Effect Of Vibration On The Performance Of PEMFCJAYDEEP DESHPANDE*, TAPOBRATA DEY^, P. C . GHOSH^

*- PUNE VIDYARTHI GRIHA’S COLLEGE OF ENGINEERING AND TECHNOLOGY, PUNE

^- DEPARTMENT OF ENERGY SCIENCE AND ENGINEERING, I IT BOMBAY

Agenda1. Problem Definition

2. Modelling

3. Setup

4. Results and Discussion

5. Conclusion

6. Future Scope

Problem DefinitionVibrating body experiences two forces which reduce the vibrations, spring force and damping force given by;

The force acting body is given by,

The external excitation force is give by,

External excitation force produces the case of forced vibrationsFig. 1

Problem Definition

Thus, by D’Alembert's principle, the motion of equation is given by,

On solving the equation for the boundary conditions, the steady state solution is obtained as,

The steady state amplitude of vibration is given by,

Fig. 1

Problem DefinitionANSYS solves the equation in the matrix form by finite element discretization

For damping ratio ( ratio of damping coefficient to critical damping coefficient)

Vibrations are transferred from one component to other by the transmissibility relation;

Modelling• The model is created in

SOLIDWORKS• Endplates x2 – SS316• Current Collectors x2 – Copper • Graphite Plates x2 – Graphite • Gaskets x2 – PTFE• Membrane x1 – Nafion®• GDL x2 – Carbon Paper

Fig. 2

Setup Initially a modal analysis of the entire cell is performed to evaluate the natural frequencies

The bottom plate fixed and all modes are scanned up to 1KHz frequency

Using the obtained frequencies the model is exported for harmonic analysis with acceleration at 4g for 1 hour

The bottom plate is fixed

Deformations are noted

Final step of the analysis takes into account the loosening of bolts due to vibrations

Bottom plate is fixed for structural analysis

Change in bolting torques is applied to bolts and changes in contact pressure profiles is plotted

Results and Discussions Modal Analysis:

Zones with maximum modal displacements are indicated in the Fig. 3Fig. 3

Results and Discussions Frequencies

Mode Frequency [Hz]1 474.712 476.483 476.884 793.395 796.016 839.257 844.47

Table. 1

Results and Discussion

Fig. 4

Results and Discussion Estimation of Hydrogen Leakage Rate

Operation at natural frequencies will result into large displacements at the zones shown in Fig. 3

Thus ,

From harmonic analysis displacement at resonance point=1.0338e-08 m

Area of the micro-pore= max. Displacement * width of the micro-pore

Area of the micro-pore = (1.0338e-08 * 0.003)

A= 3.1014e-11 m2

Results and Discussion Estimation of Hydrogen Leakage Rate

Now considering the Hydrogen side pressure 2 bar and atmospheric pressure 1 bar, applying basic Bernoulli’s theo-rem we get,

 (P1 / dg) = (P2 / dg) + (V2 / 2g);

(Neglecting change in Enthalpy, Internal Energy of Hydrogen)

Where,

P1 - Pressure at Hydrogen side

P2- Atmospheric Pressure

d- Density of Hydrogen = 0.08988 g/L

g- Acceleration due to gravity

V- Velocity of leaking Hydrogen

  On substituting the values and solving we get, V= 1502.853 m/s

Thus, leakage Hydrogen flow rate = A*V= 0.16778 L/ hr

ConclusionThe paper outlines natural frequencies which should be avoided during the operation of fuel cells

It also points out reduction in the contact pressure due to reduction in the bolting torque under vibration. This will directly reflect on the performance of the fuel cell through increases losses and leakages.

Study calculates the hydrogen leakage rate after vibration. Although the estimation is crude, it gives some idea on the volume loss of hydrogen after and during the operation under vibrating conditions.

Future ScopeDetailed hydrogen leakage estimation by consideration thermodynamic parameters

Safety framework for fuel cell design for mobile applications for safer operation in vibration environment

References References

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Transmissibility Ratio