CN115859851B - Calculation method for conjugate heat transfer of liquid metal coupling supercritical carbon dioxide - Google Patents
Calculation method for conjugate heat transfer of liquid metal coupling supercritical carbon dioxide Download PDFInfo
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Abstract
The invention discloses a method for calculating the conjugate heat transfer of liquid metal coupled supercritical carbon dioxide, belongs to the field of hydraulic calculation of thermal engineering of liquid metal cooling reactors, and solves the problems of poor calculation precision and difficult coupling of a heat flux model when liquid metal with low-privet turbulence heat exchange characteristics is coupled with supercritical carbon dioxide with supercritical flow heat transfer characteristics. According to the invention, the liquid metal and the supercritical carbon dioxide can be automatically distinguished, and the turbulent thermal diffusion calculation and correction of the fluid in two are respectively carried out by applying a two-equation thermal turbulent model and a turbulent Plandter number empirical model, so that a liquid metal coupling supercritical carbon dioxide high-fidelity three-dimensional conjugated heat transfer analysis platform is established. The method uses an advanced two-equation thermal turbulence model of the liquid metal to correct CFD heat transfer calculation of the liquid metal, and can use a Plandter number experimental model of turbulence to correct transcritical CFD heat transfer calculation of supercritical carbon dioxide.
Description
Technical Field
The invention belongs to the field of liquid metal cooling reactor thermal hydraulic calculation, and particularly relates to a liquid metal coupling supercritical carbon dioxide conjugate heat transfer calculation method.
Background
To meet the safety and economical requirements of the fourth generation stack, highly efficient compact supercritical carbon dioxide (S-CO 2 ) The brayton cycle was proposed for use in power conversion designs for liquid metal cooled nuclear reactors, and thus liquid metal and S-CO were studied 2 Is of great significance for guiding the design of advanced liquid metal cooling nuclear energy system. However, liquid metal and S-CO 2 Belongs to two kinds of fluid with large difference of molecular prandtl numbers (Pr), and CFD turbulent heat exchange models simulating flow heat transfer of the two kinds of fluid are also large in difference. To support liquid metal and S-CO 2 The heat exchanger design and the mastering of the enthalpy matching coupling heat exchange mechanism of the heat exchanger need to further develop a proper CFD method to conduct fine conjugated heat transfer research.
Liquid metals, such as lead (Pb), whose smaller Pr, as shown in fig. 1, means a large difference between their velocity and temperature fields, which results in the reynolds assumption, i.e., the turbulent plannd (Pr t ) A 0.85 is no longer suitable and would affect the CFD heat transfer accuracy of Pb. To solve this problem, many scholars focus on two equations k θ -ε θ Study of the model. Compared with Pr t Model=0.85, two equations k θ -ε θ Model by transporting temperature pulsation k θ Dissipation ratio epsilon θ Combining the dynamic turbulence model and the thermal turbulence model to transport and calculate the turbulent planter number Pr of the liquid metal t The CFD heat transfer calculation accuracy of Pb is expected to be improved.
S-CO in a quasi-critical zone 2 The physical properties change drastically, and the Pr is high Pr fluid, as shown in FIG. 2 t Model=0.85 affects its flow heat transfer calculation in the critical section; whereas S-CO is far from critical section 2 The physical property change is smooth, the flowing state is gradually classified into the category of the conventional fluid (Pr-1), pr t The =0.85 model can generally meet its flow heat transfer calculation in the far-from critical region. To meet S-CO 2 Is a transcritical flow heat transfer calculation of (1), many scholars developed a turbulent planner number Pr based on different local turbulent parameter decisions t Relational expression for improving S-CO in different temperature areas 2 Flow heat transfer CFD calculation.
FIG. 3 is Pb and S-CO 2 Conjugate heat transfer Pr in a printed Circuit Board Heat exchanger (PCHE) heat exchange channel t Schematic change. Pb with low Pr and S-CO with high Pr 2 Heat transfer coupled in large temperature differential, high heat flow heat exchange channelsThe process has dissimilation phenomenon (Pb is mainly molecular heat conduction, S-CO 2 Based on turbulent thermal diffusion), although the above two equations heat turbulent k θ -ε θ Model and Pr t Empirical relationships have been developed for liquid metal and S-CO, respectively 2 But due to the complexity of differential numerical form, boundary condition and the like of the two-equation thermal turbulence model and the physical property difference of liquid metal and supercritical fluid, the traditional commercial CFD software is difficult to develop and simultaneously couples the two-equation thermal turbulence k θ -ε θ Model and Pr t Empirical relationship of liquid metal to S-CO 2 Therefore, the establishment of a liquid metal two-equation-based thermal turbulence model and S-CO is urgent 2 A high-fidelity refined three-dimensional conjugate heat transfer numerical analysis method for liquid metal and supercritical carbon dioxide corrected by a turbulent flow Plandter number empirical model.
Disclosure of Invention
The invention aims to provide a calculation method for coupling supercritical carbon dioxide conjugate heat transfer by liquid metal, which aims to solve the problems of poor calculation precision and difficult coupling of a heat flux model when the liquid metal with low-pride turbulent heat transfer characteristics is coupled with the supercritical carbon dioxide conjugate heat transfer with supercritical flow heat transfer characteristics.
The technical scheme of the invention is as follows: a calculation method for liquid metal coupling supercritical carbon dioxide conjugate heat transfer comprises the following steps:
step 1: in OpenFOAM, a user-defined conjugate heat transfer solver is established based on a built-in fluid-solid conjugate heat transfer solver;
step 2: in the user-defined conjugate heat transfer solver established in the step 1, a turbulent flow thermal diffusion coefficient variable alpha is established t And transporting a temperature pulsation variable k that calculates the turbulent thermal diffusion coefficient θ Dissipation ratio variable ε θ The method comprises the steps of carrying out a first treatment on the surface of the Calling temperature-pressure and physical variables in a thermophysical function library, including temperature T, pressure P and fluid density ρ f Specific heat capacity C of fluid pf Coefficient of thermal conductivity lambda of fluid f Kinematic viscosity v of fluid molecules f Density ρ of solid s Specific heat capacity C of solid ps And solid thermal conductivity lambda s The method comprises the steps of carrying out a first treatment on the surface of the Invoking speed and turbulence variables in a turbulence function library, including speed u i Turbulent motion viscosity v t And calculating turbulence energy k and dissipation rate epsilon of the turbulence kinematic viscosity by transport;
step 3: adding physical property judgment, adding a supercritical carbon dioxide energy conservation equation, and adding a liquid metal energy conservation equation and a two-equation thermal turbulence k θ -ε θ The model comprises the following specific steps:
step 3-1: adding physical property judgment conditions in an original energy equation EEqn.H file, wherein the judgment conditions are as follows: traversing the density values represented by the fluid domain grids, and judging whether the maximum density value in the fluid domain grids is smaller than the minimum density value of the current calculation step of the liquid metal;
step 3-2: if the maximum density value in the fluid domain grid is smaller than the minimum density value of the current calculation step of the liquid metal, calculating a supercritical carbon dioxide energy conservation equation, defining a turbulent flow Plantt number empirical model suitable for supercritical carbon dioxide transcritical heat transfer calculation, and adding the supercritical carbon dioxide energy conservation equation;
step 3-3: if the maximum density value in the fluid domain grid is greater than the minimum density value of the current calculation step of the liquid metal, calculating a liquid metal energy conservation equation, adding the liquid metal energy conservation equation, and adding a liquid metal turbulence thermal diffusion coefficient alpha for calculating t Two equations k of (2) θ -ε θ A thermal turbulence model program segment;
step 4: adding two equations k for calculating liquid metal θ -ε θ The related function head file of the thermal turbulence model is added into the main program file of the user-defined conjugate heat transfer solver established in the step 1;
step 5: according to the actual calculation problem, applying proper OpenFOAM standard physical conditions to the fluid and solid thermal physical variables called in the step 2 in a fluid physical dictionary file under a user calculation example folder; specifying turbulence models required to be used for each fluid in a fluid turbulence model dictionary file under a user calculation folder; designating the size and direction of gravity in a gravity dictionary file under a user's example folder;
step 6: and (3) applying proper numerical simulation boundary conditions to the physical quantities called and established in the step (2) under the initial folder of the user computing example, wherein the specific steps are as follows:
step 6-1: physical quantities for the following calls: temperature T, pressure P, speed u i Turbulent motion viscosity v t Turbulence energy k and dissipation ratio epsilon or specific dissipation ratio omega and turbulence heat diffusion coefficient alpha thereof t Invoking a standard OpenFOAM boundary condition;
step 6-2: for temperature pulsation k on fluid-solid coupling surface θ Dissipation ratio epsilon θ Applying a zero fixed gradient value boundary condition of an OpenFOAM standard;
step 7: setting a calculation step length, output control, a numerical discrete format and a numerical solution algorithm in a calculation control dictionary file, a numerical discrete format dictionary file and a numerical solution dictionary file under a user calculation example folder respectively;
step 8: reading a fluid domain grid model, respectively solving a mass conservation equation (1), a momentum conservation equation (2) and a supercritical carbon dioxide fluid energy conservation equation (3) or a liquid metal fluid energy conservation equation (4) of the liquid metal fluid and the supercritical carbon dioxide fluid by adopting an OpenFOAM built-in PIMPLE algorithm,
the mass conservation equation (1) is:
momentum conservation equation (2) is:
the supercritical carbon dioxide fluid energy conservation equation (3) is:
the liquid metal fluid energy conservation equation (4) is:
wherein:
h- -the specific enthalpy of the liquid metal;
k is the specific kinetic energy of the liquid metal;
g i -gravitational acceleration;
the method comprises the following specific steps:
reading physical properties of the fluid domain, performing judgment calculation according to the step 3-1, and performing the following steps a) -c) if a supercritical carbon dioxide energy conservation equation is calculated:
a) Solving a momentum conservation equation (2), and updating a speed field;
b) Combining the updated speed field of the step a) and the turbulent flow Plandter number empirical model suitable for supercritical carbon dioxide transcritical heat transfer calculation, which is described in the step 3-2, iteratively solving a supercritical carbon dioxide fluid energy conservation equation (3), and updating a temperature field and fluid thermophysical properties;
c) Based on the updated speed field of the step a) and the updated fluid thermophysical property of the step b), carrying out iterative solution on a pressure poisson equation which is derived by combining a fluid mass conservation equation (1) and a fluid momentum conservation equation (2) under the PIMPLE algorithm, judging whether the set PIMPLE iteration number is reached, if so, judging that the current iteration step PIMPLE pressure-speed coupling iterative solution is finished, and carrying out the next step after updating the supercritical carbon dioxide pressure field and the speed field;
if the liquid metal energy conservation equation is calculated, the following steps a) -d) are performed:
a) Solving a momentum conservation equation (2), and updating a speed field;
b) Iteratively solving a liquid metal fluid energy conservation equation (4) by combining the updated speed field in the step a), and updating a temperature field and fluid thermophysical properties;
c) IterationSolving two equations k of liquid metal turbulence thermal diffusion coefficient θ -ε θ Thermal turbulence model for iteratively solving temperature pulsation k θ And dissipation ratio epsilon θ Differential transport equation and updating the liquid metal turbulence thermal diffusion coefficient alpha t ；
d) Based on the updated speed field in the step a) and the updated fluid thermophysical property in the step b), carrying out iterative solution on a pressure poisson equation which is derived by combining a fluid mass conservation equation (1) and a fluid momentum conservation equation (2) under the PIMPLE algorithm, judging whether the set PIMPLE iteration number is reached, if so, judging that the current iteration step PIMPLE pressure-speed coupling iterative solution is finished, and carrying out the next step after updating the liquid metal speed field and the liquid metal pressure field;
step 9: according to the turbulence model set in the step 5, respectively and iteratively solving turbulence energy k and dissipation rate epsilon or specific dissipation rate omega transport equation of the liquid metal fluid and the supercritical carbon dioxide fluid to a set calculation residual error, and updating turbulence kinematic viscosity v of the two fluids t ；
Step 10: judging whether all the fluid domains are calculated, if not, jumping to the step 8 to continue calculation; if the calculation is finished, the next step is carried out;
step 11: iteratively solving an energy conservation equation (5) of the solid domain to calculate residual errors based on the fluid temperature field information and the fluid-solid coupling surface temperature information updated in the current iteration step, updating solid physical property values under a user dictionary file based on the solid domain temperature field updated in the current iteration step, judging whether all solid domains are calculated, and if so, performing the next step;
the energy conservation equation (5) for the solid domain is:
step 12: judging a fluid domain mass conservation equation (1), a momentum conservation equation (2), a supercritical carbon dioxide fluid energy conservation equation (3) or a liquid metal fluid energy conservation equation (4) updated in the step 8, and internally arranging an OpenFOAMTurbulence energy k of turbulence model and dissipation rate epsilon or specific dissipation rate omega transportation equation thereof, and temperature pulsation k of two-equation thermal turbulence model θ Dissipation ratio epsilon θ Whether the residual errors of the transport equation and the solid domain energy conservation equation (5) reach a set external residual error threshold value or not, and if so, judging that the external iteration converges; if not, updating u on the wall boundary grid according to the boundary conditions of the physical quantities set in the step 6 i 、P、T、ν t K, ε or ω, α t 、k θ 、ε θ And (3) numerical value, and repeating the steps 8-12 until the residual error threshold set by the outer iteration is reached.
After each physical quantity of the final fluid domain and the solid domain reaches the set external iteration convergence condition, two equations k based on advanced liquid metal can be obtained θ -ε θ The high-fidelity conjugate heat transfer characteristic of the supercritical carbon dioxide is coupled by the liquid metal of the thermal turbulence model and the corrected supercritical carbon dioxide transcritical turbulence Plantain number empirical model, and researches on the reinforced heat exchange rule, the enthalpy matching mechanism, the heat transfer dissimilarity and the like of the liquid metal and the supercritical carbon dioxide can be carried out based on the numerical calculation method.
The invention provides a calculation method suitable for coupling heat transfer of liquid metal with low Plandter number turbulence heat transfer characteristics and carbon dioxide with supercritical convection heat transfer characteristics in a heat exchanger solid channel, which can automatically distinguish the liquid metal from supercritical carbon dioxide and respectively apply a two-equation thermal turbulence model and a turbulence Plandter number experience model to calculate and correct turbulence thermal diffusion of two-medium fluid so as to establish a liquid metal coupling supercritical carbon dioxide high-fidelity three-dimensional conjugated heat transfer analysis platform. According to the method, an advanced two-equation thermal turbulence model of the liquid metal is used for correcting CFD heat transfer calculation of the liquid metal, and meanwhile, a Plantt number experimental model of turbulence can be used for correcting trans-critical CFD heat transfer calculation of supercritical carbon dioxide, so that a three-dimensional high-fidelity conjugate heat transfer analysis calculation method is provided for researching the problems of heat enthalpy matching heat transfer mechanism, enhanced heat exchange technology, heat exchanger structure optimization design and the like between the liquid metal and the supercritical carbon dioxide in a large temperature difference and high heat flow environment in a reactor.
Compared with the prior art, the invention has the following advantages:
1. the invention introduces the two equations k of the liquid metal with strong theory, higher theory precision and simple theory boundary into the conjugate heat transfer calculation of the liquid metal coupling supercritical carbon dioxide θ -ε θ The thermal turbulence model is based on which the liquid metal coupling supercritical carbon dioxide conjugate heat transfer problem is calculated, and meanwhile, the richer liquid metal low Plantain number turbulence heat transfer behavior is obtained.
2. According to the invention, in the conjugate heat transfer calculation of the supercritical carbon dioxide by liquid metal coupling, the supercritical carbon dioxide turbulence Plantt number empirical model with high flexibility and improved calculation accuracy is introduced, so that the numerical heat transfer result of supercritical carbon dioxide transcritical calculation can be better improved, and the supercritical convection heat transfer characteristic of carbon dioxide is obtained.
3. The user-defined conjugate heat transfer solver established by the method reserves a function of calling the OpenFOAM built-in turbulence model, can call the same or different turbulence models according to the complexity of actual calculation flow geometry, the requirements of calculation resources and the like to respectively obtain the turbulence flow behavior of the liquid metal and the supercritical carbon dioxide, can conveniently and comprehensively utilize the same or different turbulence models, and respectively combine the liquid metal two-equation thermal turbulence transport model and the supercritical carbon dioxide turbulence Plandter number empirical model to improve the conjugate heat transfer calculation result of the liquid metal coupled supercritical carbon dioxide.
4. The method is a secondary development and application of a built-in conjugate heat transfer solver which is embedded in open source CFD software together with an advanced liquid metal thermal turbulence model and a supercritical carbon dioxide turbulence Plandter number empirical model, and can provide thought for developing a high-fidelity numerical method suitable for researching liquid metal and supercritical fluid flow-solid conjugate heat transfer characteristics.
Drawings
FIG. 1 is a schematic diagram of Pr-T distribution of Pb;
FIG. 2 is a schematic diagram of Pr-T distribution of S-CO 2;
FIG. 3 is a schematic view ofPb and S-CO 2 Conjugate heat transfer Pr in PCHE heat exchange channel t A variation schematic;
FIG. 4 is a schematic diagram of a liquid metal coupled supercritical carbon dioxide conjugated heat transfer transport mechanism according to the method of the present invention;
FIG. 5 is a computational flow chart of the method of the present invention;
FIG. 6 is a schematic diagram of a geometric model of an embodiment of the present invention;
FIG. 7 is a diagram of a mesh model according to an embodiment of the present invention;
FIG. 8 is a graph showing a calculated temperature profile according to an embodiment of the present invention;
FIG. 9 is a velocity profile calculated in accordance with an embodiment of the present invention;
FIG. 10 is a graph showing a calculated pressure profile according to an embodiment of the present invention;
FIG. 11 is a graph showing calculated density profiles according to an embodiment of the present invention;
FIG. 12 is a graph of calculated turbulence energy distribution for an embodiment of the present invention;
FIG. 13 is a graph of calculated turbulence energy versus dissipation ratio for an embodiment of the present invention;
FIG. 14 is a graph showing calculated turbulent kinematic viscosity profiles according to an embodiment of the present invention;
FIG. 15 is a graph showing calculated temperature pulsation profiles according to an embodiment of the present invention;
FIG. 16 is a graph showing calculated temperature pulsation dissipation ratio profiles according to embodiments of the present invention;
FIG. 17 is a graph showing calculated turbulent thermal diffusivity profiles according to an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The conjugated heat transfer transport mechanism of the liquid metal coupling supercritical carbon dioxide is shown in figure 4. According to the method, the same or different OpenFOAM built-in turbulence models can be called as required to respectively calculate the turbulence fields of the liquid metal and the supercritical carbon dioxide, and simultaneously, two-equation thermal turbulence model is introduced to correct the turbulence thermal diffusion calculation of the liquid metal and the turbulence thermal diffusion calculation of the supercritical carbon dioxide is introduced to correct the turbulence Plandter number model. The process can fully consider the transport characteristics of heat transfer dissimilarity of the fluid with large difference between two physical properties of liquid metal and supercritical carbon dioxide. A computational flow chart of the method of the present invention is shown in fig. 5.
Example 1,
The process of calculating the coupling heat transfer of liquid metal and supercritical carbon dioxide in a straight channel of a printed circuit board heat exchanger (PCHE) is analyzed, in the embodiment, the hot fluid is liquid lead bismuth with outlet back pressure of 0.1MPa, the cold fluid is supercritical carbon dioxide with outlet back pressure of 15MPa, the solid domain is low carbon steel, the inlet temperature of the hot fluid is 773.15K, and the inlet temperature of the cold fluid is 473.15K. Fig. 6 is a schematic diagram of a geometric model of the present embodiment, and fig. 7 is a schematic diagram of a mesh model of the present embodiment. The calculation method comprises the following steps:
step 1: in OpenFOAM, a user-defined conjugate heat transfer solver is built based on a built-in fluid-solid conjugate heat transfer solver.
Step 2: in the user-defined conjugate heat transfer solver established in the step 1, a turbulent flow thermal diffusion coefficient variable alpha is established t And transporting a temperature pulsation variable k that calculates the turbulent thermal diffusion coefficient θ Dissipation ratio variable ε θ The method comprises the steps of carrying out a first treatment on the surface of the Calling temperature-pressure and physical variables in a thermophysical function library, including temperature T, pressure P and fluid density ρ f Specific heat capacity C of fluid pf Coefficient of thermal conductivity lambda of fluid f Kinematic viscosity v of fluid molecules f Density ρ of solid s Specific heat capacity C of solid ps And solid thermal conductivity lambda s The method comprises the steps of carrying out a first treatment on the surface of the Invoking speed and turbulence variables in a turbulence function library, including speed u i Turbulent motion viscosity v t And calculating turbulence energy k and dissipation rate epsilon of the turbulence motion viscosity through transportation.
Step 3: adding physical property judgment, adding a supercritical carbon dioxide energy conservation equation, and adding a liquid metal energy conservation equation and a two-equation thermal turbulence k θ -ε θ The model comprises the following specific steps:
step 3-1: adding physical property judgment conditions in an original energy equation EEqn.H file, wherein the judgment conditions are as follows: traversing the density values represented by the fluid domain grids, and judging whether the maximum density value in the fluid domain grids is smaller than the minimum density value of the current calculation step of the liquid metal;
step 3-2: if the maximum density value in the fluid domain grid is smaller than the minimum density value of the current calculation step of the liquid metal, calculating a supercritical carbon dioxide energy conservation equation, defining a turbulent flow Plantt number empirical model suitable for supercritical carbon dioxide transcritical heat transfer calculation, and adding the supercritical carbon dioxide energy conservation equation;
step 3-3: if the maximum density value in the fluid domain grid is greater than the minimum density value of the current calculation step of the liquid metal, calculating a liquid metal energy conservation equation, adding the liquid metal energy conservation equation, and adding a liquid metal turbulence thermal diffusion coefficient alpha for calculating t Two equations k of (2) θ -ε θ A thermal turbulence model program segment.
Step 4: adding two equations k for calculating liquid metal θ -ε θ And (3) the relevant wall function head file of the thermal turbulence model is added into the main program file of the user-defined conjugate heat transfer solver established in the step (1).
The step 1-4 completes the secondary development of the user-defined conjugate heat transfer solver for the liquid metal and supercritical carbon dioxide two-fluid multi-flux model differentiated calculation.
Step 5: according to the actual calculation problem, applying proper OpenFOAM standard physical conditions to the fluid and solid thermal physical variables called in the step 2 in a fluid physical dictionary file under a user calculation example folder, and in the embodiment, inputting physical relational expressions of liquid metal, supercritical carbon dioxide and solid materials according to temperature change by using a polynomial function, wherein physical data of the supercritical carbon dioxide is derived from an NIST database and physical data of the liquid lead bismuth is derived from a lead bismuth physical handbook; specifying turbulence models required to be used for each fluid in a fluid turbulence model dictionary file under a user calculation example folder, wherein in the embodiment, SST k-omega turbulence models are respectively specified in the user turbulence model dictionary file for liquid metal and supercritical carbon dioxide fluid; the size and direction of gravity is specified in a gravity dictionary file under the user's example folder.
Step 6: applying proper numerical simulation boundary conditions to each physical variable called and established in the step 2 under the initial folder of the user computing example, as shown in the table 1, and specifically comprising the following steps:
step 6-1: the following physical variables were measured: temperature T, pressure P, speed u i Turbulent motion viscosity v t Turbulent energy k and specific dissipation ratio omega and turbulent thermal diffusion coefficient alpha thereof t Invoking standard OpenFOAM wall boundary conditions;
step 6-2: for temperature pulsation k on fluid-solid coupling surface θ Dissipation ratio epsilon θ A zero fixed gradient value boundary condition of the OpenFOAM standard is applied.
TABLE 1
Step 7: and setting a calculation step length, output control, a numerical discrete format and a numerical solution algorithm in a calculation control dictionary file, a numerical discrete format dictionary file and a numerical solution dictionary file under a user calculation example folder respectively.
The steps 5-7 complete the main pretreatment flow needed by calculation.
In this embodiment, before step 8 is performed, the setting content of the rest of the preprocessing in the calculation flow shown in fig. 5 is to be completed, including: 1) Dividing high-quality mesh grids by adopting mesh division software including but not limited to GAMBIT, generating an OpenFOAM identifiable mesh file polyMesh by adopting a mesh conversion tool, wherein a mesh schematic diagram generated in the embodiment is shown in fig. 7; 2) Specifying a streaming solids type in an area parameter dictionary file under a user calculation example folder; 3) Designating a fluid domain and a solid domain time item in a numerical discrete format dictionary file under a user calculation example folder as a steady-state format, wherein a gradient item is in a Gaussian linear format, a stream item is in a bounded Gaussian windward format, and a Laplace item is in a Gaussian linear correction format; 4) The pressure of a designated fluid domain in a fluid numerical solution format dictionary file under a user calculation example folder is solved by adopting an algebraic multiple grid method (GAMG), and the rest physical quantities are solved by adopting a stable precondition conjugation method (PBiCG); 5) And designating solid specific enthalpy in the solid numerical solution format dictionary file under the user calculation example folder, and solving by adopting a symmetrical conjugation method (PCG).
After the above steps are completed, the user-defined conjugate heat transfer solver compiled in step 4 is adopted to perform conjugate heat transfer calculation on the liquid metal and the supercritical carbon dioxide PCHE in this embodiment, that is, implement the conjugate heat transfer solving calculation process in the calculation flow shown in fig. 5, that is, implement steps 8-12.
Step 8: reading a fluid domain grid model, respectively solving a mass conservation equation (1), a momentum conservation equation (2) and a supercritical carbon dioxide fluid energy conservation equation (3) or a liquid metal fluid energy conservation equation (4) of the liquid metal fluid and the supercritical carbon dioxide fluid by adopting an OpenFOAM built-in PIMPLE algorithm,
the mass conservation equation (1) is:
momentum conservation equation (2) is:
the supercritical carbon dioxide fluid energy conservation equation (3) is:
the liquid metal fluid energy conservation equation (4) is:
wherein:
h- -the specific enthalpy of the liquid metal;
k is the specific kinetic energy of the liquid metal;
g i -gravitational acceleration;
the method comprises the following specific steps:
reading physical properties of the fluid domain, performing judgment calculation according to the step 3-1, and performing the following steps a) -c) if a supercritical carbon dioxide energy conservation equation is calculated:
a) Solving a momentum conservation equation (2), and updating a speed field;
b) Combining the updated speed field of the step a) and the turbulent flow Plandter number empirical model suitable for supercritical carbon dioxide transcritical heat transfer calculation, which is described in the step 3-2, iteratively solving a supercritical carbon dioxide fluid energy conservation equation (3), and updating a temperature field and fluid thermophysical properties;
c) Based on the updated speed field of the step a) and the updated fluid thermophysical property of the step b), carrying out iterative solution on a pressure poisson equation which is derived by combining a fluid mass conservation equation (1) and a fluid momentum conservation equation (2) under the PIMPLE algorithm, judging whether the set PIMPLE iteration number is reached, if so, judging that the current iteration step PIMPLE pressure-speed coupling iterative solution is finished, and carrying out the next step after updating the supercritical carbon dioxide pressure field and the speed field;
if the liquid metal energy conservation equation is calculated, the following steps a) -d) are performed:
a) Solving a momentum conservation equation (2), and updating a speed field;
b) Iteratively solving a liquid metal fluid energy conservation equation (4) by combining the updated speed field in the step a), and updating a temperature field and fluid thermophysical properties;
c) Two equations k for iteratively solving liquid metal turbulence thermal diffusion coefficient θ -ε θ Thermal turbulence model for iteratively solving temperature pulsation k θ And dissipation ratio epsilon θ Differential transport equation and updating the liquid metal turbulence thermal diffusion coefficient alpha t ；
d) And (3) based on the updated speed field in the step a) and the updated fluid temperature field and thermophysical properties in the step b), carrying out iterative solution on a pressure poisson equation which is derived by combining a fluid mass conservation equation (1) and a fluid momentum conservation equation (2) under the PIMPLE algorithm, judging whether the set PIMPLE iteration times are reached, if so, judging that the current iteration step PIMPLE pressure-speed coupling iterative solution is finished, and carrying out the next step after updating the liquid metal speed field and the liquid metal pressure field.
Two equations k for liquid metal θ -ε θ The thermal turbulence model is illustrated as follows:
wherein:
f d2 ＝1/C d2 (C ε2 f ε -1)[1-exp(-R ε /5.7)] 2 -a temperature pulsation dissipative damping function;
f ε ＝1-0.3exp[-(R t /6.5) 2 ]-a turbulent energy dissipation damping function;
The liquid metal turbulent thermal diffusivity model is illustrated as follows:
α t ＝C λ f λ kτ u
wherein:
C λ 、C m 、Pr t∞ -model constants;
τ u =k/epsilon-dynamic time scale;
R＝τ θ /τ u mixing time scale, τ θ Is k θ /ε θ -thermal turbulence time scale;
R t is the turbulence Reynolds number, k 2 /(νε)；R ε For the characteristic Reynolds number δu ε V, delta is the distance from the wall;
pr—the molecular Plantt number of the fluid.
Step 9: according to the turbulence model set in the step 5, respectively and iteratively solving the turbulence energy k and specific dissipation rate omega transport equation of the liquid metal fluid and the supercritical carbon dioxide fluid to set residual errors, and updating the turbulence kinematic viscosity v of the two fluids t 。
Step 10: judging whether all the fluid domains are calculated, if not, jumping to the step 8 to continue calculation; if the calculation is completed, the next step is performed.
Step 11: iteratively solving an energy conservation equation (5) of the solid domain to an iteration residual error based on the fluid temperature field information and the fluid-solid coupling surface temperature information updated in the current iteration step, updating solid physical property values under a user dictionary file based on the solid domain temperature field updated in the current iteration step, judging whether all solid domains are calculated, and if so, carrying out the next step;
the energy conservation equation (5) for the solid domain is:
step 12: judging a fluid domain mass conservation equation (1), a momentum conservation equation (2), a supercritical carbon dioxide fluid energy conservation equation (3) or a liquid metal fluid energy conservation equation (4), an OpenFOAM built-in turbulence model turbulence energy k, a dissipation rate epsilon thereof or a specific dissipation rate omega transport equation thereof, and a two-equation thermal turbulence model temperature pulsation k after being updated in the step 8 θ Dissipation ratio epsilon θ Whether the residual errors of the transport equation and the solid domain energy conservation equation (5) reach a set external residual error threshold value or not, and if so, judging that the external iteration converges; if not, updating u on the wall boundary grid according to the boundary conditions of the physical quantities set in the step 6 i 、P、T、ν t K, ε or ω, α t 、k θ 、ε θ And (3) numerical value, and repeating the steps 8-12 until the residual error threshold set by the outer iteration is reached.
After the calculation is finished, the calculated result is subjected to post-processing by using open source post-processing software ParaView, and a key parameter distribution result shown in figures 8-17 is obtained. In fig. 8-17, the upper semicircle is the flow channel of supercritical carbon dioxide fluid, the lower semicircle is the flow channel of liquid metal fluid, and the rest area is the PCHE solid area. Fig. 8-14 are schematic diagrams of temperature, speed, pressure, density, turbulence energy and turbulence energy to dissipation ratio distribution obtained in the calculation of this embodiment, which indicate that the calculation method of the present invention can obtain typical coupling conjugate heat transfer characteristics of liquid metal and supercritical carbon dioxide. Fig. 15-17 are schematic diagrams of the liquid metal temperature pulsation, the temperature pulsation dissipation rate and the turbulence thermal diffusion coefficient distribution obtained in the calculation of the present embodiment, which show that the calculation method of the present invention can additionally obtain the low planter number turbulence heat exchange characteristic of the liquid metal after the two equation thermal turbulence model of the liquid metal is coupled. The calculation method of the invention introduces a turbulent flow prandtl number empirical model to calculate the supercritical convection heat transfer characteristic of supercritical carbon dioxide, so that no supercritical carbon dioxide temperature pulsation, no temperature pulsation dissipation rate and no turbulent flow thermal diffusion coefficient distribution are observed in the supercritical carbon dioxide flow channel in fig. 15-17, and the calculation method of the invention realizes the coupling application of two independent heat flux models (a liquid metal two-equation heat turbulence model and a supercritical carbon dioxide turbulent flow prandtl number empirical model) in the calculation of the conjugate heat transfer problem of the liquid metal with low prandtl number turbulent flow heat transfer characteristic and the supercritical carbon dioxide with supercritical convection heat transfer characteristic.
The invention develops a high-fidelity numerical simulation calculation method suitable for the research of the double-fluid coupling conjugate heat transfer of liquid metal and supercritical carbon dioxide, and can provide a proper numerical calculation method for the novel thermodynamic hydraulic design of a liquid metal cooling reactor heat exchanger, the basic scientific problems of dissimilarisation and enthalpy matching of the heat transfer of the liquid metal and the supercritical fluid, and the reinforced heat exchange technology of the liquid metal and the supercritical fluid.
The description of the embodiments of the invention is merely an exemplification of the manner in which the inventive concepts may be implemented, and the non-detailed description of the invention will be presented in part to those skilled in the art.
Claims (1)
1. The calculation method of the conjugate heat transfer of the liquid metal coupling supercritical carbon dioxide is characterized by comprising the following steps of:
step 1: in OpenFOAM, a user-defined conjugate heat transfer solver is established based on a built-in fluid-solid conjugate heat transfer solver;
step 2: in the user-defined conjugate heat transfer solver established in the step 1, a turbulent flow thermal diffusion coefficient variable alpha is established t And transporting a temperature pulsation variable k that calculates the turbulent thermal diffusion coefficient θ Dissipation ratio variable ε θ The method comprises the steps of carrying out a first treatment on the surface of the Calling temperature-pressure and physical variables in a thermophysical function library, including temperature T, pressure P and fluid density ρ f Specific heat capacity C of fluid pf Coefficient of thermal conductivity lambda of fluid f Kinematic viscosity v of fluid molecules f Density ρ of solid s Specific heat capacity C of solid ps And solid thermal conductivity lambda s The method comprises the steps of carrying out a first treatment on the surface of the Invoking speed and turbulence variables in a turbulence function library, including speed u i Turbulent motion viscosity v t And calculating turbulence energy k and dissipation rate epsilon of the turbulence kinematic viscosity by transport;
step 3: adding physical property judgment, adding a supercritical carbon dioxide energy conservation equation, and adding a liquid metal energy conservation equation and a two-equation thermal turbulence k θ -ε θ The model comprises the following specific steps:
step 3-1: adding physical property judgment conditions in an original energy equation EEqn.H file, wherein the judgment conditions are as follows: traversing the density values represented by the fluid domain grids, and judging whether the maximum density value in the fluid domain grids is smaller than the minimum density value of the current calculation step of the liquid metal;
step 3-2: if the maximum density value in the fluid domain grid is smaller than the minimum density value of the current calculation step of the liquid metal, calculating a supercritical carbon dioxide energy conservation equation, defining a turbulent flow Plantt number empirical model suitable for supercritical carbon dioxide transcritical heat transfer calculation, and adding the supercritical carbon dioxide energy conservation equation;
step 3-3: if the maximum density value in the fluid domain grid is greater than the minimum density value of the current calculation step of the liquid metal, calculating a liquid metal energy conservation equation, adding the liquid metal energy conservation equation, and adding a liquid metal turbulence thermal diffusion coefficient alpha for calculating t Two equations k of (2) θ -ε θ A thermal turbulence model program segment;
step 4: adding two equations k for calculating liquid metal θ -ε θ The related function head file of the thermal turbulence model is added into the main program file of the user-defined conjugate heat transfer solver established in the step 1;
step 5: according to the actual calculation problem, applying proper OpenFOAM standard physical conditions to the fluid and solid thermal physical variables called in the step 2 in a fluid physical dictionary file under a user calculation example folder; specifying turbulence models required to be used for each fluid in a fluid turbulence model dictionary file under a user calculation folder; designating the size and direction of gravity in a gravity dictionary file under a user's example folder;
step 6: and (3) applying proper numerical simulation boundary conditions to the physical quantities called and established in the step (2) under the initial folder of the user computing example, wherein the specific steps are as follows:
step 6-1: physical quantities for the following calls: temperature T, pressure P, speed u i Turbulent motion viscosity v t Turbulence energy k and dissipation ratio epsilon or specific dissipation ratio omega and turbulence heat diffusion coefficient alpha thereof t Invoking a standard OpenFOAM boundary condition;
step 6-2: for temperature pulsation k on fluid-solid coupling surface θ Dissipation ratio epsilon θ Applying a zero fixed gradient value boundary condition of an OpenFOAM standard;
step 7: setting a calculation step length, output control, a numerical discrete format and a numerical solution algorithm in a calculation control dictionary file, a numerical discrete format dictionary file and a numerical solution dictionary file under a user calculation example folder respectively;
step 8: reading a fluid domain grid model, respectively solving a mass conservation equation (1), a momentum conservation equation (2) and a supercritical carbon dioxide fluid energy conservation equation (3) or a liquid metal fluid energy conservation equation (4) of the liquid metal fluid and the supercritical carbon dioxide fluid by adopting an OpenFOAM built-in PIMPLE algorithm,
the mass conservation equation (1) is:
momentum conservation equation (2) is:
the supercritical carbon dioxide fluid energy conservation equation (3) is:
the liquid metal fluid energy conservation equation (4) is:
wherein:
h- -the specific enthalpy of the liquid metal;
k is the specific kinetic energy of the liquid metal;
g i -gravitational acceleration;
the method comprises the following specific steps:
reading physical properties of the fluid domain, performing judgment calculation according to the step 3-1, and performing the following steps a) -c) if a supercritical carbon dioxide energy conservation equation is calculated:
a) Solving a momentum conservation equation (2), and updating a speed field;
b) Combining the updated speed field of the step a) and the turbulent flow Plandter number empirical model suitable for supercritical carbon dioxide transcritical heat transfer calculation, which is described in the step 3-2, iteratively solving a supercritical carbon dioxide fluid energy conservation equation (3), and updating a temperature field and fluid thermophysical properties;
c) Based on the updated speed field of the step a) and the updated fluid thermophysical property of the step b), carrying out iterative solution on a pressure poisson equation which is derived by combining a fluid mass conservation equation (1) and a fluid momentum conservation equation (2) under the PIMPLE algorithm, judging whether the set PIMPLE iteration number is reached, if so, judging that the current iteration step PIMPLE pressure-speed coupling iterative solution is finished, and carrying out the next step after updating the supercritical carbon dioxide pressure field and the speed field;
if the liquid metal energy conservation equation is calculated, the following steps a) -d) are performed:
a) Solving a momentum conservation equation (2), and updating a speed field;
b) Iteratively solving a liquid metal fluid energy conservation equation (4) by combining the updated speed field in the step a), and updating a temperature field and fluid thermophysical properties;
c) Two equations k for iteratively solving liquid metal turbulence thermal diffusion coefficient θ -ε θ Thermal turbulence model for iteratively solving temperature pulsation k θ And dissipation ratio epsilon θ Differential transport equation and updating the liquid metal turbulence thermal diffusion coefficient alpha t ；
d) Based on the updated speed field in the step a) and the updated fluid thermophysical property in the step b), carrying out iterative solution on a pressure poisson equation which is derived by combining a fluid mass conservation equation (1) and a fluid momentum conservation equation (2) under the PIMPLE algorithm, judging whether the set PIMPLE iteration number is reached, if so, judging that the current iteration step PIMPLE pressure-speed coupling iterative solution is finished, and carrying out the next step after updating the liquid metal speed field and the liquid metal pressure field;
step 9: according to the turbulence model set in the step 5, respectively and iteratively solving turbulence energy k and dissipation rate epsilon or specific dissipation rate omega transport equation of the liquid metal fluid and the supercritical carbon dioxide fluid to a set calculation residual error, and updating turbulence kinematic viscosity v of the two fluids t ；
Step 10: judging whether all the fluid domains are calculated, if not, jumping to the step 8 to continue calculation; if the calculation is finished, the next step is carried out;
step 11: iteratively solving an energy conservation equation (5) of the solid domain to calculate residual errors based on the fluid temperature field information and the fluid-solid coupling surface temperature information updated in the current iteration step, updating solid physical property values under a user dictionary file based on the solid domain temperature field updated in the current iteration step, judging whether all solid domains are calculated, and if so, performing the next step;
the energy conservation equation (5) for the solid domain is:
step 12: judging a fluid domain mass conservation equation (1), a momentum conservation equation (2), a supercritical carbon dioxide fluid energy conservation equation (3) or a liquid state updated in the step 8Metal fluid energy conservation equation (4), openFOAM built-in turbulence model turbulence energy k, dissipation rate epsilon or specific dissipation rate omega transport equation thereof, and two-equation thermal turbulence model temperature pulsation k θ Dissipation ratio epsilon θ Whether the residual errors of the transport equation and the solid domain energy conservation equation (5) reach a set external residual error threshold value or not, and if so, judging that the external iteration converges; if not, updating u on the wall boundary grid according to the boundary conditions of the physical quantities set in the step 6 i 、P、T、ν t K, ε or ω, α t 、k θ 、ε θ And (3) numerical value, and repeating the steps 8-12 until the residual error threshold set by the outer iteration is reached.
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