JP6528115B2 - Fuel cell stack simulation method and simulation apparatus - Google Patents

Description

  The present invention relates to a fuel cell stack simulation method and simulation apparatus for efficiently simulating performance calculation of a fuel cell stack.

  Currently, cells are stacked and connected in series due to the market expansion of Enefarm (registered trademark), a fuel cell cogeneration system for home use, and the market launch and spread of fuel cell vehicles in 2015. Related companies are focusing on the performance improvement of the fuel cell stack, which is the heart of the fuel cell system.

  Under such circumstances, it is expected that the battery performance can be efficiently and accurately calculated by calculating the battery performance of the fuel cell stack by simulation.

  The purpose of the fuel cell stack simulation is to calculate the performance of the fuel cell stack based on the unit cell and the configuration of the fuel cell stack and the operating conditions. This is the largest analysis size for fuel cell related simulations.

  In this other analysis scale, there are simulation of the structure of the catalyst layer, simulation related to the preparation process thereof, and simulation of a single fuel cell, etc., but various approaches are known according to the scale.

  In the above simulation of the structure of the catalyst layer, the structure of the actual catalyst layer is reproduced by volume rendering from an image observed by SEM (scanning electron microscope) or TEM (transmission electron microscope), or the catalyst layer is represented The analytical structure necessary for simulation is determined by extracting dynamic parameters and creating a virtual catalyst structure from that, and the capacity of the catalyst layer is calculated by combining mass transport and electrochemical reaction. It is

  In addition, in the simulation related to the process of creating the catalyst layer, the application of molecular dynamics, coarse-grained molecular dynamics, dissipative particle dynamics etc. has begun to report the link between the material and the creation process and the structure of the catalyst layer. There is.

  With regard to the calculation of the performance of a single fuel cell, it is possible to simulate accurately with the platformization of the commercial tool Ansys Fluent (registered trademark) and the creation of various constitutive law models. Also in the stack, a large-scale simulation is possible by using the inventive method as described in Patent Document 1.

  Generally, the simulation of a fuel cell stack has problems in calculation time and convergence because the scale of calculation becomes very large, but the one proposed in Patent Document 1 is a simplified fuel represented by a simplified pressure loss body The calculation of the flow of gas in the fuel cell stack is performed using the cell stack model, and then the calculation of the flow of gas in the individual cells is performed to reduce the calculation time and ensure the convergence.

JP 2007-305419 A

  However, since what was proposed by patent document 1 uses the simple fuel cell stack model for calculation of a fuel cell stack, it is predicted that the calculation accuracy and the calculation time will largely change depending on the degree of the simplification. .

  It is necessary to carry out calculations on a scale close to a structure in which a large number of single cells are stacked if calculation accuracy is determined and the level of simplification is lowered, that is, if the model is close to a detailed fuel cell stack model. Because there is an increase in calculation time, there is a concern that the calculation accuracy may be degraded if the calculation speed is obtained and the level of simplification is increased, that is, if the model is simplified too much. Had.

  Therefore, an object of the present invention is to provide a fuel cell stack simulation method capable of calculating the cell performance of each cell at each stack position in the fuel cell stack while achieving both calculation accuracy and reduction of calculation time.

  In order to solve the above-mentioned conventional problems, in the fuel cell stack simulation method of the present invention, when N is an integer of 2 or more, a fuel cell stack in which N stages of fuel cells having electrolyte membranes and electrodes are stacked A fuel cell stack simulation method for calculating the cell performance of a fuel cell stack, comprising: a first end cell located at one end of the fuel cell stack; a first end cell located at the other end of the fuel cell stack The second end cell is a second end cell, which is located on both sides in the stacking direction of the fuel cell stack, and of the two end faces of the fuel cell stack orthogonal to the stacking direction, the end face on the first end cell side The first end surface is an end surface on the second end cell side, the second end surface is orthogonal to the stacking direction of the fuel cell stack, and any surface or first end surface located in the first end cell is a first end surface. Of the first reference surface The first predetermined value, which is the current density or the current density, is set, and it is located on the second end face side from the first reference face on an arbitrary plane which is orthogonal to the stacking direction of the fuel cell stack and located in the first end cell. The second reference plane is a second reference plane, and a second predetermined value which is the potential of the second reference plane is set. The second reference plane is orthogonal to the stacking direction of the fuel cell stack, and the second plane is the second plane. A first calculation step of calculating the potential and current density of the third reference surface using the first predetermined value and the second predetermined value with the surface located on the second end face side from the reference surface as the third reference surface It is

  As a result, the boundary conditions of the end cells can be rationally set, and the calculation of the performance of the fuel cell stack can be efficiently simulated while achieving both the calculation accuracy and the shortening of the calculation time.

  According to the present invention, since the boundary conditions of the end cells can be rationally set, calculation of the cell performance of each cell at each stacking position of the fuel cell stack while accurately maintaining the calculation scale of the single cell Is possible. As a result, it is possible to efficiently calculate the cell performances of the end cells of the fuel cell stack and cells other than the end portions while making the calculation accuracy and the reduction of the calculation time compatible with each other.

Explanatory drawing for demonstrating the concept of the setting method of the boundary in the 1st or 2nd calculation step of the fuel cell stack simulation method of this invention, and the (2K-1) calculation step. Flow chart showing the concept of the first embodiment of the fuel cell stack simulation method of the present invention Explanatory drawing for demonstrating the concept of the setting method of the boundary in the 1st or 2nd calculation step of the simulation method of the fuel cell stack of this invention and 2nd K calculation step. Flow chart showing the concept of the second embodiment of the fuel cell stack simulation method of the present invention Flow chart showing the concept of the third embodiment of the fuel cell stack simulation method of the present invention A flowchart showing the concept of Embodiment 4 of the fuel cell stack simulation method of the present invention

  First, we will describe the discovery facts that led to the form for carrying out the invention. As a result of intensive studies on the simulation results of the fuel cell stack, the present inventor has focused on the following two facts.

  First, even in the case where a potential difference of about 50 millivolts is generated in the separator end face of a cell in a fuel cell stack, the potential distribution on the laminated surface of the center of the electrolyte membrane of that cell is substantially flat Is a constant value.

  Second, when a large potential difference similarly occurs in the end face of the separator of a cell in the fuel cell stack, the potential is distributed on the cathode side in the direction to exactly cancel the in-plane current generated on the anode side. What is done, in other words, the potential distribution on the anode side and the potential distribution on the cathode side at the separator end face of a certain cell are in mirror symmetry with respect to the potential distribution on the electrolyte membrane surface.

  Naturally, the boundary conditions related to the potential distribution include cases where no potential difference occurs in the separator end face, and are widely applicable conditions.

  Here, the reason why each potential distribution is determined so as to cancel the in-plane current on the anode side and the cathode side will be briefly considered. Since the fuel cell stack is formed by stacking a large number of cells, the cells located at other than the ends except for the cells at both ends have approximately periodic physical quantity distributions (eg, temperature and current density) for each cell. It is predicted that

  However, if the in-plane current on the anode side and the in-plane current on the cathode side do not cancel each other, a net in-plane current is formed in the cell, and the in-plane current is accumulated in the stacking direction. And its periodicity breaks down. Therefore, in order for the cells located other than the end to have a periodic distribution of physical quantities, in-plane currents need to be offset at both end faces.

  In addition, when the in-plane currents on the anode side and the cathode side cancel each other, it is predicted that the potential distribution on the anode side and the potential distribution on the cathode side have mirror symmetry with respect to the potential distribution on the electrolyte membrane surface. Therefore, due to the configuration of the fuel cell, the potential distribution at the center of the laminated surface of the electrolyte membrane located at the center of the cell can be easily explained as being almost flat and having a constant value.

  Next, on the basis of this heuristic fact, the present invention will be described which efficiently simulates a fuel cell stack. Here, the embodiment of the present invention will be described along the procedure of each calculation step. The present invention is not limited by this embodiment.

A first invention is a fuel cell stack simulation method for calculating the cell performance of a fuel cell stack in which N fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more. A first end cell located at one end of the fuel cell stack is referred to as a first end cell, and an Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. Among the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the end face on the second end cell side is the first An arbitrary surface or a first end surface located in the first end cell, which has two end surfaces and is orthogonal to the stacking direction of the fuel cell stack, is a potential or current density of the first reference surface. Set the first default value, stack direction of fuel cell stack A second predetermined value, which is an electric potential of the second reference surface, is a surface which is orthogonal to the first end surface and which is located on the second end surface side with respect to the first reference surface. A third reference plane is set as a third reference plane, which is an arbitrary plane that is orthogonal to the stacking direction of the fuel cell stack and located in the first end cell, and is located on the second end face side from the second reference plane. A fuel cell stack simulation method, comprising: a first calculation step of calculating a potential and a current density of a third reference surface using a value and a second predetermined value.

  By this fuel cell stack simulation method, it becomes possible to rationally set the boundary condition of the end cell by setting the potential of the second reference surface based on the above-described heuristic fact in the present invention, It is possible to efficiently simulate the performance calculation of the fuel cell stack while achieving both the calculation accuracy and the reduction of the calculation time.

  A second invention is a fuel cell stack simulation method for calculating the cell performance of a fuel cell stack in which N fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more. A first end cell located at one end of the fuel cell stack is referred to as a first end cell, and an Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. Among the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the end face on the second end cell side is the first Two end faces, an arbitrary face which is orthogonal to the stacking direction of the fuel cell stack, and is located in the first end cell, or a first end face is a first reference face, and a first predetermined potential which is a potential of the first reference face Setting the value, and orthogonal to the stacking direction of the fuel cell stack, With any surface located in the end cell, a surface located on the second end surface side from the first reference surface is set as a second reference surface, and a second predetermined value which is the current density of the second reference surface is set. The third reference plane is a plane which is orthogonal to the stacking direction of the battery stack and which is located in the first end cell and which is located on the second end face side with respect to the second reference plane. It is a simulation method of a fuel cell stack provided with the 2nd calculation step which calculates potential and current density of the 3rd reference level using default value.

  With this fuel cell stack simulation method, the current density of the second reference surface can be determined, so that the boundary conditions of the end cells can be rationally set with respect to the amount of current, which achieves both calculation accuracy and reduction of calculation time. At the same time, it is possible to efficiently simulate the performance calculation of the fuel cell stack.

  In the third invention, in particular, the first reference surface in the first or second invention is a first end surface.

  By this simulation method, the first reference plane can be set to the end face of the first end cell, and boundary conditions can be easily set.

  In the fourth invention, in particular, the second reference plane in any one of the first to third inventions is a plane located in the electrolyte membrane of the first end cell.

  With this simulation method, boundaries can be set inside the electrolyte membrane, and boundary conditions can be easily set.

  In the fifth invention, in particular, the third reference surface in any one of the first to fourth inventions is an end face on the second end face side of the first end cell.

  By this simulation method, the third reference plane can be set at the boundary between the first end cell and the second stage cell, and boundary conditions can be easily set.

  According to a sixth aspect of the invention, in particular, the first reference surface according to any one of the first to fifth aspects of the invention sets a constant predetermined potential.

  This simulation method makes it possible to use a constant predetermined potential, and to set boundary conditions suitable for the case where the first reference surface is an equipotential surface.

  In a seventh aspect of the invention, in particular, a predetermined current density is set on the first reference surface in any one of the first, third, and fifth aspects of the invention.

  This simulation method makes it possible to use a constant predetermined current density, and can easily set the current density of the first reference surface.

  According to an eighth aspect of the invention, in particular, the second reference surface according to any one of the first and third to seventh aspects of the invention sets a constant predetermined potential.

  This simulation method makes it possible to use a constant predetermined potential, and to set boundary conditions suitable for the case where the second reference surface becomes an equipotential surface.

  According to a ninth aspect of the invention, in particular, the second reference surface according to any one of the second to seventh aspects of the invention sets a predetermined current density.

  This simulation method makes it possible to use a constant predetermined current density, and the current density of the second reference surface can be easily set.

The tenth invention is adjacent to the (K-1) th cell of the fuel cell stack, in particular when K is an integer of 2 or more and N or less in any of the first to ninth inventions. A specific cell located on the side of the second end cell is referred to as the K-th cell, and an arbitrary surface located in the K-th cell and orthogonal to the stacking direction of the fuel cell stack is the (3K-2) An arbitrary plane orthogonal to the stacking direction of the fuel cell stack, which serves as a reference plane, is located in the K-th cell, and is located on the second end face side from the (3K-2) reference plane, is the (3K-1) An arbitrary plane orthogonal to the stacking direction of the fuel cell stack, which is a reference plane, located in the Kth cell and located on the second end face side from the (3K-1) reference plane, is a 3K reference plane, After the (2K-3) calculation step or (2K-2) calculation step, the potential of the (3K-3) reference plane is used to set Value of the (3K-2) reference plane and, second (3K-2) No. (3K-1) is set as the average current density of the reference plane with the value of the reference surface, the potential of the 3K reference plane And a second (2K-1) calculation step of calculating the current density.

  By this simulation method, the boundary conditions of the (3K-1) reference plane of cells other than the first end cell can be easily set, and the calculation accuracy and the reduction of the calculation time can be achieved at the same time. Performance calculation can be efficiently simulated.

  According to an eleventh aspect of the invention, in particular, in any one of the first to ninth aspects, when K is an integer of 2 or more and N or less, it is adjacent to the K-1st cell of the fuel cell stack, The specific cell located on the side of the two-end cell is the K-th cell, and an arbitrary surface located in the K-th cell and orthogonal to the stacking direction of the fuel cell stack is the (3K-2) reference plane And an arbitrary plane orthogonal to the stacking direction of the fuel cell stack, located in the K-th cell and located on the second end face side from the (3K-2) reference plane, is taken as the 3K-th reference plane. 2K-3) Calculation step or (2K-2) After the calculation step, the value of the (3K-2) reference surface set using the potential of the (3K-3) reference surface, and (3K-3) ) Calculate the potential of the third K reference surface using the current density of the third K reference surface set using the current density of the reference surface Those having a 2K calculation step.

  With this simulation method, it becomes possible to rationally set the boundary conditions of the (3K−2) reference plane and the 3rd reference plane of cells other than the first end cell, making it possible to balance calculation accuracy and calculation time. At the same time, it is possible to efficiently simulate the performance calculation of the fuel cell stack.

  In a twelfth aspect of the present invention, in particular, the (3K-2) reference plane in the tenth or eleventh aspect is used as an end face of a K-th stage cell located on the first end cell side.

  By this simulation method, the (3K-2) reference plane can be set at the boundary between the (K-1) th cell and the Kth cell, and boundary conditions can be easily set.

In a thirteenth aspect of the present invention, in particular, the (3K-1) reference plane in the tenth aspect is a surface located in the electrolyte membrane of the K-th cell.

  With this simulation method, boundaries can be set inside the electrolyte membrane, and boundary conditions can be easily set.

  In a fourteenth aspect of the present invention, in particular, the third K reference surface in the tenth or eleventh aspect is used as an end face of a K-th cell located on the second end cell side.

  By this simulation method, the 3rd K reference plane can be set at the boundary between the Kth cell and the (K + 1) th cell, and boundary conditions can be easily set.

  A fifteenth invention is a fuel cell stack simulation apparatus for calculating the cell performance of a fuel cell stack in which N fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more. A first end cell located at one end of the fuel cell stack is referred to as a first end cell, and an Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. Among the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the end face on the second end cell side is the first An arbitrary surface or a first end surface located in the first end cell, which has two end surfaces and is orthogonal to the stacking direction of the fuel cell stack, is a potential or current density of the first reference surface. Set the first default value and stack the fuel cell stack A second predetermined value which is an electric potential of the second reference surface, wherein a surface located on the second end surface side with respect to the first reference surface is an arbitrary surface which is orthogonal to the first end surface and which is located in the first end cell. The second reference surface is an arbitrary surface which is orthogonal to the stacking direction of the fuel cell stack and is located in the first end cell, and the surface located on the second end surface side with respect to the second reference surface is the third reference surface. A fuel cell stack simulation apparatus, comprising: a first calculation step of calculating a potential and a current density of a third reference surface using a default value and a second default value.

  With the above configuration, the boundary condition of the end cell can be rationally set by setting the potential of the second reference surface based on the above-described heuristic facts of the present invention, and thus the fuel cell The calculation of stack performance can be efficiently simulated.

A sixteenth invention relates to a fuel cell stack simulation apparatus for calculating the cell performance of a fuel cell stack in which fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages when N is an integer of 2 or more. A first end cell located at one end of the fuel cell stack is referred to as a first end cell, and an Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. Among the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the end face on the second end cell side is the first Two end faces, an arbitrary face which is orthogonal to the stacking direction of the fuel cell stack, and is located in the first end cell, or a first end face is a first reference face, and a first predetermined potential which is a potential of the first reference face Set the value, orthogonal to the stacking direction of the fuel cell stack, With an arbitrary surface located in one end cell, a surface located on the second end surface side from the first reference surface is set as a second reference surface, and a second predetermined value which is a current density of the second reference surface is set. The third reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the second reference plane. A fuel cell stack simulation apparatus comprising a second calculation step of calculating the potential and current density of the third reference surface using the predetermined value.

  With the above configuration, since the current density of the second reference surface is defined, the boundary condition of the end cell with respect to the amount of current can be rationally set, and simulation of performance calculation of the fuel cell stack can be efficiently simulated. Device can be used.

The seventeenth invention is the second end cell adjacent to the K-1st cell of the fuel cell stack, where K is an integer not less than 2 and not more than N, particularly in the fifteenth or sixteenth invention. A specific cell located on the side of the fuel cell is referred to as a K-th cell, an arbitrary surface located in the K-th cell and orthogonal to the stacking direction of the fuel cell stack is referred to as a (3K-2) reference plane, An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, located in the step cell and located on the second end face side from the (3K-2) reference surface, is taken as the (3K-1) reference surface, the Kth surface An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, located in the step cell and located on the second end face side from the (3K-1) reference surface, is taken as the 3rd K reference surface, the (2K-3) After the calculation step or (2K-2) calculation step, the third set using the potential of the (3K-3) reference plane 3K-2) the value of the reference plane and, using the value of the (3K-1) reference surface set as an average current density of the (3K-2) a reference plane, the potential and current density of the 3K reference plane A second (2K-1) calculation step of calculating is provided.

  With the above configuration, the boundary conditions of the (3K-1) reference plane of cells other than the first end cell can be set simply and rationally, and simulation of fuel cell stack performance calculation can be efficiently performed. It can be a possible device.

  According to an eighteenth invention, in particular, in the fifteenth or sixteenth invention, when K is an integer of 2 or more and N or less, the second end cell is adjacent to the K-1st cell of the fuel cell stack. A specific cell located on the side of the fuel cell is referred to as a K-th cell, an arbitrary surface located in the K-th cell and orthogonal to the stacking direction of the fuel cell stack is referred to as a (3K-2) reference plane, An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, located in the step cell and located on the second end face side from the (3K-2) reference surface, is taken as the 3rd K reference surface, the (2K-3) After the calculation step or (2K-2) calculation step, the value of the (3K-2) reference plane set using the potential of the (3K-3) reference plane and the value of the (3K-3) reference plane A second K for calculating the potential of the third K reference plane using the current density of the third K reference plane set using the current density Out are those provided with a step.

  With the above configuration, it is possible to rationally set the boundary conditions of the (3K−2) reference plane and the 3rd reference plane of cells other than the first end cell, and efficiency of fuel cell stack performance calculation can be achieved. Can be simulated.

  Hereinafter, when N is 2 or more and K is an integer of 2 or more and N or less, Embodiments 1 to 4 of the fuel cell stack simulation method of the present invention will be described.

Embodiment 1
FIG. 1 is an explanatory view for explaining the concept of a method of setting boundaries in the first calculation step and the (2K-1) calculation step in the fuel cell stack simulation method of the present invention, and FIG. 2 is a fuel of the present invention It is a flowchart which shows the concept of Embodiment 1 of the simulation method of a battery stack.

  First, the first calculation step in the first end cell and the (2K-1) calculation step in the K-th cell used in the first embodiment will be described, and a simulation of a fuel cell stack combining them will be described. Explain how to do it.

  In FIG. 1, the fuel cell stack 5 includes a first end cell 1, a K th cell 2, a (K + 1) th cell 3, a second end cell 4, an anode side collector plate 6 and a cathode side. Current collector plate 7, first reference surface 8, second reference surface 9, third reference surface 10, third (3K-2) reference surface 11, third (3K-1) reference surface 12, third K reference surface 13 It is configured.

  In the first calculation step, since the first end cell 1 of the fuel cell stack 5 is in contact with the current collector plate 6 on the anode side, the current collector plate 6 on the anode side and the first end cell A surface in contact with 1 is set as a first reference surface 8, and a constant potential or current density is set there. Next, a constant potential is set in the first calculation step with respect to the second reference surface 9 located in the electrolyte membrane.

  The reason why the constant value can be set to the second reference surface 9 is as described above. Furthermore, in the first calculation step, after the boundary conditions of the potentials are set to the first reference surface 8 and the second reference surface 9, calculation of the battery performance of the first end cell 1 is performed by simulation.

  The calculation of the battery performance referred to here indicates that the internal physical quantities of the battery including the potential, the current, the pressure, the temperature, and the concentration are calculated. Further, since the boundary conditions are set to the second reference surface 9, in order to carry out the present invention, it is essential to be a simulation method or apparatus capable of setting the inner boundary.

  Next, in the first calculation step, after calculation of the battery performance of the first end cell 1 is simulated, the potential and the current density are set on the third reference surface 10 using this result. This makes it possible to calculate the cell performance of the first end cell 1 of the fuel cell stack by simulation.

  Next, a method of performing calculation of the battery performance of the Kth cell as a second (2K-1) calculation step will be described.

  In the (2K-1) calculation step, the calculation result of the cell performance of the (K-1) th cell in the (2K-3) calculation step is obtained for the Kth cell 2 of the fuel cell stack. The potential and the current density are set to the (3K-2) reference surface 11 based on the above values, and the (3K-2) reference surface 11 is formed on the (3K-1) reference surface 12 located in the electrolyte membrane. Set the average current density value. After setting the boundary conditions to the (3K-2) reference surface 11 and the (3K-1) reference surface 12, calculation of the battery performance of the cell 2 of the K-th stage is performed by simulation.

  In this calculation step, since the boundary conditions are set to the (3K-1) th reference surface 12, in order to carry out the present invention, it is necessary to be a simulation method or apparatus capable of setting an inner boundary. From the simulation result of the cell 2 of the K-th stage, the potential and the current density are set to the third K reference surface 13. This makes it possible to calculate the cell performance of the K-th cell 2 in the fuel cell stack by simulation.

  A flowchart of this embodiment using the first calculation step and the (2K-1) calculation step is shown in FIG.

In this flowchart, the process starts at S001, sets the number of cell stages of the fuel cell stack at S002, and calculates the cell performance of the first end cell using the first calculation step 14 at S003 to S006.

  Next, in S007, K is set to 2, and in S008 to S012, the cell performance of the second-stage cell is calculated using the third calculation step, K = K + 1 is performed in S013, and 3 is added to the cell number K Set After that, while increasing the value of K, the (2K-1) -th calculation step 16 is repeated repeatedly.

  Also for the Nth-stage cell corresponding to the second end cell, calculation of battery performance can be performed by simulation using the (2N-1) -th calculation step. Finally, when N + 1 is set to the cell number K, the calculation is completed, and the calculation of the cell performance of all the cells of the fuel cell is completed.

  As described above, in the present embodiment, the boundary conditions of the first end cell can be set accurately, and further, the boundary conditions of the (3K-1) reference plane of cells other than the first end cell can be simplified. By being able to set, it becomes possible to calculate the cell performance of each cell at each stacking position in the fuel cell stack while making the calculation accuracy and the reduction of the calculation time compatible.

Second Embodiment
FIG. 3 is an explanatory view for explaining the concept of a method of setting boundaries in the first or second calculation step and the second K calculation step of the fuel cell stack simulation method of the present invention, and FIG. 4 is a fuel cell of the present invention It is a flowchart which shows the concept of Embodiment 2 of the simulation method of a stack | stuck.

  First, the first calculation step in the first end cell and the second K calculation step in the Kth cell used in the second embodiment will be described, and a method of simulating a fuel cell stack combining them will be described. Do.

  In FIG. 3, the fuel cell stack 5 includes the first end cell 1, the Kth cell 2, the (K + 1) th cell 3, the second end cell 4, the anode side current collector plate 6 and the cathode side. The collector plate 7, the first reference surface 8, the second reference surface 9, the third reference surface 10, the third (3K-2) reference surface 11, and the third K reference surface 13 are provided.

  In the first calculation step, since the first end cell 1 of the fuel cell stack 5 is in contact with the current collector plate 6 on the anode side, the current collector plate 6 on the anode side and the first end cell A surface in contact with 1 is set as a first reference surface 8, and a constant potential or current density is set there. Next, a constant potential is set in the first calculation step with respect to the second reference surface 9 located in the electrolyte membrane.

  The reason why the constant value can be set to the second reference surface 9 is as described above. Furthermore, in the first calculation step, after the boundary conditions of the potentials are set to the first reference surface 8 and the second reference surface 9, calculation of the battery performance of the first end cell 1 is performed by simulation. The calculation of the battery performance referred to here indicates that the internal physical quantities of the battery including the potential, the current, the pressure, the temperature, and the concentration are calculated.

  In addition, since the boundary conditions are set in the second reference surface 9, it is essential that the simulation method or apparatus be able to set the inner boundary in order to implement the present invention.

  Next, in the first calculation step, after calculation of the battery performance of the first end cell 1 is simulated, the potential and the current density are set on the third reference surface 10 using this result. This makes it possible to calculate the cell performance of the first end cell 1 of the fuel cell stack by simulation.

Next, a method of performing a calculation of the battery performance of the Kth cell as a second K calculation step will be described.

  The 2nd K calculation step is based on the value obtained as a result of the calculation of the cell performance of the (K-1) th cell in the (2K-3) calculation step with respect to the 2nd cell of the fuel cell stack. The potential and the current density are set to the (3K-2) reference plane 11 and the current density value of the 3Kth reference plane 13 is set using the value of the current density of the (3K-2) reference plane.

  Here, as described above, the current density distribution on the anode side and the current density distribution on the cathode side of the separator end face of the cell other than the end are in mirror symmetry with respect to the center plane of the electrolyte membrane. (3K-2) Based on the current density of the reference plane, the value of the current density of the third K reference plane 13 is set.

  After the boundary conditions are set to the (3K-2) reference plane 11 and the 3K reference plane 13, calculation of the battery performance of the cell 2 of the K-th stage is performed by simulation. From the simulation result of the cell 2 of the K-th stage, the potential and the current density are set to the third K reference surface 13. This makes it possible to calculate the cell performance of the K-th cell 2 in the fuel cell stack by simulation.

  A flowchart of the present embodiment using the first calculation step and the second K calculation step is shown in FIG.

  In this flowchart, the process starts in S101, sets the number of cell stages of the fuel cell stack in S102, and calculates the cell performance of the first end cell using the first calculation step 14 in S103 to S106.

  Next, in step S107, K is set to 2, and in steps S108 to S112, the cell performance of the second stage cell is calculated using the third calculation step, and in step S113, K = K + 1 is performed. Set After that, the second K calculation step 17 is repeated repeatedly while increasing the value of K.

  Also with regard to the cell of the Nth stage corresponding to the second end cell, it is possible to perform calculation of battery performance by simulation using the second N calculation step. Finally, when N + 1 is set to the cell number K, the calculation is completed, and the calculation of the cell performance of all the cells of the fuel cell is completed.

  As described above, in the present embodiment, the boundary condition of the first end cell can be set most accurately, and the boundary condition of the (3K-2) reference plane and the 3K reference plane of cells other than the first end cell is further set. By being able to set simply, it becomes possible to calculate the cell performance of each cell at each stacking position in the fuel cell stack while achieving both calculation accuracy and reduction of calculation time.

Third Embodiment
Here, the case of applying the second calculation step instead of the first calculation step in the first embodiment will be described. FIG. 5 is a flowchart showing the concept of the third embodiment of the fuel cell stack simulation method of the present invention.

  First, the second calculation step in the first end cell and the (2K-1) calculation step in the Kth cell used in the third embodiment will be described, and a simulation of a fuel cell stack combining them will be described. Explain how to do it.

In the second calculation step, since the first end cell 1 of the fuel cell stack 5 is in contact with the current collector plate 6 on the anode side, the current collector plate 6 on the anode side and the first end cell A surface in contact with 1 is set as a first reference surface 8, and a constant potential or current density is set there. Next, a constant current density is set in the second calculation step with respect to the second reference surface 9 located in the electrolyte membrane.

  The reason why the constant value can be set to the second reference surface 9 is as described above. Furthermore, in the second calculation step, after the boundary conditions of the potential or the current density are set to the first reference surface 8 and the second reference surface 9, calculation of the battery performance of the first end cell 1 is performed by simulation.

  The calculation of the battery performance referred to here indicates that the internal physical quantities of the battery including the potential, the current, the pressure, the temperature, and the concentration are calculated. In addition, since the boundary conditions are set in the second reference surface 9, it is essential that the simulation method or apparatus be able to set the inner boundary in order to implement the present invention.

  Next, in a second calculation step, calculation of the battery performance of the first end cell 1 is simulated, and then the potential and current density are set on the third reference surface 10 using this result. This makes it possible to calculate the cell performance of the first end cell 1 of the fuel cell stack by simulation.

  Next, a method of performing calculation of the battery performance of the Kth cell as a second (2K-1) calculation step will be described.

  In the (2K-1) calculation step, the calculation result of the cell performance of the (K-1) th cell in the (2K-3) calculation step is obtained for the Kth cell 2 of the fuel cell stack. The potential and the current density are set to the (3K-2) reference surface 11 based on the above values, and the (3K-2) reference surface 11 is averaged on the (3K-1) reference surface 12 located in the electrolyte membrane. Set the current density value.

  After setting the boundary conditions to the (3K-2) reference surface 11 and the (3K-1) reference surface 12, calculation of the battery performance of the cell 2 of the K-th stage is performed by simulation.

  In this calculation step, since the boundary conditions are set to the (3K-1) th reference surface 12, in order to carry out the present invention, it is necessary to be a simulation method or apparatus capable of setting an inner boundary. From the simulation result of the cell 2 of the K-th stage, the potential and the current density are set to the third K reference surface 13. This makes it possible to calculate the cell performance of the K-th cell 2 in the fuel cell stack by simulation.

  A flowchart of the present embodiment using the second calculation step and the (2K-1) calculation step is shown in FIG.

  In this flowchart, the process starts in S201, sets the number of cell stages of the fuel cell stack in S202, and calculates the cell performance of the first end cell using the second calculation step 15 in S203 to S206.

  Next, 2 is set to K in S207, and the cell performance of the second-stage cell is calculated using the third calculation step in S208 to S212, K = K + 1 is performed in S213, and 3 is added to the cell number K Set After that, while increasing the value of K, the (2K-1) -th calculation step 16 is repeated repeatedly.

  Also for the Nth-stage cell corresponding to the second end cell, calculation of battery performance can be performed by simulation using the (2N-1) -th calculation step. Finally, when N + 1 is set to the cell number K, the calculation is completed, and the calculation of the cell performance of all the cells of the fuel cell is completed.

As described above, in the present embodiment, by defining the current density of the second reference surface of the first end cell, the boundary condition of the end cell can be rationally set with respect to the amount of current that is most desired to be known. The boundary conditions of the third (3K-1) reference plane of cells other than the cells can be easily set, and the cell performance of each cell at each stacking position in the fuel cell stack can be achieved while achieving both calculation accuracy and reduction of calculation time. It becomes possible to calculate

Embodiment 4
Here, the case of applying the second calculation step instead of the first calculation step in the second embodiment will be described. FIG. 6 is a flow chart showing the concept of Embodiment 4 of the fuel cell stack simulation method of the present invention.

  First, the second calculation step in the first end cell and the second K calculation step in the K-th cell used in the fourth embodiment will be described, and a method of simulating a fuel cell stack combining them will be described. Do.

  In the second calculation step, since the first end cell 1 of the fuel cell stack 5 is in contact with the current collector plate 6 on the anode side, the current collector plate 6 on the anode side and the first end cell A surface in contact with 1 is set as a first reference surface 8, and a constant potential or current density is set there. Next, a constant current density is set in the second calculation step with respect to the second reference surface 9 located in the electrolyte membrane.

  The reason why the constant value can be set to the second reference surface 9 is as described above. Furthermore, in the second calculation step, after the boundary conditions of the potential or the current density are set to the first reference surface 8 and the second reference surface 9, calculation of the battery performance of the first end cell 1 is performed by simulation. The calculation of the battery performance referred to here indicates that the internal physical quantities of the battery including the potential, the current, the pressure, the temperature, and the concentration are calculated.

  In addition, since the boundary conditions are set in the second reference surface 9, it is essential that the simulation method or apparatus be able to set the inner boundary in order to implement the present invention.

  Next, in a second calculation step, calculation of the battery performance of the first end cell 1 is simulated, and then the potential and current density are set on the third reference surface 10 using this result. This makes it possible to calculate the cell performance of the first end cell 1 of the fuel cell stack by simulation.

  Next, a method of performing a calculation of the battery performance of the Kth cell as a second K calculation step will be described.

  The second K calculation step is the cell performance of the (K-1) th cell of the (2K-3) calculation step or the (2K-2) calculation step with respect to the Kth cell 2 of the fuel cell stack. The potential and the current density are set to the (3K-2) reference plane 11 based on the values obtained as a result of calculation of the 3rd K reference plane 13 using the value of the current density of the (3K-2) reference plane. Set the current density value of

  Here, as described above, the current density distribution on the anode side and the current density distribution on the cathode side of the separator end face of the cell other than the end are in mirror symmetry with respect to the center plane of the electrolyte membrane. (3K-2) Based on the current density of the reference plane, the value of the current density of the third K reference plane 13 is set. After the boundary conditions are set to the (3K-2) reference plane 11 and the 3K reference plane 13, calculation of the battery performance of the cell 2 of the K-th stage is performed by simulation.

  From the simulation result of the cell 2 of the K-th stage, the potential and the current density are set to the third K reference surface 13. This makes it possible to calculate the cell performance of the K-th cell 2 in the fuel cell stack by simulation.

  A flowchart of the present embodiment using the second calculation step and the 2K calculation step is shown in FIG.

  In this flowchart, the process starts in S301, sets the number of cell stages of the fuel cell stack in S302, and calculates the cell performance of the first end cell using the second calculation step 15 in S303 to S306.

  Next, 2 is set to K in S307, and the cell performance of the second stage cell is calculated using the third calculation step in S308 to S312, K = K + 1 is performed in S313, and 3 is added to the cell number K Set After that, the second K calculation step 17 is repeated repeatedly while increasing the value of K.

  Also with regard to the cell of the Nth stage corresponding to the second end cell, it is possible to perform calculation of battery performance by simulation using the second N calculation step. Finally, when N + 1 is set to the cell number K, the calculation is completed, and the calculation of the cell performance of all the cells of the fuel cell is completed.

  As described above, in the present embodiment, by defining the current density of the second reference surface of the first end cell, the boundary condition of the end cell can be rationally set with respect to the amount of current that is most desired to be known. The boundary conditions of the third (3K-2) reference plane and the third K reference plane of cells other than the cells can be easily set, and both calculation accuracy and reduction of calculation time can be achieved at the same time at each stacking position in the fuel cell stack. It becomes possible to calculate the battery performance of each cell.

  As mentioned above, although Embodiment 1-4 was shown, a 1st calculation step and a 2nd calculation step are steps which perform calculation of the battery performance of the 1st end cell of a fuel cell stack by simulation, and the purpose of both is It is the same but the method is different.

  However, since the potential of the center plane of the electrolyte membrane is substantially constant in the first end cell based on the facts found by us, the first calculation is for the purpose of carrying out the calculation of the cell performance of the fuel cell stack by simulation. Steps are more suitable.

  The (2K-1) calculation step and the 2nd K calculation step are steps for performing calculation of the cell performance of the Kth cell of the fuel cell stack by simulation, and the purpose of both is the same, but the method is It is different.

  However, since the current density in the Kth cell is approximately mirror-symmetrical between the (3K-2) reference plane 11 and the 3Kth reference plane 13, the calculation of the cell performance of the fuel cell stack can be simulated by simulation. For the purpose of carrying out, the second K calculation step is more suitable.

  In view of these circumstances, the one corresponding to the second embodiment is the best mode for calculating the cell performance of the fuel cell stack.

  The fuel cell stack simulation method of the present invention can efficiently simulate the performance calculation of the fuel cell stack while achieving both calculation accuracy and shortening of calculation time, so the cost reduction and development of the fuel cell stack development can be achieved. Suitable for time reduction applications.

1 1st end cell (1st cell)
2 cell of the K th stage 3 cell of the K th +1 stage 4 second end cell (cell of the N th stage)
Reference Signs List 5 fuel cell stack 6 anode side current collector plate 7 cathode side current collector plate 8 first reference surface 9 second reference surface 10 third reference surface 11 th (3K-2) reference surface 12 th (3K-1) reference Plane 13 3rd K reference plane 14 1st calculation step 15 2nd calculation step 16 2nd (2K-1) calculation step 17 2nd K calculation step

Claims (18)

A fuel cell stack simulation method for calculating the cell performance of a fuel cell stack in which fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more,
The first stage cell located at one end of the fuel cell stack is referred to as a first end cell, and the Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. ,
Of the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the second end cell side The end face of the second end face,
The electric potential or the current density of the first reference surface is an arbitrary surface which is orthogonal to the stacking direction of the fuel cell stack and located in the first end cell or the first end surface is a first reference surface. Set the first default value,
The second reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the first reference plane. 2 Set a second default value, which is the potential of the reference plane,
The third reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the second reference plane. The first calculation step of calculating the potential and the current density of the third reference surface using one predetermined value and the second predetermined value,
Fuel cell stack simulation method. A fuel cell stack simulation method for calculating the cell performance of a fuel cell stack in which fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more,
The first stage cell located at one end of the fuel cell stack is referred to as a first end cell, and the Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. ,
Of the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the second end cell side The end face of the second end face,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack and located in the first end cell, or the first end surface as a first reference surface, and a first predetermined potential at the first reference surface Set the value,
The second reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the first reference plane. 2 Set a second default value, which is the current density of the reference plane,
The third reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the second reference plane. And a second calculation step of calculating the potential and the current density of the third reference surface using the one predetermined value and the second predetermined value.
Fuel cell stack simulation method. The first reference surface is the first end surface,
A method of simulating a fuel cell stack according to claim 1 or 2. The second reference plane is a plane located in the electrolyte membrane of the first end cell,
The fuel cell stack simulation method according to any one of claims 1 to 3. The third reference plane is an end face on the second end face side of the first end cell,
The fuel cell stack simulation method according to any one of claims 1 to 4. Setting a constant predetermined potential on the first reference surface;
The fuel cell stack simulation method according to any one of claims 1 to 5. Setting a predetermined current density on the first reference surface;
A method of simulating a fuel cell stack according to any one of claims 1 to 5. Setting a constant predetermined potential on the second reference surface;
The fuel cell stack simulation method according to any one of claims 1 to 3. Setting a predetermined current density on the second reference surface;
The fuel cell stack simulation method according to any one of claims 2 to 7. When K is an integer greater than or equal to 2 and less than or equal to N, a specific cell located adjacent to the K-1st cell of the fuel cell stack and located on the second end cell side is the Kth cell. ,
An arbitrary surface located in the Kth cell and orthogonal to the stacking direction of the fuel cell stack is taken as a (3K-2) reference surface,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, which is located in the K-th cell and located on the second end face side with respect to the (3K-2) reference surface, is a (3K-1) As a reference plane,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, which is located in the Kth cell and located on the second end face side with respect to the (3K-1) reference surface, is taken as a 3K reference surface,
After the (2K-3) calculation step or the (2K-2) calculation step, the value of the (3K-2) reference surface set using the potential of the (3K-3) reference surface, and the (3K-2) A second (2K-1) calculation of calculating the potential and the current density of the third K reference surface using the value of the third (3K-1) reference surface set as the average current density of the reference surface With steps
The fuel cell stack simulation method according to any one of claims 1 to 9. When K is an integer greater than or equal to 2 and less than or equal to N, a specific cell located adjacent to the K-1st cell of the fuel cell stack and located on the second end cell side is the Kth cell. ,
An arbitrary surface located in the Kth cell and orthogonal to the stacking direction of the fuel cell stack is taken as a (3K-2) reference surface,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, which is located in the K-th cell and is located on the second end face side with respect to the (3K-2) reference surface, is taken as a 3K reference surface;
After the (2K-3) calculation step or the (2K-2) calculation step, the value of the (3K-2) reference surface and the value of the (3K-2) reference surface set using the potential of the (3K-3) reference surface 3K-3) A second K calculation step of calculating the potential of the third K reference surface using the current density of the third K reference surface set using the current density of the reference surface,
The fuel cell stack simulation method according to any one of claims 1 to 9. The (3K-2) reference plane is an end face of a Kth cell located on the first end cell side,
A method of simulating a fuel cell stack according to claim 10 or 11. The (3K-1) reference plane is a plane located in the electrolyte membrane of the K-th cell,
The fuel cell stack simulation method according to claim 10 . The third K reference plane is an end face of a K-th cell located on the second end cell side,
A method of simulating a fuel cell stack according to claim 10 or 11. A fuel cell stack simulation apparatus that calculates the cell performance of a fuel cell stack in which fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more.
The first stage cell located at one end of the fuel cell stack is referred to as a first end cell, and the Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. ,
Of the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the second end cell side The end face of the second end face,
The electric potential or the current density of the first reference surface is an arbitrary surface which is orthogonal to the stacking direction of the fuel cell stack and located in the first end cell or the first end surface is a first reference surface. Set the first default value,
The second reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the first reference plane. 2 Set a second default value, which is the potential of the reference plane,
The third reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the second reference plane. The first calculation step of calculating the potential and the current density of the third reference surface using one predetermined value and the second predetermined value,
Simulation device for fuel cell stack. A fuel cell stack simulation apparatus that calculates the cell performance of a fuel cell stack in which fuel cell cells having an electrolyte membrane and electrodes are stacked in N stages, where N is an integer of 2 or more.
The first stage cell located at one end of the fuel cell stack is referred to as a first end cell, and the Nth stage cell located at the other end of the fuel cell stack is referred to as a second end cell. ,
Of the both end faces of the fuel cell stack located on both sides in the stacking direction of the fuel cell stack and orthogonal to the stacking direction, the end face on the first end cell side is the first end face, and the second end cell side The end face of the second end face,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack and located in the first end cell, or the first end surface as a first reference surface, and a first predetermined potential at the first reference surface Set the value,
The second reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the first reference plane. 2 Set a second default value, which is the current density of the reference plane,
The third reference plane is a plane which is orthogonal to the stacking direction of the fuel cell stack and which is located in the first end cell and which is located on the second end face side with respect to the second reference plane. And a second calculation step of calculating the potential and the current density of the third reference surface using the one predetermined value and the second predetermined value.
Simulation device for fuel cell stack. When K is an integer greater than or equal to 2 and less than or equal to N, a specific cell located adjacent to the K-1st cell of the fuel cell stack and located on the second end cell side is the Kth cell. ,
An arbitrary surface located in the Kth cell and orthogonal to the stacking direction of the fuel cell stack is taken as a (3K-2) reference surface,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, which is located in the K-th cell and located on the second end face side with respect to the (3K-2) reference surface, is a (3K-1) As a reference plane,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, which is located in the Kth cell and located on the second end face side with respect to the (3K-1) reference surface, is taken as a 3K reference surface,
After the (2K-3) calculation step or the (2K-2) calculation step, the value of the (3K-2) reference surface set using the potential of the (3K-3) reference surface, and the (3K-2) A second (2K-1) calculation of calculating the potential and the current density of the third K reference surface using the value of the third (3K-1) reference surface set as the average current density of the reference surface With steps
The fuel cell stack simulation apparatus according to claim 15 or 16. When K is an integer greater than or equal to 2 and less than or equal to N, a specific cell located adjacent to the K-1st cell of the fuel cell stack and located on the second end cell side is the Kth cell. ,
An arbitrary surface located in the Kth cell and orthogonal to the stacking direction of the fuel cell stack is taken as a (3K-2) reference surface,
An arbitrary surface orthogonal to the stacking direction of the fuel cell stack, which is located in the K-th cell and is located on the second end face side with respect to the (3K-2) reference surface, is taken as a 3K reference surface;
After the (2K-3) calculation step or the (2K-2) calculation step, the value of the (3K-2) reference surface and the value of the (3K-2) reference surface set using the potential of the (3K-3) reference surface 3K-3) A second K calculation step of calculating the potential of the third K reference surface using the current density of the third K reference surface set using the current density of the reference surface,
The fuel cell stack simulation apparatus according to claim 15 or 16.

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