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Research Papers

# A Model for the Freeze Start Behavior of a PEM Fuel Cell Stack

[+] Author and Article Information
Michael Mangold1

Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germanymangold@mpi-magdeburg.mpg.de

Silvia Piewek

Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstraße 1, 39106 Magdeburg, Germanypiewek@mpi-magdeburg.mpg.de

Olaf Klein

Volkswagen AG, Konzernforschung Antriebssysteme, 38436 Wolfsburg, Germanyolaf.klein@volkswagen.de

Achim Kienle

Otto von Guericke University, 39016 Magdeburg, Germanyachim.kienle@ovgu.de

Behind these two terms is the assumption that the water generated in the reaction is originally gaseous. This assumption is quite arbitrary and has no effect on the model behavior because the chemical conversion of reactants is an internal process that does not change the total energy of the system. The assumption only allows a consistent definition of the heat of reaction and the heat of sublimation. Different assumptions on the state of the reaction product would only lead to different definitions of $ΔRH$ and $hsublim$.

1

Corresponding author.

J. Fuel Cell Sci. Technol 8(3), 031006 (Feb 18, 2011) (9 pages) doi:10.1115/1.4003015 History: Received January 20, 2010; Revised October 29, 2010; Published February 18, 2011; Online February 18, 2011

## Abstract

A simple model for the start-up of a proton exchange membrane fuel cell stack is proposed. The model covers a wide temperature range from temperatures below the freezing point of water to usual operation temperatures of a low-temperature fuel cell. Model equations are derived from first principles. They account for the effects of ice and liquid water on the stack behavior. The model is validated by experimental data published by Schießwohl [2009, “Experimental Investigation of Parameters Influencing the Freeze Start Ability of a Fuel Cell System,” J. Power Sources, 193(1), pp. 107–115.], and a good qualitative agreement is found. The applicability of the model to problems of operation strategies and stack design is demonstrated by simulation studies.

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## Figures

Figure 1

(a) Measured temperature and (b) electrical power of a fuel cell stack during start-up (1); initial and ambient temperature −10°C (solid line): successful start-up; and initial and ambient temperature −12°C (dashed line): fuel cell freezes

Figure 2

Scheme of the stack model

Figure 3

Qualitative sketch of the temperature and the water phases during a start-up; case I: stack temperature below TM=0°C, frozen water in the stack; case II: stack temperature equal to TM=0°C, frozen and liquid water in the stack; and case III: stack temperature above TM=0°C, liquid water and vapor in the stack

Figure 4

Measured current-voltage curves in the model stack for a temperature range between −25°C and 90°C; dots denote measured points

Figure 5

Scheme for the calculation of the cell voltage (a) for a given stack current and (b) for a given cell voltage. Ice and liquid water in the stack reduce the active electrode area and increase the actual current density. A correction factor accounts for a reduced voltage due to depletion of reactants oxygen and hydrogen.

Figure 6

Finite state machine for the description of transitions between the model variants. TM=0°C is the melting temperature of ice; τ is an artificial delay parameter introduced for enhanced numerical robustness; τ is the time interval since the last transition event.

Figure 7

Simulation of a failed freeze start and comparison with experimental results. The initial temperature of the stack and the ambient temperature are equal to −12°C. Diagrams from top to bottom: measured and simulated temperatures of the coolant and of the stack core; measured and simulated power output; and simulated amount of ice and liquid water in the stack.

Figure 8

Simulation of a successful freeze start and comparison with experimental results. The initial temperature of the stack and the ambient temperature are equal to −10°C. Diagrams from top to bottom: measured and simulated temperatures of the coolant and of the stack core; measured and simulated power output; and simulated amount of ice, liquid water, and vapor in the stack.

Figure 9

Behavior of the model for different initial and ambient temperatures from −20°C to 0°C

Figure 10

Behavior of the model for different stack voltages at a fixed ambient temperature of −12°C: a reduced stack voltage and increased stack current improve the frost-start of a stack; V0=nominal value of the stack voltage used in the other simulations

Figure 11

Support of the cold start by an external heating of the coolant

Figure 12

Behavior of the model for different stack materials at a fixed ambient temperature of −10°C: A lower thermal capacity of the bipolar plates may improve the frost-start of a stack

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