A bidirectional coupling simulation method and system for a heat exchanger in a non-uniform thermal load environment

Abstract

The application discloses a heat exchanger bidirectional coupling simulation method and system under a non-uniform heat load environment, which establishes a three-dimensional flow field model and a one-dimensional pipe network model, performs geometric mapping and heat flow integration on wall surface units according to U-shaped pipe numbering and pipe section numbering along a path based on spatial coordinates, wall surface temperature, local heat flow density and wall surface area, generates a one-dimensional pipe section non-uniform heat input boundary, and solves the flow, pressure, fluid temperature in the pipe, equivalent pipe wall temperature and heat exchange coefficient in the pipe of the working medium in the pipe network model after loading the non-uniform heat input boundary, returns to the wall surface heat response boundary of the three-dimensional flow field model according to the same mapping relationship, and performs bidirectional iteration through sub-relaxation and convergence criterion. The method can reduce the full three-dimensional calculation cost while improving the prediction accuracy of wall temperature, heat flow and flow distribution under the non-uniform heat load.

Description

Technical Field

[0001] This invention relates to the field of heat exchanger thermal-hydraulic simulation technology, and in particular to a two-way coupled simulation method and system for heat exchangers under non-uniform heat load conditions. Background Technology

[0002] Supercritical carbon dioxide Brayton cycles offer advantages such as high system efficiency, compact equipment, and broad application prospects, attracting widespread attention in advanced energy and power systems. Shell-less U-tube heat exchangers, as key heat exchange equipment in such systems, face complex challenges including flue gas flow around the tubes, tube bundle wakes, localized heat load concentration, and significant variations in the properties of supercritical carbon dioxide within the tubes. Especially under non-uniform heat load environments, significant differences in heat transfer intensity exist between different tube banks, at different axial positions, and in different circumferential regions, thus affecting tube wall temperature distribution, flow distribution within the tubes, and equipment operational safety.

[0003] Existing heat exchanger simulation methods mainly fall into two categories: full 3D CFD simulation and one-dimensional system-level simulation. Full 3D CFD simulation can accurately describe the flue gas side flow field, temperature field, local heat flux density, and tube wall temperature distribution. However, for complex heat exchangers with multiple U-shaped tube bundles, it usually suffers from problems such as complex modeling, large mesh count, long calculation cycle, and high computational resource consumption, making it difficult to meet the efficiency requirements of multi-condition batch analysis and engineering optimization design. One-dimensional system-level simulation methods have advantages such as fast calculation speed and suitability for system-level flow distribution and thermal parameter analysis. However, they are difficult to accurately capture the effects of flue gas side flow, wake effect, and local non-uniform heat load on tube wall temperature and internal flow heat transfer, which can easily lead to inaccurate prediction of local high-temperature regions, heat flux concentration regions, and flow distribution differences. Summary of the Invention

[0004] The purpose of this invention is to address the problems in existing thermal-hydraulic simulations of shell-less U-tube heat exchangers, such as high computational overhead of full 3D CFD, difficulty in meeting the needs of rapid analysis under multiple operating conditions, inaccurate reflection of flue gas flow around the flue gas side, wake effect and local non-uniform heat load distribution by pure 1D pipe network model, reliance on manual processing for data interaction between 1D and 3D models, insufficient spatial mapping accuracy, and low efficiency of boundary condition update. The invention proposes a bidirectional coupled simulation method and system for heat exchangers under non-uniform heat load conditions to achieve efficient, accurate, and automated collaborative solution of heat exchanger temperature field, heat flow distribution and flow distribution in the tubes.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A two-way coupled simulation method for heat exchangers under non-uniform heat load conditions includes:

[0007] A three-dimensional flow field model on the flue gas side is established to obtain wall elements including local heat flux density, wall temperature, wall area and spatial coordinates. A one-dimensional pipe network model is established, and mass, momentum and energy are conserved.

[0008] The U-shaped tube number and one-dimensional tube segment number are determined based on the spatial coordinates of the wall unit. Heat flux integration is performed on the wall unit mapped to the same one-dimensional tube segment to obtain the segmented heat absorption of the one-dimensional tube segment and construct a non-uniform heat flux boundary.

[0009] The non-uniform heat flux boundary is loaded onto the one-dimensional pipe network model to calculate the mass flow rate, the fluid temperature inside the pipe, the equivalent pipe wall temperature, and the heat transfer coefficient inside the pipe. The results are then fed back to the three-dimensional flow field model to update the wall boundary of the three-dimensional flow field model.

[0010] The maximum segmented heat absorption relative change, the maximum equivalent pipe wall temperature change, and the overall energy conservation error are used as convergence criteria to output the final calculation results.

[0011] As a further preferred embodiment of the present invention, the three-dimensional flow field model includes a flue gas inlet region, a tube bundle flow region, a U-shaped tube outer wall region, and a flue gas outlet region; the flue gas inlet region is located at the inlet section upstream of the flue gas entering the tube bundle flow region, the tube bundle flow region is the region where the flue gas flows around the outer wall of each U-shaped tube after entering the tube bundle and generates flow around, wake, and mutual interference between adjacent tubes, the U-shaped tube outer wall region is the outer surface of the solid wall that exchanges heat with the working fluid inside the tube, and the flue gas outlet region is the discharge region located downstream of the tube bundle flow region;

[0012] The wall element, including local heat flux density, wall temperature, wall area, and spatial coordinates, is obtained as follows:

[0013] When discretizing the three-dimensional flow field model, the outer wall of the U-shaped tube is discretized into multiple wall elements, and each wall element records the center point coordinates of the spatial coordinates. Wall area Wall temperature and local heat flux density ;

[0014] The local heat flux density Represented as:

[0015]

[0016] in,

[0017] In the above formula, For the first Convection heat flux density of each wall element For the first The radiative heat flux density of each wall unit For equivalent emissivity, The Stefan-Boltzmann constant, The flue gas temperature near the wall unit. For the first The wall temperature of each wall unit.

[0018] As a further preferred embodiment of the present invention, the one-dimensional pipe network model is composed of multiple parallel U-shaped pipes. The U-shaped pipes are axially discretized, and each U-shaped pipe is divided into sections along the flow direction of the working fluid inside the pipe. One-dimensional pipe segment;

[0019] The mass conservation is expressed as:

[0020]

[0021] The conservation of momentum is expressed as:

[0022]

[0023] The energy conservation is expressed as:

[0024]

[0025] in, The inlet mass flow rate of the one-dimensional pipe segment. For the first U-tube mass flow rate; and The first root U-shaped tube Pressure at the inlet and outlet nodes of a one-dimensional pipe segment; This represents the frictional pressure drop along the pipe section in this one-dimensional structure. This refers to the local resistance pressure drop in this one-dimensional pipe section caused by bends, inlets, outlets, or local components. This represents the gravity pressure drop of the one-dimensional pipe segment; and The first root U-shaped tube The specific enthalpy of the working fluid at the inlet and outlet of a one-dimensional pipe section This is a correction factor for the wall heat conduction or heat loss of the one-dimensional pipe segment. This refers to the segmented heat absorption of this one-dimensional tube section.

[0026] As a further preferred embodiment of the present invention, the heat transfer coefficient inside the pipe of the one-dimensional pipe network model is... Based on the one-dimensional pipe section Reynolds number , working fluid Prandtl number thermal conductivity and tube inner diameter The calculation is as follows:

[0027]

[0028]

[0029] in, For Nusselt numbers, A coefficient related to the flow state. A correction factor to account for changes in supercritical properties or the effect of pipe bending;

[0030] The equivalent pipe wall temperature of the one-dimensional pipe section is calculated by back-calculating the convective heat transfer relationship inside the pipe. For the first... root U-shaped tube A one-dimensional pipe segment, equivalent pipe wall temperature The calculation expression is:

[0031]

[0032] in, This represents the heat exchange area inside the pipe corresponding to this one-dimensional pipe segment. The temperature of the fluid inside the pipe.

[0033] As a further preferred embodiment of the present invention, the process of determining the U-shaped tube number and the one-dimensional tube segment number based on the spatial coordinates of the wall unit is as follows:

[0034] Establish the centerline parameters for each U-shaped tube, and calculate the shortest distance from the center point of the wall unit to the centerline parameter; if the shortest distance is less than the preset distance threshold and the shortest distance is the smallest among all U-shaped tubes, then the number corresponding to the centerline parameter is taken as the U-shaped tube number.

[0035] Based on the coordinates of the wall element along the corresponding center line The inclusion relationship with the one-dimensional pipe segment along its length determines the one-dimensional pipe segment number: each U-shaped pipe is divided into... Along the one-dimensional pipe segment, the first The range along the path of each one-dimensional pipe segment is , , The coordinates along the pipe section are the starting and ending points; if satisfy Then determine the first The wall unit belongs to the first root U-shaped tube A one-dimensional pipe segment.

[0036] As a further preferred embodiment of the present invention, the step of performing heat flux integration on the wall elements mapped to the same one-dimensional pipe segment to obtain the segmented heat absorption of the one-dimensional pipe segment and constructing a non-uniform heat flux boundary includes:

[0037] For the root U-shaped tube A one-dimensional pipe section, with a range along the pipe. The heat absorption of a one-dimensional tube segment is segmented. The result is obtained by multiplying the total heat absorbed by the integral over the entire travel distance:

[0038]

[0039] in, Let be the heat distribution function. For the first The total heat absorbed by the U-shaped tube For the first Total friction length of the U-shaped tube;

[0040] Based on the input format of the one-dimensional pipe network model, the non-uniform heat input boundary is divided into segmented heat absorption areas. Segmented heat flow or segmented surface heat flow Transform using the following relational expression:

[0041]

[0042]

[0043] in, The length of a one-dimensional pipe segment. This represents the heat exchange area of ​​the outer wall of a one-dimensional pipe section.

[0044] As a further preferred embodiment of the present invention, the segmented heat absorption... The sum of the heat contributions of all wall units mapped to this pipe segment is expressed as:

[0045]

[0046] No. Total heat absorption of the U-shaped tube The summation of heat absorption in each segment of the one-dimensional tube of the U-shaped tube yields the following result:

[0047]

[0048] in, For local heat flux density, For the wall area, To map to the root U-shaped tube A set of wall elements for a one-dimensional pipe segment.

[0049] As a further preferred embodiment of the present invention, the process of loading the non-uniform heat flux boundary onto the one-dimensional pipe network model, calculating the mass flow rate, the fluid temperature inside the pipe, the equivalent pipe wall temperature, and the heat transfer coefficient inside the pipe, and then transmitting this data back to the three-dimensional flow field model to update the wall boundary of the three-dimensional model is as follows:

[0050] For mapping to the root U-shaped tube A set of wall elements for a one-dimensional pipe segment The one-dimensional solution result for this one-dimensional pipe segment, i.e., the temperature of the fluid inside the pipe. Equivalent pipe wall temperature and the heat transfer coefficient inside the pipe Postback to wall unit set Each wall unit in the;

[0051] If the three-dimensional flow field model adopts a given wall temperature form, then... This serves as the wall temperature boundary for the wall unit.

[0052] If in-tube convection heat transfer is used, the temperature of the fluid inside the tube will be... and the heat transfer coefficient inside the pipe As the boundary of wall thermal response, the wall temperature based on the wall element. This allows for heat flow across the segmented surfaces of the wall unit. satisfy:

[0053]

[0054] The one-dimensional solution results are organized into a boundary condition data table, which includes at least the U-shaped tube number. One-dimensional pipe section numbering , coordinates of the pipe section's start and end points, and the temperature of the fluid inside the pipe Equivalent pipe wall temperature and the heat transfer coefficient inside the pipe After the 3D flow field model reads the boundary condition data table, it determines the flow based on the U-shaped tube number to which the wall element belongs. One-dimensional pipe section numbering Update the wall boundary.

[0055] As a further preferred embodiment of the present invention, the relative change of the maximum segmented heat absorption, the maximum equivalent pipe wall temperature change, and the overall energy conservation error are obtained in the following manner:

[0056] No. Wheel and the first Relative change in maximum segmented heat absorption between wheels Represented as:

[0057]

[0058] Maximum equivalent pipe wall temperature change Represented as:

[0059]

[0060] Energy Imbalance Rate Represented as:

[0061]

[0062] In the above formula, and These are the first iterations in the coupled iteration process. Wheel and the first Wheel of Life root U-shaped tube The segmented heat absorption of a one-dimensional tube segment This represents the minimum positive value among all one-dimensional pipe segment heat absorptions during the current coupling iteration process; and These are the first iterations in the coupled iteration process. Wheel and the first Wheel of Life root U-shaped tube The equivalent pipe wall temperature of a one-dimensional pipe segment; For the first The total heat after integrating the heat flux contributions of all wall elements in the three-dimensional flow field model. For the first The sum of heat absorbed by all one-dimensional pipe segments in a one-dimensional pipe network model. To obtain and The maximum value in;

[0063] Indicates the first The overall energy conservation error in the wheel coupling iteration is expressed as:

[0064]

[0065] When the maximum segmental heat absorption relative change Maximum equivalent pipe wall temperature change and overall energy conservation error When all values ​​are less than the preset threshold, the coupled calculation is considered to have converged, and the final calculation result is output.

[0066] On the other hand, the present invention proposes a system for performing a two-way coupled simulation method for heat exchangers under non-uniform thermal load conditions, the system comprising:

[0067] The 3D flow field modeling module is used to establish and solve the 3D flow field model on the flue gas side.

[0068] The one-dimensional pipeline modeling module is used to build and solve the one-dimensional pipeline model corresponding to the U-shaped pipe.

[0069] The geometric mapping module is used to determine the U-shaped tube number and the one-dimensional tube segment number based on the coordinates of the center point of the wall unit space;

[0070] The heat flux integration module is used to calculate the heat contribution of the wall unit, the heat absorption of the one-dimensional pipe segment, and the total heat absorption of the U-tube.

[0071] The non-uniform boundary generation module is used to generate and load one-dimensional non-uniform heat input boundaries for pipe segments;

[0072] The thermal response feedback module is used to feed back the equivalent pipe wall temperature, pipe fluid temperature and pipe heat transfer coefficient obtained from the one-dimensional pipe network model to the three-dimensional flow field model.

[0073] The iterative control module is used to perform sub-relaxation updates, convergence checks, and result output.

[0074] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention combines three-dimensional local flow field calculation with one-dimensional system-level pipe network calculation, integrating the high-precision description capability of three-dimensional CFD for non-uniform heat loads and local flow field details with the efficient calculation capability of one-dimensional pipe network models. This significantly reduces the simulation cost of complex heat exchangers while ensuring calculation accuracy. Through spatial coordinate identification, geometric mapping, and heat flux integration methods, the local heat flux density of three-dimensional wall units is accurately mapped to one-dimensional axial pipe sections, breaking through the limitations of the uniform heat flux assumption in traditional one-dimensional models and improving the prediction accuracy of wall temperature and heat absorption under non-uniform heat load conditions. Through automated data interaction and boundary update mechanisms, bidirectional closed-loop coupling between three-dimensional and one-dimensional models is achieved, reducing errors caused by manual export, format conversion, and boundary setting, and improving the stability and efficiency of coupled simulation. Through iterative convergence judgment and boundary update, temperature field, heat flux distribution, and flow distribution results that better conform to actual flow and heat transfer laws can be obtained, providing technical support for local overheating identification, heat transfer performance analysis, structural optimization design, and engineering safety assessment of shell-less U-tube heat exchangers. Attached Figure Description

[0075] Figure 1 This is a flowchart of the bidirectional coupling simulation method for heat exchangers under non-uniform heat load conditions in this embodiment of the invention; Figure 2 This is a schematic diagram of a one-dimensional pipe network model of a shell-less U-tube heat exchanger in an embodiment of the present invention; Figure 3 This is a schematic diagram of the discrete one-dimensional pipe network model of a single U-shaped pipe in an embodiment of the present invention; Figure 4 This is a schematic diagram of the bidirectional coupling calculation process in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the changes in heat exchange and energy imbalance rate during the global coupling iteration process in an embodiment of the present invention. Detailed Implementation

[0076] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the specific embodiments of this invention will be described in detail below with reference to the accompanying drawings. These embodiments are merely preferred examples of this invention, used to aid in understanding the inventive concept, and do not constitute a limitation on the scope of protection.

[0077] This embodiment proposes a two-way coupled simulation method for heat exchangers under non-uniform heat load conditions and a system for executing the two-way coupled simulation method for heat exchangers under non-uniform heat load conditions. The system includes: a three-dimensional flow field modeling module, a one-dimensional pipe network modeling module, a geometric mapping module, a heat flux integration module, a non-uniform boundary generation module, a thermal response feedback module, and an iterative control module.

[0078] This implementation method takes a shell-less U-tube heat exchanger in a supercritical carbon dioxide Brayton cycle as the object, and uses a three-dimensional flow field model and a one-dimensional pipe network model as the calculation objects.

[0079] The execution flow of the two-way coupled simulation method for heat exchangers under non-uniform heat load conditions can be found in [reference needed]. Figure 1 First, based on the actual structure of the shell-less U-tube heat exchanger, a three-dimensional flow field model for the flue gas side is established and solved using a three-dimensional flow field modeling module. This three-dimensional flow field model includes the flue gas inlet region, the tube bundle flow region, the U-tube outer wall region, and the flue gas outlet region. The flue gas inlet region is the inlet section upstream of the tube bundle flow region. This inlet section is configured with flue gas inlet temperature and velocity distributions. The flue gas inlet velocity distribution is either a uniform velocity distribution or a non-uniform velocity distribution that varies along the transverse and longitudinal coordinates of the inlet section. The non-uniform velocity distribution is used to characterize the incoming flow deflection, local acceleration, or local stagnation of the flue gas before it enters the tube bundle flow region. The tube bundle flow region is the area where the flue gas flows around the outer wall of each U-tube after entering the tube bundle, generating flow around the tubes, wakes, and mutual interference between adjacent tube banks. The U-tube outer wall region is the outer surface of the solid wall that exchanges heat with the working fluid inside the tubes. The flue gas outlet region is the discharge region downstream of the tube bundle flow region.

[0080] When discretizing the three-dimensional flow field model, the outer wall of the U-shaped tube is discretized into multiple wall elements, and each wall element records the center point coordinates of the spatial coordinates. Wall area Wall temperature and local heat flux density For the three-dimensional flow field model, special attention needs to be paid to regions such as the near-wall region of the tube bundle, the windward side region, the leeward wake region, and the bend region, using smaller wall element sizes to capture the spatial variation of local heat flux density. The discretization and parameter recording of the above three-dimensional flow field model form the basis for subsequent geometric mapping and heat flux integration.

[0081] The flue gas inlet boundary refers to the inlet cross-sectional boundary where the flue gas enters the three-dimensional flow field model. This inlet cross-sectional boundary sets the flue gas inlet temperature. and flue gas inlet velocity The inlet velocity is set to a non-uniform velocity distribution that varies with the inlet cross-sectional coordinates, such as:

[0082]

[0083] in, For average inlet velocity, , These are the coordinates of the center of the inlet section, and These are the width and height of the inlet section, respectively. , The coefficients represent the horizontal and vertical non-uniformity; the above method can characterize the inflow deviation or local velocity non-uniformity of flue gas before it enters the tube bundle flow region.

[0084] When solving the three-dimensional flow field model, the continuity equation, momentum equation, energy equation, and turbulent closure relation are discretized and solved. The turbulent closure relation is a type of calculation relation used to estimate the turbulent viscosity and turbulent heat diffusion capacity of flue gas. Its function is to correct the momentum and heat exchange of flue gas in the flow region around the tube bundle, thereby obtaining a velocity field and temperature field that better conforms to the flow characteristics around high Reynolds numbers. The turbulent closure relation can be a relation containing turbulent kinetic energy and dissipation rate, or a relation containing turbulent kinetic energy and specific dissipation rate. This embodiment does not limit the specific form, only requiring that its output can participate in the calculation of effective viscosity, effective thermal conductivity, or turbulent Prandtl number in the momentum equation and energy equation.

[0085] When solving the three-dimensional flow field model, the continuity equation, momentum equation, and energy equation are all three-dimensional governing equations on the flue gas side, used to solve for the velocity, pressure, and temperature fields of the flue gas in the tube bundle flow region. The continuity equation describes the conservation of flue gas mass, the momentum equation solves for the flue gas velocity and pressure fields, and the energy equation solves for the flue gas temperature field and wall heat transfer.

[0086] The continuity equation can be expressed as:

[0087]

[0088] The momentum equation can be expressed as:

[0089]

[0090]

[0091] The energy equation can be expressed as:

[0092]

[0093]

[0094]

[0095] In the above formula, Represents the vector differential operator. Indicates transpose. For the density of the flue gas, For the flue gas velocity vector, For flue gas pressure, For flue gas temperature, The specific heat capacity of flue gas at constant pressure. The dynamic viscosity of flue gas molecules. For flue gas turbulent viscosity, The effective viscosity of the flue gas. The thermal conductivity of flue gas molecules, The equivalent thermal conductivity of flue gas turbulence. The effective thermal conductivity of the flue gas, For turbulent Prandtl number, For momentum source term, This is an energy source term.

[0096] The turbulent closure relation is used to calculate the turbulent kinetic viscosity of the flue gas side and further determine the effective viscosity and effective thermal conductivity of the flue gas side. The effective viscosity, effective thermal conductivity, and turbulent Prandtl number mentioned above are parameters in the turbulent closure relation, which differ from the dynamic viscosity, thermal conductivity, and Prandtl number of the working fluid calculated based on the supercritical carbon dioxide temperature and pressure inside the pipe in the one-dimensional pipe network model described later. Through the above turbulent closure relation, the additional momentum diffusion and additional heat diffusion caused by turbulence can be incorporated into the momentum control equation and energy control equation on the flue gas side, thereby correcting the momentum and heat exchange in the flow region around the tube bundle.

[0097] When the flue gas temperature is high and radiative heat transfer has a significant impact on the wall heat flux, a radiative heat flux correction can be added to the total wall heat flux. Local heat flux density of the wall element. It can be represented as:

[0098]

[0099]

[0100] in, For the first Convection heat flux density of each wall element For the first The radiative heat flux density of each wall unit For equivalent emissivity, The Stefan-Boltzmann constant, For the first Flue gas temperature near each wall unit For the first The wall temperature of each wall unit.

[0101] When fly ash deposits exist in the operating environment of the three-dimensional flow field model, the thermal resistance of the fly ash deposits can be used as a basis. Or deposition correction factor Heat flow to the wall The following formula is used for correction:

[0102] or

[0103] in, This represents the local heat transfer coefficient on the flue gas side.

[0104] The purpose of the above-mentioned radiation heat transfer correction and fly ash deposition correction is to make the local heat flux density output by the three-dimensional flow field model closer to the actual heat absorption of the outer wall of the U-shaped tube under high-temperature flue gas environment, and directly affect the heat absorption of subsequent one-dimensional tube segments.

[0105] After solving the three-dimensional flow field model, the velocity field of the flue gas side can be obtained. Flue gas side temperature field Local heat flux density Wall temperature Wall area and spatial coordinates The aforementioned local heat flux density, wall area, wall temperature, and spatial coordinates are used to construct the heat flux boundary from three dimensions to one dimension.

[0106] Among them, spatial coordinates U-shaped tube number used to identify the wall unit and one-dimensional pipe section number ; and Used to calculate the The heat contribution of each wall element is calculated, and the heat contributions of wall elements mapped to the same one-dimensional pipe segment are further accumulated to obtain the heat contribution of the first wall element. root U-shaped tube Segmented heat absorption of a one-dimensional tube segment ; Used for determining wall temperature convergence and comparing three-dimensional wall temperature results in subsequent coupled iterations.

[0107] It should be noted that, It is the first in the three-dimensional flow field model The wall temperature of each wall element, and then the output of the one-dimensional pipe network model. It is the first root U-shaped tube The equivalent pipe wall temperature of a one-dimensional pipe segment differs in physical location and discrete level. They are correlated through the same geometric mapping: when the... The wall element is mapped to the first... root U-shaped tube When a one-dimensional pipe segment is used Can be used with By performing corresponding comparisons, error evaluations, or sub-relaxation updates, a clear data source is provided for the subsequent generation of non-uniform heat input boundaries for one-dimensional pipe segments.

[0108] See Figure 2 and Figure 3 Based on the tube bundle structure of the shell-less U-tube heat exchanger, a one-dimensional pipe network model corresponding to the U-tubes is established and solved using a one-dimensional pipe network modeling module. This one-dimensional pipe network model consists of multiple parallel U-tubes, each U-tube including an inlet node, a left straight pipe section, a bend section, a right straight pipe section, an outlet node, heat transfer elements, and local resistance elements.

[0109] The U-shaped tubes are axially discretized, and each U-shaped tube is divided into sections along the flow direction of the working fluid inside the tube. A one-dimensional pipe segment, It can be set according to the required calculation accuracy, for example, each U-shaped tube can be divided into 20 one-dimensional tube segments.

[0110] Each one-dimensional pipe segment is set to a length. , pipe inner diameter , tube outer diameter Wall thickness Roughness External wall heat exchange area Elevation Inlet pressure Inlet temperature Inlet quality flow And the thermophysical properties of the working fluid. Elevation. The parameters are used to calculate the gravity pressure drop under the operating conditions of vertical U-shaped pipes, avoiding the simplification of vertically arranged pipelines as horizontal pipelines, which would cause pressure drop errors. For the first... root U-shaped tube For a one-dimensional pipe segment, the gravitational pressure drop is expressed as:

[0111]

[0112] in, The density of the working fluid inside the pipe, It is the acceleration due to gravity. and These are the elevations of the outlet and inlet nodes of the one-dimensional pipe segment, respectively.

[0113] The thermophysical properties of the working fluid for supercritical carbon dioxide inside the tube can be determined by temperature and pressure, including density, specific heat capacity, dynamic viscosity, and thermal conductivity. These can be obtained through pre-set property functions, property table interpolation, or calculation using equations of state. For each round of one-dimensional solution, after obtaining the temperature and pressure of the supercritical carbon dioxide inside the tube in the current iteration, the density, specific heat capacity, dynamic viscosity, and thermal conductivity of each one-dimensional tube segment are updated, and the Reynolds number, Prandtl number of the working fluid, and heat transfer coefficient inside the tube are calculated accordingly.

[0114] The one-dimensional pipe network model establishes mass conservation, momentum conservation, and energy conservation relationships for each U-shaped pipe and each one-dimensional pipe segment.

[0115] For parallel U-tube inlet and outlet manifolds, the total inlet mass flow rate must equal the sum of the mass flow rates of each U-tube. For each U-tube connected at the same node, the inlet node pressure... and export node pressure Satisfying pipeline connection constraints, the mass conservation principle can be expressed as:

[0116]

[0117] in, The inlet mass flow rate of the one-dimensional pipe segment. For the first U-tube mass flow rate;

[0118] For the root U-shaped tube For a one-dimensional pipe segment, the conservation of momentum can be expressed as:

[0119]

[0120] in, and The first root U-shaped tube Pressure at the inlet and outlet nodes of a one-dimensional pipe segment; This represents the frictional pressure drop along the pipe section in this one-dimensional structure. This refers to the local resistance pressure drop in this one-dimensional pipe section caused by bends, inlets, outlets, or local components. This represents the gravity pressure drop of the one-dimensional pipe section.

[0121] Frictional pressure drop along the friction path and local resistance pressure drop can be determined by the friction factor. Pipe section length , pipe inner diameter Density of working fluid inside the pipe and average flow velocity Confirmed, the expression is:

[0122]

[0123]

[0124] in, This represents the local drag coefficient.

[0125] Energy conservation is used to calculate the segmented heat absorption of the one-dimensional pipe section based on the aforementioned three-dimensional flow field model. Calculate the enthalpy rise and temperature change of the working fluid within this one-dimensional pipe section. Specifically, calculate the heat absorbed in each section. This represents the known heat input obtained through heat flux integration using three-dimensional wall elements and applied to the one-dimensional pipe segment. For the... root U-shaped tube The energy conservation relationship for a one-dimensional pipe segment can be expressed as:

[0126]

[0127] in, and The first root U-shaped tube The specific enthalpy of the working fluid at the inlet and outlet of a one-dimensional pipe section This is a correction factor for the wall heat conduction or heat loss of the one-dimensional pipe segment; when heat loss is ignored, Option 1 is acceptable.

[0128] In-tube heat transfer coefficient It can be based on the Reynolds number of a one-dimensional pipe section. , working fluid Prandtl number thermal conductivity and tube inner diameter The calculation method, taking the commonly used forced convection in pipes as an example, is as follows:

[0129]

[0130]

[0131] in, For Nusselt numbers, A coefficient related to the flow state. A correction factor is added to account for supercritical property changes or the effect of tube bending. The resulting heat transfer coefficient inside the tube is... It is used both in the calculation of the equivalent pipe wall temperature of a one-dimensional pipe segment and as the boundary parameter of the wall thermal response fed back to the three-dimensional flow field model.

[0132] No. root U-shaped tube Equivalent pipe wall temperature of a one-dimensional pipe segment The heat transfer can be determined by the convective heat transfer relationship inside the tube and the heat absorption at the wall surface. When the heat absorption is segmented... For the first to be introduced from the flue gas side root U-shaped tube For the first segment, the equivalent pipe wall temperature can be calculated back based on the convective heat transfer relationship within the pipe. For the second segment... root U-shaped tube The convective heat transfer relationship inside a one-dimensional pipe segment can be expressed as:

[0133]

[0134] Equivalent pipe wall temperature The calculation expression is:

[0135]

[0136] in, This represents the heat exchange area inside the pipe corresponding to this one-dimensional pipe segment. The temperature of the fluid inside the pipe is the average temperature or node temperature of the working medium within this one-dimensional pipe section.

[0137] After solving the 3D flow field model and the 1D pipe network model, a correspondence is established between the 3D wall elements and the 1D pipe segments. This correspondence is mainly determined by the geometric structure and does not depend on the 1D solution results of the 1D pipe network model; the 1D solution results are only used when subsequently propagating back the wall thermal response boundary.

[0138] When establishing a three-dimensional coordinate system, the x-direction can be defined as the lateral arrangement direction of the tube bundle, the y-direction as the mainstream direction of the flue gas, and the z-direction as the height direction.

[0139] The geometric mapping module is used to determine the U-shaped pipe number and the one-dimensional pipe segment number based on the center point coordinates of the wall unit spatial coordinates. Establish centerline parameters for the U-shaped tube ,in The coordinates are along the flow direction of the working fluid inside the pipe. =0 corresponds to the input terminal. Corresponding to the export end, For the first Total friction length of the U-shaped tube. Centerline parameters. It consists of a straight pipe section on the left, a bend in the pipe section, and a straight pipe section on the right.

[0140] For the Each wall element has its center point coordinates as follows: First, calculate the coordinates of the center point of the wall element. Parameters to the centerline of each U-tube shortest distance :

[0141]

[0142] like Less than the preset distance threshold and the shortest distance If the smallest value is found among all U-shaped tubes, then the number corresponding to that centerline parameter is used as the U-shaped tube number, i.e., the number is determined. The wall unit belongs to the first Root U-shaped tube. Distance threshold. Based on the outer radius of the pipe And the wall element discrete error setting, ,in This represents the allowable geometric error.

[0143] Determining the U-tube number Then, continue to determine the coordinates of the wall elements along the corresponding center lines. For the straight pipe section on the left, if its starting height is... And the working fluid flows along the height direction from Flow direction Then it can be based on the first The center point height coordinates of each wall unit Calculate the coordinates along the corresponding centerline. :

[0144]

[0145] For the bend section, if the center of the bend is The bend radius is The starting angle of the bend is The projection angle of the center point of the wall element relative to the center of the bend is Then the friction coordinates of the bend section can be expressed as:

[0146]

[0147] For the straight pipe section on the right, the height difference of the wall element on the right straight pipe section is added to the length of the straight pipe section and the bend section on the left. This allows both the straight and bend sections to use a unified friction coordinate system. This indicates that the division is not based solely on a single vertical direction.

[0148] Each U-shaped tube is divided into Along the one-dimensional pipe segment, the first The range along the path of each one-dimensional pipe segment is , , These are the coordinates along the start and end points of the pipe section. If... satisfy Then determine the first The wall unit belongs to the first root U-shaped tube A one-dimensional pipe segment.

[0149] When dividing into equal-length sections, the one-dimensional pipe segment number can be determined using the following formula:

[0150]

[0151] For U-shaped tubes located at the tube bundle boundary, at the reference tube, or close to adjacent tube rows where mismatch is likely to occur, a geometric mask can be set as a set of coordinate filtering conditions. For example, for the 10th reference tube, its centerline transverse coordinates can be used as the filtering criteria. Vertical coordinates and outer radius of the pipe set up:

[0152] , ,

[0153] in, and Here, the lower and upper limits of the height coordinates are respectively used for the geometric mask filtering region of the 10th U-shaped tube, to limit the height range of wall elements allowed to participate in the mapping of this U-shaped tube; only when the height coordinates of the center point of the wall element are... satisfy ≤ ≤ Only then does the wall unit participate in the spatial mapping of the 10th U-shaped tube.

[0154] This method can eliminate the problem of misassignment of wall elements near adjacent pipe rows or bends, and improve the spatial matching accuracy between wall elements and one-dimensional pipe segments.

[0155] After spatial mapping is completed, wall elements belonging to the same one-dimensional pipe segment are grouped together. Heat flux integration is then performed on the wall elements mapped to the same one-dimensional pipe segment. A heat flux integration module is used to calculate the heat contribution of each wall element, the heat absorption of the one-dimensional pipe segment, and the total heat absorption of the U-shaped pipe. Heat contribution of each wall unit Due to local heat flux density With wall area Multiplying them together gives:

[0156]

[0157] If heat transfer from the flue gas side to the pipe wall is defined as positive, then >0 It is positive. For the first... root U-shaped tube Each one-dimensional tube segment absorbs heat in sections. The sum of the heat contributions from all wall units mapped to this pipe section:

[0158]

[0159] in, Indicates mapping to the first root U-shaped tube A set of wall elements for a one-dimensional pipe segment. Total heat absorption of the U-shaped tube The sum of the heat absorbed by each segment of the one-dimensional tube in the U-shaped tube is obtained as follows:

[0160]

[0161] This requires understanding the relationships between the different levels. The heat contribution of the wall unit is the heat of a single wall unit; segmented heat absorption. It is the cumulative result of the heat contribution from multiple wall units within the same one-dimensional tube segment; the total heat absorbed by the U-shaped tube. It is the cumulative result of the heat absorbed by each segment of the one-dimensional tube of the same U-shaped tube.

[0162] To describe the heat distribution of different U-shaped tubes on a uniform scale, the coordinates along the tube can be normalized. Let the first... root U-shaped tube The coordinates of the center of each one-dimensional pipe segment along the path are: Then normalize the coordinates along the path. for:

[0163]

[0164] No. root U-shaped tube Heat percentage of each one-dimensional tube segment for:

[0165]

[0166] From a set of points ( , This will establish the heat distribution relationship along the direction of the U-shaped tube.

[0167] If a one-dimensional pipe network model directly receives segmented heat input, then... , / , / The heat can be applied to the corresponding pipe segment as segmented heat absorption, segmented linear heat flux, or segmented surface heat flux, respectively. This represents the heat exchange area of ​​the outer wall of the one-dimensional pipe section.

[0168] If a one-dimensional pipe network model requires a continuous function form of heat input, then piecewise interpolation or normalized polynomial fitting can be used to construct the heat distribution function. , For the first The normalized friction coordinates of the root U-shaped pipe are defined as follows:

[0169]

[0170] in, The coordinates are along the flow direction of the working fluid inside the pipe. For the first Total friction length of the U-shaped pipe.

[0171] Heat distribution function The following normalization conditions must be met:

[0172]

[0173] In one implementation, the polynomial coefficients can be obtained using the least squares method. And construct a heat distribution function of the following form:

[0174]

[0175] in, The order of the polynomial can be set according to the required accuracy of the heat distribution fitting. When the heat distribution changes relatively smoothly, a lower-order polynomial can be used; when there are obvious local peaks or non-uniform changes in the heat distribution, the order of the polynomial can be increased. This scheme can select order 5, i.e. =5. Adjust the coefficients by normalizing the integral, so that... The integral in the range [0,1] is 1. Thus, for any x, y = 1, the integral is 1. root U-shaped tube A one-dimensional pipe segment, its travel range is: The heat absorption of a one-dimensional tube segment is segmented. can be Multiply by the interval The integral is obtained as follows:

[0176]

[0177] in, For the first The total heat absorbed by the U-shaped tube.

[0178] Due to the segmented heat absorption of different one-dimensional tube sections There may be differences. In this embodiment, the non-uniform heat input boundary refers to the non-uniform heat input boundary loaded onto each one-dimensional pipe segment of the one-dimensional pipe network model using the non-uniform boundary generation module. It is used to describe the heat transferred from the three-dimensional flue gas side to that one-dimensional pipe segment. Based on the input form that the one-dimensional pipe network model can recognize, the non-uniform heat input boundary generated by the non-uniform boundary generation module is divided into segmented heat absorption areas. Segmented heat flow or segmented surface heat flow The three can be converted according to the following relationship:

[0179]

[0180]

[0181] in, This is the length of the one-dimensional pipe segment. This represents the heat transfer area of ​​the outer wall of the one-dimensional pipe segment. This non-uniform heat input boundary differs from the wall boundary that propagates back from one-dimensional to three-dimensional. The non-uniform heat input boundary represents the heat input from the flue gas side to the one-dimensional model, while the wall boundary represents the heat transfer response within the pipe that the one-dimensional model feeds back to the three-dimensional model.

[0182] See Figure 1 and Figure 4 The input operating parameters are passed to the one-dimensional pipe network model and the three-dimensional flow field model. These parameters include the mass flow rate, temperature, and pressure on the working fluid side, and the flue gas velocity and temperature on the flue gas side. After the three-dimensional flow field model completes the flow and heat transfer solution on the flue gas side, it outputs the spatial coordinates of the wall elements, local heat flux density, wall area, and wall temperature. Through the aforementioned geometric mapping and heat flux integration, the segmented heat absorption of each one-dimensional pipe segment of each U-shaped pipe is obtained. This generates a non-uniform heat input boundary. The heat flux integral in this step refers only to the heat contribution to the wall element, which is determined by the local heat flux density. With wall area Multiply them to collect and sum them.

[0183] After loading a non-uniform heat input boundary onto the one-dimensional pipe network model, the solution is obtained according to the pipe network connection relationships, mass conservation, momentum conservation, and energy conservation relationships. The specific calculation method has been explained in the above introduction to the pipe network connection relationships, mass conservation, momentum conservation, and energy conservation relationships. For each parallel U-shaped pipe, the inlet node pressure... Export node pressure The mass flow rate of each branch U-shaped tube is determined by the frictional pressure drop, local resistance pressure drop, and gravity pressure drop along each branch. ; for the first root U-shaped tube Each one-dimensional tube segment absorbs heat in sections. As a known heat input, the enthalpy rise of the working fluid inside the pipe and the temperature of the fluid inside the pipe are determined. and equivalent pipe wall temperature After iterative solution, the thermal response parameters inside the pipe, including the mass flow rate of each U-tube, are obtained. Each root U-shaped tube Nodal pressure of a one-dimensional pipe segment Fluid temperature inside the pipe Equivalent pipe wall temperature One-dimensional pipe section Reynolds number , working fluid Prandtl number and the heat transfer coefficient inside the pipe .

[0184] The purpose of the one-dimensional to three-dimensional backhaul is to ensure that the wall boundary of the three-dimensional flow field model no longer uses a fixed wall temperature or empirically given heat transfer conditions inside the pipe, but instead reflects the changes in mass flow rate, pressure, temperature, and heat transfer capacity inside the pipe under the current non-uniform heat load. This backhaul is not a simple conversion of the one-dimensional model results into a three-dimensional data field, but rather the assignment of the pipe thermal response parameters obtained from solving each one-dimensional pipe segment to the corresponding three-dimensional wall element according to the aforementioned three-dimensional to one-dimensional mapping relationship.

[0185] The equivalent pipe wall temperature, internal fluid temperature, and internal heat transfer coefficient obtained from the one-dimensional pipe network model are fed back to the three-dimensional flow field model using the thermal response feedback module. This is done by mapping the U-shaped pipe number to the pipe segment number... root U-shaped tube A set of wall elements for a one-dimensional pipe segment The one-dimensional solution result of this one-dimensional pipe segment, i.e., the mass flow rate. Fluid temperature inside the pipe Equivalent pipe wall temperature and the heat transfer coefficient inside the pipe Return to collection Each wall element in the model. If the 3D flow field model uses a given wall temperature, then... This serves as the wall temperature boundary for the wall unit; if in-tube convection heat transfer is adopted, for the temperature mapped to the first... root U-shaped tube The wall elements of a one-dimensional pipe segment can then be used to obtain the one-dimensional pipe network model. and As the boundary of the wall thermal response, a value is assigned to the wall element to control the segmented surface heat flux of the wall element. satisfy:

[0186]

[0187] In practice, the one-dimensional solution results can be fed back and organized into a boundary condition data table. This boundary condition data table should include at least the U-tube number. One-dimensional pipe section numbering , coordinates of the pipe section's start and end points, and the temperature of the fluid inside the pipe Equivalent pipe wall temperature and the heat transfer coefficient inside the pipe After reading the boundary condition data table, the 3D flow field model determines the flow based on the U-shaped tube number to which the wall element belongs. One-dimensional pipe section numbering Update the wall boundary.

[0188] To avoid heat flow or pipe wall temperature oscillations caused by direct and large updates of the wall boundary in adjacent calculations, a sub-relaxation factor is introduced. This technical solution performs sub-relaxation updates, convergence judgments, and result outputs for at least one of the non-uniform heat input boundary and the wall boundary through an iterative control module.

[0189] With equivalent pipe wall temperature For example, the first The equivalent pipe wall temperature boundary used for three-dimensional flow field model calculations can be expressed as:

[0190]

[0191] in, It is the sub-relaxation factor, 0 < ≤1; For the first After one round of iterative processing, the equivalent pipe wall temperature for the next round of iteration is determined. For the first The equivalent tube wall temperature before smoothing in the round of iteration. For the first The equivalent tube wall temperature that is adopted and saved after the round of iterations.

[0192] When oscillations occur in coupled calculations, they can be reduced. When the calculation process is stable, the value can be increased. For segmented heat absorption or heat transfer coefficient inside the pipe The same method can also be used for smooth updates.

[0193] During the coupled iteration process, the relative change of the maximum segmented heat absorption, the maximum equivalent pipe wall temperature change, and the overall energy conservation error can be selected as convergence criteria. Wheel and the first Relative change in maximum segmented heat absorption between wheels It can be represented as:

[0194]

[0195] Maximum equivalent pipe wall temperature change It can be represented as:

[0196]

[0197] Energy Imbalance Rate It can be represented as:

[0198]

[0199] in, and These are the first iterations in the coupled iteration process. Wheel and the first Wheel of Life root U-shaped tube The segmented heat absorption of a one-dimensional tube segment This is the minimum positive value among all one-dimensional pipe segment heat absorptions in the current coupling iteration process, used to avoid amplification of normalization error due to an excessively small denominator; and These are the first iterations in the coupled iteration process. Wheel and the first Wheel of Life root U-shaped tube The equivalent pipe wall temperature of a one-dimensional pipe segment; For the first The total heat after integrating the heat flux contributions of all wall elements in the three-dimensional flow field model. For the first The sum of heat absorbed by all one-dimensional pipe segments in a one-dimensional pipe network model; This means taking the maximum value between the total heat of the three-dimensional flow field model and the sum of the heat absorbed by each segment of the one-dimensional pipe network model under their respective reference heat conditions. and The maximum value in the equation should be equal to the maximum value in an ideal mapping. .

[0200] Indicates the first The overall energy conservation error in the wheel coupling iteration can be expressed as:

[0201]

[0202] In actual calculations, due to the existence of interpolation errors, spatial discretization errors, and wall boundary update errors, it is permissible to... It fluctuates within a preset threshold range.

[0203] The preset threshold can be set according to the accuracy requirements of the coupling calculation. In one embodiment:

[0204] The threshold for the relative change in segmented heat absorption can be taken as 10. -3 ~10 -2 ;

[0205] The threshold for relative temperature change in pipe walls can be taken as 10. -4 ~ 10 -3 ;

[0206] The energy conservation error threshold can be taken as 10. -3 ~10 -2 .

[0207] To determine whether the convergence criterion is met, i.e., when the relative change in the maximum segmental heat absorption... Maximum equivalent pipe wall temperature change and overall energy conservation error If all values ​​are less than the preset threshold, the coupled computation can be considered to have converged; otherwise, the iteration continues.

[0208] The final calculation results output after convergence include the flue gas side velocity field, flue gas side temperature field, wall temperature field, and heat flux density distribution output from the three-dimensional flow field model, as well as the mass flow rate, pressure, fluid temperature inside the pipe, equivalent pipe wall temperature, and heat transfer coefficient inside the pipe for each U-shaped tube output from the one-dimensional pipe network model. In other words, the final result is not the result of a single model, but a coupled simulation result composed of the three-dimensional flue gas side result and the one-dimensional working fluid side result of the pipe segment.

[0209] In a verification embodiment, boundary conditions were set as follows: the working fluid in the one-dimensional pipe segment was supercritical carbon dioxide; the working fluid pressure at the inlet node of the one-dimensional pipe network model was 8 MPa; the working fluid temperature at the inlet node of the one-dimensional pipe network model was 350°C; and the inlet mass flow rate was 0.6 kg / s. In the three-dimensional flow field model, the flue gas temperature at the flue gas inlet section was 600°C; and the average flue gas inlet velocity was 12 m / s.

[0210] Based on the above boundary conditions, execute Figure 1 The bidirectional coupling calculation process is shown. In each iteration, the local heat flux density and wall area of ​​the wall element are first obtained from the three-dimensional flow field model. Then, the segmented heat absorption is calculated through the one-dimensional discrete relationship and loaded into the one-dimensional pipe network model. After the one-dimensional pipe network model obtains the fluid temperature, pipe wall temperature and heat transfer coefficient in the pipe, the wall thermal response boundary is returned.

[0211] like Figure 5 As shown, with the increase of the number of global coupling iterations, the heat exchange gradually stabilizes and the energy imbalance rate gradually decreases. After 18 global coupling iterations, the relative change of the maximum segmented heat absorption, the change of the maximum equivalent pipe wall temperature, and the overall energy conservation error all meet the preset convergence criteria, indicating that the coupling process has good stability.

[0212] The coupled calculation of the 3D flow field model and the 1D pipe network model can output temperature field distribution, heat flux distribution, and residual distribution. The temperature field distribution characterizes the temperature changes on the outer wall of the U-shaped pipe and in the nearby flue gas region; the heat flux distribution characterizes the local heat absorption differences between different pipe bundles, at different axial positions, and at different circumferential positions; and the residual distribution characterizes the local deviations in wall temperature or heat flux after updates in the coupled calculation. Validation results show that, influenced by the 3D flue gas sideflow and wake effect, there is a significant temperature difference between the windward and leeward sides of the pipe bundle, with a maximum wall temperature difference of approximately 28℃; the maximum flow deviation between parallel pipe bundles reaches 11.2%. Compared with the full 3D baseline calculation results, the average error of the coupled wall temperature calculation results is approximately 2.1%, with a maximum error not exceeding 3.5%, while the calculation time is approximately 16.7% of the full 3D baseline calculation.

[0213] Building upon the aforementioned embodiments, further coupled simulations can be conducted on operating parameters such as the working fluid pressure at the inlet node of the one-dimensional pipe network model, the working fluid temperature at the inlet node of the one-dimensional pipe network model, the inlet mass flow rate, the flue gas temperature at the flue gas inlet section of the three-dimensional flow field model, and the average flow velocity at the flue gas inlet. Through batch operation, a database of the temperature field, heat flux distribution, and flow rate allocation of the shell-less U-tube heat exchanger under different operating conditions can be generated, providing a data foundation for heat exchanger structure optimization, operational safety assessment, and identification of local overheating risks.

[0214] Although the steps in the above embodiments are described in the above order, those skilled in the art will understand that in order to achieve the effect of this embodiment, different steps do not need to be executed in such an order. They can be executed simultaneously (in parallel) or in a reverse order. These simple variations are all within the protection scope of this invention.

[0215] Those skilled in the art will understand that although some embodiments described herein include certain features but not others included in other embodiments, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the claims of this invention, any of the claimed embodiments can be used in any combination.

[0216] It should be noted that the above embodiments are illustrative of the invention and not restrictive, and that those skilled in the art can devise alternative embodiments without departing from the scope of the appended claims. In the claims, the word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention can be implemented by means of hardware comprising several different elements and by means of a suitably programmed PC.

[0217] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it should be noted that the parts not covered in this invention are the same as or can be implemented using existing technology. It will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions resulting from these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A two-way coupled simulation method for heat exchangers under non-uniform thermal load conditions, characterized in that, include: A three-dimensional flow field model on the flue gas side is established to obtain wall elements including local heat flux density, wall temperature, wall area and spatial coordinates. A one-dimensional pipe network model is established, and mass, momentum and energy are conserved. The U-shaped tube number and one-dimensional tube segment number are determined based on the spatial coordinates of the wall unit. Heat flux integration is performed on the wall unit mapped to the same one-dimensional tube segment to obtain the segmented heat absorption of the one-dimensional tube segment and construct a non-uniform heat flux boundary. The non-uniform heat flux boundary is loaded onto the one-dimensional pipe network model to calculate the mass flow rate, the fluid temperature inside the pipe, the equivalent pipe wall temperature, and the heat transfer coefficient inside the pipe. The results are then fed back to the three-dimensional flow field model to update the wall boundary of the three-dimensional flow field model. The maximum segmented heat absorption relative change, the maximum equivalent pipe wall temperature change, and the overall energy conservation error are used as convergence criteria to output the final calculation results.

2. The bidirectional coupling simulation method for heat exchangers under non-uniform thermal load conditions according to claim 1, characterized in that, The three-dimensional flow field model includes a flue gas inlet region, a tube bundle flow region, a U-shaped tube outer wall region, and a flue gas outlet region. The flue gas inlet region is located at the inlet section upstream of the tube bundle flow region. The tube bundle flow region is the area where the flue gas flows around the outer wall of each U-shaped tube after entering the tube bundle, generating flow around the tubes, wake, and mutual interference between adjacent tubes. The U-shaped tube outer wall region is the outer surface of the solid wall that exchanges heat with the working fluid inside the tube. The flue gas outlet region is the discharge region located downstream of the tube bundle flow region. The wall element, including local heat flux density, wall temperature, wall area, and spatial coordinates, is obtained as follows: When discretizing the three-dimensional flow field model, the outer wall of the U-shaped tube is discretized into multiple wall elements, and each wall element records the center point coordinates of the spatial coordinates. Wall area Wall temperature and local heat flux density ; The local heat flux density Represented as: ； in, ; In the above formula, For the first Convection heat flux density of each wall element For the first The radiative heat flux density of each wall unit For equivalent emissivity, The Stefan-Boltzmann constant, For the first Flue gas temperature near each wall unit For the first The wall temperature of each wall unit.

3. The bidirectional coupling simulation method for heat exchangers under non-uniform thermal load conditions according to claim 1, characterized in that, The one-dimensional pipe network model consists of multiple parallel U-shaped pipes. The U-shaped pipes are axially discretized, and each U-shaped pipe is divided along the flow direction of the working fluid inside the pipe. One-dimensional pipe segment; The mass conservation is expressed as: ； The conservation of momentum is expressed as: ； The energy conservation is expressed as: ； in, The inlet mass flow rate of the one-dimensional pipe segment. For the first U-tube mass flow rate; and The first root U-shaped tube The pressure at the inlet and outlet nodes of a one-dimensional pipe segment. This represents the frictional pressure drop along the pipe section in this one-dimensional structure. This refers to the local resistance pressure drop in this one-dimensional pipe section caused by bends, inlets, outlets, or local components. This represents the gravity pressure drop of the one-dimensional pipe segment. and The first root U-shaped tube The specific enthalpy of the working fluid at the inlet and outlet of a one-dimensional pipe section This is a correction factor for the wall heat conduction or heat loss of the one-dimensional pipe segment. This refers to the segmented heat absorption of this one-dimensional tube section.

4. The bidirectional coupling simulation method for heat exchangers under non-uniform heat load conditions according to claim 3, characterized in that, The heat transfer coefficient inside the pipes of the one-dimensional pipe network model Based on the one-dimensional pipe section Reynolds number , working fluid Prandtl number thermal conductivity and tube inner diameter The calculation is as follows: ； ； in, For Nusselt numbers, A coefficient related to the flow state. A correction factor to account for changes in supercritical properties or the effect of pipe bending; The equivalent pipe wall temperature of a one-dimensional pipe section is calculated by back-calculating the convective heat transfer relationship inside the pipe. For the first... root U-shaped tube A one-dimensional pipe segment, equivalent pipe wall temperature The calculation expression is: ； in, This represents the heat exchange area inside the pipe corresponding to this one-dimensional pipe segment. The temperature of the fluid inside the pipe.

5. The bidirectional coupling simulation method for heat exchangers under non-uniform heat load conditions according to claim 1, characterized in that, The process of determining the U-shaped pipe number and one-dimensional pipe segment number based on the spatial coordinates of the wall unit is as follows: Establish the centerline parameters for each U-tube and calculate the shortest distance from the center point of the wall unit to the centerline parameter. If the shortest distance is less than the preset distance threshold and the shortest distance is the smallest among all U-tubes, then the number corresponding to the centerline parameter is used as the U-tube number. Based on the coordinates of the wall element along the corresponding center line The inclusion relationship with the one-dimensional pipe segment along its length determines the one-dimensional pipe segment number: each U-shaped pipe is divided into... Along the one-dimensional pipe segment, the first The range along the path of each one-dimensional pipe segment is , , The coordinates along the pipe section are the starting and ending points; if satisfy Then determine the first The wall unit belongs to the first root U-shaped tube A one-dimensional pipe segment.

6. The bidirectional coupling simulation method for heat exchangers under non-uniform thermal load conditions according to claim 1, characterized in that, The process of integrating the heat flux of wall elements mapped to the same one-dimensional pipe segment to obtain the segmented heat absorption of the one-dimensional pipe segment and constructing a non-uniform heat flux boundary includes: For the root U-shaped tube A one-dimensional pipe section, with a range along the pipe. The heat absorption of a one-dimensional tube segment is segmented. The result is obtained by multiplying the total heat absorbed by the integral over the entire travel distance: ； in, Let be the heat distribution function. For the first The total heat absorbed by the U-shaped tube For the first Total friction length of the U-shaped tube; Based on the input format of the one-dimensional pipe network model, the non-uniform heat input boundary is divided into segmented heat absorption areas. Segmented heat flow or segmented surface heat flow Transform using the following relational expression: ； ； in, The length of a one-dimensional pipe segment. This represents the heat exchange area of ​​the outer wall of a one-dimensional pipe section.

7. The bidirectional coupling simulation method for heat exchangers under non-uniform thermal load conditions according to claim 6, characterized in that, The segmented heat absorption The sum of the heat contributions of all wall elements mapped to this one-dimensional pipe segment is expressed as: ； No. Total heat absorption of the U-shaped tube The summation of heat absorption in each segment of the one-dimensional tube of the U-shaped tube yields the following result: ； in, For local heat flux density, For the wall area, To map to the root U-shaped tube A set of wall elements for a one-dimensional pipe segment.

8. The bidirectional coupling simulation method for heat exchangers under non-uniform thermal load conditions according to claim 1, characterized in that, The process of loading a non-uniform heat flux boundary onto a one-dimensional pipe network model, calculating the mass flow rate, fluid temperature inside the pipe, equivalent pipe wall temperature, and heat transfer coefficient inside the pipe, and then feeding it back to the three-dimensional flow field model to update the wall boundary of the three-dimensional model is as follows: For mapping to the root U-shaped tube A set of wall elements for a one-dimensional pipe segment The one-dimensional solution result for this one-dimensional pipe segment, i.e., the temperature of the fluid inside the pipe. Equivalent pipe wall temperature and the heat transfer coefficient inside the pipe Postback to wall unit set Each wall unit in the; If the three-dimensional flow field model adopts a given wall temperature form, then... This serves as the wall temperature boundary for the wall unit. If in-tube convection heat transfer is used, the temperature of the fluid inside the tube will be... and the heat transfer coefficient inside the pipe As the boundary of wall thermal response, the wall temperature based on the wall element. This allows for heat flow across the segmented surfaces of the wall unit. satisfy: ； The one-dimensional solution results are organized into a boundary condition data table, which includes at least the U-shaped tube number. One-dimensional pipe section numbering , coordinates of the pipe section's start and end points, and the temperature of the fluid inside the pipe Equivalent pipe wall temperature and the heat transfer coefficient inside the pipe After the 3D flow field model reads the boundary condition data table, it determines the flow based on the U-shaped tube number to which the wall element belongs. One-dimensional pipe section numbering Update the wall boundary.

9. The bidirectional coupling simulation method for heat exchangers under non-uniform thermal load conditions according to claim 1, characterized in that, The relative change of the maximum segmented heat absorption, the maximum equivalent pipe wall temperature change, and the overall energy conservation error are obtained using the following methods: No. Wheel and the first Relative change in maximum segmented heat absorption between wheels Represented as: ； Maximum equivalent pipe wall temperature change Represented as: ； Energy Imbalance Rate Represented as: ； In the above formula, and These are the first iterations in the coupled iteration process. Wheel and the first Wheel of Life root U-shaped tube The segmented heat absorption of a one-dimensional tube segment This represents the minimum positive value among all one-dimensional pipe segment heat absorptions during the current coupling iteration process; and These are the first iterations in the coupled iteration process. Wheel and the first Wheel of Life root U-shaped tube The equivalent pipe wall temperature of a one-dimensional pipe segment; For the first The total heat after integrating the heat flux contributions of all wall elements in the three-dimensional flow field model. For the first The sum of heat absorbed by all one-dimensional pipe segments in a one-dimensional pipe network model. To obtain and The maximum value in; Indicates the first The overall energy conservation error in the wheel coupling iteration is expressed as: ； When the maximum segmental heat absorption relative change Maximum equivalent pipe wall temperature change and overall energy conservation error When all values ​​are less than the preset threshold, the coupled calculation is considered to have converged, and the final calculation result is output.

10. A system for performing a two-way coupled simulation method for a heat exchanger under non-uniform thermal load conditions as described in any one of claims 1 to 9, characterized in that, The system includes: The 3D flow field modeling module is used to establish and solve the 3D flow field model on the flue gas side. The one-dimensional pipeline modeling module is used to build and solve the one-dimensional pipeline model corresponding to the U-shaped pipe. The geometric mapping module is used to determine the U-shaped tube number and the one-dimensional tube segment number based on the coordinates of the center point of the wall unit space; The heat flux integration module is used to calculate the heat contribution of the wall unit, the heat absorption of the one-dimensional pipe segment, and the total heat absorption of the U-tube. The non-uniform boundary generation module is used to generate and load one-dimensional non-uniform heat input boundaries for pipe segments; The thermal response feedback module is used to feed back the equivalent pipe wall temperature, pipe fluid temperature and pipe heat transfer coefficient obtained from the one-dimensional pipe network model to the three-dimensional flow field model. The iterative control module is used to perform sub-relaxation updates, convergence checks, and result output.

Images