Analytical Assessment of the Mechanical Design of a Metal Getter Bed for Hydrogen Storage

8/20/2019 Analytical Assessment of the Mechanical Design of a Metal Getter Bed for Hydrogen Storage

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Analytical assessment of the mechanical design of a metal getter bed

for hydrogen storage

Rupsha Bhattacharyya*

Heavy Water Division, Bhabha Atomic Research Centre, Mumbai-400 085, Maharashtra, INDIA

Abstract

Compact solid state hydrogen storage systems using metal or alloy based getter beds have gained worldwide attention. The

vessels containing the metallic getter are required to operate under both external and internal pressure conditions, with

accompanying cooling and heating cycles. Thus the mechanical design of these vessels must take care of several kinds of loads

some of which are addressed in this work. Selection of optimal dimensions, closures and suitable supports for the vessel are

considered, followed by the preliminary steady state thermal stress and seismic analyses to ensure a stable and robust

mechanical design under usual operating conditions. A method of evaluation of the cyclic loads acting on the vessel has also

been demonstrated which will be useful for fatigue analysis of the vessel. These checks are recommended at the vessel design

stage itself since they do not necessitate expenditure of large amounts of computational time, which would be required for a ful

finite element based stress analysis of the vessel.

Keywords: getter bed, pressure vessel, stress analysis, cyclic loads

* Author for correspondence: Email: [email protected], Tel: +91-22-2559-2962

INTRODUCTION

The extensive use of hydrogen as a fuel for the future depends significantly on the available technologies to store it

Hydrogen immobilized on a solid matrix by physical or chemical adsorption has been used as a compact, reversible

storage technique for the gas [1]. Out of various solids available for the storage and on demand recovery of hydrogen

metal and metallic alloy based getter materials have been studied and employed most extensively, both for automobileapplications as well as for various applications in the nuclear industry [2, 3].

The pressure vessel employed to contain the solid getter experiences a wide range of operating conditions as it goes

through hydriding and dehydriding steps. During hydriding a given quantity of gas at ambient conditions or at somewhat

elevated temperature and pressure is filled into this vessel. As soon as the hydriding reaction starts the pressure falls and

ultimately the equilibrium pressure at the corresponding hydriding temperature is attained. For various metals or alloys

like uranium, ZrCo this equilibrium pressure is in the moderately high vacuum range at near ambient conditions, with a

value of 1 atm being attained in the vicinity of 430 to 450 deg C [4, 5]. So during recovery of hydrogen, the getter

material must be heated to cause dissociation of the hydride and release the adsorbed gas. The gas can then be removed by

continuous evacuation, thus leading to creation and maintenance of vacuum conditions inside the vessel. So alternating

cycles of high pressure and low temperature followed by low pressure, high temperature are encountered by the vessel

containing the getter bed. The high pressure phase may actually be of a very short duration compared with the entire

cycle, since the reaction kinetics is very fast and the pressure drops rather rapidly during hydriding if the metal is in a

sufficiently active state [6]. So for most of the time, the vessel must withstand external pressure loads. But it must be

designed to operate safely and reliably under both sets of conditions.

It has been reported that for thermonuclear fusion reactor systems, there is a need to store various quantities of hydrogen

isotopes at the reactor site. Some of the larger vessels can contain up to 60 gm of the isotopes per vessel [7] with severalkilograms of uranium or ZrCo acting as the solid storage medium. This indicates the scale of the vessel volume

considered in this work and the vessel dimensions are determined and analysis is carried out accordingly.


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Analytical assessment of getter bed design Rupsha Bhattacharyya__________________________________________________________________________________________________

This work presents an analysis of the mechanical design considerations for a getter bed vessel using analytical expressions

available in literature for cylindrical vessels. The volume of the vessel is fixed from the quantity of hydrogen to be stored

Further mechanical details like the selection of dimensions of the vessel, the closures and the supports are subsequentlyaddressed through simple optimization criteria. Thermal stresses and seismic loads are addressed next to ensure that the

design is robust and safe. Cyclic loads acting on the vessel and fatigue issues are also addressed in the paper. The majorobjective is to utilize the necessary analytical formulations available for stress analysis in simplified vessel geometries to

check that the design can be at least theoretically established to be safe and capable of reliable operation under the design

conditions.

MECHANICAL DESIGN OF A METAL GETTER BED

Design basis

The hydriding process on uranium is represented by the following chemical reaction:

U + 1.5H2 = UH3, HRx = -97.5 kJ mol-1 H2 (1)

This reaction was used to estimate the stoichiometric quantity of uranium necessary for storing a given amount (in this

case 60 gm) of hydrogen. The mass of solid actually to be loaded into the vessel was decided by the percentage loading of

hydrogen on uranium, which was taken as 60% in this work. Thus hydrogen was allowed to be the limiting reactant. The

volume expansion of uranium and change in powder density on hydriding were considered in estimating the maximum

solid volume to be accommodated inside the vessel. The space available for gas was taken as 9 times the calculated solidvolume. This gives a rather conservative value of the vessel volume. Once the total vessel volume was fixed, the other

dimensions were calculated as shown in the following sub-sections. The material of construction of the vessel was taken

as SS 316L and the design temperature was fixed at 400oC on the basis of maximum allowable operating temperature for

it from ASME Section VIII, Division 2, which is about 450oC. At 450

oC, the equilibrium pressure of hydrogen over

uranium is known to be 1.47 bar (a) [4]. Thus at this temperature, the maximum gas pressure cannot rise beyond theequilibrium value. For calculation of wall thicknesses the design pressure is taken as 40 bar (a).

General assumptions

Certain assumptions have been made in carrying out the design of the vessel and the subsequent analyses. These are listed

below:

(i) The vessel has been designed as a thin walled vessel and all analyses have been carried out by considering the

membrane stresses.

(ii) Only vertical alignment of the vessel has been considered for support design.

(iii) Elastic deformation and behaviour of the vessel under mechanical and thermal loads have been studied in this work.

Creep and fatigue issues have been separately addressed.

(iv) The material of construction is ductile and has been assumed to be free of flaws and defects that could lead to

localized stress concentration, crack propagation and failure. Discontinuity stresses at the vessel-end closure junction arethe only secondary stresses considered here.

(v) Bi-axial stress conditions (i.e. along the circumference of the shell and along the axis) have been taken into account in

the analyses, unless otherwise mentioned.

(vi) All welded connections have been assumed to have been 100% radiographically examined, so all the joint efficiencies

have been taken as unity.


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(vii) The material of construction has been taken as SS316L (owing to its suitability for hydrogen service and welded

construction) and it has been assumed to be homogeneous and isotropic.

(viii) Piping reaction loads on the vessel nozzles have not been considered in this work since the detailed layout of piping

connected to the vessel would be required for that. No eccentric loads due to offset piping have been considered here.

Selection of optimal vessel dimensions and end closures

The fixing of the vessel volume i.e. the shell volume was followed by selection of a length to diameter ratio for the shellbased on which the shell thickness was calculated. The thickness of the shell had to be so chosen that the vessel can

operate safely under internal as well as external pressure i.e. the vessel has to be capable of withstanding the internal

tensile stress when pressurized during the filling of gas or during the dehydriding if pressure build up is allowed before

gas recovery is started, as well as the external compressive load when it is left under vacuum conditions after hydriding at

ambient conditions. The most conservative vessel thickness thus calculated was taken for evaluating the shell weight.Based on the design equations from the ASME code, the formula of the cylindrical shell thickness for withstanding the

selected design pressure is given by [8]

=

(2)

The four types of vessel closures considered for the getter bed were the flat head, torispherical head, ellipsoidal head and

the hemispherical head. For each type of head, the head thickness was evaluated from well established equations in design

codes, which are shown in Equations 3 to 6 below [8, 9]:

Flat head:

= / (3)Torispherical Head

= (4)Ellipsoidal Head

= (5)Hemispherical Head

= (6)The cost of fabrication of the shell was estimated from the cost per unit weight of its material of construction, the cost of

the end closure was calculated the diameter of the blank plate required to form the closure as well as the forming cost

Thus the total cost of vessel fabrication was arrived at. The cost was calculated at various L/D ratios for each type of head

and the configuration that gave the minimum total cost at a particular value of L/D was selected for further analysis. Thustotal vessel cost (ignoring the cost of vessel support at this point) is thus taken as the basis for choosing the optimal L/D

ratio for a fixed shell volume. Results are presented in Figure 1.

It is seen that for any length to diameter ratio and identical design conditions, the vessel with the hemispherical end

closures has the minimum weight. The dependence of vessel weight and hence total vessel cost on L/D ratio is rather

weak at L/D greater than about 2 and a flat curve is obtained. Thus there is no clear optimal value of L/D ratio and a value

of 4 is chosen to fix the vessel dimensions as per standard pipe sizes. The calculated values of the shell thickness were

rounded off to the wall thickness of Sch 40 pipe having inner diameter closest to the calculated vessel diameter, as it is


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proposed to fabricate the beds out of standard pipe sections. The end closures will be fabricated out of standard plates of

required thickness.

Figure 1: Calculated vessel weight as a function of L/D ratio for various end closures

The vessel wall thickness for a given L/D ratio was also calculated for withstanding 1 bar (a) of external pressure while

the inside of the vessel remains under full vacuum, using Equation 7 [9] and the values of shell or head thickness were

found to be much less than that for withstanding internal design pressure of 40 bar (a).

=

(7)

Values of K and m depend on the L/D ratio of the vessel and they are equal to 0.381 and 2.46 for the chosen L/D of 2[Bhattacharyya]. The head and shell thicknesses are kept identical to facilitate ease of welding and reduce discontinuity

stresses along the junction.

Thus the finally selected thicknesses for both shell and head were based on the internal design pressure. The dimensions

are shown in Table 1.

Table 1: Major dimensions of the getter bed vessel

Inner

diameter

Outer

diameter

Shell

thickness

Shell

length

End closure

type

End

closure

thickness

Total

vessel

volume

Vessel weight

with contents

0.255 m 0.273 m 9.27 mm 0.5 m Hemisphericalhead 8.18 mm 22 L 25 kg

From Table 1, the ratio of shell thickness to inside radius is 0.073 which justifies assumption of the getter bed as a thin

walled vessel [10].

Design of vessel supports

0.5 1 1.5 2 2.5 3 3.5 410

20

30

40

50

60

70

80

90

100

Length to diameter ratio

T o t a l v e s s e l w e i g h t ( k g )

Flat head

Torispherical headElliptical head

Hemispherical head


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The getter bed vessels are generally required to be aligned vertically as this requires less floor space. Thus leg type vessel

supports directly welded to the shell were selected for them. The pertinent data for support design are provided below [8]:

Diameter of vessel: 0.273 m

Height of vessel: 0.5 m

Clearance of vessel bottom from foundation: 0.3 m

Weight of vessel with contents: 25 kg

Number of supports: 4

Diameter of anchor bolt circle: 0.35 m (based on standard dimensions)

Height of leg from foundation: 0.52 m

Permissible stresses for structural steel support material: Tension-140 N/mm2, Compression-123.3 N/mm

2

Bending-157.5 N/mm2

Permissible bearing stress for concrete: 3.5 N/mm2

The getter bed vessel is supposed to be placed indoors in the facility; hence no wind or snow loads are considered to be

acting on it.

Maximum compressive load on a single leg = weight of vessel/number of legs = 25*9.8/4 = 62 N

Assuming the vessel support to be fabricated out of standard channel sections, it is decided to take ISMC 75 X 40

channels for the supports. Four (4) such channels are to be welded directly to the shell at an elevation of 520 mm from the

floor level. Using the properties of the section and the vessel dimensions, it can be shown that the combined compressiveloading on the supports (which are taken as columns) is much lower than the permissible compressive stress for the

channel. Thus the selection of the support is appropriate. For the base plate of the channel support, it is assumed that the

plate extends on each side of the channel to a distance of 20 mm. The bearing pressure on each base plate can then becalculated and shown to be much less than the safe bearing pressure for the concrete foundation. Thus the base plate

dimensions are also adequately determined. The base plate thickness is taken to be 4 mm, from standard plate thicknesses.

The results of the design calculations for the getter bed are consolidated in Table 1.

Table 2: Base case design and operating parameters for the getter bed

Serial

NumberDesign Parameter Value

1 Design pressure (internal) 40 bar (a)

2 Design pressure (external) 1 bar (a), full vacuuminside

3 Design temperature 400oC

4 Ambient temperature 25oC

5 Material of construction SS 316L

6 Maximum allowable stress at 100 MPa [13]


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design temperature

7 Poisson’s ratio 0.33

8 Young’s Modulus 190 GPa [13]

9 Efficiency of welded joints100% (fully radiographed welds)

10 Inner diameter 0.255 m

11 Length of shell 0.5 m

12 Vessel wall thickness 9.27 mm

13 Head type Hemispherical

14 Thickness of head 9.27 mm

15 Type of support Welded leg support

16 Support length 0.52 m

17Coefficient of thermal expansion

of SS 316L18.4*10

-6 m/m K [18]

EVALUATION OF MECHANICAL STRESSES

The vessel internal pressure, external pressure and the dead weight create various stresses in the shell, the end closure and

the welded junction region. For simple vessel geometries as has been considered in this study, analytical solutions forshear stresses and bending moments are available in literature for the shell and end closures. These solutions were used to

evaluate the various load combinations for the getter bed. The calculated results for various loads, based on the condition

in Table 2 are presented in this section [9]. For internal pressure, the maximum fill pressure of hydrogen is used to

calculate the stresses, but in practice the internal pressure varies as gas is depleted during hydriding phase. For externa

loading, 1 atm pressure is assumed to act uniformly over the shell and heads of the vessel. Piping and nozzle reactionloads have not been considered in this work as that will require detailed knowledge of the associated piping connections

for the vessel.

a) Stresses due to internal pressure and vessel dead weight

The maximum axial tensile stress due to internal pressure is

= () (8)The maximum axial compressive stress during vacuum condition is

= () (9)The axial compressive stress induced by the vessel’s dead weight (neglecting weight of insulation) is


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= () (10)b) Discontinuity stresses due to end closures

The evaluation of discontinuity stresses arising at the junction of the shell and hemispherical heads of the vessel is

performed using the concept of the deformation of a beam on an elastic foundation. [9].

The damping factor for a cylindrical vessel is calculated as [9]

= () (11)The longitudinal stress in the cylinder at any distance from the location of the junction is given as

=

(12)

where = ().The total hoop stress in the cylinder at any distance from the location of the junction is given as

=

− (13)

where = () The calculated maximum mechanical stresses are shown in Table 3.

c) Compressive load during vacuum conditions

The vessel remains under high vacuum conditions for a significant part of the load cycle. During this time compressive

tresses due to external pressure act on it and can cause elastic failure. The safe external pressure that it can withstand

without buckling and local distortion effects like lobe formation can be calculated from Equation 7 above, using the actuavessel thickness in place of tv. For the pressure vessel dimensions shown in Tables 1 and 2, the value of the safe external

pressure is calculated to be around 17.7 MPa, which is much larger than the ambient pressure which the vessel will be

subjected to. Thus buckling of the vessel is not likely under normal operating conditions.

THERMAL STRESS ANALYSIS

Determination of one-dimensional radial thermal gradient in the getter bed

A simple, one dimensional, steady state radial heat conduction analysis was performed for obtaining the temperature drop

across the vessel wall. This is only an approximation since the real hydriding or dehydriding step is a batch operation and

not a continuous, steady process. Axial heat conduction was neglected, assuming the vessel closures to be well insulated,and the shell was assumed to be diathermal. The simplified, conservative calculations were used to estimate the maximum

temperature gradients across the wall, which in turn will enable the calculation of the thermal stresses acting on the shell

Similar temperature gradients were assumed to be present in the vessel closures as well. The entire thermal analysis was

performed to arrive at the likely worst case scenarios for thermal stress evaluation.


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Figure 2: Simplified model of the getter bed for thermal stress analysis

For hydriding, the peak heat generation rate during the reaction under adiabatic condition was set equal to the heatconduction rate through the wall at steady state in order to calculate the temperature gradient across the wall. This may be

expressed as [11]

= ∆ ( ) (14)

The value of Qr was calculated to be around 1600 W for the vessel under consideration [6]. The calculated vale of Twalfor this condition was about 0.8 deg C.

For dehydriding it was assumed that a 1.5 kW heater was available to supply the heat necessary for causing the hydride to

dissociate. The thermal gradient was in opposite direction as compared to hydriding (i.e. outer wall temperature higher

than inner wall) and its value was similarly calculated to be about 0.75 deg C.

Calculation of thermal stresses

The getter bed vessel is a thin walled vessel and hence the temperature distribution in the radial direction may be assumed

to be linear across the wall thickness. Expressions for radial, longitudinal and circumferential thermal stresses for a linear

wall temperature gradient are available in literature [12] which may be used to evaluate the thermal stress distribution in

the walls. The results are shown in Figure 3 for the hydriding phase when the inner wall temperature is higher than the

outer wall temperature. The radial thermal stress is seen to be about two orders of magnitude lower than the tangential and

axial thermal stresses. During the dehydriding phase the nature of the stresses will be opposite since then the outer wall

would be at higher temperature on account of heat being supplied externally to the vessel.


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Figure 3: Wall thermal stresses in the getter bed during hydriding

VIBRATIONAL BEHAVIOUR

For a vessel placed indoors in a facility, vibrational loads are imposed during a seismic event. The fundamental

frequencies of vibration of the vessel depend upon its configuration and dimensions. Vertical vessels supported on legs

bolted to the floor are generally considered as cantilever beams supported rigidly at one end and this concept is used toarrive at expressions for the time period of vibration of the vessel []. The floor response spectrum of the building or

location which will house the getter bed should be available for assessing the impact of the design basis earthquake on the

vessel. Wind loads have not been considered for the getter bed since it will be housed inside a building.

a) Time period of vibration of the vessel [9]

For a vertically supported vessel, the time period of vibration is given by the following equation:

= .

(15)

where = .The seismic coefficient Cs for a medium intensity seismic zone and for the calculated value of T has the value of 0.1[9].

b) Stresses due to seismic loads

Seismic activity produces a horizontal shear stress on the vessel which leads to a bending moment about the vessel base.

The bending moment can be calculated as [8]

= (16)The resultant bending stress due to seismic activity is given by [8]

0.115 0.12 0.125 0.13 0.135 0.14 0.145-1.5

-1

-0.5

0

0.5

1

1.5x 10

7

T h e r m a l s t r e s s ( P a )

Radial position along the wall (m)

Radial stress

Tangential st ress

Axial stress


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= (17)Table 3: Magnitudes of maximum mechanical stresses acting on the getter bed vessel

Stress Magnitude (Pa) Stress Ratio 8.57*106 0.0857 1.15*107 0.115 3.43*104 3.43*10-4 3.61*104 3.61*10-4

x = 0.0 m 8.91*106

0.0891

x = 0.1 m 8.87*10 0.0887

x = 0.2 m 8.91*10 0.0891

x = 0.3 m 8.91*10 0.0891

x = 0.4 m 8.91*10 0.0891

x = 0.5 m 8.91*106 0.0891

x = 0.0 m 4.46*10 0.0446

x = 0.1 m 8.94*10 0.0891

x = 0.2 m 8.91*10 0.0891

x = 0.3 m 8.91*10 0.0891

x = 0.4 m 8.91*106 0.0891

x = 0.5 m 8.91*10 0.0891

FATIGUE CONSIDERATIONS FOR THE GETTER BED

Estimation of cyclic loads

Fatigue issues are important for any piece of equipment under cyclic loading conditions [14]. In case of metal getter beds

for hydrogen storage, there are pressure as well as thermal cycles for the hydriding and dehydriding steps. The cyclicpressure variation for the bed was considered to be as follows:

i) Initial filling of the hydrogen into the pressure vessel to the desired fill pressure. The time for filling the gas in the

vessel depends on the pressure of the source of hydrogen and the flow conductance of the associated tubing and fittings in

the line. Typically this time duration will be quite less than the time taken for the actual hydriding or dehydriding reaction

step.

ii) Drop in pressure due to reaction of hydrogen with the getter material, leading to vacuum conditions inside the vesselThis is based on the assumption of hydrogen adsorption at near ambient temperature when the equilibrium hydrogen

pressure over uranium is in the high vacuum range. Under this condition the vessel is under compressive load due to

ambient pressure. The time taken for the reaction to be completed is about 500 seconds [6].

iii) Evacuation of the vessel with heating for complete recovery of the adsorbed hydrogen, during which vacuumconditions are maintained inside the vessel. No pressure build up is considered by first allowing the vessel to be heated to

a certain temperature, due to which the equilibrium pressure of hydrogen will rise inside the vessel. Tensile thermal stress

and compressive stress on the vessel walls due to atmospheric pressure are the major stresses prevailing during this phaseof the cycle. The time taken for this step is of the order of 10 to 12 hours.

iv) Cooling of the vessel, during which compressive thermal stresses will act on it followed by re-filling to the initial fillpressure for the next cycle.


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No time lags were assumed in between any two stages of the pressure cycle, though in actual practice the recovery of

stored hydrogen would depend on the requirements at a given time for a particular application. A portion of the pressure

cycle is illustrated in Figure 4 for clarity and to highlight the pressure variation during hydriding step. Otherwise the

vessel internally remains under vacuum conditions and is therefore under compressive stress from ambient air.

For each pressure value at different times in the cycle, the equivalent shell, junction and closure stresses can be calculated

in a straightforward manner using the formulations presented in the section on mechanical stress analysis.

For the temperature cycle it was considered that during the hydriding or the dehydriding step a constant temperature

difference existed across the vessel wall. The gradient is assumed to be linear since the getter bed is housed in a thin

walled vessel. The inner wall temperature is lower than the outer wall temperature when external heating is done to raise

the vessel temperature; while the outer wall temperature is lower when the vessel is being cooled and when hydriding

reaction is taking place inside the vessel. A typical approximate simulated representation of the time- temperature history

of the getter bed walls for a heating with dehydriding cycle followed by a cooling cycle and hydriding step is shown in

Figure 5. The rather small temperature difference means that thermal stresses will be quite low as well. The temperature

difference can be used to calculate the time dependent thermal stresses acting on the vessel walls.

Thus it can be said that during a complete hydriding and dehydriding cycle, the getter bed will be under a superposition of

pressure and thermal loads which will together govern the fatigue behaviour of the vessel.

Use of S-N curves for getter bed life prediction

The S-N method is one of the most well known and widely applied, albeit simplified technique of fatigue analysis of a

pressure vessel or any mechanical component in general [14, 15]. The S-N curve for a particular material enables one to

determine the endurance limit i.e. the stress level at which the component will not fail even after an infinite number of

load cycles applied to it. It may be assumed that if the maximum stress anywhere in the vessel at any point in the load

cycle remains below the endurance limit, the vessel should not fail due to fatigue. From the maximum thermal and

mechanical stresses calculated for the getter bed in the previous sections, it is seen that the stress values remain below the

endurance limit of SS 316L for both hydriding and dehydriding cases. Even when considering stress concentration zones

around the nozzle opening on the head through the use of a stress concentration factor, it can be seen that that even then

the stress remains below the endurance limit which is about 2.60*108 Pa for SS 316L [19]. Hence this eliminates any

possibility of fatigue failure of the vessel within the limited number of cycles which a getter bed will be expected to

endure, based on the getter material’s ability to retain the storage properties after a certain number of cycles. Stress

concentration factors have been calculated from charts available in literature [16] and for the assumed nozzle size of ½’’

NPS, Sch 40, to be located on each of the hemispherical end closures and the value is about 3 for the getter bed vessel

considered in this work.

Creep and embrittlement issues

Creep damage of the vessel is not explicitly considered in this work since it is reported extensively in literature that creep

becomes a major consideration for prolonged operations at temperatures between 30 to 60% of the absolute meltingtemperature of the material of the vessel [14]. In this work, the maximum material temperature considered for the design

is about 450oC which is less than 30% of the melting temperature of SS 316L [13]. Thus long term creep damage is no

likely to be significant under the getter bed operating policy considered here, since the vessel is not constantly under hightemperature conditions during use.

The getter bed vessel is intended for use in a hydrogen environment. Constant exposure of hydrogen leads to a high

possibility of hydrogen embrittlement of the material of construction of the vessel and thus lowers its strength [17]. The

hydrogen concentration in the metal depends on the pressure of the gas and the operating temperature and the total time ofexposure [18]. For long term operation of the getter bed vessel, the progressive loss in strength of the material due to the

embrittling effects of hydrogen must be factored in the vessel design. Similar to a corrosion allowance, additional vesse

wall thickness may be provided to combat the lower strength of the embrittled metal when prolonged use of the getter bed

is envisaged.


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Figure 4: Simulated internal pressure-time cycle for the getter bed

Figure 5: Simulated temperature-time cycle for the getter bed

SUMMARY AND CONCLUSIONS

The work focuses on the mechanical aspects that must be considered during the design of a metal getter based hydrogenstorage bed. The vessel has to be designed for both internal and external pressure loads for hydriding and dehydriding

phases respectively, and the most conservative wall thicknesses thus calculated have to be taken for the shell and the end

5.9 5.95 6 6.05 6.1 6.15

x 104

0

2

4

6

8

10

12

14x 10

5

TIME(SEC)

G A S

P R E S S U R E

( P a ( g a u g e ) )

Evacuation and

dehydridingPreservation after

hydriding

Hydriding reaction

Undervacuum

from time = 0

Under

vacuum till

time = 105 sec

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 10

5

0

50

100

150

200

250

300

350

400

Time(sec)

T e m p e r a t u r e ( C

)

Outer wal l temperature Inner wall temperature


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closures. Selection of optimal closures for the vessel depends on both cost and stress considerations. The nature and

design of the vessel support determines the behaviour of the vessel under seismic conditions. A basic thermal analysis of

the getter bed system has also been done to estimate the magnitudes of the temperature gradients likely to be encountered

across the shell during operation, which in turn enables the calculation of possible thermal stresses in that region. Because

of the time dependent cyclic thermal and pressure loads, the vessel may be subjected to fatigue, especially when the

storage bed is intended to be used for a long duration, provided the getter material retains its storage capacity after asignificantly large number of cycles. Complete analysis of the stresses in such a system can be carried out with

commercially available software packages but it can be quite time consuming and involved, in which case the simplified

analysis carried out in this work may be useful for checking and validating preliminary design calculations.

ACKNOWLEDGEMENTS

The author wishes to thank Shri Kalyan Bhanja and Dr Sadhana Mohan of the Heavy Water Division, BARC for an

introduction to the field of metal getter beds for hydrogen storage and for inspiration in writing this paper.

NOMENCLATURE

Symbol Significance

Bβx Dimensionless constant for discontinuity stress calculation

Ce Edge fixity constant for flat head, dimensionless

Cs Seismic coefficient, dimensionless

Dm Diameter of the major axis of the elliptical head, m

Dβx Dimensionless constant for discontinuity stress calculation

Di Vessel inside diameter, m

Do Vessel outside diameter, m

E Young’s Modulus, Pa

g Acceleration due to gravity, m s-2

H Total height of the vessel including supports, m

I Moment of inertia of the shell, m4

K Dimensionless constant

k steel Thermal conductivity of steel, W/m K

L Length of vessel, m

m Dimensionless constant

Ms Bending moment induced due to seismic load, N m

p Internal pressure, Pa

pe External pressure, Pa

Qr Electrical heat supply rate, W

qs” Surface electrical heat flux, W/m2

Rc Crown radius for torispherical head, m

Ri Vessel inside radius, m

Ro Vessel outside radius, m

S Maximum allowable stress for vessel material of construction, Pa

teh Thickness of elliptical head, m

tfh Thickness of flat head, m

thh Thickness of hemispherical head, m

tshell Thickness of cylindrical shell, m

tth Thickness of torispherical head, m


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tv Thickness of shell for external pressure load, m

T Time period of vibration of the vessel, s

V Stress intensification factor for elliptical head, dimensionless

w Stress intensification factor for torispherical head, dimensionless

W Total weight of the vessel, kgWs Weight of the shell, kg

x Axial location along the shell from the shell-head junction, m

β Damping factor for cylindrical vessel, m-1

Twall Temperature drop across vessel wall, K

µ Poisson’s ratio, dimensionless

Φr Volumetric reaction heat generation rate, W/m3

σb Stress due to bending moment, Pa

σh Hoop stress due to shell-head discontinuity, Pa

σl Longitudinal stress due to shell-head discontinuity, Pa

σzp Axial stress due to internal pressure in the vessel, Pa

σzs Axial stress due to dead weight of the vessel, Pa

σzv Axial stress due to external pressure on the vessel in vacuum conditions, Pa

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Analytical Assessment of the Mechanical Design of a Metal Getter Bed for Hydrogen Storage

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