CN111581838B - Performance prediction semi-analysis method for U-shaped underground heat exchanger - Google Patents
Performance prediction semi-analysis method for U-shaped underground heat exchanger Download PDFInfo
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Abstract
The invention discloses a semi-analytic method for predicting the performance of a U-shaped underground heat exchanger, which aims at the U-shaped underground heat exchanger widely used in the application process of geothermal energy, and realizes the rapid prediction of the performance of the U-shaped underground heat exchanger such as outlet water temperature, heat exchange quantity and the like by utilizing the size parameters, the rock-soil thermophysical parameters and the aquifer physical parameters of the underground heat exchanger in practical engineering based on the basic heat conduction and convection heat transfer rules of the heat transfer science. The method can help people to master the overall performance of the U-shaped buried heat exchanger in advance before the heating project is developed, provides a theoretical basis for the design process and the operation process, and is beneficial to reducing the cost and improving the utilization efficiency of geothermal energy. The method can be applied before engineering development, and has the characteristics of rapidness and easy implementation.
Description
Technical Field
The invention relates to a performance prediction semi-analysis method for a U-shaped underground heat exchanger, and belongs to the technical field of heat exchanger performance prediction.
Background
Geothermal energy is a clean, environment-friendly and pollution-free energy source, has the advantages of wide distribution, huge reserves and the like, and is paid more and more attention by people at present. The U-shaped buried heat exchanger is a common heat-taking device in the process of utilizing geothermal energy. In the process of utilizing the U-shaped underground heat exchanger for heat extraction, the heat exchanger may penetrate different rock-soil layers and a plurality of aquifers, and uncertainty is brought to prediction of the performance of the heat exchanger. At present, the relevant theory of the heat exchanger in the form is not mature, and the existing numerical algorithm has the defects of long calculation time consumption, complex modeling and the like. Therefore, the method for rapidly, efficiently and accurately predicting the performance of the U-shaped underground heat exchanger is mastered, and has very important theoretical significance and engineering value.
Disclosure of Invention
The invention aims to provide a performance prediction semi-analytic method for a U-shaped underground heat exchanger, which is used for estimating the heat exchange performance of the heat exchanger before project development by utilizing the basic heat conduction and convection heat transfer principles of heat transfer science and based on energy conservation.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a performance prediction semi-analysis method for a U-shaped buried heat exchanger comprises the following steps:
s1: determining the structure and thermophysical parameters of the U-shaped buried heat exchanger;
s2: calculating the equivalent outer diameter of the U-shaped buried heat exchanger after two branch pipes are equivalent to a single round pipe;
s3: determining thermophysical parameters of rock and soil at different depths;
s4: determining system operating parameters and other related parameters;
s5: calculating the flow velocity of the working medium in the U-shaped buried heat exchanger according to the mass flow of the heat exchange working medium;
calculating the heat conduction resistance between the pipe wall in the equivalent circular pipe and the surrounding rock soil;
s6: let i =1, let the inlet water temperature of the first calculation section be equal to the inlet temperature of the heat exchange working medium entering the heat exchanger, i.e. T in (1)＝T in ；
S7: setting an initial value T for the outlet water temperature of the ith calculation section out (i)＝50℃；
S8: calculating the qualitative temperature of the heat exchange working medium in the current calculation section;
calculating the heat change of the fluid working medium after flowing through the current calculation section;
s9: calculating the Reynolds number Re and the Plantt number Pr of the heat exchange working medium in the current calculation section;
calculating the convection heat transfer resistance between the heat exchange working medium and the inner wall surface of the heat exchanger;
s10: judging whether the current calculation section is positioned in the aquifer, if so, obtaining the temperature T of the outer wall surface of the heat exchanger of the current calculation section by utilizing the existing moving line heat source and column heat source formulas based on the parameters b (i) (ii) a If not, then based on the above parameters, use the existingObtaining the outer wall surface temperature T of the heat exchanger at the current calculation section by a finite long line heat source and column heat source formula b (i)；
S11: calculating the heat exchange quantity of fluid heat exchange working media in the heat exchanger and surrounding rock and soil;
s12: judging | q 1 –q 2 Whether | is less than β:
if yes, q 2 I.e. the T calculated by the accurate solution of the heat exchange quantity of the heat exchange working medium in the current calculation section and the surrounding rock soil out (i) Namely, the temperature of the outlet of the heat exchange working medium at the current calculation section is accurately solved;
if not, repeating S8-S12 until the result satisfies | q 1 –q 2 |<Beta, obtaining the heat exchange quantity and the outlet water temperature of the current calculation section;
s13: the calculation of the next calculation segment is performed: let i = i +1, let the heat exchange working medium inlet temperature of the next calculation section equal to the heat exchange working medium outlet temperature of the current calculation section, that is: t is in (i+1)＝T out (i) (ii) a Repeating S7 to S12;
s14: judging whether i is more than or equal to n:
if not, repeating S7-S13; if yes, the calculation is finished.
As a further improvement of the invention, in S2, the equivalent outer diameter of two branch pipes of the U-shaped buried heat exchanger after being equivalent to a single round pipe is calculated by the following formula:
wherein r is eq,o Is an equivalent radius; r is o Is the heat exchanger tube radius; d is the center distance of the water supply and return pipe.
As a further improvement of the invention, the specific method for determining the thermophysical parameters of the rock and soil at different depths in S3 comprises the following steps:
dividing the heat exchanger and surrounding rock and soil into n calculation sections from the ground downwards along the depth direction of the heat exchanger; wherein the length of the ith calculation section is L (i), and the temperature of the rock-soil layer is T soil (i) Thermal conductivity of rock-soil layer is k soil (i) Density of rock and soil is rho soil (i) Specific heat of rock and soil c soil (i) The thermal diffusivity of rock-soil α (i);
if the calculated segment is located in the aquifer, the flow rate of the water is u (i).
As a further improvement of the present invention, in S5
Wherein u is fluid The working medium flow velocity; m is the mass flow of the fluid working medium; d pipe The wall thickness of the heat exchanger pipe;
calculating the heat conduction resistance between the pipe wall in the equivalent circular pipe and the surrounding rock soil by adopting the following formula:
wherein R is c Is the heat conduction thermal resistance between the heat exchange pipeline and the surrounding rock soil; r is a radical of hydrogen b Is the borehole radius; k is a radical of pipe 、k grout The heat conductivity coefficient of the heat exchanger pipeline and the heat conductivity coefficient of the backfill material are respectively; l (i) is the length of the current computed segment.
As a further improvement of the invention, in S8, the qualitative temperature of the heat exchange working medium in the current calculation section is calculated by using the following formula:
calculating the heat change of the fluid working medium after flowing through the current calculation section by using the following formula:
q 1 ＝mc[T out (i)-T in (i)]
wherein, T m The average temperature of the working medium inlet and outlet of the current calculation section is calculated; t is a unit of out (i)、T in (i) Respectively calculating the outlet temperature and the inlet temperature of the working medium of the current calculation section; q. q.s 1 The heat absorbed by the heat exchange working medium after flowing through the first calculation section; c is the specific heat of the heat exchange working medium.
As a further improvement of the invention, in S9, the Reynolds number Re and the Plantt number Pr of the heat exchange working medium at the current calculation section are respectively calculated by the following formulas:
Pr＝-0.000023T m 3 +0.005073T m 2 -0.39525T m +13.344266
calculating the convective heat transfer resistance between the heat exchange working medium and the inner wall surface of the heat exchanger by adopting the following formula:
wherein Re is Reynolds number; pr is the Plantt number; r f Is thermal resistance for convective heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ] fluid Is the heat conductivity coefficient of the heat exchange working medium.
As a further improvement of the present invention, if the determination result is yes, the following finite-length moving-line heat source formula is adopted in S10 to perform calculation:
wherein, T b For borehole wall surface temperature, T soil (i)、k soil (i) And alpha (i) is the temperature, the heat conductivity coefficient and the thermal diffusion coefficient of the rock-soil layer where the first calculation section is located respectively; u (i) is the flow rate of water in the aquifer; x, y and z are position coordinates of the wall surface under the condition that the center of the section of the inlet of the pipe section is taken as an origin; t is the running time; z' is an integral variable;
in the above-mentioned formula, the compound has the following structure,
erfc is a complementary error function;
if the judgment result is negative, calculating by adopting the following formula:
where ρ is soil (i) The density of rock soil; c. C soil (i) Specific heat of rock soil; r is the distance between the wall surface and the axis of the heat exchanger; z is the depth of the calculated position; z 'and t' are integral variables.
As a further improvement of the invention, in S11, the heat exchange quantity between the fluid heat exchange working medium in the heat exchanger and the surrounding rock soil is obtained by adopting the following formula:
wherein q is 2 To calculate the amount of heat exchange between the segment and the surrounding rock and soil.
As a further improvement of the present invention, T calculated in S12 by the following formula out (i) Namely, the accurate solution of the outlet temperature of the heat exchange working medium at the current calculation section is as follows:
wherein, T out (i) The working medium outlet temperature of the current calculation section.
As a further improvement of the invention, the obtained heat exchange working medium outlet temperatures of all the calculation sections are the temperature distribution of the fluid heat exchange working medium in the heat exchanger, and the working medium outlet temperature of the last calculation section is the working medium outlet temperature of the U-shaped buried heat exchanger; and the sum of the heat exchange quantity of all the calculation sections is the total heat exchange quantity of the U-shaped underground heat exchanger and the surrounding rock soil in the operation process.
Compared with the prior art, the invention has the following beneficial effects:
according to the performance prediction semi-analysis method for the U-shaped underground heat exchanger, the thermophysical property change of underground rock and soil is brought into the setting process of the calculated boundary conditions, and the actual heat exchange process of the heat exchanger and the surrounding rock and soil can be accurately reflected by a model; by adopting a mode of combining an analytical algorithm with numerical iteration calculation, on the basis of ensuring the calculation precision, the calculation time is greatly reduced, and the calculation efficiency is improved. The method can be used for quickly calculating the heat exchange performance of the U-shaped underground heat exchangers with different sizes under different geological conditions, and can predict parameters such as outlet water temperature and heat exchange quantity of the heat exchangers. The performance of the heat exchanger can be estimated before actual engineering is carried out based on the U-shaped underground heat exchanger structure and geological condition information, the heat exchanger structure is favorably optimized, the engineering cost is reduced, and the efficiency of a geothermal energy system is improved. The method can provide theoretical basis and data reference for the efficient operation of a heating system of the underground heat exchanger, the calculation method is efficient and rapid, the development of the geothermal energy application theory is promoted, and the efficient utilization of geothermal energy and the reduction of cost are promoted.
Drawings
The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way. In addition, the shapes, the proportional sizes, and the like of the respective members in the drawings are merely schematic for facilitating the understanding of the present invention, and do not specifically limit the shapes, the proportional sizes, and the like of the respective members of the present invention. Those skilled in the art, having the benefit of the teachings of this invention, may choose from the various possible shapes and proportional sizes to implement the invention as a matter of case. In the drawings:
FIG. 1 is a flow chart of a method of the present invention;
fig. 2 is a schematic diagram of the equivalent structure and the calculation segment division of the U-shaped underground heat exchanger.
Detailed Description
In order to make those skilled in the art better understand the technical solutions of the present invention, 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 only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments in the present invention, shall fall within the protection scope of the present 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. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
As shown in fig. 1, the invention aims to provide a performance prediction semi-analytic method for a U-shaped buried heat exchanger, which has clear thought, is convenient to calculate, and is fast, and provides a reference theoretical guidance for performance prediction of the heat exchanger in actual engineering.
In order to realize the purpose, the technical scheme adopted by the invention is as follows: a performance prediction semi-analysis method for a U-shaped buried heat exchanger comprises the following specific calculation steps:
s1: determining the structure and thermophysical parameters of the U-shaped buried heat exchanger, including the depth H (unit: m) of the heat exchanger and the outer diameter r of the heat exchanger pipeline o (unit: m), heat exchanger tube wall thickness d pipe (unit: m), bore wall diameter r b (unit: m), the center distance D (unit: m) of the water supply and return pipe, and the heat conductivity coefficient k of the heat exchanger pipeline pipe (unit: W/m.K).
S2: calculating the equivalent outer diameter of the U-shaped buried heat exchanger after two branch pipes are equivalent to a single round pipe by adopting the following formula:
wherein r is eq,o Is the equivalent radius (unit: m); r is a radical of hydrogen o Is the heat exchanger pipe radius (unit: m); d is the center distance (unit: m) of the water supply and return pipe.
S3: and determining the thermophysical parameters of the rock and soil at different depths. The specific method comprises dividing the heat exchanger and surrounding rock and soil into n calculation sections from ground surface to ground along the depth direction of the heat exchanger. Wherein the length of the ith calculation section is L (i) (unit: m), and the temperature of the rock-soil layer is T soil (i) (unit:. Degree. C.) and the thermal conductivity of rock-soil layer is k soil (i) (unit: W/m.K) and rock density is rho soil (i) (unit: kg/m) 3 ) Specific heat of rock and soil c soil (i) (unit: J/kg. Cndot.). Degree.C, rock-soil thermal diffusivity alpha (i) (unit: m) 2 In s). If the calculated section is located in the aquifer, the flow rate of the water is u (i) (unit: m/s).
S4: system operating parameters and other relevant parameters are determined. The method specifically comprises the following steps: inlet temperature T of heat exchange working medium entering underground heat exchanger in (unit: DEG C), the mass flow rate m (unit: kg/s) of the heat exchange working medium, and the density rho (unit: kg/m) of the heat exchange working medium 3 ) Specific heat c of the heat exchange working medium (unit: j/kg · c), the system run time t (unit: s), thermal conductivity k of the borehole backfill material grout (unit: W/m · K), and a small amount β (e.g., β = 0.1) set in advance for the judgment error.
S5: according to the mass flow m of the heat exchange working medium, the flow velocity of the working medium in the U-shaped buried heat exchanger is calculated by adopting the following formula:
wherein u is fluid The flow rate of the working medium (unit: m/s); m is the mass flow (unit: kg/s) of the fluid working medium; d is a radical of pipe For heat exchanger pipe wall thickness (unit: m)
Calculating the heat conduction resistance between the pipe wall in the equivalent circular pipe and the surrounding rock soil by adopting the following formula:
wherein R is c Is the heat conduction thermal resistance (unit: K/W) between the heat exchange pipeline and the surrounding rock soil; r is b Is the borehole radius (unit: m); k is a radical of pipe 、k grout The heat conductivity coefficient of the heat exchanger pipeline and the heat conductivity coefficient of the backfill material (unit: W/m.K) are respectively; l (i) is the length of the current calculation segment(unit: m).
S6: let i =1, let the inlet water temperature of the first calculation section be equal to the inlet temperature of the heat exchange working medium entering the heat exchanger, i.e. T in (1)＝T in 。
S7: giving an initial value T to the outlet water temperature of the ith calculation section out (i)＝50℃。
S8: and calculating the qualitative temperature of the heat exchange working medium at the current calculation section by using the following formula:
wherein, T m The average temperature (unit: DEG C) of the working medium inlet and outlet of the current calculation section is calculated; t is a unit of out (i)、T in (i) Respectively the working medium outlet temperature and inlet temperature (unit:. Degree. C.) of the current calculation section. .
Calculating the heat change of the fluid working medium after flowing through the current calculation section by using the following formula:
q 1 ＝mc[T out (i)-T in (i)]
wherein q is 1 The heat absorbed by the heat exchange working medium after flowing through the first calculation section (unit: W); c is the specific heat of the heat exchange working medium (unit: J/kg. DEG C.).
S9: respectively calculating the Reynolds number Re and the Plantt number Pr of the heat exchange working medium at the current calculation section by using the following formulas:
Pr＝-0.000023T m 3 +0.005073T m 2 -0.39525T m +13.344266
wherein Re is Reynolds number; pr is the prandtl number.
Calculating the convective heat transfer resistance between the heat exchange working medium and the inner wall surface of the heat exchanger by adopting the following formula:
wherein R is f Is the heat resistance (unit: K/W) of the convection heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ] fluid The heat conductivity coefficient (unit: W/m.K) of the heat exchange working medium.
S10: judging whether the current calculation section is positioned in the aquifer, if so, obtaining the temperature T of the outer wall surface of the heat exchanger of the current calculation section by utilizing formulas of existing moving line heat sources, column heat sources and the like based on the parameters b (i) In that respect For example, the following finite-length moving-line heat source formula is adopted for calculation:
wherein, T b The temperature of the wall surface of the drilled hole (unit:. Degree. C.), T soil (i)、k soil (i) And alpha (i) is the temperature (unit: DEG C) of the rock-soil layer where the first calculation section is located, the heat conductivity coefficient (unit: W/m.K) and the heat diffusion coefficient (unit: m 2/s) respectively; u (i) is the flow rate of water in the aquifer (unit: m/s); x, y and z are position coordinates of the wall surface under the condition that the center of the section of the inlet of the pipe section is taken as an origin; t is the running time (unit: s); z' is an integral variable.
Wherein, the first and the second end of the pipe are connected with each other,
erfc is a complementary error function.
In the above formula, the first and second carbon atoms are,
if not, based on the parameters, the current calculation section heat exchanger outer wall surface temperature T is obtained by using the existing formulas of limited long-line heat sources, column heat sources and the like b (i) .1. The For example, the following formula is used for calculation:
where ρ is soil (i) Is the density of rock soil (unit: kg/m) 3 )；c soil (i) The specific heat of rock and soil (unit: J/kg DEG C); r is the distance between the wall surface and the axis of the heat exchanger; z is the depth of the calculated position; z ', t' are integral variables.
S11: the heat exchange quantity of fluid heat exchange working media in the heat exchanger and surrounding rock soil is obtained by the following formula:
wherein q is 2 To calculate the heat exchange quantity (unit: W) between the segment and the surrounding rock and soil.
S12: judging | q 1 –q 2 Whether | is less than β. If so, q 2 Namely the accurate solution of the heat exchange quantity of the heat exchange working medium in the current calculation section and the surrounding rock soil, and the T calculated by the following formula out (i) Namely, the temperature of the outlet of the heat exchange working medium at the current calculation section is accurately solved:
wherein, T out (i) The working medium outlet temperature (unit:. Degree. C.) of the current calculation section.
If not, repeating S8-S12 until the result satisfies | q 1 –q 2 |<Beta, obtaining the heat exchange quantity and the outlet water temperature of the current calculation section.
S13: the calculation of the next calculation segment is performed. Let i = i +1, let the heat exchange working medium inlet temperature of the next calculation section equal to the heat exchange working medium outlet temperature of the current calculation section, that is: t is a unit of in (i+1)＝T out (i) In that respect And repeating S7 to S12.
S14: and judging whether i is larger than or equal to n. If not, repeating S7-S13; if yes, the calculation is finished, the obtained heat exchange working medium outlet temperatures of all the calculation sections at the moment are the temperature distribution of the fluid heat exchange working medium in the heat exchanger, and the working medium outlet temperature of the last calculation section is the working medium outlet temperature of the U-shaped buried heat exchanger. Meanwhile, the sum of the heat exchange quantity of all the calculation sections is the total heat exchange quantity of the U-shaped underground heat exchanger and surrounding rock and soil in the operation process.
Examples
In order to more clearly illustrate the technical scheme of the invention, the following embodiment is described by taking a butted heat exchange well which is 200 meters deep, has a center distance of a water supply and return pipe of 200 meters, and takes a heat exchange working medium as water as a calculation object, and operating for 1 day (t =86400 s) as an example.
S1: and determining the structure and thermophysical parameters of the U-shaped buried heat exchanger. The depth H =200m of the heat exchanger and the outer diameter r of the heat exchanger pipeline o =0.016m, heat exchanger pipeline wall thickness d pipe =0.003m, borehole wall radius r b =0.065m, the center distance D of the water supply and return pipe =0.06m, and the heat conductivity coefficient k of the heat exchanger pipeline pipe ＝2.0W/m·K。
S2: calculating the equivalent outer diameter of the U-shaped buried heat exchanger after two branch pipes are equivalent to a single round pipe by adopting the following formula:
wherein r is eq,o Is the equivalent radius (unit: m); r is o Is the heat exchanger tube radius (unit: m); d is the center distance (unit: m) of the water supply and return pipe. Each parameter is substituted into a calculation to obtain r eq,o ＝0.031m。
S3: and determining the thermophysical parameters of the rock and soil at different depths. The heat exchanger and the surrounding rock soil are divided into 4 calculation sections along the depth direction of the heat exchanger from the ground downwards. Wherein the length L (i) =50m of each calculation section, the temperature of the soil layer at the inlet position is 15 ℃, the temperature of the rock soil at the deepest part of the heat exchanger is 25 ℃, and the temperature T of the soil in each calculation section in the middle is soil (i) Values are taken according to a linear distribution. When i is less than or equal to 2, calculating the thermal conductivity k of the rock-soil layer where the section is located soil (i) Density of rock and soil rho = 1.76W/m.K soil (i)＝1949kg/m 3 Specific heat of c soil (i) Thermal diffusion coefficient alpha (i) =8 =1080J/kg · DEG C.39×10 -7 m 2 S; when i is>2, calculating the thermal conductivity k of the rock-soil layer where the section is located soil (i) Density of rock and soil (2.20W/m.K) = 2.20W/m.K soil (i)＝1663kg/m 3 Specific heat of c soil (i) Temperature of 1361J/kg DEG C, thermal diffusion coefficient alpha (i) = 9.72X 10 -7 m 2 And s. The 2 nd calculation segment is located in the aquifer, and the flow rate u (2) =10 of water -7 m/s。
S4: system operating parameters and other relevant parameters are determined. The method specifically comprises the following steps: inlet temperature T of heat exchange working medium entering underground heat exchanger in =5 ℃, mass flow rate m of heat exchange working medium =2.78kg/s, density rho of water =1000kg/m 3 The specific heat of water c =4200J/kg DEG C, the system operation time t =86400s, and the thermal conductivity k of the drill hole backfill material grout =1.5W/m · K, small amount β =0.1 for determination error.
S5: according to the mass flow m of the heat exchange working medium, the flow velocity of the working medium in the U-shaped buried heat exchanger is calculated by adopting the following formula:
wherein u is fluid The flow velocity of the working medium (unit: m/s); m is the mass flow (unit: kg/s) of the fluid working medium; d pipe Is the heat exchanger tube wall thickness (unit: m). All parameters are substituted into the calculation fluid ＝0.66m/s。
Calculating the heat conduction resistance between the pipe wall in the equivalent circular pipe and the surrounding rock soil by adopting the following formula:
wherein R is c Is the heat conduction resistance (unit: K/W) between the heat exchange pipeline and the surrounding rock soil; r is b Is the borehole radius (unit: m); k is a radical of formula pipe 、k grout Respectively the heat conductivity coefficient of the heat exchanger pipeline and the heat conductivity coefficient (unit: W/m.K) of the backfill material; l (i) is the length (in m) of the current computed segment. Each parameter is substituted into a calculation to obtain R c ＝1.73×10 -3 K/W。
S6: let i =1, let the inlet water temperature of the first calculation section equal to the inlet temperature of the heat exchange working medium entering the heat exchanger, i.e. T in (1)＝T in ＝5℃。
S7: setting an initial value T for the outlet water temperature of the ith calculation section out (i)＝50℃。
S8: and calculating the qualitative temperature of the heat exchange working medium at the current calculation section by using the following formula:
wherein, T m The average temperature (unit: DEG C) of the working medium inlet and outlet of the current calculation section is calculated; t is a unit of out (i)、T in (i) Respectively the working medium outlet temperature and inlet temperature (unit:. Degree. C.) of the current calculation section. Calculated to obtain, T m ＝27.5℃。
Calculating the heat change of the fluid working medium after flowing through the current calculation section by using the following formula:
q 1 ＝mc[T out (i)-T in (i)]
wherein q is 1 The heat quantity (unit: W) absorbed by the heat exchange working medium after flowing through the first calculation section; c is the specific heat (unit: J/kg. Degree. C.) of the heat exchange working medium. Each parameter is brought into calculation to obtain q 1 ＝11760W。
S9: respectively calculating the Reynolds number Re and the Plantt number Pr of the heat exchange working medium in the current calculation section by using the following formulas:
Pr＝-0.000023T m 3 +0.005073T m 2 -0.39525T m +13.344266
wherein Re is Reynolds number; pr is the prandtl number. Calculated, re =70599, pr =3.73.
Calculating the convective heat transfer resistance between the heat exchange working medium and the inner wall surface of the heat exchanger by adopting the following formula:
wherein R is f Is the heat resistance (unit: K/W) of the convection heat transfer between the heat exchange working medium and the pipeline; lambda fluid Is the heat conductivity coefficient (unit: W/m.K) of the heat exchange working medium. All parameters are substituted and calculated to obtain 3.37 multiplied by 10 -5 K/W。
S10: the current calculation segment is the first calculation segment, not located in the aquifer, and therefore the borehole wall temperature is calculated using the following formula:
wherein, T b The temperature (unit:. Degree. C.) of the wall surface of the drilled hole, T soil (i)、k soil (i) And alpha (i) is the temperature (unit: DEG C) of the rock-soil layer where the first calculation section is located, the heat conductivity coefficient (unit: W/m.K) and the heat diffusion coefficient (unit: m 2/s) respectively; r is the distance between the wall surface and the axis of the heat exchanger; z is the depth of the calculated position; z 'and t' are integral variables; t is the running time (unit: s). Substituting each parameter into a calculation, T b ＝16.25℃。
S11: the heat exchange quantity of fluid heat exchange working media in the heat exchanger and surrounding rock soil is obtained by the following formula:
wherein q is 2 The heat exchange quantity (unit: W) between the section and the surrounding rock soil is calculated. Calculated to obtain q 2 ＝-325.44W。
S12: calculating the outlet temperature of the current working medium in the calculation section by adopting the following formula:
wherein, T out (i) The working medium outlet temperature (unit:. Degree. C.) of the current calculation section. Calculated to obtain, T out (i)＝8.06℃。
At this time, | q 1 -q 2 |>β, therefore, S8 to S12 are repeated. Calculated q before convergence 2 The values of (a) are in order: 80.96W,67.42W,67.87W and 67.85W. When q is 2 If =67.85W, | q 1 -q 2 |<Beta is used as the reference. At this time, the outlet working medium temperature T of the current calculation section can be obtained out (1) And the heat exchange quantity q between the heat exchanger at the current calculation section and the surrounding rock soil is not less than 10.40 DEG C 2 ＝67.85W。
S13: the calculation of the next calculation segment is performed. Let i =2, let the heat exchange working medium inlet temperature of the second calculation section equal to the heat exchange working medium outlet temperature of the current calculation section, that is: t is a unit of in (2)＝T out (1) =10.40 ℃. S7 to S12 are repeated. At this time, the calculation section is located in the aquifer, and the temperature of the wall surface of the borehole is calculated by adopting the following formula:
wherein, T b The temperature of the wall surface of the drilled hole (unit:. Degree. C.), T soil (i)、k soil (i) And alpha (i) is the temperature (unit: DEG C) of the rock-soil layer where the first calculation section is located, the heat conductivity coefficient (unit: W/m.K) and the heat diffusion coefficient (unit: m 2/s) respectively; u (i) is the flow rate of water in the aquifer (unit: m/s); x, y and z are position coordinates of the wall surface under the condition that the center of the section of the inlet of the pipe section is taken as an origin; t is the running time (unit: s); z' is an integral variable.
Wherein, the first and the second end of the pipe are connected with each other,
erfc is a complementary error function. The parameters are substituted into the calculation to obtain T b ＝18.75℃。
Repeating S8-S12 to obtain the accurate outlet working medium temperature T of the second calculation section out (2) And the second calculates the heat exchange quantity q between the heat exchanger and the surrounding rock and soil at 10.52 DEG C 2 ＝19.04W。
S14: and judging whether i is greater than or equal to 4. If not, repeating S7-S13; if yes, the calculation is finished, and the obtained heat exchange working medium outlet temperatures of all the calculation sections are the temperature distribution of the fluid heat exchange working medium in the heat exchanger. The working medium outlet temperature of the last calculation section is the working medium outlet temperature of the U-shaped buried heat exchanger, and the value T of the working medium outlet temperature out ＝T out (4) =12.02 ℃. Meanwhile, the sum of the heat exchange quantity of all the calculation sections is the total heat exchange quantity of the U-shaped underground heat exchanger and surrounding rock and soil in the operation process.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
It should be noted that, in the description of the present invention, the terms "first", "second", etc. are used for descriptive purposes only and to distinguish similar objects, and there is no order between the two, and no indication or implication of relative importance should be understood. In addition, in the description of the present invention, "a plurality" means two or more unless otherwise specified.
It is to be understood that the above description is intended to be illustrative, and not restrictive. Many embodiments and many applications other than the examples provided would 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 pending 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 applicant consider that such subject matter is not considered part of the disclosed subject matter.
Claims (10)
1. A performance prediction semi-analysis method for a U-shaped buried heat exchanger is characterized by comprising the following steps:
s1: determining the structure and thermophysical parameters of the U-shaped buried heat exchanger;
s2: calculating the equivalent outer diameter of the U-shaped buried heat exchanger after two branch pipes are equivalent to a single round pipe;
s3: determining thermophysical parameters of rock and soil at different depths;
s4: determining system operating parameters and other related parameters;
s5: calculating the flow velocity of the working medium in the U-shaped buried heat exchanger according to the mass flow of the heat exchange working medium;
calculating the heat conduction resistance of the middle pipe wall of the equivalent circular pipe and the surrounding rock soil;
s6: let i =1, let the inlet water temperature of the first calculation section be equal to the inlet temperature of the heat exchange working medium entering the heat exchanger, i.e. T in (1)＝T in ；
S7: giving an initial value T to the outlet water temperature of the ith calculation section out (i)＝50℃；
S8: calculating the qualitative temperature of the heat exchange working medium in the current calculation section;
calculating the heat change of the fluid working medium after flowing through the current calculation section;
s9: calculating the Reynolds number Re and the Plantt number Pr of the heat exchange working medium in the current calculation section;
calculating the convection heat transfer resistance of the heat exchange working medium and the inner wall surface of the heat exchanger;
s10: judging whether the current calculation section is positioned in the aquifer, if so, obtaining the temperature T of the outer wall surface of the heat exchanger of the current calculation section by utilizing the existing moving line heat source and column heat source formulas based on the parameters b (i) (ii) a If not, based on the parameters, the existing finite-length-line heat source and column heat source formula is utilized to obtain the temperature T of the outer wall surface of the heat exchanger at the current calculation section b (i)；
S11: calculating the heat exchange quantity of fluid heat exchange working media in the heat exchanger and surrounding rock and soil;
s12: determine | q 1 –q 2 Whether | is less than β:
if so, q 2 Namely the T calculated by the accurate solution of the heat exchange quantity of the heat exchange working medium in the current calculation section and the surrounding rock soil out (i) Namely, the temperature of the outlet of the heat exchange working medium at the current calculation section is accurately solved;
if not, repeating S8-S12 until the result satisfies | q 1 –q 2 |<Beta, obtaining the heat exchange quantity and the outlet water temperature of the current calculation section;
s13: the calculation of the next calculation segment is performed: let i = i +1, let the heat exchange working medium inlet temperature of the next calculation section equal to the heat exchange working medium outlet temperature of the current calculation section, that is: t is in (i+1)＝T out (i) (ii) a Repeating S7 to S12;
s14: judging whether i is more than or equal to n:
if not, repeating S7-S13; if yes, the calculation is finished.
2. The semi-analytic method for performance prediction of a U-shaped underground heat exchanger according to claim 1, wherein in S2, the equivalent outer diameters of two branch pipes of the U-shaped underground heat exchanger after being equivalent to a single circular pipe are calculated by using the following formula:
wherein r is eq,o Is an equivalent radius; r is o Is the heat exchanger tube radius; d is the center distance of the water supply and return pipe.
3. The performance prediction semi-analytic method for the U-shaped buried heat exchanger according to claim 1, wherein the specific method for determining the thermophysical parameters of rock and soil at different depths in S3 is as follows:
dividing the heat exchanger and surrounding rock and soil into n calculation sections from the ground downwards along the depth direction of the heat exchanger; wherein the length of the ith calculation segment is L (i), and the rock-soil layer temperature is T soil (i) And the thermal conductivity of rock-soil layer is k soil (i) Density of rock and soil is rho soil (i) Specific heat of rock and soil c soil (i) The thermal diffusivity of rock-soil α (i);
if the calculated segment is located in the aquifer, the flow rate of the water is u (i).
4. The method for semi-analyzing performance prediction of U-shaped underground heat exchanger according to claim 1, wherein S5 is
Wherein u is fluid The flow rate of the working medium; m is the mass flow of the fluid working medium; d is a radical of pipe The wall thickness of the heat exchanger pipeline;
calculating the heat conduction resistance between the pipe wall in the equivalent circular pipe and the surrounding rock soil by adopting the following formula:
wherein R is c Is the heat conduction thermal resistance between the heat exchange pipeline and the surrounding rock soil; r is b Is the borehole radius; k is a radical of pipe 、k grout The heat conductivity coefficient of the heat exchanger pipeline and the heat conductivity coefficient of the backfill material are respectively; l (i) is the length of the current computed segment.
5. The performance prediction semi-analytic method for the U-shaped buried heat exchanger according to claim 1, wherein in S8, the qualitative temperature of the heat exchange working medium in the current calculation section is calculated by using the following formula:
calculating the heat change of the fluid working medium after flowing through the current calculation section by using the following formula:
q 1 ＝mc[T out (i)-T in (i)]
wherein, T m The average temperature of the working medium inlet and outlet of the current calculation section is calculated; t is out (i)、T in (i) Are respectively a current meterCalculating the outlet temperature and the inlet temperature of the working medium of the section; q. q.s 1 The heat absorbed by the heat exchange working medium after flowing through the first calculation section; c is the specific heat of the heat exchange working medium.
6. The performance prediction semi-analytic method for the U-shaped buried heat exchanger according to claim 1, wherein in S9, the Reynolds number Re and the Plantt number Pr of the heat exchange working medium at the current calculation section are calculated by using the following formulas respectively:
Pr＝-0.000023T m 3 +0.005073T m 2 -0.39525T m +13.344266
calculating the convective heat transfer resistance between the heat exchange working medium and the inner wall surface of the heat exchanger by adopting the following formula:
wherein Re is Reynolds number; pr is the Plantt number; r f Is thermal resistance for convective heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ] fluid Is the heat conductivity coefficient of the heat exchange working medium.
7. The method for semi-analyzing performance prediction of a U-shaped underground heat exchanger according to claim 1, wherein if the determination result is yes, the following finite length moving line heat source formula is used for calculation in S10:
wherein, T b For borehole wall surface temperature, T soil (i)、k soil (i) And alpha (i) is the temperature, the heat conductivity coefficient and the heat diffusion coefficient of the rock-soil layer where the first calculation section is located respectively; u (i) is the flow rate of water in the aquifer; x, y, z are tubesPosition coordinates of the wall surface under the condition that the center of the section entrance section is an original point; t is the running time; z' is an integral variable;
in the above formula, the first and second carbon atoms are,
erfc is a complementary error function;
if the judgment result is negative, calculating by adopting the following formula:
where ρ is soil (i) The density of rock soil; c. C soil (i) Specific heat of rock soil; r is the distance between the wall surface and the axis of the heat exchanger; z is the depth of the calculated position; z ', t' are integral variables.
8. The performance prediction semi-analytic method for the U-shaped underground heat exchanger according to claim 1, wherein in S11, the heat exchange amount between the fluid heat exchange working medium in the heat exchanger and the surrounding rock soil is obtained by adopting the following formula:
wherein q is 2 To calculate the amount of heat exchange between the segment and the surrounding rock and soil.
9. The method according to claim 1, wherein T is calculated in S12 by using the following formula out (i) Namely, the accurate solution of the outlet temperature of the heat exchange working medium at the current calculation section is as follows:
wherein, T out (i) The working medium outlet temperature of the current calculation section.
10. The performance prediction semi-analytic method for the U-shaped buried heat exchanger according to claim 1, wherein the obtained heat exchange working medium outlet temperatures of all the calculation sections are temperature distributions of a fluid heat exchange working medium in the heat exchanger, and the working medium outlet temperature of the last calculation section is the working medium outlet temperature of the U-shaped buried heat exchanger; and the sum of the heat exchange quantity of all the calculation sections is the total heat exchange quantity of the U-shaped underground heat exchanger and the surrounding rock soil in the operation process.
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