2003 ABAQUS Users’ Conference 1

Heat Transfer and Thermal-Stress Analysis to Support the Design of Vaporizers in Fuel Cell

Engines with ABAQUS

K. Schwab1, U. Benz2, D. Borst3, H. Krause4 and M. Weisser2

1DaimlerChrysler D-71059 Sindelfingen, 2Ballard Power Systems AG D-73230 Kirchheim/Teck-Nabern, 3Modine D-70794 Filderstadt ,4KOLT Engineering D-71034 Böblingen

Abstract: Ballard is developing fuel cell engines for automotive applications. To allow its light-duty fuel cell engines to utilize not only hydrogen but also hydrocarbon fuels, for example methanol, fuel processors are also being developed. An on-board fuel processor allows operational ranges similar to those of conventional vehicles.

The steam reforming process starts with the vaporization of liquid methanol and water. Heat produced in the reforming process is used to accomplish this. Critical to the design of high performance evaporators is a complete understanding of the thermal-stresses involved. The contribution of finite element analysis to the vaporizer development is shown through the example of an oil heated test reactor.

The task of calculating the stress distribution in the vaporizer is solved with the help of an uncoupled heat transfer analysis. In the first step - pure heat transfer analysis - the temperature field caused by forced convection is calculated. The streaming media through the mesh are defined by the mass current density and the specific weight. The turbulent flow and the related improvement in heat transfer are taken into account by the heat-transfer coefficient.

The heat-transfer coefficients are investigated experimentally with the help of a test reactor. The reactor is designed so that flow and heat transition conditions represent the conditions in developed evaporators. Temperatures can be measured along the run length both in the medium flow channel and in the metal sheet.

The method of effective heat capacity was selected to model the phase change (evaporation). To model the flow direction change at corners a special mass current distribution which avoids an enthalpy loss is chosen. The sequentially coupled thermal-stress analysis is then completed by generating and reading the temperature solution into a stress analysis as a predefined field.

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1. Introduction

DaimlerChrysler introduced the Necar 3 and 5 prototype automobiles, powered by Ballard® fuel cells, in 1997 and 2000. These fuel cell passenger cars utilize methanol as a fuel, converting liquid methanol fuel on board into hydrogen through water-steam reformation. Figure 1 shows the XCELLSISTM ME-75 light-duty fuel cell engine integrated in the floor of a passenger car.

PEM (Proton Exchange Membrane) fuel cells are power generation units which directly, and with high efficiency, convert the chemically stored energy of hydrogen into electrical energy via an electrochemical process (figure 2). To obtain the desired amount of electrical power, individual fuel cells are combined to form a fuel cell stack.

A fuel cell engine requires hydrogen to operate. The process of fuel reforming (figure 2) allows the extraction of hydrogen on-board the vehicle from other fuels including methanol, gasoline, ethanol, natural gas, petroleum or renewable sources.

The steam reforming process starts with the vaporization of liquid methanol and water. The reformer breaks the molecular bonds of the gas mixture at a reaction temperature of 250 to 300 °C and creates hydrogen and carbon dioxide. Carbon monoxide formed at the same time (harmful to the hydrogen fuel cell) is further reformed by a selective CO oxidation into carbon dioxide. Additional process heat for the steam reforming process is produced by a catalytic burner, using surplus hydrogen as fuel.

The quantity of the hydrogen provided is determined by the position of the accelerator pedal and related control unit which regulates the drive (DaimlerChrysler, 2000).

Figure 1. XCELLSISTM light-duty fuel cell engine including air-, fuel cell - , periphery module and methanol fuel processor (Ballard Power Systems AG).

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Figure 2. PEM fuel cell and flow chart of a methanol fuel processor (Ballard Power Systems AG).

2. Task and procedure

The requirements on volume, weight as well as cost reduction at increased efficiency and reliability result from the installation of the fuel cell engine into passenger cars. Under efficiency, among other things the reaction time of the drive on the activity of the accelerator pedal has to be understood. Pressure and temperature field fluctuations can appear in the reactors over the operating range.

An essential prerequisite for the development of the aggregates is the knowledge of the appearing thermal-stress distribution in the operating range. The example of an oil heated test reactor shows the contribution of the finite element analysis to the vaporizer development to solve this task.

The evaporators looked at are plate heat exchangers. The separating metal sheets are provided with microstructures. Through this the heat transfer area is increased and therefore a high power density is obtained. With acceptable effort a flow simulation is not feasible because of the channel height to length ratio.

The component heats liquid, vaporizes and overheats the steam. Heat energy, provided by heat carrier oil, is transferred by heat transition and thermal conduction to the water methanol mixture. An essential identification value for the heat transition is the heat-transfer coefficient alpha. This specific value is dependent on different parameters, like flow speed, temperature, viscosity, pressure etc..

The task of calculating the stress distribution in the vaporizer is solved with the help of an uncoupled heat transfer analysis. To size the finite element analysis the heat-transfer coefficients are investigated experimentally with the help of a test reactor.

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In the first step of the finite element analysis - pure heat transfer - the temperature field caused by forced convection is calculated. The streaming media through the mesh are defined by the mass current density and the specific weight. The turbulent flow and with that the improved heat transfer is taken into account by the heat-transfer coefficient.

The method of the effective heat capacity was selected to model the phase change (evaporation). To model the flow direction change at corners a special mass current distribution which avoids an enthalpy loss is chosen. The sequentially coupled thermal-stress analysis is finished by generating and reading the temperature solution into a stress analysis as a predefined field.

3. Basics of heat transfer and evaporation

During heat transfer heat from a substance is transferred to a different one. The heat transfer can be provided by conduction (more high-energy molecules transfer a part of the energy to close-by molecules), convection (figure 3) and radiation (electromagnetic waves).

Thermal conduction, i.e. the heat flux through a cross section A, is described by Fourier’s law (Beitz, 1987)

dxdT

AQ ⋅⋅−= λ& (1)

with the heat fluxQ& , the heat conductivity λ and the temperature gradient in the heat conducting

body in x direction dxdT

.

The convectional heat transition between wall and medium depends on the flow of the media (type of the fluid as well as the flow, flow speed and condition of the wall) and is described by

)( WFl TTAQ −⋅⋅= α& (2)

where α is the heat-transfer coefficient (film coefficient), FlT the temperature of the fluid and

WT the surface temperature of the solid field.

The influence of the thermal radiation can be neglected in the case in hand.

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0

50

100

150

200

250

0 0,2 0,4 0,6 0,8 1

Direction of heat transfer: oil -metal sheet - water

Tem

pera

ture

/ °C

metal sheet

Figure 3. Heat transfer (oil-heated test reactor).

The evaporation process can be subdivided into three steps. Warming the liquid up to the boiling-point, vaporize and overheat of the vapor. In steady operation the vapor production usually takes place under a constant pressure. The liquid absorbs heat - up to reaching the boiling temperature. At a further heat supply the liquid vaporizes at constant temperature (wet steam). The temperature of vapor without liquid increases at heat absorption, see temperature-entropy diagram on figure 4.

s

T

s''

q Ü

s'

q f

T'

K

Figure 4. Temperature-entropy diagram of the evaporation process (Beitz, 1987).

4. Experimental investigations

On figure 5 the test vaporizer is pictured in the longitudinal section. The separating metal sheets are micro-structured. The water to be vaporized flows in the in channels, heated by a heat carrier oil on both sides. The reactor is designed so that flow and heat transition conditions represent the conditions in developed vaporizers. Temperatures can be measured throughout the run length both in the medium space and in the metal sheet. By the lengths-/ width relationship of the vaporizer the flow and heat transition characteristics are variable in the measurement range during stationary states almost only in lengthways direction.

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Figure 5. Test vaporizer in the longitudinal section.

The experimental investigations were carried out at an existing test rig (figure 6). Volume currents, pressures, temperatures as well as steam quality can be adjusted/measured.

Figure 6. Test vaporizer during measuring.

Figure 7 shows the measured temperature distribution in the flow channel of vaporizing water over standardized mass flow and run length.

The experimentally investigated heat-transfer coefficients are represented on figure 8. The identification values determined for the evaporation area diversify more strongly than in the liquid and overheating phase. This can be explained by the effect of the coexisting liquid and vapor phase.

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28,3 55

,5 82,7 10

9,9 137,

1

164,

3 191,

5

218,

7

0,10,2

0,30,4

0,50,6

0,70,8

0,91,0

90

105

120

135

150

165

180

195

210

225

240

255

270

Tem

pera

ture

/ °C

Run lengthStandardized mass flow / -

Figure 7. Experimentally investigated temperature distribution in the flow channel of vaporizing water over standardized mass flow and run length.

0

0,25

0,5

0,75

1

0 0,25 0,5 0,75 1

Standardized mass flow / -

Sta

ndar

dize

d he

at-t

rans

fer

coef

ficie

nt /

-

heat-transfer coefficient -vaporization

heat-transfer coefficient -superheated steam

heat transfer coefficient -heating

Figure 8. Standardized experimentally investigated heat transfer coefficients depending of the mass current.

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5. Uncoupled heat transfer analysis with ABAQUS

The task of calculating the stress distribution in the vaporizer is solved with the help of an uncoupled heat transfer analysis. In the first step - pure heat transfer analysis - the temperature field caused by forced convection is calculated. The sequentially coupled thermal-stress analysis is finished by generating and reading the temperature solution into a stress analysis as a predefined field.

The crucial points of the task as well as the solutions are summarized in table 1.

Table 1. Crucial points and solutions.

Crucial point Solution Turbulent flow The ratio of channel height to length excludes a flow simulation (with acceptable effort feasible).

Uncoupled heat transfer analysis - heat transfer, turbulent flow and fins are of taken into account by the heat transfer coefficient and increasing the heat conductivity of the fluid by factor 10. Sizing of the finite element analysis with the help of experimental investigations.

During the vaporization process appear forced convection and phase change (latent heat) simultaneously. Latent heat effects cannot be combined with ABAQUS convective heat transfer elements (Hibbit, 1998)

The phase change is modelled with the method of the effective heat capacity (Huang, 1994).

Reduction of the model quantity and the computing time when straight flow channels are analysed.

Different models for heat transfer analysis (two-dimensional solid elements) and thermal stress analysis (shell elements) Transfer of the node temperatures by identical node coordinates and numbering (middle node row of the metal sheet). The node temperatures vertical to the flow are assigned by thermal conduction (orthotropic material).

Change of the flow direction at corners. A special mass current density distribution which avoids an enthalpy loss is chosen (figure 9).

5.1 Pure heat transfer analysis

The heat transfer analysis is carried out in iterative loops, caused by strong variation of characteristic values during the evaporation process. The characteristic values of the liquid phase are assigned to the fluid to be vaporized. With the help of the temperatures in the result file the geometric line of the phase change is determined and the analysis is repeated up to reaching the exact boiling temperature. The characteristic values for the evaporation process are assigned to the following elements. The procedure is repeated for the overheating area until the chosen temperature difference is reached (see below).

5.2 Phase change

The phase change is modelled with the method of the effective heat capacity (H. Huang, 1994). From the heat flux equation

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)(

)(

12

12

hhmQ

TTcmQ

−⋅=⇔

−⋅⋅=

&&&&

(3)

where m& is the mass current and h the specific enthalpy results the specific heat capacity

)()(

12

12

TThh

c−−

= . (4)

The evaporation enthalpy can be used for the difference (h2-h1) for the respective state. For the difference (T2-T1) a small temperature value is chosen. The effective heat capacity therefore is

)2( Kchosen

nevaporatioeff T

hc

∆

∆= .

(5)

It is allowed that the evaporation process doesn't proceed isothermal. The influence of the chosen temperature difference on the following stress analysis is negligible at the application on hand.

5.3 Change of the flow direction

When the flow direction changes the mass currents (quotient mass current / area) are investigated with Excel and stipulated one by one at every node. In the respective channel the partial mass current as well as the flow direction at the single node is taken into account. At the corners (figure 13), a special mass current distribution which avoids an enthalpy loss was chosen (figure 9).

m/A 2m/A -> --> 0 ------o--------o--------o | | | | | | | | | | | | | ------o--------o--------o | 2m/A -> 0 | | v m/A | | | | | | | | m/A v o--------o v m/A | | | |

.

. .

.

..

Figure 9. Modelling of the flow direction change at corners.

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5.4 To pass the parameters into the ABAQUS -code

The finite element model for the heat transfer analysis, consisting of two-dimensional continuum elements, is shown on figure 10. The flow channels are modelled with type DCC2D4 elements, the metal sheets by type DC2D4 elements. The substantial parameters for the heat transfer analysis -keyword *HEAT TRANSFER, STEADY STATE - are the substance quantities density, heat conductivity and heat capacity - keywords *DENSITY, *CONDUCTIVITY and *SPECIFIC HEAT - the heat transfer coefficients - keyword *GAP CONDUCTANCE - effective with contact - keyword *SURFACE DEFINITION, *CONTACT PAIR and *SURFACE INTERACTION.

The used mass currents result from the flow channel geometry and the entire mass currents – keyword *MASS FLOW RATE. The boundary conditions - keyword *BOUNDARY - pass the inlet temperatures of water and oil.

Figure 10. Finite element model – heat transfer analysis.

5.5 Results of the heat transfer analysis

On figure 11 the calculated temperature distributions in the fluid as well as in the separating metal sheet - oil- and waterside - can be seen.

0

50

100

150

200

250

Run length

Tem

pera

ture

/ °C

sheet - oilside

sheet - waterside

water

oil

Figure 11. Calculated temperature distributions in the fluid an the metal sheet.

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5.6 Thermal stress analysis

To reduce effort, degrees of freedom and computing time, for the heat transfer analysis a model of two-dimensional solid elements and for the thermal stress analysis two nearly identical models of shell elements were generated. The node temperatures are transferred by identical node coordinates and numbering (middle node row of the metal sheet) via report file. By a thermal conductivity analysis - keyword *HEAT TRANSFER, STEADY STATE - the node temperatures vertical to the flow are assigned to the shell element model, element type DS4 (orthotropic material with thermal conduction only vertical to the flow - keyword *CONDUCTIVITY, TYPE=ORTHO).

Figure 12 shows a thermal-stress distribution calculated by reading the temperature solution into a stress analysis - element type S4R5, as a predefined field - keyword *TEMPERATURE, FILE=name.

Figure 12. Thermal-stress distribution – metal sheet.

6. Results of a „first generation“ vaporizer

The calculated fluid and metal temperatures as well as the metal sheet stress distribution of an oil-heated “first generation” vaporizer are represented on figures 13 and 14. The structure and fluids are modelled with the help of three-dimensional continuum elements.

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Figure 13. Calculated temperature distributions – fluids.

Figure 14. Calculated temperature and thermal-stress distributions - metal sheet.

7. Conclusions

With the help of an uncoupled heat transfer analysis, temperature and thermal-stress distributions during stationary evaporation processes can be analysed. The analysis of stationary states identifies highly stressed areas in vaporizers at the appropriate mass currents. It is possible to evaluate measures for the reduction of the stress.

Through “homogenization processes” geometry and flow were simplified, the phase change is modelled with the method of the effective heat capacity. Necessary characteristic values were determined experimentally. The characteristic values and procedure can be transferred to further applications under the prerequisite that flow and heat transition conditions do not strongly differ. It is possible to model the flow direction change at corners with a special mass current distribution to avoid an enthalpy loss.

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In future, the analysis of evaporation processes during dynamic events (start and shut down, activity of the accelerator pedal) would be challenging. Considerably more efficient hardware and steady further developments in the analysis code ABAQUS are promising.

Summarizing, it can be said, that the non-linear finite element code ABAQUS is well suited to define the stress distribution in vaporizers during stationary processes. Under the described conditions it is very important to combining finite element analysis and experimental investigations in the early phase of the vaporizer development.

8. References

1. Beitz, W., K. H. Kütter, „Dubbel – Taschenbuch für den Maschinenbau“, Springer Verlag, 1987

2. DaimlerChrysler Research & Technology, D-70546 Stuttgart, „necar 5 – fahren mit Methanol“, 2000

3. Hibbit, Carlson & Sorensen Inc., „Abaqus/Standard, User’s Manual“, 1998

4. Huang, H.C., “Finite Element Analysis for Heat Transfer”, Springer Verlag, 1994

5. Ballard Power Systems AG, „http://www.ballard.com/pdfs/transportation/XCS-ME-75-APR5_4.1.2.2.PDF“

9. Appendix

α W/m2K heat-transfer coefficient (film coefficient)

λ W/mK heat conductivity

A m2 cross section

c J/kgK specific heat capacity

h J/kg specific enthalpy

m& kg/s2 mass current

Q& W heat flux

T K temperature

x m x-coordinate

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Indices

eff effective

Fl Fluid

W Wall

10. Acknowledgement

The authors are grateful to Professor Martin Pitzer. A great deal of the introduced publication is part of Daniel Borst’s master thesis advised by him.