CN113704961B - Method for predicting transient operation performance of proton exchange membrane fuel cell - Google Patents
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Abstract
The invention discloses a method for predicting transient operation performance of a proton exchange membrane fuel cell, which comprises the following steps: s01, acquiring operation parameters to be predicted, which are required to be regulated and controlled, of the proton exchange membrane fuel cell, and calculating a boundary condition of gas transmission and a balance threshold value of phase change; s02, calculating the transmission quantity of dynamic physical parameters in the proton exchange membrane fuel cell to be predicted in the transmission process; s03, calculating gas transient parameters of a catalytic layer in the proton exchange membrane fuel cell to be predicted according to a pre-constructed model for simulating transient load change of the proton exchange membrane fuel cell; s04, calculating real-time output performance parameters of the proton exchange membrane fuel cell to be predicted according to various parameters obtained by calculation in the steps S01-S03 and a pre-constructed output performance parameter calculation model. The invention can simulate the transient voltage overshoot phenomenon of the proton exchange membrane fuel cell and has the advantages of simple realization method, high prediction efficiency, high prediction precision and the like.
Description
Technical Field
The invention relates to the technical field of fuel cells, in particular to a method for predicting transient operation performance of a proton exchange membrane fuel cell.
Background
The energy and environmental problems in the world are becoming more serious, and proton exchange membrane fuel cells are receiving more and more attention due to the characteristics of high energy density, zero emission, low noise, high economy and the like. Proton exchange membrane fuel cells are devices that convert chemical energy into electrical energy by consuming hydrogen and oxygen, and have found wide application in the fields of autopilot, rail transit, mobile power sources, and the like. As a complex energy conversion system, multiphase multi-substance coupling transmission and dynamic change such as electricity, gas, liquid, heat and the like exist in the proton exchange membrane fuel cell, and the mechanical structure and the output performance are difficult to optimally design by an experimental method by combining the limitation of factors such as cost feasibility and the like. Therefore, the simulation and emulation of the operation process of the proton exchange membrane fuel cell by a numerical simulation method are particularly important.
The current numerical simulation performance prediction model is mainly focused on the steady-state operation condition of the proton exchange membrane fuel cell in terms of performance prediction, but does not pay attention to the transient change process of external load, so that the description of output performance during the transient change of the load is lacking. The voltage overshoot phenomenon caused by the transient change of the load power has important influence on the stability and the durability of the proton exchange membrane fuel cell, and the transient overshoot phenomenon of the performance of the proton exchange membrane fuel cell is difficult to accurately carry out numerical simulation by the traditional prediction model, namely the accuracy of predicting the running performance of the proton exchange membrane fuel cell under the transient load is not high by directly using the traditional numerical simulation performance prediction model.
As disclosed in patent application CN111313056B, the method performs recursive computation by substituting a small amount of experimental data into a mathematical model, performs online estimation on model data of a polarization curve, realizes accurate online estimation on the performance of the fuel cell, can update the parameter value of the polarization curve of the fuel cell in real time, and reduces the requirement on configuration of a controller from the aspects of reducing data storage space and improving operation speed. However, the method mainly predicts the performance condition of the fuel cell in a stable state, but cannot accurately estimate the performance change condition of the fuel cell under load transient change, and the accuracy of predicting the whole operation cycle performance of the proton exchange membrane fuel cell is not high.
And patent application CN106848351B discloses a method for establishing a proton exchange membrane fuel cell performance prediction model, which establishes a one-dimensional analysis model vertical to the direction of a polar plate or establishes a quasi three-dimensional analysis model, and obtains the dynamic condition of the output performance of a fuel cell by establishing a dynamic equation of gas transmission and water transmission in the fuel cell system. However, as such, this method can only realize prediction of the output performance of the fuel cell in the steady state, but cannot realize prediction of the performance change in the unsteady state period.
In summary, in the prior art, when predicting the steady-state operation condition of the proton exchange membrane fuel cell, only the performance prediction accuracy of the steady-state operation condition is concerned, but the accurate estimation of the performance change condition of the fuel cell under the load transient change cannot be realized, so that the performance change prediction accuracy of the proton exchange membrane fuel cell in the whole operation period process is not high.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the technical problems existing in the prior art, the invention provides the prediction method for the transient operation performance of the proton exchange membrane fuel cell, which has the advantages of simple implementation method, high prediction efficiency and high prediction precision.
In order to solve the technical problems, the technical scheme provided by the invention is as follows:
a method for predicting transient operation performance of proton exchange membrane fuel cell includes the following steps:
s01, determining operation parameters to be predicted to be regulated and controlled of the proton exchange membrane fuel cell, and calculating boundary conditions and phase change balance threshold values of gas transmission according to the operation parameters;
s02, calculating the transmission quantity of dynamic physical parameters in the proton exchange membrane fuel cell to be predicted in the transmission process so as to obtain the variation quantity of the dynamic physical parameters;
S03, calculating gas transient parameters of a catalytic layer in the proton exchange membrane fuel cell to be predicted according to a pre-constructed model for simulating transient load change of the proton exchange membrane fuel cell;
S04, calculating real-time output performance parameters of the proton exchange membrane fuel cell to be predicted according to various parameters obtained by calculation in the steps S01-S03 and a pre-constructed output performance parameter calculation model.
Further, the operation parameters in the step S01 specifically include an inlet gas pressure, an inlet gas relative humidity and a heat source temperature, the boundary conditions include a local gas concentration, and the phase change equilibrium threshold includes a saturated water vapor pressure and an equilibrium film water content.
Further, the local gas concentration is specifically calculated by a local gas pressure, and the local gas pressure is specifically calculated according to the following formula:
Wherein the method comprises the steps of Is the partial hydrogen pressure,/>P a is the anode inlet pressure, p c is the cathode inlet pressure, p sat is the saturated water vapor pressure, RH a is the anode relative humidity, RH c is the cathode relative humidity, I is the current density, T is the cell temperature, and R is the ideal gas constant;
The calculation expression of the local gas concentration is as follows:
Wherein the method comprises the steps of Is the local hydrogen concentration,/>Is the local oxygen concentration;
the saturated water vapor pressure is calculated as follows:
wherein T c = T-273.15K;
The calculation expression of the water content of the balance film is as follows:
a＝RH+2s
wherein lambda eq is the water content of the balance film, a is the water activity, and s is the liquid water saturation.
Further, in the step S02, the transmission process specifically includes a gas transmission process, a water transmission process and a temperature transmission process, in the gas transmission process, the local gas concentration of the gas at the designated position in the proton exchange membrane fuel cell is specifically calculated according to the net flow rate of the gas, in the water transmission process, the liquid water saturation at the designated position in the proton exchange membrane fuel cell is specifically calculated according to the liquid water saturation transmission amount, the net flow rate of the liquid water saturation and the liquid water pressure, and the membrane water content at the designated position in the proton exchange membrane fuel cell is specifically calculated according to the net flow rate of the membrane water content transmission amount and the membrane water content, and in the temperature transmission process, the temperature is specifically calculated according to the volumetric heat capacity and the heat net flow rate.
Further, the gas delivery process is calculated specifically according to the following formula:
Wherein i represents a gas species and includes hydrogen, oxygen and water vapor; x, y and z represent the parts in the proton exchange membrane fuel cell and comprise a runner, a diffusion layer, a microporous layer, a catalytic layer and a proton exchange membrane, Representing the local gas concentration of the current gas i at the location y,/>Representing the local gas concentration of gas i at location y at the previous step,/>Representing the net flux of gas i from location x to location y at the present time, S i,y is the source term for gas i at location y, t represents time;
The expression for calculating the liquid water saturation in the water transmission process is as follows:
wherein, Representing the liquid water saturation at the current location y,/>Represents the liquid water saturation at the location y at the last step time, M represents the liquid water molar mass, ε y represents the porosity at the location y,/>Representing the current net flux of liquid water saturation from location x to location y, S lq,y represents the source term of liquid water saturation at location y;
The expression for calculating the net flux of liquid water saturation is:
Where ρ lq is the liquid water density, The effective penetration rate of liquid water between the position x and the position y is shown; /(I)The liquid water pressures of the current position x and the current position y are respectively, and mu lq is the liquid hydrodynamic viscosity;
The expression for calculating the moisture content of the film is:
Wherein the method comprises the steps of For the film moisture content of the current time part y,/>For the film moisture content at time position y of the previous step,For the net flux of membrane water content from site x to site y at the current time, S mw is the membrane water content source term, EW is the membrane equivalent mass, ω y is the electrolyte volume fraction;
The temperature transfer process is calculated according to the following formula:
wherein, For the heat net flux of the current time part x, S T,x is the temperature source term, (ρc p)x is the volumetric heat capacity of the part x.
Further, the step S02 further includes calculating source items required for the gas transfer process, the water transfer process, and the temperature transfer process.
Further, the gas transient parameter in the step S03 includes a concentration of the gas in the catalytic layer and an effective gas diffusion coefficient when the gas transient parameter is instantaneously changed.
Further, the calculation expression of the gas concentration in the catalytic layer is:
wherein, Is the instantaneous concentration of the gas in the catalytic layer after load change,/>For the instantaneous concentration of the gas in the catalytic layer at the previous step, u is a coefficient, u=Δt (I 1-I0)/I1, Δt is the time period required for the gas concentration replenishment to fail to respond;
the effective gas diffusion coefficient is calculated as follows:
wherein, For the diffusion coefficient of gas i between sites x and y, sher is the Shewand constant, 4.8,/>The diffusion coefficient of the gas i at the site x is coe, which is the correction coefficient.
Further, in the step S04, the output performance parameter is an output voltage.
Further, the output voltage is calculated according to the following formula:
Wherein, E out is output voltage, E nernst is Nernst voltage, E act activation polarization, E ohmic is ohmic polarization, E conc is concentration polarization, deltaG is Gibbs free energy variation, deltaS is entropy variation, T ref is reference temperature, alpha a and alpha c are conversion coefficients, n a and n c are the number of electrons transferred by reaction, I 0,a and I 0,c are exchange current densities of an anode and a cathode, and I lim,a and I lim,c are limit current densities of the anode and the cathode.
Compared with the prior art, the invention has the advantages that:
(1) The invention considers the characteristics of the proton exchange membrane fuel cell in transient change, and on the basis of calculating the gas transmission boundary condition, the phase change balance threshold value and the transmission quantity of dynamic physical parameters of the proton exchange membrane fuel cell, the invention mainly characterizes the time delay change of the instantaneous parameters of the gas in the catalytic layer in transient change of load, can quickly simulate the steady-state operation condition and transient voltage overshoot phenomenon of the proton exchange membrane fuel cell, realizes the performance prediction of the full operation period, and solves the problem that the performance prediction of the traditional proton exchange membrane fuel cell only pays attention to the steady-state condition.
(2) The invention can separate from the limitation of the traditional prediction model, analyze and combine the operation mechanism of the fuel cell in the two states of steady state and transient state, and can explore the dynamic change condition of the internal dynamic physical parameters in the whole operation period while describing the steady state performance, thereby being convenient for realizing the performance analysis and optimization of the follow-up proton exchange membrane fuel cell and the optimal operation condition optimization.
(3) According to the invention, the prediction model of the operation performance of the proton exchange membrane fuel cell is constructed based on the mathematical relationship among the operation parameters, the dynamic physical parameters and the output performance, and compared with the traditional model, the control and influence of the single or multiple coupling operation parameters on the dynamic physical parameters and the output performance can be more highlighted. (4) When the transient model of the proton exchange membrane fuel cell is further constructed, the disturbance influence of the phase change of the water content of the inner membrane and the convection diffusion on the performance is considered, and the transient overshoot phenomenon of the output voltage of the proton exchange membrane fuel cell under the transient load can be accurately described.
Drawings
Fig. 1 is a schematic implementation flow chart of a method for predicting transient operation performance of a proton exchange membrane fuel cell according to the present embodiment.
FIG. 2 is a graphical representation of steady state performance results obtained using the predictive method of the present invention in a specific application example versus experimental data.
Fig. 3 is a schematic diagram comparing the results of the performance mutation under transient load obtained by the prediction method of the present invention with experimental data in a specific application example.
Detailed Description
The invention is further described below in connection with the drawings and the specific preferred embodiments, but the scope of protection of the invention is not limited thereby.
As shown in fig. 1, the method for predicting transient operation performance of a proton exchange membrane fuel cell according to the present embodiment includes the steps of:
S01, determining operation parameters to be predicted to be regulated and controlled by the proton exchange membrane fuel cell, and calculating boundary conditions and phase change balance thresholds of gas transmission according to the operation parameters;
s02, calculating the transmission quantity of dynamic physical parameters in the proton exchange membrane fuel cell to be predicted in the transmission process so as to obtain the variation quantity of the dynamic physical parameters;
S03, calculating gas transient parameters of a catalytic layer in the proton exchange membrane fuel cell to be predicted according to a pre-constructed model for simulating transient load change of the proton exchange membrane fuel cell;
S04, calculating real-time output performance parameters of the proton exchange membrane fuel cell to be predicted according to various parameters obtained by calculation in the steps S01-S03 and a pre-constructed output performance parameter calculation model.
Because the running state of the proton exchange membrane fuel cell tends to be stable when the load power is kept constant, and the internal dynamic transmission process also tends to be stable, the diffusion amount of hydrogen and oxygen from the microporous layer to the catalytic layer in unit time is equal to the reaction consumption amount caused by the current generated by the cell; when the load current changes, the gas consumption in unit time also changes, and the supplement of hydrogen and oxygen is blocked due to the phase change of the water content of the membrane and the convection diffusion between the porous layers, so that the gas concentration in the catalytic layer changes temporarily, thereby causing an overshoot phenomenon. According to the embodiment, the characteristics of the proton exchange membrane fuel cell in transient change are considered, the time delay change of the instantaneous parameters of the gas in the catalytic layer in the transient change of the load is emphasized on the basis of calculating the gas transmission boundary condition, the phase change balance threshold and the transmission quantity of the dynamic physical parameters of the proton exchange membrane fuel cell, the steady-state operation condition and the transient voltage overshoot phenomenon of the proton exchange membrane fuel cell can be rapidly simulated, the full-operation periodic performance prediction is realized, and the problem that the current traditional proton exchange membrane fuel cell performance prediction only focuses on the steady-state condition is solved.
The present embodiment classifies predictions into: the method comprises the following specific steps of operation parameter calculation, dynamic physical parameter transmission calculation, transient performance correction and output performance calculation:
And S01, calculating operation parameters.
In this embodiment, the air inlet pressure, the air inlet relative humidity and the heat source temperature are specifically used as the control objects, and the operation parameters specifically include the local air pressure, the saturated water vapor pressure, the water content of the balance film, and the like.
The partial gas pressure is calculated specifically according to the following formula:
wherein, Is the partial hydrogen pressure,/>P a is the anode inlet pressure, p c is the cathode inlet pressure, p sat is the saturated water vapor pressure, RH a is the anode relative humidity, RH c is the cathode relative humidity, I is the current density, T is the cell temperature, and R is the ideal gas constant;
The partial gas concentration is calculated as:
Wherein the method comprises the steps of Is the local hydrogen concentration,/>Is the local oxygen concentration;
The specific calculation expression of the saturated water vapor pressure is as follows:
wherein T c = T-273.15K;
in this embodiment, the expression for calculating the water content of the balance film is specifically:
a＝RH+2s
wherein lambda eq is the water content of the balance film, a is the water activity, and s is the liquid water saturation.
The selection of the operation parameters and the specific calculation formula can be selected according to actual requirements.
S02, dynamic physical parameter transmission calculation
The transmission process in this embodiment specifically includes a gas transmission process, a water transmission process, and a temperature transmission process, that is, the transmission calculation of dynamic parameters includes gas transmission, water transmission, and temperature transmission, and iterative calculation is performed with time as an iteration step, so as to obtain the dynamic parameter variation of each part in the proton exchange membrane fuel cell. The method comprises the steps of calculating local gas concentration of gas at a designated part in a proton exchange membrane fuel cell according to gas net flux in a gas transmission process, calculating liquid water saturation at the designated part in the proton exchange membrane fuel cell according to liquid water saturation transmission quantity, liquid water saturation net flux and liquid water pressure in a water transmission process, calculating membrane water content at the designated part in the proton exchange membrane fuel cell according to membrane water content transmission quantity and membrane water content net flux, and calculating temperature according to volume heat capacity and heat net flux in a temperature transmission process.
The specific calculation steps of each transmission process are as follows:
① Gas delivery process calculation
The embodiment specifically calculates the gas transmission process according to the following formula:
Wherein i represents a gas species and includes hydrogen, oxygen and water vapor; x, y and z represent the parts in the proton exchange membrane fuel cell and comprise a runner, a diffusion layer, a microporous layer, a catalytic layer and a proton exchange membrane, Representing the local gas concentration of the current gas i at the location y,/>Representing the local gas concentration of gas i at location y at the previous step,/>Representing the net flux of gas i from location x to location y at the present time, S i,y is the source term for gas i at location y, and t represents time.
The specific expression for calculating the net flux of gas is:
wherein h x denotes the thickness of the portion x, Indicating the effective gas diffusion coefficient.
② Calculation of Water Transmission Process
The expression for calculating the liquid water saturation is specifically:
wherein, Representing the liquid water saturation at the current location y,/>Represents the liquid water saturation at the location y at the last step time, M represents the liquid water molar mass, ε y represents the porosity at the location y,/>Representing the current net flux of liquid water saturation from location x to location y, S lq,y represents the source term of liquid water saturation at location y.
The specific expression for calculating the net flux of liquid water saturation is:
Wherein ρ lq is the liquid water density, The effective penetration rate of liquid water between the position x and the position y is shown; /(I)The liquid water pressures of the current position x and the current position y are respectively, and mu lq is the liquid hydrodynamic viscosity.
The embodiment specifically calculates the liquid water pressure according to the Leverett-J function:
wherein p g is the pressure of the incoming air, Delta lq is the surface tension coefficient, and theta is the contact angle, which is the capillary pressure at the current time point x.
The specific expression for calculating the surface tension coefficient is:
δlq＝-0.0001676T+0.1218(273.15K≤T373.15K) (10)
In this embodiment, the specific expression for calculating the water content of the film is:
wherein, For the film moisture content of the current time part y,/>For the film moisture content at time position y of the previous step,For the net flux of membrane water content from site x to site y at the current time, S mw is the membrane water content source term, EW is the membrane equivalent mass, ω y is the electrolyte volume fraction.
The film moisture diffusion coefficient is calculated specifically as follows:
③ Temperature transmission process calculation
In this embodiment, the temperature transmission process is specifically calculated according to the following:
wherein, For the heat net flux of the current time part x, S T,x is the temperature source term, (ρc p)x is the volumetric heat capacity of the part x.
The specific calculation expression of the volumetric heat capacity is as follows:
(ρCp)x＝εx(sxρlq(Cp)lq+(1-sx)ρg(Cp)g)+(1-εx-ωx)ρs(Cp)s+ωxρm(Cp)m (15)
the expression for calculating the net flux of heat is:
Wherein k x-y is the thermal conductivity between the part x and the part y;
Where k x is the thermal conductivity of the part x.
In this embodiment, step S02 further includes calculating source items required for the gas transmission process, the water transmission process, and the temperature transmission process, where the specific calculation process of each source item is:
① The gas source term is calculated according to the following formula:
Wherein CH, MPL, GDL, CL is runner, micropore layer, diffusion layer, catalytic layer respectively, and prefix A that adds indicates the positive pole side, prefix C indicates the negative pole side, and F is faradaic constant, and R lv is the conversion rate between gaseous water and liquid water, and R mv is the conversion rate between membrane state water and gaseous water.
The conversion rate between the gaseous water and the liquid water is specifically calculated as follows:
Where γ evap is the evaporation rate and p vap is the local water vapor pressure.
The expression for calculating the conversion rate between membrane water and gaseous water is:
② The liquid water source term was calculated as follows:
Wherein R ml is the conversion rate between the membrane water and the liquid water, and:
③ The film moisture content source term was calculated as follows:
Wherein R per is the rate of liquid water penetration across the membrane, and:
Wherein Pe MEM is the penetration coefficient of liquid water across the membrane.
④ The temperature source term is calculated according to the following formula:
Where σ x is the conductivity at site x and LH is the latent heat of evaporation of water.
The calculation of the dynamic parameters in each transmission process can select a specific calculation formula according to actual requirements.
Through the steps, the steady state of the proton exchange membrane fuel cell can be simulated, and parameter acquisition in the steady state is realized.
S03, correcting transient performance
As described above, considering that the operation state of the proton exchange membrane fuel cell tends to be stable when the load power is kept constant, and the internal dynamic transmission process also tends to be stable, the amount of diffusion of hydrogen and oxygen from the microporous layer to the catalytic layer per unit time is equal to the amount consumed by the reaction when the cell generates current; when the load current changes, the gas consumption in unit time also changes, and the supplement of hydrogen and oxygen is blocked due to the phase change of the water content of the membrane and the convection diffusion between the porous layers, so that the gas concentration in the catalytic layer changes temporarily, thereby causing an overshoot phenomenon. The embodiment further corrects transient performance, wherein the gas transient parameters comprise gas concentration in the catalytic layer and effective gas diffusion coefficient in transient change, and the overshoot phenomenon of the output voltage of the proton exchange membrane fuel cell under transient load can be accurately described by focusing on the time delay change of the gas concentration in the catalytic layer in transient change, so that the performance prediction of the proton exchange membrane fuel cell under transient operation state is realized.
In this embodiment, the calculation expression of the gas concentration in the catalytic layer is:
wherein, Is the instantaneous concentration of the gas in the catalytic layer after load change,/>For the instantaneous concentration of the gas in the catalytic layer at the previous step, u is a coefficient, u=Δt (I 1-I0)/I1, Δt is the time period required for the gas concentration replenishment to fail to respond;
the effective gas diffusion coefficient is calculated as:
wherein, For the diffusion coefficient of gas i between sites x and y, sher is the Shewand constant, 4.8,/>The diffusion coefficient of the gas i at the site x is coe, which is the correction coefficient.
The correction factor coe is a power function over time:
wherein t transient is the time required for the recovery of the voltage overshoot.
According to the embodiment, the transient model of the proton exchange membrane fuel cell is constructed by adopting the steps, the disturbance influence of phase change and convection diffusion of the water content of the inner membrane on the performance is considered, and the overshoot phenomenon of the output voltage of the proton exchange membrane fuel cell under the transient load can be accurately described.
S04, calculating output performance parameters
In this embodiment, the output performance parameter is an output voltage, which is specifically calculated according to the following formula:
Wherein, E out is output voltage, E nernst is Nernst voltage, E act activation polarization, E ohmic is ohmic polarization, E conc is concentration polarization, deltaG is Gibbs free energy variation, deltaS is entropy variation, T ref is reference temperature, alpha a and alpha c are conversion coefficients, n a and n c are the number of electrons transferred by reaction, I 0,a and I 0,c are exchange current densities of an anode and a cathode, and I lim,a and I lim,c are limit current densities of the anode and the cathode.
The specific calculation expression of the exchange current density is as follows:
wherein, Exchange current density for anodic reference,/>Exchange current density for cathodic reference,/>Is the hydrogen reference concentration,/>Is the reference concentration of oxygen.
The specific expression of the limiting current density is:
the calculation formulas of the parameters can be selected according to actual requirements.
According to the invention, the operation mechanisms of the fuel cell in the steady state and the transient state are analyzed and combined, a calculation model for forming the output performance parameter of the proton exchange membrane fuel cell is constructed based on the mathematical relation among the operation parameters, the dynamic physical parameters and the output performance, compared with the traditional calculation model, the limitation of the traditional prediction model can be removed, the control and influence of single or multiple coupling operation parameters on the dynamic physical parameters and the output performance can be more highlighted, and the dynamic change condition of the internal dynamic physical parameters and the output performance in the whole operation period can be explored, so that the accuracy of the output performance prediction of the proton exchange membrane fuel cell is effectively improved, more accurate performance prediction is realized, and meanwhile, the performance analysis and the optimization of the proton exchange membrane fuel cell and the optimal operation condition optimization are conveniently realized.
In order to verify the effectiveness of the present invention, the above method of the present invention was used in the specific application examples to perform a predictive test on the operation performance of a proton exchange membrane fuel cell, and the test results are shown in fig. 2 and 3. As can be seen from FIG. 2, the relative error of the steady-state output performance obtained by the method for predicting the running performance of the proton exchange membrane fuel cell according to the invention is 0.4732% compared with the experimental data, and as can be seen from FIG. 3, the relative error under transient change is 0.4% by the method for predicting the running performance of the proton exchange membrane fuel cell according to the invention. The method for predicting the running performance of the proton exchange membrane fuel cell can accurately predict the full-cycle running output performance.
The foregoing is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. While the invention has been described with reference to preferred embodiments, it is not intended to be limiting. Therefore, any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention shall fall within the scope of the technical solution of the present invention.
Claims (7)
1. The method for predicting the transient operation performance of the proton exchange membrane fuel cell is characterized by comprising the following steps:
S01, determining operation parameters to be predicted to be regulated and controlled by the proton exchange membrane fuel cell, and calculating boundary conditions and phase change balance thresholds of gas transmission according to the operation parameters;
s02, calculating the transmission quantity of dynamic physical parameters in the proton exchange membrane fuel cell to be predicted in the transmission process so as to obtain the variation quantity of the dynamic physical parameters;
s03, calculating gas instantaneous parameters of a catalytic layer in the proton exchange membrane fuel cell to be predicted according to a pre-constructed model for simulating transient load change of the proton exchange membrane fuel cell, wherein the gas instantaneous parameters comprise gas concentration and effective gas diffusion coefficient in the catalytic layer during the instantaneous change;
S04, calculating real-time output performance parameters of the proton exchange membrane fuel cell to be predicted according to various parameters obtained by calculation in the steps S01-S03 and a pre-constructed output performance parameter calculation model, wherein the output performance parameters are output voltages and are obtained by calculation according to the following formula:
Wherein, E out is output voltage, E nernst is Nernst voltage, E act activation polarization, E ohmic is ohmic polarization, E conc is concentration polarization, deltaG is Gibbs free energy variation, deltaS is entropy variation, T ref is reference temperature, alpha a and alpha c are conversion coefficients, n a and n c are the number of electrons transferred by reaction, I 0,a and I 0,c are exchange current densities of an anode and a cathode, and I lim,a and I lim,c are limit current densities of the anode and the cathode.
2. The method according to claim 1, wherein the operation parameters in the step S01 include gas inlet pressure, gas inlet relative humidity and heat source temperature, the boundary conditions include local gas concentration, and the phase change equilibrium threshold includes saturated water vapor pressure and equilibrium membrane water content.
3. The method for predicting transient operating performance of a proton exchange membrane fuel cell according to claim 2, wherein the local gas concentration is calculated specifically from a local gas pressure, and the local gas pressure is calculated specifically according to the following formula:
Wherein the method comprises the steps of Is the partial hydrogen pressure,/>P a is the anode inlet pressure, p c is the cathode inlet pressure, p sat is the saturated water vapor pressure, RH a is the anode relative humidity, RH c is the cathode relative humidity, I is the current density, T is the cell temperature, and R is the ideal gas constant;
The calculation expression of the local gas concentration is as follows:
Wherein the method comprises the steps of Is the local hydrogen concentration,/>Is the local oxygen concentration;
the saturated water vapor pressure is calculated as follows:
wherein T c = T-273.15K;
The calculation expression of the water content of the balance film is as follows:
a＝RH+2s
wherein lambda eq is the water content of the balance film, a is the water activity, and s is the liquid water saturation.
4. The method according to claim 1, wherein in the step S02, the transmission process specifically includes calculating a gas transmission process, a water transmission process, and a temperature transmission process, the gas transmission process specifically calculates a local gas concentration of the gas at a specified location in the proton exchange membrane fuel cell according to a gas net flux, the water transmission process specifically calculates a liquid water saturation at the specified location in the proton exchange membrane fuel cell according to a liquid water saturation transmission amount, a liquid water saturation net flux, and a liquid water pressure, and calculates a membrane water content at the specified location in the proton exchange membrane fuel cell according to a membrane water content transmission amount and a membrane water content net flux amount, and the temperature transmission process specifically calculates a temperature amount according to a volume heat capacity and a heat net flux amount.
5. The method for predicting transient operating performance of a PEM fuel cell of claim 4,
The gas delivery process is calculated specifically according to the following formula:
Wherein i represents a gas species and includes hydrogen, oxygen and water vapor; x, y and z represent the parts in the proton exchange membrane fuel cell and comprise a runner, a diffusion layer, a microporous layer, a catalytic layer and a proton exchange membrane, Representing the local gas concentration of the current gas i at the location y,/>Representing the local gas concentration of gas i at location y at the previous step,/>Representing the net flux of gas i from location x to location y at the present time, S i,y is the source term for gas i at location y, t represents time;
The expression for calculating the liquid water saturation in the water transmission process is as follows:
wherein, Representing the liquid water saturation at the current location y,/>Represents the liquid water saturation at the location y at the last step time, M represents the liquid water molar mass, ε y represents the porosity at the location y,/>Representing the current net flux of liquid water saturation from location x to location y, S lq,y represents the source term of liquid water saturation at location y;
The expression for calculating the net flux of liquid water saturation is:
Where ρ lq is the liquid water density, The effective penetration rate of liquid water between the position x and the position y is shown; /(I)The liquid water pressures of the current position x and the current position y are respectively, and mu lq is the liquid hydrodynamic viscosity;
The expression for calculating the moisture content of the film is:
Wherein the method comprises the steps of For the film moisture content of the current time part y,/>The water content of the film at the time part y of the last step,/>For the net flux of membrane water content from site x to site y at the current time, S mw is the membrane water content source term, EW is the membrane equivalent mass, ω y is the electrolyte volume fraction;
The temperature transfer process is calculated according to the following formula:
wherein, For the heat net flux of the current time part x, S T,x is the temperature source term, (ρc p)x is the volumetric heat capacity of the part x.
6. The method according to any one of claims 1 to 5, wherein the step S02 further comprises calculating source items required for the gas transfer process, the water transfer process, and the temperature transfer process.
7. The method for predicting transient operating performance of a proton exchange membrane fuel cell as recited in claim 1, wherein the calculation expression of the gas concentration in the catalytic layer is:
wherein, Is the instantaneous concentration of the gas in the catalytic layer after load change,/>For the instantaneous concentration of the gas in the catalytic layer at the previous step, u is a coefficient, u=Δt (I 1-I0)/I1, Δt is the time period required for the gas concentration replenishment to fail to respond;
the effective gas diffusion coefficient is calculated as follows:
wherein, For the diffusion coefficient of gas i between sites x and y, sher is the Shewand constant, 4.8,/>The diffusion coefficient of the gas i at the site x is coe, which is the correction coefficient.
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