Gas distribution characteristic prediction method for multi-scale coupling heat and mass transport of fuel cell stack

Abstract

The invention discloses a gas distribution characteristic prediction method for multi-scale coupling heat and mass transport of a fuel cell stack, and relates to the technical field of fuel cell stack distribution. The flow area network on any side of the fuel cell stack is divided into a fuel cell stack inlet distribution unit, a fuel cell stack outlet confluence unit and flow units in each single-layer cell; constructing a multi-scale reaction gas distribution and heat and mass transport dynamic coupling model, and respectively establishing a function relationship between input parameters and output parameters of a fuel stack inlet distribution unit and a reaction gas flowing unit along each single-layer cell inner flow unit; determining inlet and outlet fluid parameters of each fluid unit in the distribution main pipe, inlet and outlet fluid parameters of each single-layer battery and outlet pressure of each layer of battery; therefore, the reaction gas in each single-layer cell in the fuel cell stack is distributed, and the overall performance of the cell stack, especially the air at the cathode side, is greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of fuel cell stack distribution technology, and in particular to a method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack. Background Art

[0002] With the increasing global demand for clean energy, hydrogen fuel cells, as a highly efficient and environmentally friendly energy conversion technology, have garnered widespread attention. Hydrogen fuel cells convert hydrogen and oxygen into electricity and water through electrochemical reactions, offering advantages such as zero emissions and high efficiency. They exhibit significant potential for application in transportation, particularly in hydrogen-powered heavy trucks. However, practical applications of hydrogen fuel cells still face numerous technical challenges, one of which is the distribution of reactant gases within the fuel cell stack.

[0003] Fuel cell stacks are typically composed of multiple single-layer cells connected in series. The performance of each single-layer cell directly affects the output efficiency and stability of the entire stack. The uniformity of the distribution of reactant gases (such as hydrogen and oxygen) in the stack is crucial. If the reactant gases are unevenly distributed, some single-layer cells may have excess or insufficient reactant gases, which in turn can cause local overheating, membrane dehydration, gas deficiency, and other problems, seriously affecting the performance and life of the stack. Especially in high-power fuel cell stacks, where there are many cells, the uneven distribution of reactant gases is more pronounced, becoming a key factor restricting the performance improvement of the fuel cell stack.

[0004] Developing accurate prediction methods for the distribution characteristics of fuel cell stack reaction gases is the first and most critical step in optimizing distribution. The extremely complex distribution characteristics of fuel cell stacks are reflected in: huge scale differences (the scale of the macroscopic flow field and the scale of the coupling of multi-physical fields within the microscopic single-layer battery), complex flow channel structure (involving the flow channel design of the polar plate (BP), the porous characteristics of the gas diffusion layer (GDL), the electrochemical reaction active area of the catalyst layer (CL), the ion conduction characteristics of the proton exchange membrane (PEM), and the connection structure between the bipolar plates), and the complex coupling of influencing factors (including chemical reaction kinetics, proton exchange efficiency, concentration gradients, heat and mass transport, current density distribution, phase change processes, and multi-component diffusion kinetics). Accurately predicting the distribution characteristics of fuel cell stacks is a major challenge.

[0005] Existing prediction methods often ignore the multi-field coupling mechanism within single-layer batteries, or simplify it to a porous medium layer, only considering local flow parameters and unable to fully reflect the dynamic impact of uneven distribution on electrochemical output performance, such as local overheating, membrane dehydration and reactant concentration imbalance. Summary of the Invention

[0006] In response to the problem that the existing technology only considers local flow parameters and cannot fully reflect the dynamic impact of uneven distribution on electrochemical output performance, the present invention proposes a method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack, thereby solving the problems existing in the existing technology.

[0007] A method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack comprises the following steps:

[0008] Obtaining a flow network of the fuel cell stack, and dividing the flow area network on any side of the fuel cell stack into a fuel cell stack inlet distribution unit, an outlet confluence unit, and flow units within each single-layer cell;

[0009] The Harris Eagle optimization algorithm was used to optimize the artificial neural network. By performing a global 3D modeling simulation of each single-layer battery, the simulation results were used as training data to train the optimized artificial neural network and determine the functional relationship between the input parameters and output parameters of the flow unit of the reactant gas along each single-layer battery.

[0010] The parameter changes of the fuel cell stack inlet distribution unit and outlet confluence unit are analyzed based on the mass conservation equation and the momentum conservation equation, and the functional relationship between the input parameters and output parameters of the fuel cell stack inlet distribution unit and the functional relationship between the input parameters and output parameters of the outlet confluence unit are respectively constructed; the inlet and outlet fluid parameters of each fluid unit in the fuel cell stack main pipe and the inlet and outlet fluid parameters of each single-layer cell are determined based on the three functional relationships, and based on the inlet and outlet fluid parameters of each single-layer cell, discrete control equations are sequentially established within each fluid grid in the confluence main pipe, and the outlet pressure of each single-layer cell is obtained based on each discrete control equation;

[0011] Based on the obtained outlet pressure of each single-layer cell, the distribution characteristics of the reaction gas within each single-layer cell in the fuel cell stack are predicted.

[0012] Furthermore, the analysis of parameter changes of the fuel cell stack inlet distribution unit and outlet confluence unit according to the mass conservation equation and the momentum conservation equation specifically includes the following steps:

[0013] The inlet distribution unit or outlet confluence unit includes two types of units, namely the flow distribution unit A at the inlet of each battery and the flow unit B between two adjacent layers of batteries;

[0014] For the flow unit B between two adjacent layers of batteries, the mass conservation equation and momentum conservation equation at the unit inlet and outlet are expressed as follows:

[0015] M in =M out

[0016]

[0017] Where, u is the flow velocity; M in is the unit inlet mass flow rate, M out is the unit outlet mass flow rate; ΔP f is the friction pressure drop along the process; P in is the unit inlet momentum, P out is the unit outlet momentum, λ is the friction coefficient along the way; l is the length of the pipeline; d is the inner diameter of the pipeline; ρ is the density of the fluid;

[0018] For the diversion unit A at each battery inlet, part of the reaction gas enters the battery, and the other part continues to flow downstream; the pressure drop at the inlet and outlet of the diversion unit A includes the local resistance loss caused by the change in flow structure due to diversion or confluence, and the increase or decrease in fluid static pressure due to diversion or confluence;

[0019] Then the inlet and outlet mass conservation equations and energy conservation equations of the shunt unit A at each battery inlet are expressed as:

[0020] M in =M out +M 电池

[0021]

[0022] Among them, K d is the static pressure recovery coefficient of the distribution unit, M 电池 For battery quality, is the unit inlet flow rate, is the unit outlet flow rate;

[0023] According to the inlet and outlet mass conservation equations and energy conservation equations of the diversion unit A and the flow unit B, the parameter changes of the fuel cell inlet distribution unit and the outlet confluence unit are analyzed.

[0024] Furthermore, the global three-dimensional modeling simulation of each single-layer battery specifically includes establishing a global three-dimensional model of the bipolar plates, flow channels, cathode and anode diffusion layers, cathode and anode catalyst layers, and electrolyte membranes of the single-layer battery; the distribution data inside the single-layer battery is obtained by numerically simulating the multi-physical field coupling mechanism inside the single-layer battery; the distribution data inside the single-layer battery includes the single-layer battery inlet pressure, the single-layer battery outlet pressure and the single-layer battery inlet reaction gas flow rate, the single-layer battery outlet reaction gas flow rate, the fluid velocity field, pressure field, and temperature field distribution in the flow channel and porous medium area, the current density generated by the electrochemical reaction of the catalytic layer, the output voltage, and the component concentrations of hydrogen and oxygen reactants and products.

[0025] Furthermore, the method performs a global three-dimensional modeling simulation on the single-layer battery, uses the simulation results as training data to train the ANN-HHO neural network algorithm, and determines the functional relationship between the input parameters and output parameters of the single-layer battery, specifically including the following steps:

[0026] Setting initial parameters of an artificial neural network (ANN), including weight factors and corresponding biases; the ANN includes an input layer, a hidden layer, and an output layer; the input layer includes neurons corresponding to the inlet reaction gas flow and inlet pressure of a single-layer battery, respectively; the output layer includes neurons corresponding to the outlet pressure, outlet reaction gas flow, current density, and output voltage of the single-layer battery, respectively; the hidden layer activation function uses a ReLU function;

[0027] The initial parameters of the Harris Hawk Optimization algorithm (HHO) are set, including the population size, the maximum number of iterations, and the upper and lower bounds of the parameters. The weight factors and corresponding biases of the ANN are updated by calculating the minimum value of the fitness function using the Harris Hawk Optimization algorithm (HHO). When the maximum number of iterations is reached, the update is completed to obtain the updated ANN weight factors and corresponding biases. The fitness function is the root mean square error (RMSE) between the predicted value and the simulated result.

[0028] The results of global three-dimensional modeling simulation of the single-layer battery are input into the ANN after the weight factor and corresponding bias are updated, and the functional relationship between the single-layer battery inlet reaction gas flow and inlet pressure and the single-layer battery outlet pressure, outlet reaction gas flow, current density and output voltage is obtained.

[0029] Furthermore, according to the inlet and outlet fluid parameters of each single-layer battery, discrete control equations in each fluid grid in the collecting main pipe are sequentially established, and the outlet pressure of each single-layer battery is obtained according to each discrete control equation, which specifically includes the following steps:

[0030] Set the inlet reaction gas flow rate of each single-layer cell and the total number of cells;

[0031] Based on the principles of conservation of mass and momentum, the continuous flow of the reactant gas is discretized into the governing equations for each fluid grid. By inputting the outlet reactant gas flow rate of each single-layer cell as a boundary condition in the discrete governing equations, the pressure distribution of all grid nodes of the fluid grid is solved.

[0032] The outlet pressure of each single-layer battery is obtained based on the pressure distribution of all grid nodes.

[0033] Furthermore, the flow network method is used to equivalently divide the fuel cell stack into a series of nodes and units for connection, thereby obtaining the flow network of the fuel cell stack.

[0034] The present invention provides a method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack, which has the following beneficial effects:

[0035] The present invention constructs a multi-scale coupling model to divide the flow network of the fuel cell stack into an inlet distribution unit, an outlet confluence unit, and a flow unit within a single-layer cell, and establishes a functional relationship between the input and output parameters of each unit. By introducing an artificial neural network (ANN) and the Harris Eagle optimization algorithm (HHO), combined with three-dimensional numerical simulation and machine learning techniques, the distribution characteristics of the reaction gas in the fuel cell stack and its impact on the cell performance are accurately predicted. This method considers the coupling between the distribution process between each single-layer cell and the electrochemical reaction within the cell, as well as the scale differences between the heat and mass transport processes in each region of the stack. From the perspective of global optimization of the reaction gas distribution, it provides theoretical guidance and technical support for further improving the output performance and operational stability of high-power fuel cells and solving the range problem of hydrogen heavy trucks. By improving the distribution characteristics of the reaction gas in each single cell of the stack, the overall performance of the stack, especially the cathode air, can be greatly improved. At the same time, it can alleviate the problem of cell aging to a certain extent, which is of great significance to improving the output performance and life cycle of high-power fuel cell stacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of the flow area network division of a fuel cell stack in an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of the inlet distribution unit in an embodiment of the present invention;

[0038] Figure 3 A schematic diagram illustrating the construction of a unit input-output equation for a single-layer battery in an embodiment of the present invention;

[0039] Figure 4 A schematic diagram of the ANN-HHO neural network algorithm solution process in an embodiment of the present invention;

[0040] Figure 5 Schematic diagram of the relationship between the input vector and output vector of the artificial neuron in an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0042] The present invention proposes a method for predicting the gas distribution characteristics of a fuel cell stack by multi-scale coupled heat and mass transport. By constructing a multi-scale research method suitable for analyzing the reaction gas distribution and heat and mass transport characteristics in a hydrogen fuel cell stack, the transient change law of the reaction gas distribution and transport characteristics in a high-power hydrogen fuel cell stack under vehicle-mounted operating conditions is explored, the conditions and laws for the occurrence of uneven distribution of the reaction gas flow in the fuel cell stack are revealed, and the dynamic coupling mechanism between the reaction gas distribution characteristics and the electrochemical output performance in a high-power hydrogen fuel cell stack under vehicle-mounted operating conditions is explored, providing theoretical and technical support for improving the output performance and operating stability of the hydrogen fuel cell stack in a heavy-duty truck service environment. The method specifically includes the following steps:

[0043] S1. Construct a multi-scale dynamic coupling model of reaction gas distribution and heat and mass transport at multiple scales. First, considering that the flow structure of the fuel cell stack is relatively complex and the number of cells is extremely large, up to hundreds of pieces, the present invention intends to divide the entire fuel cell stack into a series of nodes and units connected by a flow network based on the flow network method. Figure 1 The flow area network on either side of the fuel cell stack is divided into multiple links from the stack inlet to the outlet, including the following three parts:

[0044] Fuel cell inlet distribution section: In this section, the reactant gas enters the gas distribution pipe and is distributed to each single-layer cell in sequence during the flow process.

[0045] Fuel cell outlet confluence section. In this section, each reaction gas is sequentially fed into the gas confluence pipe and then flows out.

[0046] The flow process within each single-layer cell. Here, the reactant gases enter the double-layer plates inside the cell and flow along the flow channels within the plates. During this process, they gradually penetrate the diffusion layer and catalytic layer, participate in the electrochemical reaction, and then flow out of the plates. The flow within a single cell is the most difficult and complex to determine.

[0047] S2. For the flow units at the fuel stack inlet distribution link and at each link along the reaction gas process, establish the input and output equations of the unit parameters respectively, introduce the time term into the equation, and calculate the flow changes under transient conditions.

[0048] The input and output equations for the inlet distribution unit and outlet confluence unit of a fuel cell stack are relatively simple. The input parameters are the unit's inlet reactant gas flow rate and inlet pressure, and the output parameters are the outlet pressure and outlet gas flow rate. These changes can be described by constructing mass conservation equations and momentum conservation equations. The momentum conservation equation primarily describes how the unit's inlet and outlet pressure drop varies with flow rate. The calculation process for the outlet confluence unit is identical to that for the inlet distribution unit. The calculation equations for the inlet distribution unit are listed below, taking the example of the inlet distribution unit.

[0049] Import distribution units include two types of units, such as Figure 2 As shown; for the flow unit B between two adjacent layers of batteries, the mass and momentum conservation equations of the unit inlet and outlet are as follows:

[0050] M in =M out

[0051]

[0052] u is the flow velocity, M is the mass flow rate; ΔP f is the friction pressure drop along the process; subscript in is the unit inlet, and subscript out is the unit outlet.

[0053] For the diversion unit A at each cell inlet, part of the reactant gas enters the cell, while the other part continues to flow downstream. The pressure drop at the inlet and outlet consists of two parts: one is the local resistance loss caused by the change in flow structure due to diversion or confluence, and the other is the increase or decrease in fluid static pressure due to diversion or confluence. The mass and energy conservation equations at the unit inlet and outlet are as follows:

[0054] M in =M out +M 电池

[0055]

[0056] K d is the static pressure recovery coefficient of the distribution unit.

[0057] S3. Explore the multi-field coupling mechanism inside the fuel cell at the single-layer cell scale. First, a scheme for constructing the input-output equation of the single-layer cell is required, such as Figure 3 The specific steps are as follows: First, a three-dimensional thermal, electrical, fluid-solid coupled numerical simulation of a single-layer battery is performed. Then, based on mechanism exploration and machine learning, the input-output characteristic equations of the single-layer battery are constructed, and finally, the unit input-output equation of the single-layer battery is derived.

[0058] S3.1. Establish input and output equations for unit parameters. The PEM fuel cell system is a highly complex, dynamic, multiphase, three-dimensional system. The fuel cell's operation involves gas diffusion in the porous medium, fluid flow, water phase change, water transport in the proton exchange membrane, electron and ion transfer, and electrochemical reactions in the catalyst layer. These processes are interconnected and mutually influential. Taking a PEM fuel cell as an example, a three-dimensional coupled thermal, electrical, fluidic, and solid-state numerical simulation of a single-layer PEM fuel cell is performed.

[0059] S3.1.1 A PEMFC in service is a complex multi-physics system involving heat and mass transfer, component diffusion, and electron and proton transport in gas, liquid, and solid phases. This includes electrochemical reactions, heat transfer, and multi-component mass transport associated with fluid flow. The dynamic numerical modeling of these phenomena involves describing the continuity equation, conservation of momentum, conservation of energy, electrochemical and Maxwell-Stafen differential governing equations. The specific equations are as follows:

[0060] In the simulation, assuming the fluid is a continuous medium and flows at a low speed, the mass conservation equation is:

[0061]

[0062] Where ρ represents density; ε represents porosity; u represents velocity vector; S m Represents the mass primitive. In different computational domains, S m There are different solution values. For the flow field and gas diffusion layer at the two poles, the S value is 0; for the catalyst layer at the two poles, S m The expression is:

[0063]

[0064] Where i represents the current density (A / cm 2 ); F represents the Faraday constant (96485 C / mol); M represents the molar mass (g / mol); the subscripts a and c represent the anode and cathode, respectively.

[0065] For Newtonian fluid, the momentum conservation equation (NS equation) is:

[0066]

[0067] Where p is pressure (Pa); & is porosity; ε is fluid dynamic viscosity (Pa·s); S u represents the momentum source term, where ε = 1 in the flow channel.

[0068] The energy equation of a fuel cell can be expressed as:

[0069]

[0070] Where c p represents the specific heat capacity at constant pressure (J / kg·K); T represents the temperature (K); k eff Indicates effective thermal conductivity (W / m·K); S Q represents the energy source term. And S QIt can be expressed by the following formula, which mainly considers the ohmic polarization heat, heat release or heat absorption during phase change, chemical reaction heat and heat generated by overpotential:

[0071]

[0072] Where i s Indicates the current density on the surface (A / cm 2 );R ohm represents the resistivity (Ω·m); β represents the ratio of chemical energy to thermal energy; Indicates the generation rate of gaseous water (kg / s); h reaction represents the reaction enthalpy (J / mol); r w represents the phase change rate of water (mol / s); h 1g represents the phase change enthalpy of water (J / mol); S a,c The exchange current density of the anode and cathode (A / m 3 ); η represents the overpotential (V).

[0073] The component conservation equation is expressed as:

[0074]

[0075] Where c k Indicates the concentration of the component (kmol / m 3 ); ε represents the porosity; represents the effective diffusion coefficient of the component (m 2 / s); S k Indicates the component source term; subscript k indicates the component code, representing oxygen, nitrogen, and water at the cathode, and hydrogen and water at the anode. k The values in the flow field and gas diffusion layer are all 0, and hydrogen, oxygen and water in the catalyst layer are expressed as:

[0076]

[0077] i in the formula a Indicates the anode volume current density (A / m 3 );i c Indicates cathode volume current density (A / m 3 ).

[0078] The electrochemical reaction in the PEM fuel cell mainly occurs in the catalytic layer. During simulation, the Buter-Volmer equation is mainly used to describe the electrochemical reaction process.

[0079] The Butler-Volmer equations for the anode and cathode are:

[0080]

[0081] Where, η represents the overpotential; C i represents the local molar concentration of component i (kmol / m 3 ); Indicates the reference volume exchange current density (A / m 3 ); γ represents the concentration index, γ = 0.5 for the anode and γ = 1 for the cathode; C iref The parameter molar concentration of component i (kmol / m 3 ); α represents the transfer coefficient.

[0082] Taking PEM fuel cells as an example, the charge conservation equation can be expressed as:

[0083]

[0084] Where: σ s represents the solid phase conductivity; σ m Represents the membrane phase conductivity; φ s represents the solid phase potential; φ m represents the membrane phase potential; represents the electron current source term; represents the proton current source term; in the anode catalyst layer, S s =-j a 、S m =j a , in the cathode catalyst layer S s =j c 、S m =-j c , in the remaining area S s 、S m Both are 0.

[0085] According to the law of conservation of current, the total current collected by the anode catalyst layer is equal to the total current collected by the cathode catalyst layer, that is:

[0086]

[0087] The value of the exchange current j is related to the overpotential η on the surface of the catalyst layer and the electrochemical reaction on the surface of the catalyst layer. The overpotential η can be expressed as:

[0088] η act =φ s -φ m -V ref

[0089] Where V ref It represents the reference voltage, which is 0 on the anode side and equal to the theoretical voltage of the fuel cell at a given temperature and pressure on the cathode side:

[0090]

[0091] According to the above formula, the overpotential η is negative at the cathode and positive at the anode, where the battery voltage is the difference between the solid phase potentials of the cathode and anode:

[0092] V cell =φ s.m -φ s.a

[0093] The relationship between the exchange current density j and the activation overpotential is expressed by the Butler-Volmer equation, and the anode and cathode expressions are:

[0094]

[0095] Where: α represents the transmission coefficient, and its value depends on the symmetry of the activation energy barrier.

[0096] At different pressures and temperatures, the exchange current density is corrected to:

[0097]

[0098] Where: P r represents the partial pressure of the reactants; represents the reference pressure; γ represents the concentration coefficient, which is 0.5 at the anode and 1 at the cathode; E c represents the activation energy, E c =66kJImol.

[0099] According to Faraday's theorem, the relationship between current and consumption of reactants (or generation of products) can be deduced as follows:

[0100]

[0101] Then, the consumption of hydrogen and oxygen and the generation rate of water are:

[0102]

[0103] The concentration difference diffusion water flux in the membrane can be expressed by the formula:

[0104]

[0105] Where, c represents concentration; represents the diffusion coefficient of water; and

[0106] D λ =10 -10 (λ<2)

[0107] D λ =10 -10 ×[1+2(λ-2)](2≤λ≤3)

[0108] D λ =10 -10 ×[3-1.67(λ-3)](3<λ<4.5)

[0109] The amount of water that migrates due to pressure difference in the membrane can be expressed by the following formula:

[0110]

[0111] Where k p Indicates the permeability coefficient of water in the membrane; c w represents the concentration of water vapor; μ represents the viscosity of water; p represents the pressure; y represents the thickness of the proton exchange membrane (cm). According to the deduction of Bernardi et al., the pressure change in the membrane is linear, that is:

[0112]

[0113] Where p c Indicates cathode pressure; d m is the thickness of the proton exchange membrane; p a is the anode pressure.

[0114] In summary, the overall water transport equation in the membrane can be summarized as:

[0115] φ w =φ wh +φ wb +φ wp .

[0116] S3.1.2. Perform a global 3D model of the single battery, including the proton exchange membrane, catalyst layer, gas diffusion layer, and bipolar plate. Use a structured meshing method to construct the mesh, refining the mesh in the porous media and proton exchange membrane regions.

[0117] S3.1.3. Based on S3.1.1, establish descriptive models for the bipolar plates, flow channels, cathode / anode diffusion layers, cathode / anode catalyst layers, and electrolyte membranes.

[0118] S3.2. Construction of single-layer battery input-output characteristic equations based on mechanism exploration + machine learning.

[0119] The present invention introduces the ANN-HHO neural network algorithm to construct the input and output characteristic equations of a single-layer fuel cell. The present invention determines the main form and key influencing factors of the input-output equation of a single-layer battery through theoretical research and mechanism exploration in step S3. A large number of simulation results calculated based on the simulation model established in step S3.1.1 are used as training data. The input-output equation parameter relationship that is affected by multiple coupling factors and difficult to determine is determined by the ANN-HHO neural network algorithm, thereby achieving a closed-loop solution to the entire input-output equation. Specifically, Figure 4 shown.

[0120] Figure 5 This is a schematic diagram of the relationship between the input vector and output vector of an artificial neuron. The artificial neural network establishes a linearly weighted relationship between the input vector and the output vector between each unit layer through the activation function. Based on the training samples, the network from the input layer to the hidden layer, between different hidden layers, and from the hidden layer to the output layer is trained. The essence of the learning process is to explore the mapping relationship between the input vector and the output vector by adjusting the weight value and the related bias value, so that the mapping relationship continuously approaches the optimal mapping relationship between the input vector and the output vector.

[0121] When using ANNs to solve nonlinear problems, sample data is typically randomly divided into training data, test data, and validation data. The training data is used to train the artificial neural network. During the training process, an appropriate optimization algorithm is used to update the weight factors and corresponding biases. The performance of the artificial neural network is evaluated by calculating the minimum value of the fitness function of the training data. The fitness function is:

[0122]

[0123] Where y i is the true value, is the corresponding predicted value, and N is the sample size of the training data.

[0124] When the termination condition is met (reaching the maximum number of iterations or the fitness function reaches a certain indicator), the update process is completed and the optimal solution is found. Thus, the ANN can determine the mapping relationship between inputs and corresponding outputs through the learning process. ANN validation data is used to ensure the accuracy and generalization of the developed neural network during the training process. After the training phase, the test data is used to judge the performance of the trained artificial neural network.

[0125] The learning process of ANN is achieved by adjusting the weight values. However, for traditional artificial neural network algorithms, if the weight values and corresponding bias values of artificial neurons are not properly selected, the artificial neural network may converge slowly or easily fall into the dilemma of local minimum. Therefore, a certain method is usually used to optimize the weight values and corresponding bias values. The present invention uses the Harris Hawk optimization algorithm to optimize the weight values of ANN. The present invention combines artificial neural networks (ANN) with the Harris Hawk optimization algorithm (HHO) to achieve high-precision parameterized modeling of the input and output equations of a single-layer fuel cell. The specific steps are as follows:

[0126] (1) Data generation and preprocessing: Generate a training data set based on a global three-dimensional multi-physics field coupled simulation model of a single-layer battery. The simulation model covers key areas such as bipolar plates, flow channels, catalyst layers, and proton exchange membranes. The input parameters are the single-cell inlet reaction gas flow rate Q in and inlet pressure P in , output parameters include outlet pressure P out , export flow Q out , current density j, and output voltage V. Simulation data is obtained by numerically solving mass, momentum, and energy conservation equations and electrochemical models (such as the Butler-Volmer equation). The input and output data are then normalized to eliminate dimensionality and proportionally divided into training, validation, and test sets.

[0127] (2) Construct a three-layer feedforward neural network, the input layer contains 2 neurons (corresponding to Q in and P in ), the hidden layer uses a 16-32-16 neuron configuration, and the output layer contains 4 neurons (corresponding to P out ,Q out ,j,V). The ReLU function is used as the hidden layer activation function to enhance nonlinear expression capabilities, and the output layer uses a linear activation function. The network weights and biases are randomly initialized using the Xavier method, and the objective function is defined as the root mean square error (RMSE) between the predicted value and the simulated data.

[0128] (3) HHO algorithm optimization weight and bias: Set the HHO initial parameters, including population size (50-100), maximum number of iterations (200-500) and weight search space ([-1,1]). The optimization process is divided into three stages:

[0129] Global search phase: During the search process, they will continuously change their positions according to two different strategies to approach the target. According to the random probability: when q ≥ 0.5, the Harris's hawk will randomly perch on a tree based on the position of a random hawk in the population. When q < 0.5, the Harris's hawk will perch based on the average position of the population, the position of the prey, and a random position within the field of view as a reference target. The specific mathematical expression is:

[0130]

[0131] Where, X rand (t) represents an individual randomly selected from the population, X(t) represents the Harris hawk individual whose position needs to be updated in this iteration, and X best (t) represents the optimal individual position of the population obtained after the last iteration. It is only the global optimal individual of the current iteration rather than the global optimal of the search space. It is used to represent the prey position, q and c i (i=1,2,3,4) are all random numbers uniformly distributed between 0 and 1, which are used to improve the randomness of the algorithm during the search process. LB and UB are the lower and upper bound vectors of the search space. X mean (t) represents the average position of all individuals in the population, and its evaluation formula is as follows:

[0132]

[0133] The transition from global search to local exploitation: In this transition, the two search states are switched mainly based on the prey escape energy E, which is defined as:

[0134]

[0135] In the above formula, E0 is the initial escape energy of the prey, which is a random number uniformly distributed between -1 and 1, and the escape energy convergence factor is It is used to simulate the prey becoming exhausted during the hunting process. As the algorithm iterates, E1 will converge to 0, t is the current iteration number, and T is the total iteration number.

[0136] Localized Exploitation: During this phase, Harris's hawks begin to surround and ambush their prey. Unfortunately, the prey often escapes before the Harris's hawks can. Therefore, Harris's hawks have developed four attack strategies, depending on the prey's escape energy and their own pursuit strategies.

[0137] Soft Encirclement: When r ≥ 0.5 and |E| ≥ 0.5, the prey still has enough energy. The Harris Hawk lingers around the prey, wearing down its patience and tiring it out before pouncing.

[0138] X(t+1)=ΔX(t)-E[JX best(txt)]

[0139] In the above formula, J represents the jump distance of the target prey to simulate its escape step length, and is a random number uniformly distributed between 0 and 2, which is defined as J = 2(1-r), r∈(0,1), where ΔX(t) is defined as:

[0140] ΔX(t)=X best (txt)

[0141] Tough Encirclement: When r ≥ 0.5 and |E| < 0.5, the prey is very tired and the Harris Hawk attacks directly:

[0142] X(t+1)=X best (t)-E|ΔX(t)|

[0143] Sequential Rapid Dive Soft Encirclement: When r < 0.5 and |E| ≥ 0.5, the prey has a certain amount of escape energy and has a probability of escaping. In this case, the Harris Hawks will perform a sequential rapid dive soft encirclement before the siege. The specific update formula is as follows:

[0144] Y=X best (t)-E|[X best (txt)]

[0145] After this update, if the individual fitness value does not improve, the individual may have fallen into a local optimum. Then the algorithm will continue to execute another Lévy flight strategy based on the greedy strategy to perform a random walk in order to jump out of the local optimum:

[0146] Z=Y+S×LF(D)

[0147] Sequential rapid swooping, hard-hitting encirclement: When r < 0.5 and |E| < 0.5, although the prey has less energy to escape, it still has a chance to escape. At this time, the hawks will collectively adjust their average position to form a tighter encirclement to prevent the prey from escaping. This situation is set because if a strong attack is carried out, the search radius will be rapidly reduced, which will help the prey save energy and take the opportunity to escape:

[0148] Y=X best (t)-E[JX best (t)-X mean (t)]

[0149] Similarly, if the fitness value does not improve, continue to execute the new update strategy:

[0150] Z=Y+S×LF(D).

[0151] (4) Model training and validation: The weights and biases are iteratively optimized using the HHO algorithm, with the objective function being to minimize the RMSE. The termination condition is when the maximum number of iterations is reached or the RMSE falls below a set threshold (e.g., 0.01). During the training process, the validation set is used to monitor overfitting and adjust hyperparameters, and the test set is used to evaluate the generalization performance of the model to ensure that the prediction results are consistent with the simulation data.

[0152] (5) Input-output equation construction and application: The trained neural network directly maps the input parameters (Q in ,P in ) and output parameters (P out ,Q out ,j,V), forming a nonlinear relationship between the two, forming a function expression:

[0153] (P out ,Q out ,j,V)=f(Q in ,P in )

[0154] This equation implicitly accounts for heat and mass transport, electrochemical reactions, and multi-field coupling within a single cell. Ultimately, the equation is embedded in a fuel cell stack flow network model. By iteratively solving for each unit parameter (such as the pressure drop in the distribution main pipe and the outlet pressure of a single cell), a high-precision prediction of the reaction gas distribution characteristics of the entire stack is achieved.

[0155] S3.3. Obtain the variation patterns of the main parameters of a single-layer battery, such as the inlet and outlet pressure drop, output current, voltage, and outlet working fluid flow rate, as a function of the inlet gas flow rate, and understand the heat and mass transport mechanism inside the fuel cell.

[0156] The input parameter is the reaction gas flow rate Q at the inlet of the single cell in and inlet pressure P in , the output parameter is the single cell outlet pressure P out , outlet gas flow Q out , current density j, and output voltage V. Because this unit involves complex physical and chemical processes, a functional relationship is constructed by combining mechanism exploration with machine learning. Let the functional relationship be f. First, through global three-dimensional modeling and numerical calculation of a single cell, the heat and mass transport mechanism is understood. Then, using the ANN-HHO neural network algorithm and a large amount of simulation data, the relationship between the unit input-output equation is determined, thereby determining the specific form of function f. The unit input-output equation for a single-layer fuel cell is obtained as:

[0157] (P out ,Q out ,j,V)=f(Q in ,P in ).

[0158] Among them, the neural network architecture design: build a three-layer feedforward neural network, the input layer contains 2 neurons (corresponding to Q in and P in ), the hidden layer uses a 16-32-16 neuron configuration, and the output layer contains 4 neurons (corresponding to P out ,Q out ,j,V). The ReLU function is used as the hidden layer activation function to enhance nonlinear expression capabilities, and the output layer uses a linear activation function. The network weights and biases are randomly initialized using the Xavier method, and the objective function is defined as the root mean square error (RMSE) between the predicted value and the simulated data.

[0159] HHO algorithm optimizes weights and biases: Set the HHO initial parameters, including population size (50-100), maximum number of iterations (200-500), and weight search space ([-1,1]). The optimization process is divided into three stages:

[0160] Global search phase: Explore the global optimal solution through random strategies (such as based on the average position of the population or random individual positions) to avoid falling into the local optimum. Transition phase: Dynamically adjust the search range based on the prey escape energy (E), and the energy value decays with the number of iterations, gradually shifting from global search to local optimization. Local mining phase: Use four attack strategies (soft encirclement, hard encirclement, etc.) to fine-tune the weights. For example, when the prey energy is high, the soft encirclement strategy is used to gradually approach the optimal solution; if a local optimum is detected, the Lévy flight random perturbation is introduced to break out of the stagnant state.

[0161] Model training and validation: The HHO algorithm is used to iteratively optimize weights and biases, with the objective function being to minimize the RMSE. Termination conditions are either reaching the maximum number of iterations or when the RMSE falls below a set threshold (e.g., 0.01). During training, the validation set is used to monitor overfitting and adjust hyperparameters. The test set is used to ultimately evaluate the model's generalization performance and ensure that predictions are consistent with the simulated data.

[0162] The trained neural network directly maps the nonlinear relationship between input parameters and output parameters to form a function expression:

[0163] (P out ,Q out ,j,V)=f(Q in ,P in ).

[0164] This equation implicitly accounts for heat and mass transport, electrochemical reactions, and multi-field coupling within a single cell. Ultimately, the equation is embedded in a fuel cell stack flow network model. By iteratively solving for each unit parameter (such as the pressure drop in the distribution main pipe and the outlet pressure of a single cell), a high-precision prediction of the reaction gas distribution characteristics of the entire stack is achieved.

[0165] S4. With the main goal of improving fuel cell output performance, the existing distribution structure of the fuel cell stack is globally optimized to improve the flow distribution characteristics of the fuel cell stack reaction gas, and a multi-scale reaction gas distribution and heat and mass transport dynamic coupling model is constructed.

[0166] S4.1. The model solution process is as follows:

[0167] S4.1.1, Assume that the inlet reaction gas flow rate M of each layer of cells i (I), I = 1, 2, 3, ..., N is the total number of batteries.

[0168] S4.1.2. Calculate the discrete governing equations for each fluid unit in the distribution main in sequence to obtain the inlet and outlet fluid parameters of each fluid unit in the distribution main;

[0169] S4.1.3. From battery 1 to battery NB, where NB represents the total number of single-layer batteries, calculate the control equations of each single-layer battery in turn to obtain the inlet and outlet fluid parameters of the single-layer battery, including the outlet pressure P of each layer of battery. out (I) and outlet reaction gas flow M out (I).

[0170] S4.1.4. According to the outlet reaction gas flow of each layer of battery, the discrete control equations of each fluid grid in the collecting main pipe are calculated in turn. In the flow network of the fuel cell stack, the discrete control equations of the fluid grid of the collecting main pipe are used to calculate the outlet pressure of each single-layer battery. Specifically, based on the principles of conservation of mass and momentum, the continuous flow process is discretized into algebraic equations of each fluid grid. The core role of the discrete control equation is to avoid the errors caused by the simplification of local effects by traditional methods by dynamically correlating the microscopic parameters such as the current density and temperature of the single-layer battery with the pressure drop characteristics of the macroscopic flow network, and to achieve multi-scale coupling; at the same time, accurately quantify the pressure distribution of the reaction gas in the collecting main pipe, and provide a quantitative basis for evaluating the distribution uniformity; the pressure distribution results can also be used to reversely correct the inlet flow distribution strategy, guide the optimization of the flow channel structure, and improve the overall performance of the battery stack. This method realizes multi-physics field coupling simulation from the single cell scale to the stack scale, and provides a high-precision tool for the prediction and optimization design of the distribution characteristics of the fuel cell stack. The outlet pressure of each layer of battery is obtained to distinguish it from the outlet pressure P of each single-layer battery obtained. out The difference between (I) is expressed here as follows: the two pressure values should be equal when the iteration converges, and the relative deviation of the outlet pressure of each layer of battery is defined as:

[0171]

[0172] S4.1.5. If the relative deviation of the outlet pressure of each layer of batteries satisfies: δP outIf (I)<ξ (ξ is a given threshold that is sufficiently small), the iterative process is considered to have converged. Otherwise, if the relative deviation of the outlet pressure of any battery does not meet the convergence condition, return to step S4.1.1, use the formula to correct the assumed value of the inlet working fluid flow of the corresponding battery, and repeat steps S4.1.1 to S4.1.5 until the iterative process converges.

[0173] M in (I)=M in (I)+σ·δP out (I)

[0174] Where: σ is the relaxation coefficient.

[0175] S4.1.6. Finally, output the result parameters.

[0176] S4.2. Input boundary conditions (including fuel cell structure parameters, total stack inlet flow, pressure and other operating parameters) and use the global iterative method to solve all control equations.

[0177] S5. Based on a large number of simulation results calculated based on the simulation model established in step S4, as training data, the ANN-HHO neural network algorithm is used to determine the key coefficients in the final unit input-output equation of the single battery that are affected by multiple coupling factors and are difficult to determine, thereby achieving a closed-loop solution to the entire input-output equation.

[0178] The present invention constructs a multiscale coupling model, dividing the fuel cell stack's flow network into an inlet distribution unit, an outlet confluence unit, and a flow unit within a single-layer cell. Functional relationships between the input and output parameters of each unit are established. By introducing an artificial neural network (ANN) and the Harris Hawk Optimizer (HHO) algorithm, combined with three-dimensional numerical simulation and machine learning techniques, the distribution characteristics of reactant gases in the fuel cell stack and their impact on cell performance are accurately predicted. This multiscale coupling prediction method not only considers the reactant gas distribution process between each single-layer cell in the fuel cell stack, but also couples the heat and mass transport mechanisms within the single-layer cells, achieving multiscale coupling simulation from macro to micro scales, resulting in more accurate prediction results. This provides more accurate and effective data support and theoretical basis for subsequent fuel cell stack structural optimization, operating parameter optimization, and performance improvement. By accurately predicting the reactant gas distribution characteristics in the fuel cell stack and its impact on cell performance, researchers can help optimize fuel cell stack design in a targeted manner, such as optimizing the intake manifold structure and plate flow channel structure, thereby improving the reactant gas flow distribution characteristics, further enhancing the fuel cell stack's output performance and operational stability, and extending its service life. The present invention can provide theoretical guidance and technical support for the design and optimization of fuel cell stacks, solve the problems of hydrogen fuel cells in application scenarios such as heavy trucks, and promote the further development and application of hydrogen fuel cell technology.

[0179] The present invention can greatly improve the overall performance of the battery stack, especially the cathode side air, by improving the distribution characteristics of the reaction gas in each single cell of the battery stack. At the same time, it can alleviate the battery aging problem to a certain extent, which is of great significance to improving the output performance and life cycle of the high-power fuel cell stack. The present invention will also adopt a method that combines numerical modeling, experimental verification and mechanism analysis, and fully consider the special service environment of hydrogen heavy trucks from the aspects of collaborative simulation at the battery stack scale and single-layer battery scale, transient change characteristics under variable working conditions, and the coupling effect of various heat and mass transport processes, and conduct a systematic study on the dynamic distribution characteristics of the reaction gas in the high-power fuel cell under vehicle-mounted working conditions and the electrochemical heat and mass transport coupling mechanism. From the perspective of global optimization of reaction gas distribution, the present invention provides theoretical guidance and technical support for further improving the output performance and operating stability of high-power fuel cells and solving the problem of hydrogen heavy truck cruising range. It also enriches the research methods and content of gas-liquid two-phase flow and heat transfer disciplines. Existing researchers studying the distribution and transport of reactant gases between cells often overlook the complex heat and mass transport processes within individual cells (including gas flow and heat transfer within the bipolar plate surface channels, gas diffusion within the membrane electrode assembly, electrochemical reactions, and so on). These processes are often oversimplified, either by adopting a porous medium assumption or by simply reducing a single cell to a single flow channel. This invention, however, considers the coupling between the distribution process between individual cells and the electrochemical reactions within the cells, as well as the significant scale differences between heat and mass transport processes in various regions within the stack.

[0180] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack, characterized in that: The following steps are involved: Obtaining a flow network of the fuel cell stack, and dividing the flow area network on any side of the fuel cell stack into a fuel cell stack inlet distribution unit, an outlet confluence unit, and flow units within each single-layer cell; The Harris Eagle optimization algorithm was used to optimize the artificial neural network. By performing a global 3D modeling simulation of each single-layer battery, the simulation results were used as training data to train the optimized artificial neural network and determine the functional relationship between the input parameters and output parameters of the flow unit of the reactant gas along each single-layer battery. The parameter changes of the fuel cell stack inlet distribution unit and outlet confluence unit are analyzed based on the mass conservation equation and the momentum conservation equation, and the functional relationship between the input parameters and output parameters of the fuel cell stack inlet distribution unit and the functional relationship between the input parameters and output parameters of the outlet confluence unit are respectively constructed; the inlet and outlet fluid parameters of each fluid unit in the fuel cell stack main pipe and the inlet and outlet fluid parameters of each single-layer cell are determined based on the three functional relationships, and based on the inlet and outlet fluid parameters of each single-layer cell, discrete control equations are sequentially established within each fluid grid in the confluence main pipe, and the outlet pressure of each single-layer cell is obtained based on each discrete control equation; Based on the obtained outlet pressure of each single-layer cell, the distribution characteristics of the reaction gas within each single-layer cell in the fuel cell stack are predicted.

2. The method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack according to claim 1, characterized in that: The analysis of parameter changes of the fuel cell stack inlet distribution unit and outlet confluence unit according to the mass conservation equation and the momentum conservation equation specifically includes the following steps: The inlet distribution unit or outlet confluence unit includes two types of units, namely the flow distribution unit A at the inlet of each battery and the flow unit B between two adjacent layers of batteries; For the flow unit B between two adjacent layers of batteries, the mass conservation equation and momentum conservation equation at the unit inlet and outlet are expressed as follows: M in =M out Where, u is the flow velocity; M in is the unit inlet mass flow rate, M out is the unit outlet mass flow rate; ΔP f is the friction pressure drop along the process; P in is the unit inlet momentum, P out is the unit outlet momentum, λ is the friction coefficient along the way; l is the length of the pipe; d is the inner diameter of the pipe; ρ is the density of the fluid; For the diversion unit A at each battery inlet, part of the reaction gas enters the battery, and the other part continues to flow downstream; the pressure drop at the inlet and outlet of the diversion unit A includes the local resistance loss caused by the change in flow structure due to diversion or confluence, and the increase or decrease in fluid static pressure due to diversion or confluence; Then the inlet and outlet mass conservation equations and energy conservation equations of the shunt unit A at each battery inlet are expressed as: M in =M out +M 电池 Among them, K d is the static pressure recovery coefficient of the distribution unit, M 电池 For battery quality, is the unit inlet flow rate, is the unit outlet flow rate; According to the inlet and outlet mass conservation equations and energy conservation equations of the diversion unit A and the flow unit B, the parameter changes of the fuel cell inlet distribution unit and the outlet confluence unit are analyzed.

3. The method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack according to claim 1, characterized in that: The method performs global three-dimensional modeling and simulation on each single-layer battery, specifically including establishing global three-dimensional modeling of the bipolar plates, flow channels, cathode and anode diffusion layers, cathode and anode catalyst layers, and electrolyte membranes of the single-layer battery; obtains distribution data inside the single-layer battery by numerically simulating the multi-physical field coupling mechanism inside the single-layer battery; the distribution data inside the single-layer battery includes the single-layer battery inlet pressure, the single-layer battery outlet pressure, the single-layer battery inlet reaction gas flow rate, the single-layer battery outlet reaction gas flow rate, the fluid velocity field, pressure field, and temperature field distribution in the flow channel and porous medium area, the current density and output voltage generated by the electrochemical reaction of the catalytic layer, and the component concentrations of hydrogen and oxygen reactants and products.

4. The method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack according to claim 3, characterized in that: The method involves performing a global three-dimensional modeling simulation on a single-layer battery, using the simulation results as training data to train the ANN-HHO neural network algorithm, and determining the functional relationship between the input parameters and output parameters of the single-layer battery, specifically comprising the following steps: Setting initial parameters of an artificial neural network (ANN), including weight factors and corresponding biases; the ANN includes an input layer, a hidden layer, and an output layer; the input layer includes neurons corresponding to the inlet reaction gas flow and inlet pressure of a single-layer battery, respectively; the output layer includes neurons corresponding to the outlet pressure, outlet reaction gas flow, current density, and output voltage of the single-layer battery, respectively; the hidden layer activation function uses a ReLU function; The initial parameters of the Harris Hawk Optimization algorithm (HHO) are set, including the population size, the maximum number of iterations, and the upper and lower bounds of the parameters. The weight factors and corresponding biases of the ANN are updated by calculating the minimum value of the fitness function using the Harris Hawk Optimization algorithm (HHO). When the maximum number of iterations is reached, the update is completed to obtain the updated ANN weight factors and corresponding biases. The fitness function is the root mean square error (RMSE) between the predicted value and the simulated result. The results of global three-dimensional modeling simulation of the single-layer battery are input into the ANN after the weight factor and corresponding bias are updated, and the functional relationship between the single-layer battery inlet reaction gas flow and inlet pressure and the single-layer battery outlet pressure, outlet reaction gas flow, current density and output voltage is obtained.

5. The method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack according to claim 4, characterized in that: The discrete control equations in each fluid grid in the collecting main pipe are sequentially established according to the inlet and outlet fluid parameters of each single-layer battery, and the outlet pressure of each single-layer battery is obtained according to each discrete control equation. Specifically, the following steps are included: Set the inlet reaction gas flow rate of each single-layer cell and the total number of cells; Based on the principles of conservation of mass and momentum, the continuous flow of the reactant gas is discretized into the governing equations for each fluid grid. By inputting the outlet reactant gas flow rate of each single-layer cell as a boundary condition in the discrete governing equations, the pressure distribution of all grid nodes of the fluid grid is solved. The outlet pressure of each single-layer battery is obtained based on the pressure distribution of all grid nodes.

6. The method for predicting gas distribution characteristics of multi-scale coupled heat and mass transport in a fuel cell stack according to claim 1, characterized in that: The flow network method is used to divide the fuel cell stack into a series of nodes and units for connection to obtain the flow network of the fuel cell stack.

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