CN112597639B - Heat transfer dimension reduction analysis method and system for porous buried pipe heat exchanger - Google Patents
Heat transfer dimension reduction analysis method and system for porous buried pipe heat exchanger Download PDFInfo
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Abstract
The invention provides a heat transfer dimension reduction analysis method and a heat transfer dimension reduction analysis system for a porous buried pipe heat exchanger. Determining parameters of the porous buried pipe heat exchanger; calculating and assigning an initial temperature distribution in the stratum, assigning an initial temperature distribution of fluid in each borehole, and determining an initial temperature distribution of the borehole wall; calculating the temperature distribution of the fluid in each borehole heat exchanger at the next moment according to the mathematical model of heat transfer in the borehole; according to the temperature distribution of the fluid in each borehole heat exchanger, calculating the temperature response of each single-hole buried pipe heat exchanger in the rock and soil at the next moment by using a single-hole buried pipe heat exchanger heat transfer model; based on the temperature response of each single-hole buried pipe heat exchanger in the rock and soil, the temperature response of the multi-hole buried pipe heat exchangers in the rock and soil under the combined action is calculated by using the superposition principle, and the change of the temperature of the fluid inlet and outlet along with the time is obtained.
Description
Technical Field
The invention belongs to the technical field of geothermal energy utilization and calculation, and particularly relates to a heat transfer and dimension reduction analysis method and system for a porous buried pipe heat exchanger.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The ground source heat pump heat supply air conditioning system takes the ground as a cold source and a heat source, so that a heat carrier serving as an intermediate medium circularly flows in a closed loop buried in the rock soil to exchange heat with the ground, and heat supply and cold supply of a building are realized through the heat pump. Energy saving and CO saving for building by ground source heat pump technology 2 The emission reduction and the prevention and treatment of the atmospheric pollution play an important role, and in general, the system consists of a buried pipe heat exchanger, a heat pump host and an end system in a building. The ground heat exchanger is the biggest characteristic of the ground heat pump air conditioning system with the ground source, which is different from other heat supply air conditioning systems. The heat transfer in the buried pipe heat exchanger is the heat exchange between the fluid in the pipe and the surrounding rock and soil, and can be regarded as a heat accumulating type heat exchanger. The arrangement mode of the ground heat exchanger must be according to the local conditions, and can be various, so that the geometric condition of the ground heat exchanger can be complex; the heat transfer process in a buried heat exchanger is a complex, non-steady state heat transfer process involving a long time scale, at least months to years. Therefore, the research on heat transfer of the ground heat exchanger is always a technical difficulty of the ground source heat pump air conditioning system, and is also a core and application foundation of the technical research.
The inventors have appreciated that heat transfer analysis methods for buried heat exchangers can be broadly divided into two broad categories, analytical solutions and numerical solutions, which each have their own advantages and limitations, and that hybrid methods can be used in practical applications. The basic starting point of the analytic solution method is to research the heat transfer rule of a single borehole buried pipe in an infinite or semi-infinite medium, at the moment, the buried pipe heat exchanger is simplified into a linear heat source or a cylindrical heat source, and the analytic solution of the temperature response of the buried pipe heat exchanger under the action of constant heat flow is obtained. The research scholars put forward a new thinking of superposition principle, based on describing the temperature response of a single borehole in an infinite medium under the condition of constant heat flow heating, and then the superposition principle is utilized to obtain the actual temperature response of the buried pipe heat exchanger formed by a plurality of boreholes under the action of variable load. The method has clear physical concept and simple calculation, can consider the complex geometric configuration and the change of load of the buried pipe heat exchanger along with time, and has been widely applied to actual engineering design calculation and energy consumption analysis. One disadvantage of this analytical solution is the need to assume that the subsurface rock is a homogeneous medium and has a homogeneous initial temperature. The medium-deep buried pipe heat exchanger goes deep into the ground for thousands of meters, and the ground temperature gradient becomes a main factor affecting the heat transfer process, so that it is obviously unsuitable to continuously assume that the whole underground rock and soil is a uniform medium and neglect the ground temperature gradient. In addition, in the analytical solution analysis method of heat transfer of the buried pipe heat exchanger, the heat transfer of the buried pipe heat exchanger needs to be divided into two areas to be treated respectively, and in the traditional analytical solution method, the interface between the two areas, namely the borehole wall, needs to be connected through simplifying the assumption. It is common practice to assume uniform borehole wall temperature for problems inside the borehole and uniform heat flow on the borehole wall for problems outside the borehole. Such simplifying assumptions are clearly unreasonable, but because of the complex and time-consuming heat transfer calculations of the borehole heat exchanger, such inaccurate interfacing conditions have to be employed in order to be able to employ a concise analytical solution formula. Researchers have also investigated the heat transfer of single bore buried pipe heat exchangers under conditions of non-uniform initial temperature. In order to discard the simplifying assumption on the connection interface and simultaneously keep the solving route of the analytic solution formula in the area outside the drill hole, the method performs discretization processing on the space (depth direction) and time on the heat source in the drill hole. Their work only involves single bore buried pipe heat exchanger heat exchangers; moreover, for the problems of deep holes and long time, the method has huge calculation workload, and the advantage of simple and direct calculation of the traditional analytical solution method is lost. In addition, the assumption that an overall uniform medium is inevitably adopted is not practical due to the adoption of analytic solutions.
The second type of heat transfer analysis of the buried pipe heat exchanger is to use a discretized numerical calculation-based heat transfer model, solve the temperature response in underground and fluid by using a finite element or finite difference method, and perform heat transfer analysis. With the progress of computer technology, the numerical calculation method has become a basic means of heat transfer analysis due to the characteristic of strong adaptability, and has become an important tool for theoretical research of the buried pipe heat exchanger. This approach allows for relatively realistic conditions such as non-uniformity of the subsurface medium and geothermal gradients, and allows for relatively realistic boundary connection conditions to be followed without simplifying assumptions when dealing with coupling of heat transfer between the two regions inside and outside the borehole. However, the heat transfer problem of the buried pipe heat exchanger relates to large span of the space range, and geometric configuration is complex from millimeter magnitude of pipe wall thickness to kilometer magnitude of depth; the span of the time range involved in the problem is also large, the change of load along with time and the characteristic time of flow can be in the order of minutes, and the time span of the system operation is longer than ten years. Thus, numerical modeling of this type of heat transfer problem would require dividing the area into a large number of units and consuming a large amount of computation time. The heat transfer of a single-hole buried pipe heat exchanger can be described by using a two-dimensional problem in cylindrical coordinates, but when solving the heat transfer of a buried pipe heat exchanger group consisting of more than two drilling holes, the heat transfer of the buried pipe heat exchanger group is related to a three-dimensional unsteady heat transfer problem, the calculation workload is often intolerable, and the basic heat transfer analysis or the direct solving of engineering problems are difficult. Therefore, the existing numerical analysis and research on heat transfer of the buried pipe heat exchanger (particularly the medium-deep buried pipe heat exchanger) mainly relates to a single-hole buried pipe heat exchanger, and is not suitable for the scene of a multi-hole buried pipe heat exchanger.
Disclosure of Invention
In order to solve the problems, the invention provides a heat transfer dimension reduction analysis method and a heat transfer dimension reduction analysis system for a porous buried pipe heat exchanger.
According to some embodiments, the present invention employs the following technical solutions:
a heat transfer and dimension reduction analysis method for a porous buried pipe heat exchanger comprises the following steps:
(1) Determining parameters of the porous buried pipe heat exchanger;
(2) Calculating and assigning an initial temperature distribution in the stratum, assigning an initial temperature distribution of fluid in each borehole, and determining an initial temperature distribution of the borehole wall;
(3) Calculating the temperature distribution of the fluid in each borehole heat exchanger at the next moment according to the mathematical model of heat transfer in the borehole;
(4) According to the temperature distribution of the fluid in each borehole heat exchanger, calculating the temperature response of each single-hole buried pipe heat exchanger in the rock and soil at the next moment by using a single-hole buried pipe heat exchanger heat transfer model;
(5) And calculating the temperature response in the rock and soil under the combined action of the porous buried pipe heat exchangers based on the temperature response of each single-hole buried pipe heat exchanger in the rock and soil by using the superposition principle.
As an alternative embodiment, the specific process of the step (1) includes: the geometry, physical configuration, flow and load changes of the porous borehole heat exchanger over time, the planar placement of each borehole, parameters of the formation and geothermal heat flow are obtained.
In an alternative embodiment, in the step (2), when performing the temperature assignment, an initial temperature distribution of the fluid in each borehole is the same as an initial temperature distribution in the formation; the initial temperature profile of the borehole wall is the same as the initial temperature profile in the formation.
In the step (3), the whole area is divided into two parts, namely an inner part and an outer part of the drill hole, in the process of establishing the heat transfer model, heat transfer sub-models are respectively established, and real connection conditions of the inner part and the outer part of the drill hole are considered.
As a further defined embodiment, in the step (3), the heat transfer model in the borehole in the heat transfer model employs a corrected quasi-three-dimensional model taking into account the change of the fluid temperature with time and the thermal capacity of the material.
As a further defined embodiment, in the step (3), the heat transfer model outside the borehole in the heat transfer model satisfies the following assumption condition:
the heat transfer mechanism in the medium outside the drilled hole only considers heat conduction, and does not consider other heat transfer caused by fluid seepage and the like;
the outer region of the drill hole consists of a plurality of stratum which are horizontally layered, each layer is a uniform medium, and the thermal physical properties of the stratum are not changed along with the temperature;
uniform geothermal flow is present in the region under investigation;
the outer boundary of the region in the horizontal direction is far away from the borehole of the buried pipe heat exchanger and is an adiabatic boundary;
the temperature distribution is maintained in a steady state in the initial time domain without being disturbed everywhere.
In the step (4), a heat transfer control equation and boundary conditions of the single-hole buried pipe heat exchanger are constructed, and solutions of steady-state initial temperature distribution of the rock-soil area outside the drill hole are substituted into the control equation and boundary conditions to obtain a problem formula, and then the problem formula is solved.
In the solving process, when the two-dimensional transient heat conduction problem on each time step is processed, a catch-up method is adopted to solve a linear algebraic equation set, and the discretization of the variable step is adopted in the radial direction.
Alternatively, in the step (5), the three-dimensional temperature response generated by the porous borehole heat exchanger is the sum of the temperature responses generated by each single-hole borehole heat exchanger under the zero initial condition and the sum of the steady-state initial temperature distribution.
The temperature rise of the porous buried pipe heat exchanger under the zero initial condition is equal to the sum of the temperature rises of the single-hole buried pipe heat exchangers.
Alternatively, steps (3) - (5) are cyclically performed to obtain the temperature profile of the fluid in the earth and in each borehole at any one time.
A porous buried pipe heat exchanger heat transfer dimension reduction analysis system, comprising:
the parameter configuration module is configured to determine parameters of the porous buried pipe heat exchanger, assign values to initial temperature distribution in the stratum, assign values to initial temperature distribution of fluid in each borehole, and determine initial temperature distribution of the borehole wall;
the temperature distribution calculation module is configured to calculate the temperature distribution of the fluid in each borehole heat exchanger at the next moment according to the mathematical model of heat transfer in the borehole;
the temperature response calculation module is configured to calculate the temperature response of each single-hole buried pipe heat exchanger in the rock and soil at the next moment by using the heat transfer model of the single-hole buried pipe heat exchanger according to the temperature distribution of the fluid in each drilling heat exchanger;
and the superposition module is configured to calculate the temperature response in the rock soil under the combined action of the porous buried pipe heat exchangers based on the temperature response of each single-hole buried pipe heat exchanger in the rock soil by utilizing the superposition principle.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, under the initial conditions and boundary conditions (including connection conditions inside and outside the drilling holes) as real as possible, the three-dimensional heat transfer problem of the porous buried pipe heat exchanger is decomposed into superposition of a plurality of single-hole two-dimensional problems by utilizing the superposition principle, and the numerical calculation of dimension reduction is realized, so that the calculation efficiency is improved.
When the heat transfer calculation of the single-hole buried pipe heat exchanger is performed, a heat transfer control equation and boundary conditions of the single-hole buried pipe heat exchanger are constructed, the solution of the steady-state initial temperature distribution of the rock-soil area outside the drilling hole is substituted into the original control equation and boundary conditions to obtain a problem type, the problem type is solved, a catch-up method is adopted to solve a linear algebraic equation set when the two-dimensional transient heat conduction problem on each time step is processed, and the calculation efficiency is greatly improved; meanwhile, discretization processing of variable step length is adopted in the radial direction, so that the number of nodes is greatly reduced.
The invention effectively improves the calculation speed and provides powerful support for simulating the heat transfer of the porous buried pipe heat exchanger.
In order to make the above objects, features and advantages of the present invention more comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a schematic view of a sleeve type borehole heat exchanger;
FIG. 2 is a schematic plan view of a group of porous borehole heat exchangers;
FIG. 3 is a flow chart of the dimension reduction value calculation of the porous buried pipe heat exchanger;
FIG. 4 is a schematic view of the temperature distribution of the rock and soil of a dual borehole heat exchanger;
FIG. 5 is a schematic diagram of the temperature of the circulating water outlet of the double borehole buried pipe heat exchanger as a function of time.
The specific embodiment is as follows:
the invention will be further described with reference to the drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof.
In this embodiment, the heat transfer process of the buried pipe heat exchanger is considered to be divided into two parts, namely, the inside part and the outside part of the borehole, and the two parts have different heat transfer rules and characteristics, so that mathematical models are respectively built. The connection condition of the two areas is that the temperature and the normal heat flow of the two areas are equal. The important means of the research is to decompose the heat transfer problem of the porous buried pipe heat exchanger into a plurality of stacks of single-hole buried pipe heat exchangers by using the stacking principle, and to process the initial temperature distribution with temperature gradient by using the stacking principle. The heat transfer model of the single-hole buried pipe heat exchanger under the condition of having a ground temperature gradient is mainly discussed below, and according to the superposition principle, the temperature rise generated by the multi-hole buried pipe heat exchanger under the zero initial condition is equal to the sum of the temperature rises generated by the single-hole buried pipe heat exchangers.
As shown in fig. 3, the specific steps of the method provided in this embodiment include:
step one: given system parameters, including borehole heat exchanger geometry, physical configuration, flow and load changes over time, borehole plan layout, formation parameters, geothermal flows, etc.
Step two: an initial temperature distribution in the formation is calculated.
Step three: the initial temperature profile of the fluid in each borehole is assigned a value that may be assumed to be the same as the initial temperature profile in the formation.
Step four: the initial temperature profile of a given borehole wall is the same as the initial temperature profile in the formation.
Step five: and calculating the temperature distribution of the fluid in each borehole heat exchanger at the next moment according to the mathematical model of heat transfer in the borehole.
Step six: and calculating the temperature response of each single-hole buried pipe heat exchanger in the rock and soil at the next moment by using a heat transfer model of the single-hole buried pipe heat exchanger according to the temperature distribution of the fluid in each drilling heat exchanger.
Step seven: and calculating the temperature response in the rock and soil under the combined action of the porous buried pipe heat exchanger by using the superposition principle.
Step eight: and repeating the steps five to seven to obtain the temperature distribution of the fluid in the rock soil and each borehole at any moment, and also obtain the outlet temperature of the fluid which is concerned in engineering.
Specifically, first, a heat transfer model in a borehole is introduced:
the heat transfer in the borehole of the buried pipe heat exchanger is basically characterized in that the convection heat transfer of fluid in the flowing direction in a closed pipeline (U-shaped pipe or sleeve) is balanced with the radial heat transfer between the fluid and the borehole wall through the pipe wall and the material in the borehole.
A definite solution to the convective heat transfer problem within a given tube is typically required, most often the variation of the inlet temperature or heat transfer capacity of a given fluid over time. In practical engineering calculations, the heat transfer quantity (load) of the heat exchanger is an input parameter that is more readily available; most heat exchange calculation software requires inlet temperature as an input parameter. After the temperature distribution of the borehole wall is known, the heat transfer within the borehole can be calculated virtually independently.
Heat transfer simulations for U-pipe or sleeve type borehole heat exchangers have developed many models ranging from the simplest method of estimation using the concept of thermal resistance to some CFD software that models flow and convective heat transfer in the pipeline in detail. These various models of varying degrees of refinement and accuracy should all be an integral part of the present porous borehole heat exchanger heat transfer model. However, for the flow and heat transfer in the ultra-long straight pipeline involved in the ground heat exchanger, the accuracy of the one-dimensional model can meet the actual needs, so that the complex and time-consuming three-dimensional CFD simulation is not recommended.
In conventional analytic solutions of borehole heat exchangers, the heat transfer within the borehole is typically performed using a so-called "quasi-three-dimensional" model, i.e. taking into account the change in fluid temperature in the depth direction and the convective heat transfer in the axial direction, taking into account the two-dimensional (or one-dimensional) heat transfer across the borehole interior cross-section. Because of the special slender characteristic of the heat exchanger structure of the drilling, in order to keep the simplicity of the model, the axial heat conduction of the solid part in the drilling is ignored; at the same time, the heat capacity of the material in the borehole (including backfill material, tubing and water in the tubing) is also negligible. This latter simplifying assumption effectively treats the heat transfer within the borehole as a steady state problem, primarily to enable analytical solutions. However, this assumption is clearly a departure from the actual situation, which can be significant, especially at system start-up and load fluctuations.
The present embodiment will generally be solved using a numerical calculation method, where one term of the change in fluid temperature over time is added to the equation, while using a simplified assumption, ignoring the temperature differences of the inner tube wall and the inner tube fluid, ignoring the temperature differences of the outer tube wall and the backfill material and the outer tube fluid. Such assumptions improve the fidelity of the model without increasing the number of variables, while having little impact on the computational effort.
Therefore, the heat transfer in the borehole in the heat transfer model provided in this embodiment employs a quasi-three-dimensional model that takes into account the change in flow-through temperature over time and the modification of the thermal capacity of the material. The mathematical model of heat transfer in the borehole of the sleeve type buried pipe heat exchanger, namely the model which takes the precision and the calculation efficiency of the model into consideration, is given below, and the temperature distribution of fluid in the inner pipe and the outer pipe is determined according to the known temperature distribution of the borehole wall.
The temperature of the outer tube is noted as Tf1 and the temperature of the inner tube is noted as Tf2. The sleeve type ground heat exchanger can have two flow forms: an outer inlet and an inner outlet and an inner inlet and an outer outlet; different flow patterns will result in different temperature profiles and different amounts of heat transfer.
According to the balance of energy, the flow form of internal inlet and external outlet can be written
Wherein c is the specific heat of the fluid, kJ/kg.K, M is the mass flow of the fluid in the tube, kg/s; c (C) 1 ，C 2 The heat capacities of the outer and inner tube sections per unit length, respectively; r is R 1 ，R 12 The thermal resistance between the outer tube fluid and the borehole wall and the thermal resistance between the inner and outer tube fluid, respectively.
The solution condition is that the inner tube and the outer tube are communicated at the bottom of the drilling hole, and the temperature is the same.
z＝H,T f1 ＝T f2 (2)
Inlet conditions may be given by temperature
z＝0,T f2 ＝T′ f (3)
Or a given heat transfer amount (here, provision is made for taking heat from the ground to be positive)
Wherein Q is the heat extraction rate of the heat exchanger, W and M are the flow rate of the circulating liquid, kg/s and c is the specific heat of the circulating liquid, J/kg.K.
When the flow form is changed into the external input and the internal output, the last term on the right in the equation (1), namely the sign of the flow term is changed, and the solution condition (3) or (4) is correspondingly changed.
The heat transfer model outside the borehole is described as follows:
the heat conduction problem in the hollow cylindrical domain as shown in fig. 1, the heat transfer to the region outside the borehole uses the following basic assumption:
the heat transfer mechanism in the medium outside the borehole is only considered for heat conduction, and other heat transfer caused by fluid seepage and the like is not considered.
The outer zone of the borehole consists of horizontally layered formations, each of which is a homogeneous medium of thermophysical properties (coefficient of thermal conductivity k i Thermal diffusivity a i ) Is not changed with temperature.
With uniform geothermal flow, q, in the region under investigation g ,W/m2。
The outer boundary of the zone in the horizontal direction is away from the borehole of the borehole heat exchanger and is an adiabatic boundary.
The temperature distribution is maintained in a steady state in the initial time domain without being disturbed everywhere.
In order to study the heat transfer of a porous borehole heat exchanger, a single hole must be analyzed. The problem of rock-soil stratification is not addressed in the mathematical description below to preserve the brevity of the expression. In practice, while this layering situation will cause great difficulty in resolving solutions, there is little impact on numerical solutions.
The mathematical description of the problem includes:
control equation
Where T is the temperature, r and z are the radial and axial coordinates, respectively, and τ is the time.
Boundary conditions:
the earth surface generally adopts a first type of boundary condition, namely, the earth surface temperature is assumed to be a fixed value t 0 ；
T＝t 0 ,r b ≤r≤r boundary ,z＝0,τ≥0 (6)
The bottom boundary of the zone is located deep away from the bottom of the borehole, and a second type of boundary condition may be employed.
The radial boundaries of the zones are located sufficiently far from the borehole and adiabatic boundaries may be employed.
On the borehole wall, the connection conditions of the two areas inside and outside the borehole are:
T＝T b ,r＝r b ,0≤z≤H,τ≥0 (9)
wherein r is b Is the radius of the drilling hole, T b Is the temperature distribution on the borehole wall.
The rock and soil part below the bottom of the drilling hole is simplified into radial boundary conditions
Initial conditions: the initial temperature distribution in the rock and soil is usually the temperature distribution without interference, and satisfies the steady-state heat conduction equation, the initial temperature distribution is
When the rock layer is assumed to be composed of a plurality of horizontal strata, the initial temperature distribution is
And (3) superposition dimension reduction calculation:
for the heat transfer problem of the single hole buried pipe heat exchanger described by the mathematical model above, the solution of the temperature response of the rock and soil region outside the borehole can be expressed as a superposition of the two parts
T(r,z,τ)＝θ(r,z,τ)+T 0 (r,z) (13)
Where θ is a new temperature function defined according to the present formula, T 0 ＝t 0 +q g z/k is the steady-state initial temperature profile. Substituting the above expression into the solution problem of the formulas (5) to (12), it is known that θ (r, z, τ) is a solution to the following zero initial condition problem.
That is, θ (r, z, τ) will satisfy the heat conduction differential equation, the zero initial condition, and the homogeneous boundary condition of the upper and lower boundaries; the two-dimensional heat conduction problem can be combined with a mathematical model in a drilling hole to carry out quick numerical solution.
For the heat transfer problem of the porous borehole heat exchanger, the arrangement of the pores on a flat surface is shown in FIG. 2. For a group of porous borehole heat exchangers consisting of n boreholes, the boreholes may have different geometric and physical structures and different load characteristics, but the temperature response that they produce together may also be derived from the superposition principle, as long as all of the boreholes are in the same formation. The temperature response in the subsurface rock must now be represented by a three-dimensional function. According to the superposition principle, the temperature response of any point (x, y, z) in the rock-soil outside the borehole at any moment tau can be expressed as
Wherein the method comprises the steps of
T 0 Is the steady-state initial temperature distribution, θ i (r, z, τ), (i=1, 2, …, n) are solutions of the temperature response of the ith borehole heat exchanger under conditions satisfying the solution equation (14), respectively.
For calculations within a borehole, the temperature of the borehole wall is of primary concern. According to the above formula, the temperature distribution on the borehole wall of the jth borehole is
Wherein r is ij Is the distance between the centers of the i-th borehole and the j-th borehole,
thus, the three-dimensional heat transfer problem of the porous buried pipe heat exchanger can be solved by solving the two-dimensional heat transfer problem of a plurality of single-hole buried pipe heat exchangers. The obtained calculation result can be the temperature distribution in the rock and soil at any moment, and the outlet temperature of any buried pipe heat exchanger at any moment which is more concerned in engineering can be given.
Through the above detailed process, it can be seen that the present embodiment abandons multiple simplified assumptions in the conventional heat transfer model, realizes high fidelity of the model, and simultaneously decomposes the three-dimensional heat conduction problem of the porous buried pipe heat exchanger into superposition of two-dimensional heat conduction problems of a plurality of single-hole buried pipe heat exchangers according to the concept of superposition principle, so that the efficiency of numerical calculation is improved by orders of magnitude. The method not only has important progress in the field of numerical calculation, but also has important promotion effect on the development and application of the deep ground source heat pump technology.
The porous middle-deep buried pipe heat exchanger is provided with more than one buried pipe heat exchanger. The heat exchange between the working medium and the ground is realized by drilling holes in the stratum and then burying the buried pipe therein to form a circulation loop of the heat exchange working medium. The medium-deep buried pipe heat exchanger related to the embodiment is generally buried by adopting a sleeve heat exchanger consisting of an inner pipe and an outer pipe, but the principle and the method are also applicable to other forms of devices buried in the stratum for realizing heat exchange between the circulating working medium and the underground rock soil.
The mathematical model outside the borehole of the embodiment considers the geothermal gradient in the rock and soil layer generated by the geothermal flow; and the assumption that the whole area is required to be a single uniform stratum in the traditional model is abandoned, and the fact that the rock-soil area is a plurality of layers of mediums which are uniform respectively can be considered. The various boreholes involved in the model may have different geometric and physical configurations and different load characteristics, but require that all borehole heat exchangers be disposed in the same formation.
The superposition principle provided by the embodiment can be extended to occasions where the ground temperature gradient is considered.
The embodiment abandons the simplified assumption of uniform temperature and heat flow of the wall of the drilling hole in the traditional model, and considers the real connection conditions of the inner area and the outer area of the drilling hole. For the related two-dimensional heat transfer sub-problem of the single-hole buried pipe heat exchanger, a finite difference method in cylindrical coordinates can be adopted, a catch-up method is adopted to solve the generated linear algebraic equation set, and the numerical calculation efficiency can be greatly improved.
As a verification, software was developed for the provided dimension reduction calculation method, and calculation was performed for one example. The system considered by the calculation example is a buried pipe heat exchanger consisting of two middle-deep sleeve type drilling holes, the geometric parameters and physical conditions of the two drilling holes are identical, and the buried pipe heat exchanger is buried in rock soil consisting of three layers of horizontal stratum. The main parameters of the system are listed in table 1. The system was run for 8000 hours under constant load conditions.
TABLE 1 principal parameters of a double bore buried pipe heat exchanger system in an example
10.412s for completing the above operation on a desktop (Intel (R) Core (TM) i7-8700CPU@320GHZ 3.19GHZ), it can be seen that the method provided in this embodiment reduces the number of nodes, greatly improves the calculation efficiency, and the temperature distribution in the rock and soil at the end of the operation is plotted in fig. 4. Figure 5 shows the variation of fluid inlet and outlet temperatures over time throughout operation and compared to the calculation for a single bore borehole heat exchanger. The result is accurate, and a powerful support is provided for simulating the heat transfer of the porous buried pipe heat exchanger.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.
Claims (8)
1. A heat transfer and dimension reduction analysis method for a porous buried pipe heat exchanger is characterized by comprising the following steps: the method comprises the following steps:
(1) Determining parameters of the porous buried pipe heat exchanger;
(2) Calculating and assigning an initial temperature distribution in the stratum, assigning an initial temperature distribution of fluid in each borehole, and determining an initial temperature distribution of the borehole wall;
(3) Calculating the temperature distribution of the fluid in each borehole heat exchanger at the next moment according to the mathematical model of heat transfer in the borehole;
(4) According to the temperature distribution of the fluid in each borehole heat exchanger, calculating the temperature response of each single-hole buried pipe heat exchanger in the rock and soil at the next moment by using a single-hole buried pipe heat exchanger heat transfer model;
(5) Calculating the temperature response in the rock and soil under the combined action of the porous buried pipe heat exchangers based on the temperature response of each single-hole buried pipe heat exchanger in the rock and soil by utilizing the superposition principle;
in the step (3), in the process of establishing the heat transfer model, dividing the whole area into two parts, namely an inner part and an outer part of a drill hole, respectively establishing a heat transfer sub-model, and considering the real connection condition of the inner part and the outer part of the drill hole;
in the step (3), the heat transfer model outside the drilling hole in the heat transfer model meets the following assumed conditions:
the heat transfer mechanism in the medium outside the drilled hole only considers heat conduction, and does not consider other heat transfer caused by fluid seepage and the like;
the outer region of the drill hole consists of a plurality of stratum which are horizontally layered, each layer is a uniform medium, and the thermal physical properties of the stratum are not changed along with the temperature;
uniform geothermal flow is present in the region under investigation;
the outer boundary of the region in the horizontal direction is far away from the borehole of the buried pipe heat exchanger and is an adiabatic boundary;
the temperature distribution is maintained in a steady state in the initial time domain without being disturbed everywhere.
2. The heat transfer and dimension reduction analysis method for the porous buried pipe heat exchanger as set forth in claim 1, wherein the heat transfer and dimension reduction analysis method is characterized in that: the specific process of the step (1) comprises the following steps: the geometry, physical configuration, flow and load changes of the porous borehole heat exchanger over time, the planar placement of each borehole, parameters of the formation and geothermal heat flow are obtained.
3. The heat transfer and dimension reduction analysis method for the porous buried pipe heat exchanger as set forth in claim 1, wherein the heat transfer and dimension reduction analysis method is characterized in that: in the step (2), when the temperature assignment is performed, the initial temperature distribution of the fluid in each borehole is the same as the initial temperature distribution in the stratum; the initial temperature profile of the borehole wall is the same as the initial temperature profile in the formation.
4. The heat transfer and dimension reduction analysis method for the porous buried pipe heat exchanger as set forth in claim 1, wherein the heat transfer and dimension reduction analysis method is characterized in that: in the step (3), the heat transfer model in the borehole in the heat transfer model adopts a corrected quasi-three-dimensional model taking into consideration the change of the fluid temperature with time and the thermal capacity of the material.
5. The heat transfer and dimension reduction analysis method for the porous buried pipe heat exchanger as set forth in claim 1, wherein the heat transfer and dimension reduction analysis method is characterized in that: in the step (4), a heat transfer control equation and boundary conditions of the single-hole buried pipe heat exchanger are constructed, and solutions of steady-state initial temperature distribution of a rock-soil area outside a drilling hole are substituted into the control equation and the boundary conditions to obtain a problem, and the problem is solved;
in the solving process, when the two-dimensional transient heat conduction problem on each time step is processed, a catch-up method is adopted to solve a linear algebraic equation set, and the discretization of the variable step is adopted in the radial direction.
6. The heat transfer and dimension reduction analysis method for the porous buried pipe heat exchanger as set forth in claim 1, wherein the heat transfer and dimension reduction analysis method is characterized in that: in the step (5), the three-dimensional temperature response generated by the porous buried pipe heat exchanger is the sum of the temperature responses generated by each single-hole buried pipe heat exchanger under the zero initial condition and the sum of the steady-state initial temperature distribution;
the temperature rise of the porous buried pipe heat exchanger under the zero initial condition is equal to the sum of the temperature rises of the single-hole buried pipe heat exchangers.
7. The heat transfer and dimension reduction analysis method for the porous buried pipe heat exchanger as set forth in claim 1, wherein the heat transfer and dimension reduction analysis method is characterized in that: and (5) circularly executing the steps (3) - (5) to obtain the temperature distribution of the fluid in the rock soil and each borehole at any moment.
8. A heat transfer dimension reduction analysis system for a porous buried pipe heat exchanger applying the heat transfer dimension reduction analysis method for the porous buried pipe heat exchanger according to any one of claims 1 to 7, which is characterized in that: comprising the following steps:
the parameter configuration module is configured to determine parameters of the porous buried pipe heat exchanger, assign values to initial temperature distribution in the stratum, assign values to initial temperature distribution of fluid in each borehole, and determine initial temperature distribution of the borehole wall;
the temperature distribution calculation module is configured to calculate the temperature distribution of the fluid in each borehole heat exchanger at the next moment according to the mathematical model of heat transfer in the borehole;
the temperature response calculation module is configured to calculate the temperature response of each single-hole buried pipe heat exchanger in the rock and soil at the next moment by using the heat transfer model of the single-hole buried pipe heat exchanger according to the temperature distribution of the fluid in each drilling heat exchanger;
and the superposition module is configured to calculate the temperature response in the rock soil under the combined action of the porous buried pipe heat exchangers based on the temperature response of each single-hole buried pipe heat exchanger in the rock soil by utilizing the superposition principle.
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| CN113515863B (en) * | 2021-07-14 | 2022-11-29 | 中煤科工集团西安研究院有限公司 | Method for calculating heat quantity of middle-deep sleeve type heat exchanger based on numerical inversion |
| 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 |
| CN113704941B (en) * | 2021-09-01 | 2024-06-07 | 北京中地金石科技有限公司 | Calculation method for heat transfer model of deep sleeve heat exchanger |
| CN113656986B (en) * | 2021-09-16 | 2024-06-21 | 深能科技(山东)有限公司 | Method for rapidly calculating long-term running heat exchange performance of middle-deep geothermal buried pipe |
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