CN110147639B - Finite element time-by-time simulation method for underground heat exchanger of ground source heat pump U-shaped pipe - Google Patents
Finite element time-by-time simulation method for underground heat exchanger of ground source heat pump U-shaped pipe Download PDFInfo
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- CN110147639B CN110147639B CN201910498022.8A CN201910498022A CN110147639B CN 110147639 B CN110147639 B CN 110147639B CN 201910498022 A CN201910498022 A CN 201910498022A CN 110147639 B CN110147639 B CN 110147639B
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Abstract
The invention belongs to the technical field of ground source heat pumps, and discloses a finite element time-by-time simulation method of a ground source heat pump U-shaped tube underground heat exchanger, which comprises the steps of constructing a one-dimensional finite element heat transfer model of the underground heat exchanger and carrying out simulation calculation on the underground heat exchanger, wherein the simulation calculation method comprises the following steps: inputting the heat load of the underground heat exchanger; step two: judging whether the load is zero: if yes, calculating the soil temperature by adopting a one-dimensional finite element numerical model, and then entering the sixth step; if not, entering the third step; step three: calculating the soil temperature by adopting a one-dimensional finite element numerical model; step four: calculating thermal resistance in the hole; step five: calculating the water temperature at the inlet and the outlet; step six: and updating the initial temperature of the soil by using the calculated soil temperature to prepare for the calculation of the next time step. The finite element time-by-time simulation method of the ground source heat pump U-shaped tube underground heat exchanger directly carries out time-by-time simulation calculation based on the time-by-time load of a building, and both calculation accuracy and calculation efficiency can be guaranteed.
Description
Technical Field
The invention belongs to the technical field of ground source heat pumps, and particularly relates to a finite element time-by-time simulation method for a U-shaped tube underground heat exchanger of a ground source heat pump.
Background
The ground source heat pump is considered as an air conditioner mode utilizing shallow renewable geothermal energy, has the advantages of high efficiency, energy conservation and environmental protection, and is widely applied at home and abroad.
The ground source heat pump system comprises the following parts: (1) terminal air treatment equipment and a fan; (2) The load side water pump is used for distributing cold and hot water generated by the heat pump unit to the tail end equipment; and (3) a heat pump unit for realizing refrigeration and heating. Comprises four parts of an evaporator, a condenser, a compressor and an expansion device and other auxiliary and control parts; (5) The source side water pump is used for realizing water circulation between the heat pump and the underground heat exchanger; (6) The underground heat exchanger transfers the heat of the room to the ground in summer and absorbs the heat from the soil in winter to supply the room for heating.
The ground source heat pump air conditioner is different from the conventional air conditioner in the components of an underground heat exchanger, and whether the ground source heat pump air conditioner is reasonable in design is the key of whether the ground source heat pump engineering is successful or not. The key for judging whether the underground heat exchanger is reasonable is to carry out analog calculation on the heat transfer of the underground heat exchanger. The underground heat exchanger has large structural size, and the heat transfer has the characteristics of unsteadiness, large time span and the like, so the heat transfer calculation of the underground heat exchanger has the following differences with the calculation of a common system: (1) dynamic calculation needs to be carried out for 1 year or even 30 years; (2) In addition to accuracy, the calculation speed needs to meet the progress requirements of engineering design.
Because the building load changes time by time, the time by time simulation calculation of the underground heat exchanger is the most practical method. The domestic "planet of geothermy" adopts an approximate analytical model, but in order to ensure the calculation speed, the calculation is not carried out time by time, but is carried out on the basis of the monthly average load and the peak load of the building. The existing three-dimensional numerical heat transfer simulation software can be used for time-by-time unsteady state simulation of the ground source heat pump underground heat exchanger, but the calculation cost is too high, and the engineering design calculation is not practical enough.
Considering engineering practice, the simulation of the ground source heat pump scheme is preferably directly based on the time-by-time load of the building, and the calculation efficiency is high, so that the result can be quickly obtained to evaluate the design scheme.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a finite element time-by-time simulation method for an underground heat exchanger of a ground source heat pump U-shaped pipe.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a finite element time-by-time simulation method of an underground heat exchanger of a ground source heat pump U-shaped pipe comprises the following steps:
(1) Constructing a one-dimensional finite element heat transfer model of the underground heat exchanger:
the underground heat exchanger adopts a radial one-dimensional numerical model under column coordinates: the wall of the heat exchange hole in the model is set as a hot flow boundary; the far boundary of the heat exchange hole is set as a heat insulation boundary; nodes and limited units are uniformly distributed from the wall of the heat exchange hole to the far boundary of the heat exchange hole, and a linear temperature distribution hypothesis is adopted in each limited unit; establishing a discrete equation by adopting a Galerkin method;
(2) Simulation calculation of the underground heat exchanger:
the method comprises the following steps: inputting the heat load of the underground heat exchanger;
step two: judging whether the load is zero: if yes, calculating the soil temperature by adopting a one-dimensional finite element numerical model, and then entering the sixth step; if not, entering the third step;
step three: calculating the soil temperature by adopting a one-dimensional finite element numerical model;
step four: calculating thermal resistance in the hole;
step five: calculating the water temperature at the inlet and the outlet;
step six: and updating the initial temperature of the soil by using the calculated soil temperature to prepare for the calculation of the next time step.
Further, the discrete equation is ([ C ]]+Δτ[K]){T j+1 }＝[C]{T j }+Δτ{f j+1 }; wherein, the first and the second end of the pipe are connected with each other,
the C matrix is:
in the formula: i and j are nodes of each of the finite elements; c. C p -specific heat capacity of the soil, J-(kg. DEG. C.); rho-soil density, kg/m3; lambda s -soil thermal conductivity, W/(K · m); l is the finite element length, m; a. The e ＝(2πr i +2πr j ) The/2 is the calculated heat transfer area of the cell, m2; r is i Is the radius of the ith node, m; r is j Is the radius of the jth node, m.
The K matrix is:
the f matrix is:
wherein:
in the formula: m is the mass flow of the circulating water in the pipe, kg/s; c p -specific heat capacity of circulating water, J/(kg. DEG C); l is the drilling depth, m; t is a unit of in -inlet water temperature in the tube, ° c; t is a unit of out -outlet water temperature in the tube, ° c; q. q.s w -heat flow density, W/m 2 ；r b -borehole radius, m; q. q.s l The thermal load of the drill hole with unit depth is W/m; Δ τ is the time step, s.
Compared with the prior art, the technical scheme provided by the invention has the following beneficial effects or advantages:
the finite element time-by-time simulation method of the underground heat exchanger of the ground source heat pump U-shaped pipe directly performs time-by-time simulation calculation based on the time-by-time load of the building, not only can improve the calculation accuracy, but also can guarantee the calculation efficiency and save the calculation time.
Specific embodiments of the present invention are disclosed in detail with reference to the following description and drawings, indicating the manner in which the principles of the invention may be employed. It should be understood that the embodiments of the invention are not so limited in scope. The embodiments of the invention include many variations, modifications and equivalents within the spirit and scope of the appended claims.
Features that are described and/or illustrated with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments, in combination with or instead of the features of the other embodiments.
It should be emphasized that the term "comprises/comprising" when used herein, is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers, steps or components.
Drawings
FIG. 1 is a flow chart of a heat transfer calculation algorithm for an underground heat exchanger of the present invention;
FIG. 2 is a schematic representation of a subterranean heat exchanger useful in the present invention;
FIG. 3 is a schematic diagram of a limited cell of an underground heat exchanger employed in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be 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 some, but not all embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined or explained in subsequent figures.
In the description of the embodiments of the present invention, it should be noted that the indication of the orientation or the positional relationship is based on the orientation or the positional relationship shown in the drawings, or the orientation or the positional relationship which is usually placed when the product of the present invention is used, or the orientation or the positional relationship which is usually understood by those skilled in the art, or the orientation or the positional relationship which is usually placed when the product of the present invention is used, is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the indicated device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the present invention should not be construed as being limited. Furthermore, the terms "first" and "second" are used merely to distinguish one description from another, and are not to be construed as indicating or implying relative importance.
In the description of the embodiments of the present invention, it should be further noted that the terms "disposed" and "connected" are to be interpreted broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected, unless explicitly stated or limited otherwise; may be directly connected or indirectly connected through an intermediate. For those skilled in the art, the drawings of the embodiments with specific meanings of the terms in the present invention can be understood in specific situations, and the technical solutions in the embodiments of the present invention are clearly and completely described. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
In addition, it should be further noted that, in the description of the embodiment of the present invention, except for the devices with the types specifically indicated, the other devices are conventional devices in the field, such as "water pump", "heatable water tank", and the like, and those skilled in the art may adopt the corresponding conventional devices according to actual situations, and are not described herein again.
The embodiment of the invention provides a finite element time-by-time simulation method of a ground source heat pump U-shaped tube underground heat exchanger, which comprises the following steps:
the first step is as follows: constructing a one-dimensional finite element heat transfer model of the underground heat exchanger:
the underground heat exchanger adopts a radial one-dimensional numerical model under a column coordinate: the wall of the heat exchange hole in the model is set as a hot fluid boundary; the far boundary of the heat exchange hole is set as a heat insulation boundary; uniformly arranging nodes and dividing limited units from the heat exchange hole wall to the far boundary of the heat exchange hole, wherein the nodes of each limited unit e are i and j, and a linear temperature distribution hypothesis is adopted in each limited unit e as shown in fig. 2 and 3; and establishing a discrete equation by adopting a Galerkin method.
The discrete equation established by the Galerkin method is specifically as follows:
([C]+Δτ[K]){T j+1 }＝[C]{T j }+Δτ{f j+1 }
wherein:
the C matrix is:
in the formula: c. C p -specific heat capacity of the soil, J/(kg. DEG C); rho-soil density, kg/m3; lambda s -soil thermal conductivity, W/(K · m); l is the finite element length, m; a. The e ＝(2πr i +2πr j ) The/2 is the calculated heat transfer area of the cell, m2; r is a radical of hydrogen i Is the radius of the ith node, m; r is j Is the radius of the jth node, m.
The K matrix is:
the f matrix is:
in the formula:
in the formula: m represents the mass flow of circulating water in the pipe, kg/s; c p Circulating water specific heat capacity, J/(kg. DEG. C.); l is the drilling depth, m; t is in -inlet water temperature in the tube, ° c; t is a unit of out -outlet water temperature in the tube, ° c; q. q of w -heat flow density, W/m 2 ；r b -the borehole radius, m; q. q of l The thermal load of the unit depth drill hole is W/m; Δ τ is the time step, s.
After the one-dimensional finite element heat transfer model of the underground heat exchanger is constructed, the second step is executed: the calculation process of the simulation calculation of the underground heat exchanger is shown in figure 1:
the method comprises the following steps: inputting the heat load of the underground heat exchanger;
step two: judging whether the load is zero: if yes, calculating the soil temperature by adopting a one-dimensional finite element numerical model, and then entering the sixth step; if not, entering the third step;
step three: calculating the soil temperature by adopting a one-dimensional finite element numerical model;
step four: calculating thermal resistance in the hole;
step five: calculating the water temperature at the inlet and the outlet;
step six: and updating the initial temperature of the soil by using the calculated soil temperature to prepare for the calculation of the next time step.
Wherein, it should be noted that, in the first step of the embodiment of the present invention, the heat load of the underground heat exchanger is calculated from the building load and the energy efficiency ratio of the heat pump machine; the building load is obtained by existing building load simulation software.
In addition, the method for calculating the thermal resistance in the hole in the fourth step and the method for calculating the water temperature at the inlet and the outlet in the fifth step in the embodiment of the present invention are both calculation methods in the existing specification, and will be obvious to those skilled in the art, and will not be described in detail herein.
The finite element time-by-time simulation method of the ground source heat pump U-shaped tube underground heat exchanger provided by the embodiment of the invention directly carries out time-by-time simulation calculation based on the time-by-time load of the building, thereby not only improving the calculation accuracy, but also ensuring the calculation efficiency and saving the calculation time.
Finally, it should be noted that: the foregoing description is for the purpose of illustration and is not for the purpose of limitation. Many embodiments and many applications other than the examples provided will be apparent to those of skill in the art upon reading the above description. The scope of the present teachings should, therefore, be determined not with reference to the above description, but should instead be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. The disclosures of all articles and references, including patent applications and publications, are hereby incorporated by reference for all purposes. The omission in the foregoing claims of any aspect of subject matter that is disclosed herein is not intended to forego such subject matter, nor should the inventors be construed as having contemplated such subject matter as being part of the disclosed subject matter.
Claims (2)
1. A finite element time-by-time simulation method of an underground heat exchanger of a ground source heat pump U-shaped pipe is characterized by comprising the following steps:
(1) Constructing a one-dimensional finite element heat transfer model of the underground heat exchanger:
the underground heat exchanger adopts a radial one-dimensional numerical model under column coordinates: the wall of the heat exchange hole in the model is set as a hot flow boundary; the far boundary of the heat exchange hole is set as a heat insulation boundary; uniformly arranging nodes and dividing limited units from the wall of the heat exchange hole to the far boundary of the heat exchange hole, wherein the inside of each limited unit adopts a linear temperature distribution hypothesis; establishing a discrete equation by adopting a Galerkin method;
(2) Simulation calculation of underground heat exchanger:
the method comprises the following steps: inputting the heat load of the underground heat exchanger;
step two: judging whether the load is zero: if yes, calculating the soil temperature by adopting a one-dimensional finite element numerical model, and then entering the sixth step; if not, entering the third step;
step three: calculating the soil temperature by adopting a one-dimensional finite element numerical model;
step four: calculating thermal resistance in the hole;
step five: calculating the water temperature of an inlet and an outlet;
step six: and updating the initial temperature of the soil by using the calculated soil temperature to prepare for the calculation of the next time step.
2. A finite element time-by-time simulation method of a ground source heat pump U-tube underground heat exchanger according to claim 1, characterized in that the discrete equation is ([ C)]+Δτ[K]){T j+1 }＝[C]{T j }+Δτ{f j+1 }; wherein the content of the first and second substances,
the C matrix is:
in the formula: i and j are nodes of each of the finite elements; c. C p -specific heat capacity of the soil, J/(kg. DEG C); rho-soil density, kg/m3; lambda [ alpha ] s -soil thermal conductivity, W/(K · m); l is the finite element length, m; a. The e ＝(2πr i +2πr j ) The/2 is the calculated heat transfer area of the cell, m2; r is i Is the radius of the ith node, m; r is j Is the radius of the jth node, m;
the K matrix is:
the f matrix is:
wherein:
in the formula: m represents the mass flow of circulating water in the pipe, kg/s; c p Circulating water specific heat capacity, J/(kg. DEG. C.); l is the drilling depth, m; t is a unit of in -inlet water temperature in the tube, ° c; t is a unit of out -outlet water temperature in the pipe, ° c; q. q of w -heat flow density, W/m 2 ；r b -borehole radius, m; q. q.s l The thermal load of the drill hole with unit depth is W/m; Δ τ is the time step, s.
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| CN111639378A (en) * | 2020-05-27 | 2020-09-08 | 西华大学 | Method for simulating hourly numerical value of heat exchange performance of underground air pipe |
| CN111814320B (en) * | 2020-06-23 | 2023-06-09 | 四川大学华西医院 | Dynamic operation simulation test method for variable flow ground source heat pump system |
| CN113505454B (en) * | 2021-07-14 | 2022-12-06 | 中煤科工集团西安研究院有限公司 | Method for calculating heat quantity of middle-deep geothermal well casing type heat exchanger |
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