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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- CN110059389A CN110059389A CN201910285545.4A CN201910285545A CN110059389A CN 110059389 A CN110059389 A CN 110059389A CN 201910285545 A CN201910285545 A CN 201910285545A CN 110059389 A CN110059389 A CN 110059389A
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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 present invention relates to technical field of solar utilization technique more particularly to a kind of solar cross-season soil thermal storage POD are quick
Prediction technique.
Background technique
The method of value solving such as traditional finite difference calculus (FDM), Finite Volume Method for Air (FVM) are solving heat transfer and flowing side
Cheng Shi, often freedom degree (equation number or grid number) with higher, numerical solution expend many memories and time, are difficult
Meets the needs of complex engineering problems.POD method (Proper Orthogonal Decomposition) is thrown in conjunction with Galerkin
Shadow method can by original high dimensional nonlinear physical problem carry out depression of order processing, be converted into the less ordinary differential system of freedom degree into
Row solves, and accelerates solving speed.This method collects the numerical simulation results under a large amount of given boundary conditions as sample, and from sample
The basic function that can portray simulated domain feature is extracted in this, obtains the corresponding system of basic function by solving POD lower-order model
Number realizes the quick meter to the physical problem except sample boundary condition finally by the linear superposition of basic function and corresponding coefficient
It calculates.
And aiming at the problem that solar cross-season soil thermal storage, since solar cross-season soil thermal storage has accumulation of heat scale
Greatly, the features such as time span is long, boundary condition is complicated, so that conventional numeric analogy method in the prior art expends a large amount of meter
It calculates resource and consumes a large amount of time, what this did not allowed often on engineer application.
Summary of the invention
The object of the present invention is to provide a kind of solar cross-season soil thermal storage POD method for quick predicting, this method can be with
Efficient across the season soil of analog solar stores exothermic process, to meet the real needs of engineering.
The purpose of the present invention is what is be achieved through the following technical solutions:
A kind of solar cross-season soil thermal storage POD method for quick predicting, which comprises
Step 1 establishes solar cross-season soil thermal storage physical model, carries out grid dividing to physical model and side is arranged
Boundary's condition；
Step 2 establishes percolation equationk and heat exchange equation, and carries out discrete solution to percolation equationk and heat exchange equation, obtains
Multiple groups solar cross-season soil thermal storage analog sample；
Step 3 extracts corresponding temperature field basic function, velocity field basic function and pressure field base letter from the analog sample
Number；
Step 4 rewrites the percolation equationk and heat exchange equation, and temperature, percolation flow velocity and the pressure in equation are write respectively
The form being superimposed at corresponding basic function；
Step 5 introduces the percolation equationk to percolation flow velocity basic function space projection, and by a series of mathematical derivations
Pressure boundary condition establishes the POD lower-order model of percolation equationk；
Step 6, by the heat exchange equation to temperature basic function space projection, pass through a series of mathematical derivations and introduce temperature side
Boundary's condition establishes the POD lower-order model of heat exchange equation；
The POD lower-order model of the POD lower-order model of percolation equationk described in step 7, simultaneous and the equation that exchanges heat, obtains solar energy
POD lower-order model across season soil thermal storage；
The POD lower-order model of step 8, the POD lower-order model of the iterative solution percolation equationk and the equation that exchanges heat, is seeped
Flowing pressure and percolation flow velocity spectral coefficient bk(k=1,2...N) and temperature spectral coefficient ak(k=1,2...M)；
Step 9 substitutes into the obtained spectral coefficient of step 8 and step 3 obtained basic function in the formula of step 4, obtains
To reconstruct approximate temperature field and seepage field；
Step 10 post-processes calculated result based on obtained reconstruct approximate temperature field and seepage field, measures in advance
To temperature field, velocity field and pressure field, the prediction result of solar cross-season soil thermal storage is obtained.
As seen from the above technical solution provided by the invention, the above method can efficient analog solar across season
Soil stores exothermic process, to meet the real needs of engineering.
Detailed description of the invention
In order to illustrate the technical solution of the embodiments of the present invention more clearly, required use in being described below to embodiment
Attached drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for this
For the those of ordinary skill in field, without creative efforts, it can also be obtained according to these attached drawings other
Attached drawing.
Fig. 1 is solar cross-season soil thermal storage POD method for quick predicting flow diagram provided in an embodiment of the present invention；
Fig. 2 is the schematic diagram of physical model grid dividing and corresponding boundary condition setting in the embodiment of the present invention.
Specific embodiment
With reference to the attached drawing in the embodiment of the present invention, technical solution in the embodiment of the present invention carries out clear, complete
Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
The embodiment of invention, every other implementation obtained by those of ordinary skill in the art without making creative efforts
Example, belongs to protection scope of the present invention.
The embodiment of the present invention is described in further detail below in conjunction with attached drawing, is implemented as shown in Figure 1 for the present invention
The solar cross-season soil thermal storage POD method for quick predicting flow diagram that example provides, which comprises
Step 1 establishes solar cross-season soil thermal storage physical model, carries out grid dividing to physical model and side is arranged
Boundary's condition；
In this step, physical model grid dividing and corresponding boundary condition in the embodiment of the present invention is illustrated in figure 2 to set
The schematic diagram set, the embodiment physical model use unstructured grid in the horizontal direction, use structure in vertical direction
The non-uniform grid of change divides 15 layers close to 1.5 meters of vertical directions at ground；And then divide on downward 10 layers of grid vertical direction
Be not 0.1 meter, 0.2 meter,, 1 meter；It is still further below 1.0 meters on 95 layers of grid vertical direction；Last 5 layers of grid vertical direction point
Be not 1.0 meters, 1.5 meters,, 3.0 meters.
Corresponding boundary condition setting are as follows: be cross-ventilation boundary condition above model；Model outermost tubular boundary is
Adiabatic boundary condition；It is boundary condition below model；1.5 meters are exhausted with 10 meters of lower section above internal double U pipe vertical directions
Thermal boundary condition；Internal double pipe vertical direction middle sections U are Convection Heat Transfer Boundary Conditions.
Step 2 establishes percolation equationk and heat exchange equation, and carries out discrete solution to percolation equationk and heat exchange equation, obtains
Multiple groups solar cross-season soil thermal storage analog sample；
The percolation equationk established in the step are as follows:
Wherein, ρ is the density of fluid in soil；cfFor the compressed coefficient；K is second order permeability tensor；μ is fluid in soil
Dynamic viscosity；P is the gross pressure of fluid in soil being subject to.
The heat exchange equation established in the step are as follows:
Wherein,(ρcp)eff=φ (ρ cp)f+(1-φ)(ρcp)s, φ is porosity, and subscript eff is indicated
Coefficient is imitated, f indicates that fluid, s indicate solid；T is temperature；τ is the time；keffFor effective coefficient of heat transfer；
In the specific implementation, numerical simulation result of the obtained analog sample under several given boundary conditions.
Step 3 extracts corresponding temperature field basic function, velocity field basic function and pressure field base letter from the analog sample
Number；
Step 4 rewrites the percolation equationk and heat exchange equation, and temperature, percolation flow velocity and the pressure in equation are write respectively
At corresponding basic function be superimposed form, specifically:
In formula,Respectively temperature field basic function, velocity field basic function and pressure field basic function,
It changes with space；akIt (t) is the corresponding coefficient of temperature field basic function, bkIt (t) is velocity field basic function and pressure field basic function
Coefficient, change at any time；M, N are the numbers of corresponding basic function, can be varied according to different boundary conditions, but want
Guarantee that the number of taken basic function makes cumlative energy contribution rate sufficiently large, cumlative energy contribution rate is closer to 100%, linearly
The accuracy of the approximate field obtained after superposition is higher, but basic function take excessively will affect solving speed, therefore will be according to reality
Border situation obtains suitable basic function number.
In the specific implementation, temperature field basic function is approximate with the temperature field of simulation, the feature of sample temperature field is reacted, has been passed through
The temperature field of the available soil of the linear superposition of different temperature fields basic function；Velocity field basic function is close with the velocity field of simulation
Seemingly, the feature for having reacted sample velocity field passes through fluid in the available soil of linear superposition of friction speed field basic function
Percolation flow velocity field；Pressure field basic function is approximate with the pressure field of simulation, has reacted the feature of sample pressure field, has passed through different pressures
The seepage pressure field of fluid in the available soil of linear superposition of field basic function.
Step 5 again draws the percolation equationk to percolation flow velocity basic function space projection, and by a series of mathematical derivations
Enter pressure boundary condition, and then establishes the POD lower-order model of percolation equationk；
In the step, the POD lower-order model for the percolation equationk established is seepage pressure and percolation flow velocity spectral coefficient bk(k
=1,2...N) the multinomial equation group of second order, specifically:
Wherein, Aik、Bilk、CiRespectively percolation equationk rewrites the merging item obtained after projection.
Step 6, by the heat exchange equation to temperature basic function space projection, pass through a series of mathematical derivations and introduce temperature side
Boundary's condition establishes the POD lower-order model of heat exchange equation.
In this step, the POD lower-order model for the heat exchange equation established is temperature spectral coefficient ak(k=1,2...M) and
Seepage flow spectral coefficient bkThe multinomial equation group of the second order of (k=1,2...N), specifically:
Wherein, Dik、Eilk、Fik、GiRespectively heat exchange equation rewrites the merging item obtained after projection.
The POD lower-order model of the POD lower-order model of percolation equationk described in step 7, simultaneous and the equation that exchanges heat, obtains solar energy
POD lower-order model across season soil thermal storage；
The POD lower-order model of step 8, the POD lower-order model of the iterative solution percolation equationk and the equation that exchanges heat, is seeped
Flowing pressure and percolation flow velocity spectral coefficient bk(k=1,2...N) and temperature spectral coefficient ak(k=1,2...M)；
In this step, specific solution procedure are as follows:
Velocity field and pressure field sample obtained in analytical procedure 2 first obtains velocity field and pressure using " snapshot " method
Velocity field and pressure field basic function are substituted into percolation equationk POD lower-order model by field basic function, introduce boundary condition, iterative solution
Percolation equationk POD lower-order model obtains seepage pressure and percolation flow velocity spectral coefficient bk(k=1,2...N)；
Then temperature field sample obtained in analytical procedure 2 obtains temperature field basic function using " snapshot " method, by temperature field
Basic function substitutes into heat exchange equation, then by seepage flow spectral coefficient bk(k=1,2...N) substitutes into heat exchange equation, introduces boundary condition, iteration
The POD lower-order model of solving heat exchange equation finally obtains temperature spectral coefficient ak(k=1,2...M).
Step 9 substitutes into the obtained spectral coefficient of step 8 and step 3 obtained basic function in the formula of step 4, obtains
To reconstruct approximate temperature field and seepage field；
In this step, obtained temperature field indicates are as follows:
Obtained seepage field is expressed as
In formula,Respectively temperature field basic function, velocity field basic function and pressure field basic function,
It changes with space；akIt (t) is the corresponding coefficient of temperature field basic function, bkIt (t) is velocity field basic function and pressure field basic function
Coefficient, change at any time；M, N are the numbers of corresponding basic function.
Step 10 post-processes calculated result based on obtained reconstruct approximate temperature field and seepage field, measures in advance
To temperature field, velocity field and pressure field, the prediction result of solar cross-season soil thermal storage is obtained.
So far, it completes using the sample obtained under given boundary condition come the feelings except quick predict sample boundary condition
Condition.
In practical projects, it in order to carry out the optimization of structural parameters and operating parameter, generally requires to do many cases and goes to obtain
Temperature field and seepage field are obtained with the changing rule of external condition, and then obtains Optimal Parameters, and these cases are substantially similar, pass through
Selected part case obtains the temperature field under the conditions of other counterpart boundaries and seepage field as sample according to the method described above,
Simulated time can be shortened, improve the period of engineering optimization.
It is worth noting that, the content being not described in detail in the embodiment of the present invention belongs to professional and technical personnel in the field's public affairs
The prior art known.
In conclusion the present embodiment the method can carry out predictive simulation, energy to solar cross-season soil thermal storage process
It is enough that numerical simulation result under the Outer Boundary Conditions of sample is gone out according to the sample quick predict for giving numerical simulation under boundary condition.
Convenient for before construction heat exchanging device structure and layout optimize, to engineering site implement have important references value, can also be real
When monitor underground heat exchange situation, auxiliary adjustment equipment operating parameter runs equipment high efficiency.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Within the technical scope of the present disclosure, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims
Subject to enclosing.
Claims (6)
1. a kind of solar cross-season soil thermal storage POD method for quick predicting, which is characterized in that the described method includes:
Step 1 establishes solar cross-season soil thermal storage physical model, carries out grid dividing to physical model and perimeter strip is arranged
Part；
Step 2 establishes percolation equationk and heat exchange equation, and carries out discrete solution to percolation equationk and heat exchange equation, obtains multiple groups
Solar cross-season soil thermal storage analog sample；
Step 3 extracts corresponding temperature field basic function, velocity field basic function and pressure field basic function from the analog sample；
Step 4 rewrites the percolation equationk and heat exchange equation, and temperature, percolation flow velocity and the pressure in equation are written respectively as phase
The form for answering basic function to be superimposed；
The percolation equationk is introduced pressure to percolation flow velocity basic function space projection, and by a series of mathematical derivations by step 5
Boundary condition establishes the POD lower-order model of percolation equationk；
Step 6, by the heat exchange equation to temperature basic function space projection, pass through a series of mathematical derivations and introduce temperature boundary item
Part establishes the POD lower-order model of heat exchange equation；
The POD lower-order model of the POD lower-order model of percolation equationk described in step 7, simultaneous and the equation that exchanges heat, obtains solar cross season
Save the POD lower-order model of soil thermal storage；
The POD lower-order model of step 8, the POD lower-order model of the iterative solution percolation equationk and the equation that exchanges heat, obtains seepage flow pressure
Power and percolation flow velocity spectral coefficient bk(k=1,2...N) and temperature spectral coefficient ak(k=1,2...M)；
Step 9 substitutes into the obtained spectral coefficient of step 8 and step 3 obtained basic function in the formula of step 4, obtains weight
Structure approximate temperature field and seepage field；
Step 10 post-processes calculated result based on obtained reconstruct approximate temperature field and seepage field, and prediction obtains temperature
Field, velocity field and pressure field are spent, the prediction result of solar cross-season soil thermal storage is obtained.
2. solar cross-season soil thermal storage POD method for quick predicting according to claim 1, which is characterized in that
Numerical simulation result of the obtained analog sample under several given boundary conditions in the step 2.
3. solar cross-season soil thermal storage POD method for quick predicting according to claim 1, which is characterized in that in step 2
In, the percolation equationk established are as follows:
Wherein, ρ is the density of fluid in soil；cfFor the compressed coefficient；K is second order permeability tensor；μ is the dynamic of fluid in soil
Power viscosity；P is the gross pressure of fluid in soil being subject to；
The heat exchange equation established are as follows:
Wherein,(ρcp)eff=φ (ρ cp)f+(1-φ)(ρcp)s, φ is porosity, and subscript eff indicates effectively system
Number, f indicate that fluid, s indicate solid；T is temperature；τ is the time；keffFor effective coefficient of heat transfer.
4. solar cross-season soil thermal storage POD method for quick predicting according to claim 1, which is characterized in that in step 4
In, the temperature by equation, percolation flow velocity and pressure are written respectively as the form of corresponding basic function superposition, specifically:
In formula,Respectively temperature field basic function, velocity field basic function and pressure field basic function, with sky
Between change；akIt (t) is the corresponding coefficient of temperature field basic function；bk(t) it is for velocity field basic function and pressure field basic function
Number, changes at any time；M, N are the numbers of corresponding basic function, can be varied according to different boundary conditions.
5. solar cross-season soil thermal storage POD method for quick predicting according to claim 1, which is characterized in that in step 5
In, the POD lower-order model for the percolation equationk established is seepage pressure and percolation flow velocity spectral coefficient bk(k=1,2...N) two
The multinomial equation group of rank, is embodied as:
Wherein, Aik、Bilk、CiRespectively percolation equationk rewrites the merging item obtained after projection.
6. solar cross-season soil thermal storage POD method for quick predicting according to claim 1, which is characterized in that in step 6
In, the POD lower-order model for the heat exchange equation established is temperature spectral coefficient ak(k=1,2...M) and seepage flow spectral coefficient bk(k=1,
2...N the multinomial equation group of second order), is embodied as:
Wherein, Dik、Eilk、Fik、GiRespectively heat exchange equation rewrites the merging item obtained after projection.
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| CN110968967A (en) * | 2019-12-02 | 2020-04-07 | 西安交通大学 | Heat transfer coupling simulation order reduction method for underground pipe heat exchanger |
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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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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110489912A (en) * | 2019-08-27 | 2019-11-22 | 北京石油化工学院 | A kind of method of solar cross-season soil thermal storage hierarchy slicing numerical simulation |
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| CN110968967A (en) * | 2019-12-02 | 2020-04-07 | 西安交通大学 | Heat transfer coupling simulation order reduction method for underground pipe heat exchanger |
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| CN113553790A (en) * | 2021-07-30 | 2021-10-26 | 上海安悦节能技术有限公司 | Temperature prediction method for machining workshop of automobile industry |
| 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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