Flow field simulation optimization method of fused salt electric heater

Abstract

The invention discloses a flow field simulation optimization method of a fused salt electric heater. The method comprises the following steps: constructing a flow field domain geometric model of the fused salt electric heater; establishing a dynamic coupling model of molten salt density and viscosity physical property parameters changing along with temperature, and embedding the dynamic coupling model into the simulation framework; dividing the flow field domain by adopting an unstructured grid; setting boundary conditions and initial conditions of an inlet boundary, an outlet boundary and a wall surface boundary; carrying out iterative solution by adopting a fluid dynamics numerical calculation method; and a multi-dimensional flow field quality quantitative evaluation system is constructed, and the heater structure is optimized and adjusted based on an evaluation result. According to the flow field simulation optimization method of the fused salt electric heater, the change rule of the thermophysical property parameters of the fused salt along with the temperature is incorporated into a simulation framework, real-time bidirectional feedback of the thermophysical property parameters and the flow field parameters is achieved, and the problem of flow field distortion caused by fixed physical property parameters in traditional simulation is solved.

Description

Technical Field

[0001] This invention belongs to the field of molten salt electric heater simulation design technology, specifically relating to a flow field simulation optimization method for molten salt electric heaters. Background Technology

[0002] Molten salt, as a high-temperature heat transfer and heat storage medium, is widely used in fields such as solar thermal power generation and chemical reactions. Molten salt electric heaters are the core equipment for achieving rapid heating of molten salt.

[0003] The flow field characteristics of molten salt electric heaters are a key factor determining the operating efficiency and safety of the equipment: the uniformity of the molten salt velocity distribution within the heater directly affects the stability of heat transfer efficiency; localized eddies or stagnant areas can easily lead to overheating and decomposition of the molten salt, and excessively high flow resistance increases the system's circulating energy consumption. Therefore, accurately simulating the flow state of molten salt within the heater is a core prerequisite for optimizing the equipment's structural design.

[0004] Existing flow field simulation technology for molten salt electric heaters has the following key drawbacks:

[0005] 1) The changes in thermal properties such as viscosity and density of molten salt with temperature at high temperatures were not considered, i.e., the properties were taken as constant values, which led to a large deviation between the flow field simulation results and the actual working conditions.

[0006] 2) The mesh generation strategy is coarse and lacks targeted densification in complex flow areas such as around the heating tube and at the corners of the flow channel, making it impossible to capture local flow field details (such as micro-vortices and sudden changes in flow velocity).

[0007] 3) It only outputs macroscopic parameters such as average flow velocity and pressure distribution, lacking quantitative analysis of key indicators such as equipment resistance and flow velocity distribution uniformity, making it difficult to guide structural optimization.

[0008] Therefore, there is an urgent need for a high-precision and efficient flow field simulation method for molten salt electric heaters to provide reliable technical support for heater structure optimization and performance improvement. Summary of the Invention

[0009] This invention provides a flow field simulation optimization method for molten salt electric heaters to solve the aforementioned technical problems, specifically employing the following technical solution:

[0010] A flow field simulation optimization method for a molten salt electric heater includes the following steps:

[0011] Construct a geometric model of the flow field of a molten salt electric heater;

[0012] A dynamic coupled model of the changes in molten salt density and viscosity parameters with temperature was established and embedded into the simulation framework;

[0013] The flow field is divided using unstructured grids;

[0014] Set boundary conditions and initial conditions;

[0015] Iterative solutions are obtained using computational fluid dynamics numerical methods;

[0016] A multi-dimensional flow field quality quantification evaluation system was constructed, and the heater structure was optimized and adjusted based on the evaluation results.

[0017] Furthermore, the dynamic coupling model includes a density-temperature nonlinear model ρ(T) and a viscosity-temperature nonlinear model μ(T) based on experimental data fitting:

[0018] ρ(T)=a1T+a2

[0019] μ(T) = b1T 3 +b2T 2 +b3T+b4

[0020] Where T is the molten salt temperature, and a1, a2, b1, b2, b3, and b4 are fitting coefficients.

[0021] Furthermore, the geometric model retains the key structures of the heating tube array, the guide plate, and the expansion and contraction sections of the flow channel, and simplifies the non-flow field-affected structures such as bolt holes, chamfers, and flanges. The heating tubes are arranged in equilateral triangles or squares, and the guide plate adopts a ring or honeycomb structure.

[0022] Furthermore, the mesh generation adopts an unstructured mesh combining polyhedra and prisms. The main body of the model uses a polyhedral mesh with an element size of 8–32 mm, while the near-wall region uses a prism mesh with 3–5 layers, a growth rate of 1.05–1.15, and the thickness of the first layer mesh according to y. + =30 confirmed.

[0023] Furthermore, the grid division implements gradient densification around the heating pipe, the corner of the flow channel, and the flow-sensitive areas at the inlet and outlet of the guide plate, gradually increasing the grid density by 2 to 3 times from the outside to the inside. The optimal density is determined through grid independence verification, and the result is considered stable when the change rate of the core flow field index between two adjacent grids is ≤5%.

[0024] Furthermore, the boundary conditions are set as follows:

[0025] The inlet boundary is set according to the rated circulation flow rate, with a mass flow rate or velocity boundary and an inlet temperature of 200–300℃.

[0026] A pressure outlet boundary is set at the outlet boundary with a pressure value of 0.1–0.5 MPa;

[0027] The wall boundary conditions are set as no-slip boundary conditions for the heating tube wall, the inner wall of the shell and the surface of the guide plate;

[0028] The initial conditions are: the initial temperature of the flow field is set to ambient temperature, the initial flow velocity is 0, and the initial pressure is standard atmospheric pressure.

[0029] Furthermore, the numerical solution uses the three-dimensional incompressible Navier-Stokes equations as the governing equations embedded in the coupled model. The RANS k-ε turbulence model is selected, and the transport equations for turbulent kinetic energy k and turbulent dissipation rate ε are closed by solving the Reynolds stress term. The finite volume method is used for discretization, the convection term is a second-order upwind scheme, and the pressure and diffusion terms are a second-order central difference scheme. The pressure-velocity coupling is performed using the SIMPLEC algorithm.

[0030] Furthermore, the iterative solution is set to a total of 8000–12000 iterations, and the residual values ​​of all governing equations are set to be ≤10. -5 As the core convergence criterion, and monitoring the fluctuation of the average velocity and pressure drop of the characteristic section within 500 to 1000 consecutive steps as an auxiliary convergence verification, an adaptive relaxation factor strategy is adopted, gradually increasing the relaxation factor during the iteration process.

[0031] Furthermore, the quantitative evaluation system includes three dimensions: velocity field uniformity (UI), stagnation zone ratio (ζ), and pressure field gradient (β).

[0032] UI=(1-Δv / v 平均 )×100%

[0033] ζ=V1 / V

[0034] β=ΔP / L

[0035] Where Δv represents the standard deviation of the flow velocity in the internal pipe cross section, v 平均 V represents the average flow velocity of the internal pipe cross section, V1 represents the volume of the region with a flow velocity ≤ 0.1 m / s, V represents the total volume of the flow field, ΔP represents the total pressure loss of the flow field, and L represents the length of the flow field, satisfying UI ≥ 0.95, ζ ≤ 5%, and β ≤ 5 kPa / m.

[0036] Furthermore, the structural optimization follows the principle of three indicators being required to pass simultaneously. When UI < 0.95, the inlet guide structure, flow channel cross-section, or built-in turbulence elements are optimized. When ζ > 5%, dead corners in the flow channel are eliminated, local structures are optimized, or a flow channel is added. When β > 5 kPa / m, friction resistance is reduced or local resistance is decreased. After optimization, simulation verification is performed again until all three indicators simultaneously meet the threshold requirements.

[0037] The advantage of this invention lies in the flow field simulation optimization method for molten salt electric heaters, which incorporates the variation of molten salt thermophysical parameters with temperature into the simulation framework, achieving real-time bidirectional feedback between thermophysical parameters and flow field parameters. This solves the flow field distortion problem caused by fixed physical parameters in traditional simulations. Simultaneously, it achieves high-precision simulation of velocity field, pressure field, eddy current field, and stagnation zone distribution, directly outputting structural optimization schemes to improve flow field uniformity and reduce flow risks.

[0038] The advantage of this invention also lies in the flow field simulation optimization method for the molten salt electric heater provided. Based on the prediction of flow field complexity, a mapping relationship between "flow velocity gradient and mesh density" is established, and gradient densification is implemented in flow field sensitive areas such as around the heating tube, flow channel corners, and inlet and outlet of the guide plate.

[0039] The advantage of this invention also lies in the flow field simulation optimization method for the molten salt electric heater provided, which constructs a three-dimensional quantitative evaluation index of "velocity field uniformity, stagnation zone ratio, and pressure field gradient". Each index is given a clear quantitative formula and qualified threshold, so as to achieve a comprehensive and objective evaluation of the flow field quality and break through the limitations of traditional single macroscopic index evaluation. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the flow field simulation optimization method for the molten salt electric heater of this application;

[0042] Figure 2 This is a schematic diagram of a molten salt electric heater.

[0043] Figure 3 This is a schematic diagram of the density-temperature nonlinear model fitting;

[0044] Figure 4 This is a schematic diagram of the viscosity-temperature nonlinear model fitting. Detailed Implementation

[0045] Embodiments of the present invention are described in detail below. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0046] The accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0047] The flowchart shown in the attached diagram is merely an illustrative example and does not necessarily include all steps. For example, some steps may be broken down, while others may be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0048] In a specific embodiment of the present invention, the innovability and practicality of the invention are demonstrated by describing an exemplary embodiment in detail. This embodiment, in conjunction with the system architecture and flowcharts in the accompanying drawings, clearly illustrates the various key modules of the invention and their interactions. The embodiments of the present invention aim to provide those skilled in the art with a technical solution that is easy to understand and implement, while demonstrating the advantages and effects of the present invention in practical applications.

[0049] like Figure 1 The diagram illustrates a flow field simulation optimization method for a molten salt electric heater according to this application, comprising the following steps: S1: Constructing a geometric model of the flow field domain of the molten salt electric heater. S2: Establishing a dynamic coupling model of the molten salt density and viscosity properties as a function of temperature and embedding it into the simulation framework. S3: Dividing the flow field domain using an unstructured mesh. S4: Setting boundary conditions and initial conditions. S5: Iteratively solving using computational fluid dynamics numerical methods. S6: Constructing a multi-dimensional flow field quality quantification evaluation system and optimizing the heater structure based on the evaluation results. The flow field simulation optimization method for the molten salt electric heater of this application incorporates the variation law of molten salt thermal properties with temperature into the simulation framework, realizing real-time bidirectional feedback between thermal properties and flow field parameters, and solving the flow field distortion problem caused by fixed properties in traditional simulations. The above steps are described in detail below.

[0050] For step S1: Construct the geometric model of the flow field of the molten salt electric heater.

[0051] In the embodiments of this application, the geometric model retains the key structures of the heating tube array, the guide plate, and the expansion and contraction section of the flow channel, and simplifies the non-flow field-affected structures such as bolt holes, chamfers, and flanges. The heating tubes are arranged in equilateral triangles or squares, and the guide plate adopts a ring or honeycomb structure.

[0052] Specifically, the core structural parameters of the molten salt electric heater are obtained, including the shell's length, diameter, and wall thickness; the number, diameter, wall thickness, and arrangement (equilateral triangle / square) of the heating tubes; the type (annular / honeycomb), aperture, thickness, and installation position of the guide vanes; and parameters such as inlet and outlet pipe diameters, center distance, and expansion angle. A 3D modeling software (HyperMesh) is used to construct the flow field geometry model, retaining key structures affecting the flow field (heating tube array, guide vanes, flow channel expansion / contraction sections), while simplifying non-flow field-affecting structures such as bolt holes, chamfers, and flanges to ensure a balance between model accuracy and computational efficiency. Figure 2 As shown.

[0053] For step S2: Establish a dynamic coupling model of the changes in molten salt density and viscosity with temperature and embed it into the simulation framework.

[0054] Specifically, obtain the thermophysical property test data (density ρ, dynamic viscosity μ) of the target molten salt (such as sodium nitrate-potassium nitrate mixed molten salt, chloride molten salt, fluoride molten salt) within the working temperature range (200℃~650℃);

[0055] Establish a coupling model based on experimental data:

[0056] Density-temperature nonlinear model:

[0057] ρ(T)=ρ(T)=a1T+a2

[0058] Where a1 and a2 are fitting coefficients, and T is the molten salt temperature, such as Figure 3 As shown.

[0059] Viscosity-temperature nonlinear model:

[0060] μ(T) = b1T 3 +b2T 2 +b3T+b4

[0061] Where b1, b2, b3, and b4 are the fitting coefficients, and the goodness of fit R0 is... 2 ≥0.99, where T is the molten salt temperature, such as Figure 4 As shown.

[0062] Understandably, key physical properties of molten salt, such as density ρ and dynamic viscosity μ, are not constant values ​​but functions of temperature T. Therefore, fitting formulas or data tables showing the temperature-dependent properties of the molten salt need to be pre-inputted. During the solution process, the temperature distribution of each grid cell is first obtained through initial flow field calculations. Then, based on the temperature values, the corresponding μ of the element is updated using the physical property model. The updated physical property parameters are then substituted into the governing equations for the next round of solving, forming a closed-loop coupled iterative process of "flow field solution - temperature calculation - property update - flow field re-solution" until both physical properties and flow field distributions tend to stabilize.

[0063] For step S3: Use an unstructured mesh to divide the flow field.

[0064] Specifically, the geometric model was imported into the mesh generation software (Star ccm+). To accurately capture the turbulence characteristics near the wall in the molten salt flow field simulation, an unstructured mesh combining polyhedra and prisms was used for mesh generation.

[0065] Main body of the model: It adopts a polyhedral mesh with a unit size of 8-32mm.

[0066] Near-wall region: Use prismatic mesh with 3-5 layers, growth rate 1.05-1.15, first layer mesh thickness according to y + =30 confirmed.

[0067] The specific parameters and design basis are as follows, including layer and dimensional parameters:

[0068] Number of layers: Three prismatic meshes are set. The number of layers is designed based on the thickness characteristics of the turbulent boundary layer, which can cover the viscous sublayer and transition layer in the near-wall region, and meet the layer requirements of the RANS k-ε model wall function method for the near-wall mesh.

[0069] First layer mesh size: The normal dimension of the first layer prismatic mesh near the wall is 0.5 mm. The goal of determining this dimension is to ensure that the dimensionless wall distance y in the near-wall region is within the specified range. + The value remains stable at around 30. The calculation formula is:

[0070]

[0071] In the formula, u τ ρ is the wall friction velocity, y is the distance from the center of the first layer of mesh to the wall, and ρ and μ are the density and dynamic viscosity of the molten salt.

[0072] y + =30 is the optimal applicability range for the wall function method, which can accurately match the solution logic of the near-wall region of the turbulence model. + An excessively large value (>50) will cause errors in the calculation of turbulence parameters, or y + Too small (<10) increases the number of grids and computational cost.

[0073] Mesh growth rate: The size growth rate of adjacent prism mesh layers is 1.1 (i.e., the size of the subsequent mesh layer is 1.1 times that of the previous layer). Using a low growth rate ensures a smooth transition of mesh size in the near-wall region, avoids numerical diffusion caused by excessively rapid mesh expansion, and controls the total amount of mesh in the near-wall region, balancing computational accuracy and efficiency.

[0074] Furthermore, the grid division implements gradient densification around the heating pipe, the corner of the flow channel, and the flow-sensitive areas at the inlet and outlet of the guide plate, gradually increasing the grid density by 2 to 3 times from the outside to the inside. The optimal density is determined through grid independence verification. When the change rate of the core flow field index between two adjacent grids is ≤5%, the result is considered stable.

[0075] Mesh independence verification is a necessary step in flow field numerical simulation. Its core purpose is to determine the optimal mesh density, ensuring that simulation results (velocity, pressure) no longer change significantly with increasing mesh count, thereby eliminating the influence of mesh density on the calculation results and guaranteeing the reliability and accuracy of the simulation results. The specific steps of mesh independence verification are as follows:

[0076] The design of the grid density gradient set is based on the baseline grid (2×10). 7 Four mesh schemes with different densities were designed, each with a mesh number of 1×10n units. 7 (2×10) 7 (3×10) 7 (4×10) 7 ) units. The meshing rules for each group are consistent: the basic unit size of the main polyhedral mesh is scaled proportionally (1×10). 7 The basic unit size of the group is 32mm, 2×10 7 Group 24mm, 3×10 7 Group 16mm, 4×10 7 (Group size is 8mm); the number of layers, the size of the first layer, and the growth rate of the prism mesh in the near-wall region remain unchanged, and only the density of the main mesh is adjusted.

[0077] The simulation calculation conditions were unified, applying identical boundary conditions (inlet velocity, temperature, outlet pressure, etc.), turbulence model parameters, and iterative convergence criteria (residual ≤ 10) to the four mesh models. -5 This ensures that all calculation conditions are consistent except for grid density.

[0078] After completing simulation calculations for each mesh model, key evaluation indicators were extracted, including flow field evaluation indicators (inlet and outlet flow resistance of the electric heater, outlet mass flow rate, etc.), and the rate of change of these indicators was quantified and compared.

[0079] Δ=|(Xn+1-Xn) / Xn|*100%

[0080] In the formula, Xn is the index value of the nth grid group, Xn+1 is the index value of the (n+1)th grid group, and Δ is the relative rate of change of the index.

[0081] When the number of grid cells increases from group n to group n+1, the change in the core flow field parameters is less than 5%, indicating that the impact of increasing grid density on the simulation results is within an acceptable error range for engineering applications, and the flow field results tend to stabilize. The 5% threshold balances computational accuracy and cost—if the threshold is set too small (e.g., ≤1%), the optimal grid density will be too high, significantly increasing computational resource consumption; if the threshold is set too large (e.g., >10%), the accuracy of the simulation results cannot be guaranteed.

[0082] The process for determining the optimal mesh density starts from the lowest density mesh group (1×10). 7 Starting with 1×10⁻⁶, the rate of change of indices for each adjacent set of grid cells is compared sequentially. If the rate of change of indices for a given set of grid cells is ≤5% for the first time, then the preceding set of grid cells is the optimal grid density. Example: If 1×10⁻⁶... 7 With 2×10 7 If the rate of change of the group's index is 3% (≤5%), then 2×10 7 The previous group (1×10) 7 This is not optimal and needs to be judged in conjunction with the trend of change. The correct logic is that when the grid density increases to a certain value, the rate of change of the index stabilizes at ≤5%. At this time, the minimum grid density that meets the rate of change requirement is the optimal one.

[0083] If, in the preset gradient group, the rate of change of the index between two adjacent groups crosses the 5% threshold (e.g., 1×10), then... 7 With 2×10 7 The rate of change was 8%, 2×10 7 With 3×10 7 If the rate of change is 3%, then the optimal grid density is between 2×10⁻⁶. 7 With 3×10 7 Between these intervals, new grid groups (e.g., 2.5×10) need to be added. 7 Further verification will be conducted. If the rate of change of all adjacent groups in the preset gradient group is ≤5%, then the smallest grid density group is the optimal one, in order to maximize the reduction of computational cost.

[0084] For step S4: Set boundary conditions and initial conditions.

[0085] In the embodiments of this application, the boundary conditions are set as follows:

[0086] Inlet boundary: Set a mass flow rate boundary (31.1 kg / s) or a velocity boundary, determined based on the heater's rated circulation flow rate. Set the inlet temperature to the actual operating inlet temperature of the molten salt (200℃~300℃).

[0087] Outlet boundary: Set a pressure outlet boundary, and the pressure value should match the system working pressure of 0.1 to 0.5 MPa.

[0088] Wall boundary: Set no-slip boundary conditions for the heating tube wall, the inner wall of the shell and the surface of the guide plate.

[0089] Initial conditions: Set the initial temperature of the flow field to ambient temperature (generally 25℃), the initial flow velocity to 0, and the initial pressure to standard atmospheric pressure.

[0090] For step S5: use computational fluid dynamics numerical methods to perform iterative solutions.

[0091] The numerical solution employs the three-dimensional incompressible Navier-Stokes equations as the governing equations embedded in a coupled model. The RANS k-ε turbulence model is selected, and the transport equations for turbulent kinetic energy k and turbulent dissipation rate ε are solved by closing the Reynolds stress term. The finite volume method is used for discretization. A second-order upwind scheme is used for the convection term, while a second-order central difference scheme is used for the pressure and diffusion terms. The pressure-velocity coupling is achieved using the SIMPLEC algorithm. The iterative solution is set to a total of 8000–12000 iterations, and the residual values ​​of all governing equations are set to be ≤10. -5 As the core convergence criterion, and monitoring the fluctuation of the average velocity and pressure drop of the characteristic section within 500 to 1000 consecutive steps as an auxiliary convergence verification, an adaptive relaxation factor strategy is adopted, gradually increasing the relaxation factor during the iteration process.

[0092] The specific process is as follows:

[0093] (1) Control Equation

[0094] Continuity equation:

[0095]

[0096] In the formula, u, v, w are velocities in the x, y, and z directions, respectively, in m / s; ρ is the fluid density, in kg / m³. 3 .

[0097] Momentum equation:

[0098]

[0099] In the formula, μ is the dynamic viscosity (Pa·s); P is the pressure (Pa); and f is the gravitational force per unit volume (m / s). 2 .

[0100] Energy equation:

[0101]

[0102] In the formula, C p λ is the specific heat capacity, J / kg·K, T is the temperature, °C, and λ is the thermal conductivity, W / m·K.

[0103] (2) Turbulence model:

[0104] Turbulent flow is characterized by irregularity and randomness. Directly solving the instantaneous Reynolds equations results in extremely high computational costs, making it difficult to meet the efficiency requirements of engineering simulations. The RANS k-ε turbulence model solves the two transport equations—turbulent kinetic energy (k) and turbulent dissipation rate (ε)—by closing the Reynolds-averaged Reynolds equations, thus combining stability, versatility, and computational efficiency. The core principles and key parameters of the governing equations are defined below.

[0105] 1) Turbulent kinetic energy (k): Characterizes the magnitude of the kinetic energy of turbulent fluctuations and is a core parameter that determines the intensity of turbulence;

[0106] 2) Turbulent dissipation rate (ε): Characterizes the rate at which turbulent kinetic energy is converted into heat energy due to viscosity;

[0107] 3) Turbulent viscosity coefficient μ t The Reynolds stress closure is achieved through empirical correlation calculations, with the formula: μ t =ρC μ k2 / ε, where C μ ρ is an empirical constant with a value of 0.09, and ρ is the fluid density.

[0108] 4) Transport equations:

[0109] Turbulent kinetic energy k equation:

[0110]

[0111] Turbulent dissipation rate equation:

[0112]

[0113] Among them, G k G represents the turbulent kinetic energy generated by the average velocity gradient. b Y represents the turbulent kinetic energy generated by buoyancy. M σ represents the pulsating expansion dissipation term of compressible flow. k and σ μ C represents the Prandtl numbers for the k and ε equations, typically taken as 1.0 and 1.3 respectively; 1ε C 2ε Both Cε and Cε are empirical constants of the model.

[0114] (3) Discretization method and coupled solution of pressure and velocity:

[0115] The governing equations are discretized using the finite volume method. Appropriate discretization schemes are selected for different terms, and the SIMPLEC algorithm is used to achieve a coupled solution for pressure and velocity. The specific steps are as follows:

[0116] Discrete format:

[0117] Convection term: The second-order upwind scheme is used for discretization. Its core idea is to determine the physical quantities (such as velocity and temperature) at the interface by linear interpolation of the parameters of two adjacent upstream grid cells. Compared with the first-order upwind scheme, it can significantly improve the discretization accuracy of the convection term and reduce numerical diffusion error. In specific implementation, the flow direction of the flow field is first determined to determine the upstream grid cells, and then the interface flux is calculated by linear interpolation formula.

[0118] Pressure term: Discretized using a central difference scheme, which has second-order accuracy. The interface pressure is obtained by symmetrical interpolation of the pressure values ​​of adjacent grid cells, which can accurately capture the gradient changes of the pressure field and avoid non-physical oscillations in the pressure field. During the discretization process, the orthogonality of the grid in the computational domain must be ensured to improve the stability of the central difference scheme.

[0119] Diffusion term: Discretized using a second-order central difference scheme to ensure the accuracy of the diffusion term, matching the discretization accuracy of the convection and pressure terms.

[0120] SIMPLEC algorithm coupled solution process:

[0121] Initialization: Set initial values ​​for the flow field (velocity, pressure), physical property parameters, and turbulence parameters. The initial values ​​can adopt the assumption of uniform distribution or the analytical solution of the simplified flow to reduce the iteration convergence time.

[0122] Solving the momentum equation: Based on the current pressure field, solve the discretized momentum equation to obtain the intermediate values ​​of velocity (u*, v*, w*). At this time, the velocity field does not satisfy the continuity equation.

[0123] Construct and solve the pressure correction equation: Based on the discrete forms of the continuity equation and the momentum equation, derive the pressure correction equation, and obtain the pressure correction value p' by solving the pressure correction equation; Compared with the traditional SIMPLE algorithm, the SIMPLEC algorithm corrects the coefficients of the momentum equation, reduces the pressure and velocity corrections in the iteration process, and improves the convergence stability.

[0124] Update pressure and velocity: Update the pressure field using the obtained pressure correction value p' (p = p* + p'), and update the velocity field (u = u* + u', v = v* + v', w = w* + w') according to the pressure correction value, so that the updated velocity field satisfies the continuity equation.

[0125] Solve other transport equations: After updating pressure and velocity, solve the turbulent kinetic energy k, dissipation rate ε (or specific dissipation rate ω) equation, and energy equation (used to calculate the temperature field and provide data for property coupling), etc.

[0126] Convergence criterion: Check whether the residual value of the current iteration step meets the convergence criterion. If it does not meet the criterion, return to the step of solving the momentum equation and repeat the above iteration process. If it meets the criterion, the iteration converges and the current flow field result is output.

[0127] (4) Iteration settings:

[0128] To ensure the convergence of the iterative solution and the reliability of the results, the convergence criteria, the range of iteration steps, and the convergence control strategy are clearly defined, as follows:

[0129] Convergence Criterion Definition and Monitoring:

[0130] Residual convergence criterion: The residual values ​​of all governing equations (continuity equation, momentum equation, turbulence parameter equation, energy equation) are assumed to be ≤10. -5 As the core convergence criterion.

[0131] Auxiliary convergence verification: In addition to the residual criterion, the stability of key physical quantities is monitored, such as the average velocity, pressure drop, and average temperature of the characteristic cross section in the computational domain. When the fluctuation of these physical quantities within 500 to 1000 consecutive iterations is ≤1%, the flow field is considered to have reached stable convergence, thus avoiding false convergence caused by the residuals becoming too flat too early.

[0132] Iteration step setting and control:

[0133] Total number of iterations: Set to 8,000 to 12,000 steps based on the complexity of the flow field. For simple flow fields (such as straight pipe flow), convergence can be achieved in about 8,000 iterations. For complex flow fields (such as curved channels and multi-branch flow fields), 10,000 to 12,000 iterations are required to ensure that the flow field develops fully and converges.

[0134] Iterative process control: An adaptive relaxation factor strategy is adopted to accelerate convergence. In the initial iteration steps (the first 1000 steps), a small relaxation factor is used (momentum equation 0.5-0.6, pressure equation 0.3-0.4, turbulence equation 0.5) to avoid drastic fluctuations in flow field parameters. As the iteration progresses, the relaxation factor is gradually increased (momentum equation 0.7-0.8, pressure equation 0.5-0.6, turbulence equation 0.7) to improve the iteration convergence speed. If residual oscillations or divergences occur during the iteration process, the relaxation factor is immediately reduced and the number of iteration steps is increased until the flow field returns to stability.

[0135] Iteration termination condition: When both "residual ≤ 10" are satisfied. -5 When the key physical quantity fluctuation is ≤1%, the iteration can be terminated early; if the convergence criterion is not met after 12000 iterations, the mesh quality (such as mesh orthogonality and distortion), boundary condition settings, model parameter values, etc. need to be checked, and the iteration should be restarted after optimization.

[0136] For step S6: Construct a multi-dimensional flow field quality quantification evaluation system and optimize and adjust the heater structure based on the evaluation results.

[0137] The quantitative evaluation system includes three dimensions: velocity field uniformity (UI), stagnation zone ratio (ζ), and pressure field gradient (β).

[0138] The velocity uniformity UI is defined by the following formula:

[0139] UI=(1-Δv / v 平均 )×100%

[0140] Where Δv represents the standard deviation of the flow velocity in the internal pipe cross section, v 平均 This indicates the average flow velocity across the internal pipe cross-section.

[0141] Understandably, for molten salt heat transfer, the uniformity of its flow velocity directly determines the heat flux distribution on the heat exchange surface. Uneven velocity distribution can lead to insufficient heat transfer and excessively high molten salt temperatures in some areas; conversely, excessively low molten salt can cause heat stagnation or even overheating and decomposition. Setting an excellent rating (UI>95%) ensures the uniformity of the temperature field on the heat exchange surface and prevents damage to the equipment from localized thermal stress.

[0142] The percentage of the retention area ζ is defined by the following formula:

[0143] ζ=V1 / V

[0144] Where V1 represents the volume of the region with a flow velocity ≤ 0.1 m / s, and V represents the total volume of the flow field.

[0145] Understandably, for safe operation of molten salt, the molten salt in the stagnant zone is prone to localized overheating due to insufficient heat exchange. Long-term operation can lead to carbonization, coking, and even blockage of the flow channels. Simultaneously, the stagnant zone is prone to impurity deposition, affecting the heat transfer performance and flow stability of the molten salt. Setting a qualification standard of ζ≤5% can effectively mitigate these risks.

[0146] The pressure field gradient β is defined by the following formula:

[0147] β=ΔP / L

[0148] Where ΔP represents the total pressure loss in the flow field, and L represents the length of the flow field.

[0149] For system energy consumption control, the power consumption of the molten salt circulating pump is positively correlated with pressure loss. The larger the β value, the higher the pump's operating energy consumption. Furthermore, excessively high pressure gradients can easily lead to excessive local pressure in the flow channel, increasing the risk of equipment leakage. Setting a limit of β ≤ 5 kPa / m is the optimal engineering value after comprehensively considering the physical properties of molten salt (high viscosity), the strength of the flow channel structure, and the system operating cost.

[0150] Structural optimization follows the principle of mandatory compliance of three indicators: uniformity of velocity field to ensure heat transfer efficiency, proportion of stagnation zone to ensure operational safety, and pressure gradient to control system energy consumption. These three indicators correspond to the core performance requirements of molten salt flow field and none can be omitted.

[0151] When UI < 0.95, optimize the inlet guide structure, flow channel cross-section, or built-in flow-disrupting elements. It's understandable that when UI < 0.95, the velocity distribution within the flow channel exhibits excessive dispersion, with localized high / low velocity regions. Optimization measures for UI < 0.95 are as follows:

[0152] Inlet flow guidance structure optimization: Add a flow guide plate or flow straightening grid at the inlet of the flow channel to guide the fluid to enter the main flow channel evenly and eliminate the velocity concentration caused by the inlet jet effect;

[0153] Flow channel cross-section adaptation adjustment: widen the diameter of narrow cross-sections with excessively high local flow velocity, and narrow the diameter of wide cross-sections with excessively low local flow velocity, so that the flow area of ​​each cross-section matches the flow rate.

[0154] Built-in flow disturbance elements: Flow disturbance columns or porous baffles are set in areas of abrupt changes in flow velocity to reduce the flow velocity gradient through forced mixing and improve the uniformity of flow velocity in the cross section.

[0155] When ζ > 5%, eliminate dead zones in the flow channel, optimize local structure, or add drainage channels. When ζ > 5%, it indicates the presence of dead zones, vortex zones, or excessively large local flow areas in the flow channel, leading to fluid stagnation. Optimization measures are as follows:

[0156] Eliminate dead angles in the flow channel: Round the right-angle structures at bends, tees, and end caps (the radius of the rounded corners is recommended to be 0.3 to 0.5 times the pipe diameter) to avoid the formation of vortex zones.

[0157] Optimize local structure: streamline obstacles such as protrusions and supports in the flow channel to reduce flow obstruction; reduce the diameter of areas with excessive flow area to increase local flow velocity to above 0.1m / s.

[0158] Add a diversion channel: Open an auxiliary diversion channel in the stagnation area to guide the fluid from the mainstream area into the stagnation area and break the stagnation state.

[0159] When β > 5 kPa / m, reduce the frictional resistance or decrease the local resistance. When β > 5 kPa / m, it indicates that the frictional resistance or local resistance of the flow channel is too high, leading to excessive pressure loss per unit length. Optimization measures are as follows:

[0160] Reduce friction loss: Use a flow channel material with smooth inner walls to reduce wall roughness. Optimize molten salt flow rate to avoid excessive flow rate causing a sharp increase in friction loss (friction loss is proportional to the square of the flow rate).

[0161] Reduce local resistance: Simplify the flow channel structure and reduce unnecessary bends, diameter changes, and valves; for bends that must exist, increase the turning radius (it is recommended that the turning radius be ≥ 3 times the pipe diameter) and adopt a gradual diameter change structure (diameter change angle ≤ 15°).

[0162] Optimize flow channel layout: shorten the total length of the flow channel, reduce the number of local resistance elements connected in series, and reduce the total pressure loss.

[0163] After the above optimizations, simulations were repeated until all three indicators simultaneously met the threshold requirements. By combining the three-dimensional quantitative evaluation system with the structural linkage optimization model, the uniformity of the heater velocity field can be improved by 30%–40%, the proportion of the stagnant zone can be reduced by 70%–80%, and the pressure loss can be reduced by 15%–25%.

[0164] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the present invention in any way, and all technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A flow field simulation optimization method for a molten salt electric heater, characterized in that, Includes the following steps: Construct a geometric model of the flow field of a molten salt electric heater; A dynamic coupled model of the changes in molten salt density and viscosity parameters with temperature was established and embedded into the simulation framework; Unstructured grids are used to divide the flow field. Set boundary conditions and initial conditions; Iterative solutions are obtained using computational fluid dynamics numerical methods; A multi-dimensional flow field quality quantification evaluation system was constructed, and the heater structure was optimized and adjusted based on the evaluation results.

2. The flow field simulation optimization method for the molten salt electric heater according to claim 1, characterized in that, The dynamic coupling model includes a density-temperature nonlinear model ρ(T) and a viscosity-temperature nonlinear model μ(T) based on experimental data fitting: ρ(T)=a1T+a2 μ(T)=b1T 3 +b2T 2 +b3T+b4 Where T is the molten salt temperature, and a1, a2, b1, b2, b3, and b4 are fitting coefficients.

3. The flow field simulation optimization method for the molten salt electric heater according to claim 1, characterized in that, The geometric model retains the key structures of the heating tube array, the guide plate, and the expansion and contraction sections of the flow channel, while simplifying the non-flow field-affected structures such as bolt holes, chamfers, and flanges. The heating tubes are arranged in equilateral triangles or squares, and the guide plate adopts a ring or honeycomb structure.

4. The flow field simulation optimization method for the molten salt electric heater according to claim 1, characterized in that, The mesh generation uses an unstructured mesh combining polyhedra and prisms. The main body of the model uses a polyhedral mesh, while the near-wall region uses a prism mesh.

5. The flow field simulation optimization method for the molten salt electric heater according to claim 4, characterized in that, The mesh division implements gradient densification around the heating tube, flow channel corners, and flow-sensitive areas at the inlet and outlet of the guide plate, gradually increasing the mesh density from the outside to the inside, and determining the optimal density through mesh independence verification.

6. The flow field simulation optimization method for the molten salt electric heater according to claim 1, characterized in that, The boundary conditions are set as follows: The inlet boundary is set according to the rated circulation flow rate, with a mass flow rate or velocity boundary and an inlet temperature of 200–300℃. A pressure outlet boundary is set at the outlet boundary with a pressure value of 0.1–0.5 MPa; The wall boundary conditions are set as no-slip boundary conditions for the heating tube wall, the inner wall of the shell and the surface of the guide plate; The initial conditions are: the initial temperature of the flow field is set to ambient temperature, the initial flow velocity is 0, and the initial pressure is standard atmospheric pressure.

7. The flow field simulation optimization method for the molten salt electric heater according to claim 1, characterized in that, The quantitative evaluation system includes three dimensions: velocity field uniformity (UI), stagnation zone ratio (ζ), and pressure field gradient (β). UI=(1-Δv / v 平均 )×100% ζ=V1 / V β=ΔP / L Where Δv represents the standard deviation of the flow velocity in the internal pipe cross section, v 平均 V represents the average flow velocity of the internal pipe cross section, V1 represents the volume of the region with a flow velocity ≤ 0.1 m / s, V represents the total volume of the flow field, ΔP represents the total pressure loss of the flow field, and L represents the length of the flow field, satisfying UI ≥ 0.95, ζ ≤ 5%, and β ≤ 5 kPa / m.

8. The flow field simulation optimization method for the molten salt electric heater according to claim 7, characterized in that, The structural optimization follows the principle of three indicators being required to pass simultaneously. When UI < 0.95, the inlet guide structure, flow channel cross-section, or built-in turbulence elements are optimized. When ζ > 5%, dead corners in the flow channel are eliminated, local structures are optimized, or a flow channel is added. When β > 5 kPa / m, friction resistance is reduced or local resistance is decreased. After optimization, simulation verification is performed again until all three indicators simultaneously meet the threshold requirements.

9. The flow field simulation optimization method for the molten salt electric heater according to claim 1, characterized in that, The numerical solution uses the three-dimensional incompressible Navier-Stokes equations as the governing equations embedded in the coupled model. The RANS k-ε turbulence model is selected, and the transport equations for turbulent kinetic energy and turbulent dissipation rate are closed by solving the Reynolds stress term. The finite volume method is used for discretization, the convection term is a second-order upwind scheme, and the pressure and diffusion terms are a second-order central difference scheme. The pressure-velocity coupling is performed using the SIMPLEC algorithm.

10. The flow field simulation optimization method for the molten salt electric heater according to claim 9, characterized in that, The iterative solution is set to a total of 8000–12000 iterations, and the residual values ​​of all governing equations are set to be ≤10. -5 As the core convergence criterion, and monitoring the fluctuation of the average velocity and pressure drop of the characteristic section within 500 to 1000 consecutive steps as an auxiliary convergence verification, an adaptive relaxation factor strategy is adopted, gradually increasing the relaxation factor during the iteration process.

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