b; (b) experimentally measured inlet gas temperature and pressure measured during fill 1b. list of the initial conditions, boundary conditions and material properties used to numerically simulate fill 1a are listed in Table 4. The inlet pressure and temperature boundary conditions are taken directly from the results of fill 1a. Figure 3b shows the inlet temperature and pressure measured just before the inlet to the cylinder during fill 1a. These results were curve fitted and input into the Fluent model. The sudden increase in inlet temperature at the start of the fill is the result of the compression of the gas inside of the fill line prior to forcing open the tank solenoid valve. The second increase in temperature thereafter is the 340 345

14 C. J. B. DICKEN AND W. MERIDA Table 4 Boundary, initial, and material conditions for fill 1a and 1b Value Unit Boundary condition Ambient temperature 293.4 K Convective heat transfer coefficient between the cylinder outer 10 W=m 2 K surface and the ambient air Gas inlet pressure ramp rate See Figure 3 MPa Gas inlet temperature See Figure 3 K Initial condition Gas pressure 9.3 MPa Gas temperature 293.4 K Material properties Aluminum liner Thermal conductivity 167 W=mK Density 900 kg=m 3 Specific heat 2,730 J=kgK Carbon-fiber=epoxy laminate Thermal conductivity 1.0 W=mK Density 938 Kg=m 3 Specific heat 1,494 J=kgK result of the Joule Thomson heating which is greatest at the start of the fill and declines as the pressure of the test cylinder and ground storage cylinders approach equilibrium. 350 4.2. Comparison of Experimental and Model Results The comparison of the rise in average gas temperature during the model and experiment fill is the main method used for validating the model. Figure 4 plots the mean gas temperature of the hydrogen gas for the modeled and experimental cases. The results show good agreement between the model and experiment. The 355 maximum difference between the model and experimental results is 6 K and occurs within the first 10 seconds of the fill. The difference between the model predicted and experimentally measured mean temperature of the gas at the end of the fill is 2.2 K. Qualitatively, the model correctly predicts the shape of the curve where there is a rapid rise in temperature at the onset of filling when the rate of compression of 360 the gas is greatest and the thermal mass of the gas within the cylinder is at its lowest. In order to correctly predict the temperature rise, the model must be able to accurately simulate the heat transfer between the gas and the inner wall of the cylinder. This result confirms that the CFD model accurately predicts the heat transfer during filling. 365 The Redlich-Kwong equation of state is used to solve for the density of the hydrogen gas at the end of the fill. The 2.2 K difference in temperature between the model and experiment, results in the model over estimating the density by 0.53%. A secondary means of model validation is the comparison of the model predicted gas temperature field and experimental measurements of the temperature field 370 within the cylinder. Figure 5 compares the model predicted and experimentally

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 15 Figure 4. Comparison of the model prediction and experimental measurement of the mean gas temperature during filling. measured temperature distribution throughout the cylinder at 5 s, 15 s, 25 s, and at the end of the fill. The model results predict the maximum temperature to be located at the fill end, surrounding the inlet. In general the experimental temperature fields confirm this prediction. Both the model and experiment predict a significant temperature gradient protruding from the cylinder inlet. The model predicts a larger 375 variation in temperature because it includes the cylinder inlet where incoming gas is at a much lower temperature. During the experiment the closest thermocouple to the inlet was 7 cm away along the centreline of the cylinder. Between the inlet and the location of the first thermocouple the temperature of the gas increases considerably. Outside the region of the inlet plume the variation of the temperature field 380 of the bulk gas is less than 3 K. The small variation in gas temperature in the bulk makes this region ideal for placement of a sole temperature sensor whereby the temperature measured would best reflect the mean temperature of the gas within the cylinder. While the bulk 385 region may be ideal for accuracy it is difficult to access with a sensor. Most cylinders have access ports at either end making the centreline the easiest place to locate a sensor. Figure 6 plots the model prediction of the temperature of the gas along the normalized centreline at the end of the fill. The model predicts a significant temperature gradient from the initial expansion of the inlet gas jet at 0.15 to the midpoint of the 390 centreline. From the midpoint to the tail end of the cylinder the temperature along the centreline increases slowly towards the average temperature of the gas near the end point of the cylinder. The variation in gas temperature in the radial direction is shown in Figure 7. The temperature profile at horizontal locations of x=l ¼ 0.2, 0.2, 0.35, and 0.5 are plotted for times of 5 s, 15 s, and 25 s into the fill. The plots 395 show a significant radial temperature gradient at x=l ¼ 0.2 with a diminishing gradient with distance from the gas inlet. As shown in Figure 6 the temperature at the

16 C. J. B. DICKEN AND W. MERIDA Figure 5. Comparison of the model and experimental temperature distribution within the cylinder at 5 s, 15 s, 25 s, and at the end of the fill. centreline increases with distance from the inlet. Figures 5 7 combine to describe an inlet gas plume which creates a conical region extending from the inlet to x=l ¼ 0.6 and y=r o ¼þ= 0.3; where the local gas temperature is significantly lower than the 400 mean gas temperature and where significant gas temperature gradients are present. Both of these effects diminish as the horizontal distance form the inlet increases.

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 17 Figure 6. Model predicted temperature along the centerline of the cylinder at the, end of the fill. Figure 7. Model predicted radial temperature profile at (a) x=l ¼ 0:2, (b) 0.35, and (c) 0.5 at time intervals of 5 s, 15 s and 25 s.

18 C. J. B. DICKEN AND W. MERIDA When a single temperature sensor is used to measure the mean gas temperature, the region of the inlet plume (from the inlet to x=l ¼ 0.6 and y=r o ¼þ= 0.3) should be avoided as the local temperature in this region is significantly different than the mean 405 gas temperature. Conversely the bulk region which surrounds the inlet gas plume provides an approximation of the mean gas temperature to within þ= 3 K. For this reason, a temperature probe inserted through the end port of the cylinder is an ideal location for both accuracy and accessibility. A temperature sensor can also be placed at the inlet port so long as the probe is outside the region of the inlet plume. 410 The gas velocity distribution at time intervals of 5 s, 15 s, and 25 s is shown in Figure 8. As time increases, the magnitude of the velocity at the inlet decreases due to the increase in density during the fill. With a greater density, less velocity is required at achieve the same mass flow rate of gas. As with the temperature distribution, the gas velocity is greatest and the velocity gradients are highest within the inlet gas 415 plume region. 4.3. Investigation of Heat Transfer Between the Gas and Cylinder Liner The heat transfer between the gas and cylinder liner remains the most significant obstacle for simplified models based on uniform temperature. A concise Figure 8. Model predicted velocity distribution within the cylinder at (a) 5 s, (b) 15 s, and (c) 25 s of the fill.

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 19 correlation for determining the convection coefficient based on practical and measurable parameters remains unavailable. Simplified models assume uniform temperature within the cylinder, and use Eq. (34) to calculate the heat transferred from the gas to the cylinder wall. The difficulty faced by these models is the calculation of the convective heat transfer coefficient, h. These models often use h as a tuning parameter to fit the model results to experimental data. The convection at the wall is dominated by the local velocity and turbulence of the flow near the wall, both of which are dependent on numerous experimental parameters and cylinder geometry. 420 425 Figure 9. (a) Model-predicted rate of heat transfer from the hydrogen gas to the cylinder wall and mass flow rate of gas entering the cylinder, throughout the fill; (b) Model-predicted average convection coefficient and mass flow rate of gas entering the cylinder throughout the fill.

20 C. J. B. DICKEN AND W. MERIDA A heat transfer correlation relating h to experimentally measurable parameters has yet to be developed. _q ¼ haðt gas T wall Þ ð34þ One of the major advantages of the present model is that it can be used to investigate the heat transfer processes that take place during filling. Figure 9a plots the total heat transfer from the gas to the liner and the mass flow rate of the gas entering the cylinder throughout the fill. Far from being uniform throughout the fill, the heat Figure 10. (a) Model predicted heat flux distribution and (b) convection coefficient h, around the inner wall of the cylinder at time 15 s.

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 21 transfer reaches a maximum within the first few seconds of the fill and decreases 435 steadily thereafter. The maximum rate of heat transfer is 43 kw and the mean heat transfer rate throughout the fill is 18.4 kw. From the figure it is also clear that there is a strong relationship between the rate of heat transfer and the mass flow rate of gas into the cylinder. This result is not unexpected; the rate of gas flowing into the cylinder will have a direct affect on the magnitude of both the velocity field 440 and turbulence kinetic energy within the cylinder, which will in turn, affect the rate of heat transfer through the convection coefficient at the wall. The greater the mass flow rate, the greater the increase in convection coefficient. The relationship is elucidated further in Figure 9b, where the average convection coefficient between the gas and wall is plotted along with the mass flow rate. The peak in the mean 445 convection coefficient and the peak mass flow rate occur at the same point in time and the curves follow a similar shape. The exact relationship cannot be ascertained from the present data set but it is clear that there exists a significant correlation between the mass flow rate and the mean convection coefficient. Further work in this field should seek to develop an empirical correlation for the calculation of h 450 based on measurable and practical experimental parameters. Figure 10a shows the distribution of the heat flux and convection coefficient around the inside wall of the cylinder 15 seconds into the fill. The greatest heat flux occurs at the non-fill end hemisphere while the minimum heat flux occurs at the tip of the fill end hemisphere. The increased heat flux at the non-fill end is the result of a 455 greater local convection coefficient in that region as shown in Figure 10b. The convection coefficient around the inner wall is nearly uniform except for at the non-fill end, where the convection increases significantly. This is due to the impingement of the gas jet from the inlet onto the end hemisphere and the turbulence and velocity field that results. The heat transfer coefficient decreases from the non-fill end along 460 the cylindrical portion of the liner and increases again at the fill end. 4.4. Temperature Profile in Cylinder Wall The cylinder is comprised of a highly conductive aluminum liner and a comparatively insulating carbon fiber and epoxy wrapping. For simplicity of the model, the thermal properties of both the liner and laminate were assumed to be constant. 465 This assumption is made as the effect of temperature on the thermal conductivity, density and specific heat of the aluminum liner and carbon fiber = epoxy laminate is insignificant to the overall heat transfer process. The temperature rise within a compressed gas cylinder during filling can be limited by the material properties of the liner and laminate above a certain temperature. While the present standard dictates that the mean gas temperature within the cylinder must not exceed 358 K, the 470 relationship between the gas temperature and the temperature of the liner and laminate during filling has not been clearly defined. The present model is used to determine the temperature profile within the cylinder wall. Figure 11 describes the makeup of the cylinder wall, and shows the temperature profile through the wall of 475 the cylinder at seven locations along the wall. The temperature profiles at locations 2 through 6 show the dramatic effect of the thermal diffusivity of the two different materials. The temperature within the aluminum liner is nearly uniform where as a significant temperature profile exists across the laminate. Due to the speed of the fill and

22 C. J. B. DICKEN AND W. MERIDA Figure 11. Model predicted temperature profile in the cylinder wall at the end of filling. the low thermal conductivity of the laminate, the external surface temperature of the cylinder does not see a significant change in temperature. The temperature of the liner varies significantly from one location to the next along the length of the cylinder. The liner temperature is greatest at location 6 and 7 (along the dome at the non-fill end) and the lowest at location 1 (the fill end). The locations 2 6 show a gradual decrease in liner temperature from the non-fill end towards the fill end. This is the result of the lower heat transfer rate at the fill end as the temperature of the liner is governed by the heat transfer rate from the onset of filling up until the time of the measurement. 480 485 5. CONCLUSIONS A two dimensional axissymmetric CFD model of the filling of a compressed gas cylinder has been developed and compared to experimental measurements. 490 The model is able to predict the final mean temperature of the gas at the conclusion of the fill within 2.2 K of the experimental result. The temperature distributions at 15 seconds, 25 seconds, and at the end of the fill along with the experimental measurements confirm the minimum temperature is located at the gas inlet, and there exists a large temperature gradient at the inlet of the cylinder. Both the model and experiment show significant temperature gradients within the gas inlet region, along 495 the

MODELING THE TEMPERATURE WITHIN A HYDROGEN CYLINDER 23 centreline from the inlet to x=l ¼ 0.6 and radially from the y=r o ¼þ= 0.3. The temperature in the bulk region of gas which surrounds the inlet region is much more uniform and provides the best location for a single temperature sensor to monitor the mean temperature of the gas throughout the fill. 500 The model has been used to investigate the heat transfer between the gas and inner wall and the temperature within the cylinder walls. The heat transfer reaches a maximum within the first 5 seconds and decreases steadily thereafter. The convection coefficient between the gas and inner wall is heavily influenced by the rate of mass flow into the cylinder. The local convection coefficient around the cylinder wall is 505 greatest at the non-fill end. As a result the greatest heat transfer and highest liner temperature occur at the non-fill end of the cylinder. The temperature gradient within the liner in the radial direction is shown to be small where as the laminate shows such a strong temperature gradient that the external surface temperature of the laminate does not increase significantly during the fill owing to its low thermal 510 conductivity and the short duration of the fill. REFERENCES 1. International Standard Organization, Gaseous Hydrogen and Hydrogen Blends Land Vehicule Fuel Tanks Part 1: General Requirements, ISO 15869, 2005. 2. International Standard Organization, Gas Cylinders High Pressure Cylinders for the 515 on-board Storage of Natural Gas as a Fuel for Automotive Vehicles, ISO 11439, 2005. 3. S. Charton, V. Blet, and J. P. Corriou, A Simplified Model for Real Gas Expansion between Two Reservoirs Connected by a Thin Tube, Chemi. Eng. Science, vol. 51, no. 2, pp. 295 308, 1996. 4. D. E. Daney, F. J. Edeskuty, and M. A. Daugherty, Hydrogen Vehicle Fueling Station, 520 Advances in Cryogenic Eng., vol. 41, pp. 1041 1048, 1996. 5. M. Duncan and S. Macfarlane, Fast Filling of Type 3 Hydrogen Storage Cylinders, submitted to Hydrogen and Fuel Cells Conference, June 2003. Q1 6. J. A. Eihusen, Application of Plastic-Lined Composite Pressure Vessels For Hydrogen Storage, General Dynamics Armament and Technical Products, Available at http:// 525 Q2 www.lincolncomposites.com/media.html, 2003. 7. M. A. Haque, M. Richardson, and G. Saville, Blowdown of Pressure Vessels I. Computer Model, Trans IchemE, vol. 70, pp. 3 9 part B, 1992. 8. K. Kountz, Modeling the Fast Fill Process in Natural Gas Vehicles Storage Cylinders, 207th American Chemical Society Meeting March 1994. 530 9. C. Perret, Modelling and Simulation of the Filling of a Gaseous Hydrogen Tank under very High Pressure, European Integrated Hydrogen Project Phase II, WP 3.2, DTEN=DR=2003=167, January 2004. 10. W. C. Reynolds and W. M. Kays, Blowdown and Charging Processes in a Single Gas Receiver with Heat Transfer, Transactions of the ASME, July, pp. 1160 1168, 1958. 535 11. M. Richards, W. Liss, and K. Kountz, Modeling and Testing of Fast-Fill Control Algorithms for Hydrogen Fueling, National Hydrogen Association s 14th Annual U.S. Hydrogen Conference and Hydrogen Expo USA, March 2003. 12. J. Xia, A Simplified Model for Depressurization of Gas-Filled Pressure Vessels, Int. Comm. Heat Mass Transfer, vol. 20, pp. 653 664, 1993. 540 13. M. A. Haque, M. Richardson, and G. Saville, Blowdown of Pressure Vessels II. Experimental Validation of Computer Model and Case Studies, Trans. IchemE, vol. 70, part B, pp. 10 17, 1992.

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