CN110059389A - A kind of solar cross-season soil thermal storage POD method for quick predicting - Google Patents
A kind of solar cross-season soil thermal storage POD method for quick predicting Download PDFInfo
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Abstract
The invention discloses a kind of solar cross-season soil thermal storage POD method for quick predicting, establish solar cross-season soil thermal storage physical model, carry out grid dividing to physical model and boundary condition is arranged；Discrete solution is carried out to governing equation, obtains multiple groups solar cross-season soil thermal storage analog sample；Corresponding basic function is extracted from analog sample；Rewrite governing equation；Obtain the POD lower-order model of solar cross-season soil thermal storage；Solve the POD lower-order model of the solar cross-season soil thermal storage；Obtain reconstruct approximate temperature field and seepage field；Based on obtained reconstruct approximate temperature field and seepage field, calculated result is post-processed, obtains the prediction result of solar cross-season soil thermal storage.This method efficiently can store exothermic process by across the season soil of analog solar, to meet the real needs of engineering.
Description
Technical Field
The invention relates to the technical field of solar energy utilization, in particular to a solar energy cross-season soil heat storage POD rapid prediction method.
Background
When the traditional numerical solution methods such as the Finite Difference Method (FDM) and the Finite Volume Method (FVM) are used for solving heat transfer and flow equations, the method often has higher degree of freedom (the number of equations or the number of grids), the numerical solution consumes a lot of memory and time, and the requirement of complex engineering problems is difficult to meet. The POD (product Orthogonal Decomposition) method is combined with the Galerkin projection method to reduce the order of the original high-dimensional nonlinear physical problem, and the original high-dimensional nonlinear physical problem is converted into an ordinary differential equation set with less freedom degree to be solved, so that the solving speed is increased. The method includes the steps of collecting a large number of numerical simulation results under a given boundary condition as samples, extracting a basis function capable of describing simulation region features from the samples, obtaining coefficients corresponding to the basis function by solving a POD low-order model, and finally achieving rapid calculation of physical problems outside the boundary condition of the samples through linear superposition of the basis function and the corresponding coefficients.
For the problem of solar cross-season soil heat storage, the traditional numerical simulation method in the prior art consumes a large amount of computing resources and consumes a large amount of time, which is not allowed in engineering application, because the solar cross-season soil heat storage has the characteristics of large heat storage scale, long time span, complex boundary conditions and the like.
Disclosure of Invention
The invention aims to provide a quick prediction method for solar cross-season soil heat storage POD (POD), which can efficiently simulate the process of solar cross-season soil heat storage and release so as to meet the practical requirements of engineering.
The purpose of the invention is realized by the following technical scheme:
a solar cross-season soil thermal storage POD fast prediction method, the method comprising:
step 1, establishing a solar cross-season soil heat storage physical model, carrying out grid division on the physical model and setting boundary conditions;
step 2, establishing a seepage equation and a heat exchange equation, and performing discrete solution on the seepage equation and the heat exchange equation to obtain a plurality of groups of solar seasonal soil heat storage simulation samples;
step 3, extracting corresponding temperature field basis functions, speed field basis functions and pressure field basis functions from the simulation samples;
step 4, rewriting the seepage equation and the heat exchange equation, and writing the temperature, the seepage speed and the pressure in the equation into a corresponding basic function superposition form respectively;
step 5, projecting the seepage equation to a seepage velocity basis function space, introducing a pressure boundary condition through a series of mathematical deductions, and establishing a POD low-order model of the seepage equation;
step 6, projecting the heat exchange equation to a temperature basis function space, introducing a temperature boundary condition through a series of mathematical deductions, and establishing a POD low-order model of the heat exchange equation;
step 7, combining the POD low-order model of the seepage equation and the POD low-order model of the heat exchange equation to obtain a POD low-order model of solar cross-season soil heat storage;
step 8, iteratively solving the POD low-order model of the seepage equation and the POD low-order model of the heat exchange equation to obtain seepage pressure and seepage velocity spectrum coefficient bk(k ═ 1,2.. N), and the temperature spectrum coefficient ak(k＝1,2...M)；
Step 9, substituting the spectral coefficient obtained in the step 8 and the basis function obtained in the step 3 into the formula in the step 4 to obtain a reconstructed approximate temperature field and a seepage field;
and step 10, carrying out post-processing on the calculation result based on the obtained reconstructed approximate temperature field and seepage field, predicting to obtain a temperature field, a velocity field and a pressure field, and obtaining a prediction result of solar energy cross-season soil heat storage.
According to the technical scheme provided by the invention, the method can efficiently simulate the process of heat storage and release of the solar cross-season soil, so that the practical requirements of the engineering are met.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a solar cross-season soil thermal storage POD rapid prediction method provided by an embodiment of the invention;
FIG. 2 is a diagram illustrating physical model meshing and corresponding boundary condition setting in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the present invention will be further described in detail with reference to the accompanying drawings, and as shown in fig. 1, a schematic flow chart of a solar energy trans-seasonal soil thermal storage POD rapid prediction method provided by the embodiment of the present invention is shown, where the method includes:
step 1, establishing a solar cross-season soil heat storage physical model, carrying out grid division on the physical model and setting boundary conditions;
in this step, as shown in fig. 2, a schematic diagram of physical model mesh division and corresponding boundary condition setting in an embodiment of the present invention is shown, where the physical model of this embodiment uses unstructured meshes in the horizontal direction, uses structured non-uniform meshes in the vertical direction, and divides 15 layers in the vertical direction 1.5 meters near the ground; the vertical directions of the next 10 layers of grids are respectively 0.1 meter, 0.2 meter, 1 meter; then 1.0 meter is arranged in the vertical direction of the lower 95 layers of grids; and the vertical directions of the last 5 layers of grids are 1.0 meter, 1.5 meters, 3.0 meters respectively.
The corresponding boundary conditions are set as: above the model is the air convection boundary condition; the cylindrical boundary at the outermost side of the model is an adiabatic boundary condition; isothermal boundary conditions are below the model; 1.5 meters above and 10 meters below the double U-shaped pipes in the vertical direction are used as heat insulation boundary conditions; the middle part of the internal double U-shaped tubes in the vertical direction is a convection heat exchange boundary condition.
Step 2, establishing a seepage equation and a heat exchange equation, and performing discrete solution on the seepage equation and the heat exchange equation to obtain a plurality of groups of solar seasonal soil heat storage simulation samples;
the seepage equation established in this step is:
wherein ρ is the density of the fluid in the soil; c. CfIs a compression factor; k is the second order permeability tensor; mu is dynamic viscosity of fluid in soil; p is the total pressure experienced by the fluid in the soil.
The heat exchange equation established in this step is:
wherein,(ρcp)eff＝φ(ρcp)f+(1-φ)(ρcp)sφ is porosity, subscript eff denotes the effective coefficient, f denotes the fluid, s denotes the solid; t is the temperature; τ is time; k is a radical ofeffIs the effective heat transfer coefficient;
in a specific implementation, the obtained simulation samples come from numerical simulation results under a plurality of given boundary conditions.
Step 3, extracting corresponding temperature field basis functions, speed field basis functions and pressure field basis functions from the simulation samples;
step 4, rewriting the seepage equation and the heat exchange equation, and writing the temperature, the seepage velocity and the pressure in the equation into a corresponding basic function superposition form respectively, wherein the method specifically comprises the following steps:
in the formula,the temperature field basis function, the speed field basis function and the pressure field basis function are respectively changed along with the space; a isk(t) is a coefficient corresponding to a base function of the temperature field, bk(t) is the coefficients of the velocity field basis function and the pressure field basis function, which change over time; m and N are the number of corresponding basis functions, which can be changed according to different boundary conditions, but the number of the taken basis functions is ensured to ensure that the accumulated energy contribution rate is large enough, the closer the accumulated energy contribution rate is to 100%, the higher the accuracy of the approximate field obtained after linear superposition is, but the excessive taking of the basis functions affects the solving speed, so that the proper number of the basis functions is obtained according to the actual situation.
In the specific implementation, the temperature field basis function is similar to the simulated temperature field, the characteristics of the sample temperature field are reflected, and the temperature field of the soil can be obtained through linear superposition of different temperature field basis functions; the velocity field basis function is similar to the simulated velocity field, the characteristics of the sample velocity field are reflected, and the seepage velocity field of the fluid in the soil can be obtained through the linear superposition of different velocity field basis functions; the pressure field basis function is similar to the simulated pressure field, the characteristics of the sample pressure field are reflected, and the seepage pressure field of the fluid in the soil can be obtained through the linear superposition of different pressure field basis functions.
Step 5, projecting the seepage equation to a seepage velocity basis function space, introducing a pressure boundary condition through a series of mathematical deductions, and further establishing a POD low-order model of the seepage equation;
in the step, the POD low-order model of the established seepage equation is a seepage pressure and seepage velocity spectrum coefficient bkA second-order polynomial system of (k ═ 1,2.. N), specifically:
wherein A isik、Bilk、CiAnd respectively rewriting merged terms obtained after projection for the seepage equation.
And 6, projecting the heat exchange equation to a temperature basis function space, introducing a temperature boundary condition through a series of mathematical deductions, and establishing a POD low-order model of the heat exchange equation.
In the step, the POD low-order model of the established heat exchange equation is a temperature spectrum coefficient ak(k ═ 1,2.. M) and the percolation ratio bkA second-order polynomial system of (k ═ 1,2.. N), specifically:
wherein D isik、Eilk、Fik、GiAnd respectively rewriting the merged terms obtained after projection for the heat exchange equation.
Step 7, combining the POD low-order model of the seepage equation and the POD low-order model of the heat exchange equation to obtain a POD low-order model of solar cross-season soil heat storage;
step 8, iteratively solving the POD low-order model of the seepage equation and the POD low-order model of the heat exchange equation to obtain seepage pressure and seepage velocity spectrum coefficient bk(k ═ 1,2.. N), and the temperature spectrum coefficient ak(k＝1,2...M)；
In this step, the specific solving process is as follows:
firstly analyzing the speed field and pressure field samples obtained in the step 2, obtaining speed field and pressure field basis functions by a 'snapshot' method, substituting the speed field and pressure field basis functions into a seepage equation POD low-order model, introducing boundary conditions, iteratively solving the seepage equation POD low-order model to obtain seepage pressure and seepage velocity spectrum coefficients bk(k＝1,2...N)；
Then analyzing the temperature field sample obtained in the step 2, obtaining a temperature field basis function by adopting a 'snapshot' method, substituting the temperature field basis function into a heat exchange equation, and then substituting the seepage coefficient bkSubstituting (k ═ 1,2.. N) into a heat exchange equation, introducing boundary conditions, iteratively solving a POD low-order model of the heat exchange equation, and finally obtaining a temperature spectrum coefficient ak(k＝1,2...M)。
Step 9, substituting the spectral coefficient obtained in the step 8 and the basis function obtained in the step 3 into the formula in the step 4 to obtain a reconstructed approximate temperature field and a seepage field;
in this step, the resulting temperature field is expressed as:
the resulting seepage field is denoted as
In the formula,the temperature field basis function, the speed field basis function and the pressure field basis function are respectively changed along with the space; a isk(t) is a coefficient corresponding to a base function of the temperature field, bk(t) is the coefficients of the velocity field basis function and the pressure field basis function, which change over time; m and N are the number of corresponding basis functions.
And step 10, carrying out post-processing on the calculation result based on the obtained reconstructed approximate temperature field and seepage field, predicting to obtain a temperature field, a velocity field and a pressure field, and obtaining a prediction result of solar energy cross-season soil heat storage.
By this, it is accomplished that samples obtained under given boundary conditions are used to quickly predict situations outside the sample boundary conditions.
In actual engineering, in order to optimize structural parameters and operational parameters, many cases are often needed to obtain the change rule of the temperature field and the seepage field along with external conditions, so as to obtain optimized parameters, and the cases are basically similar.
It is noted that those skilled in the art will recognize that embodiments of the present invention are not described in detail herein.
In summary, the method of the embodiment can perform prediction simulation on the solar cross-season soil heat storage process, and can quickly predict the numerical simulation result under the boundary condition outside the sample according to the numerical simulation sample under the given boundary condition. The structure and the layout of the heat exchanger are convenient to optimize before construction, important reference value is provided for engineering field implementation, underground heat exchange conditions can be monitored in real time, and operating parameters of equipment can be adjusted in an auxiliary mode, so that the equipment can operate efficiently.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. A solar cross-season soil thermal storage POD rapid prediction method is characterized by comprising the following steps:
step 1, establishing a solar cross-season soil heat storage physical model, carrying out grid division on the physical model and setting boundary conditions;
step 2, establishing a seepage equation and a heat exchange equation, and performing discrete solution on the seepage equation and the heat exchange equation to obtain a plurality of groups of solar seasonal soil heat storage simulation samples;
step 3, extracting corresponding temperature field basis functions, speed field basis functions and pressure field basis functions from the simulation samples;
step 4, rewriting the seepage equation and the heat exchange equation, and writing the temperature, the seepage speed and the pressure in the equation into a corresponding basic function superposition form respectively;
step 5, projecting the seepage equation to a seepage velocity basis function space, introducing a pressure boundary condition through a series of mathematical deductions, and establishing a POD low-order model of the seepage equation;
step 6, projecting the heat exchange equation to a temperature basis function space, introducing a temperature boundary condition through a series of mathematical deductions, and establishing a POD low-order model of the heat exchange equation;
step 7, combining the POD low-order model of the seepage equation and the POD low-order model of the heat exchange equation to obtain a POD low-order model of solar cross-season soil heat storage;
step 8, iteratively solving the POD low-order model of the seepage equation and the POD low-order model of the heat exchange equation to obtain seepage pressure and seepage velocity spectrum coefficient bk(k ═ 1,2.. N), and the temperature spectrum coefficient ak(k＝1,2...M)；
Step 9, substituting the spectral coefficient obtained in the step 8 and the basis function obtained in the step 3 into the formula in the step 4 to obtain a reconstructed approximate temperature field and a seepage field;
and step 10, carrying out post-processing on the calculation result based on the obtained reconstructed approximate temperature field and seepage field, predicting to obtain a temperature field, a velocity field and a pressure field, and obtaining a prediction result of solar energy cross-season soil heat storage.
2. The solar cross-season soil thermal storage POD fast prediction method according to claim 1,
the simulation sample obtained in the step 2 comes from numerical simulation results under a plurality of given boundary conditions.
3. The solar energy cross-season soil thermal storage POD rapid prediction method according to claim 1, characterized in that in step 2, the established seepage equation is as follows:
wherein ρ is the density of the fluid in the soil; c. CfIs a compression factor; k is the second order permeability tensor; mu is dynamic viscosity of fluid in soil; p is the total pressure experienced by the fluid in the soil;
the established heat exchange equation is as follows:
wherein,(ρcp)eff＝φ(ρcp)f+(1-φ)(ρcp)sφ is porosity, subscript eff denotes the effective coefficient, f denotes the fluid, s denotes the solid; t is the temperature; τ is time; k is a radical ofeffIs the effective heat transfer coefficient.
4. The solar energy cross-season soil thermal storage POD rapid prediction method according to claim 1, characterized in that in step 4, the temperature, the seepage velocity and the pressure in the equation are respectively written in a form of superposition of corresponding basis functions, specifically:
in the formula,the temperature field basis function, the speed field basis function and the pressure field basis function are respectively changed along with the space; a isk(t) is the coefficient corresponding to the temperature field basis function; bk(t) is the coefficients of the velocity field basis function and the pressure field basis function, which change over time; m and N are the number of corresponding basis functions and can be changed according to different boundary conditions.
5. The solar energy cross-season soil thermal storage POD rapid prediction method according to claim 1, characterized in that in step 5, the POD low-order model of the established seepage equation is seepage pressure and seepage velocity spectral coefficient bkA second order polynomial system of (k ═ 1,2.. N), specifically expressed as:
wherein A isik、Bilk、CiAnd respectively rewriting merged terms obtained after projection for the seepage equation.
6. The solar energy cross-season soil thermal storage POD rapid prediction method according to claim 1, characterized in that in step 6, the POD low-order model of the established heat exchange equation is temperature spectrum coefficient ak(k ═ 1,2.. M) and the percolation ratio bkA second order polynomial system of (k ═ 1,2.. N), specifically expressed as:
wherein D isik、Eilk、Fik、GiAnd respectively rewriting the merged terms obtained after projection for the heat exchange equation.
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| CN113569502A (en) * | 2021-07-30 | 2021-10-29 | 上海安悦节能技术有限公司 | Method for predicting air flow velocity of machining workshop of automobile industry |
| CN113836700A (en) * | 2021-09-02 | 2021-12-24 | 南方电网科学研究院有限责任公司 | Cross-season soil heat storage modeling method and device suitable for multi-energy flow system |
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