CN111581838A - 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 to 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 equal to 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. Tin(1)＝Tin；
S7: giving an initial value T to the outlet water temperature of the ith calculation sectionout(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 Prandtl number Pr of the heat exchange working medium at 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 parametersb(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 sectionb(i)；
S11: calculating the heat exchange quantity of fluid heat exchange working media in the heat exchanger and surrounding rock and soil;
s12: judging | q1–q2Whether | is less than β:
if so, q2Namely 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 soilout(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–q2|<β, 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 become i +1, make the heat transfer working medium inlet temperature of next calculation section equal to the heat transfer working medium outlet temperature of current calculation section, promptly: t isin(i+1)＝Tout(i) (ii) a Repeating S7-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 present invention, in S2, the equivalent outer diameter after two branch pipes of the U-shaped buried heat exchanger are equivalent to a single circular pipe is calculated by the following formula:
wherein r iseq,oIs an equivalent radius; r isoIs 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 rock-soil layer temperature is Tsoil(i) Thermal conductivity of rock-soil layer is ksoil(i) Density of rock and soil is rhosoil(i) Specific heat of rock and soil csoil(i) Rock-soil thermal diffusivity α (i);
if the calculated segment is located in the aquifer, the flow rate of water is u (i).
As a further improvement of the present invention, in S5
Wherein u isfluidThe flow rate of the working medium; m is the mass flow of the fluid working medium; dpipeThe 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 iscIs the heat conduction thermal resistance between the heat exchange pipeline and the surrounding rock soil; r isbIs the borehole radius; k is a radical ofpipe、kgroutThe 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 present invention, in S8, the following formula is used to calculate 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 by using the following formula:
q1＝mc[Tout(i)-Tin(i)]
wherein, TmThe average temperature of the working medium inlet and outlet of the current calculation section is calculated; t isout(i)、Tin(i) Respectively calculating the outlet temperature and the inlet temperature of the working medium of the current calculation section; q. q.s1The 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 prandtl number Pr of the heat exchange working medium in the current calculation section are calculated by the following formulas respectively:
Pr＝-0.000023Tm 3+0.005073Tm 2-0.39525Tm+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; rfIs thermal resistance for convective heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ]fluidIs 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 used in S10 to calculate:
wherein, TbFor borehole wall surface temperature, Tsoil(i)、ksoil(i) α (i) respectively represents the temperature, the heat conductivity coefficient and the heat diffusion coefficient of the rock-soil layer where the first calculation section is located, u (i) represents the flow velocity of water in the aquifer, x, y and z represent 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 represents the running time, and z' represents 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 issoil(i) The density of rock soil; c. Csoil(i) The 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.
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 is2To 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 formulaout(i) Namely, the accurate solution of the outlet temperature of the heat exchange working medium at the current calculation section is as follows:
wherein, Tout(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 and numerical iterative computation, on the basis of ensuring the computation precision, the computation time is greatly reduced, and the computation 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 section division of the U-shaped buried heat exchanger.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection 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 achieve 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 pipelineo(unit: m), heat exchanger tube wall thickness dpipe(unit: m), bore wall diameter rb(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 pipelinepipe(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 iseq,oIs the equivalent radius (unit: m); r isoIs the heat exchanger tube 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 is that the heat exchanger and the surrounding rock soil are divided 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) (unit: m), and the temperature of the rock-soil layer is Tsoil(i) (unit:. degree. C.) and the thermal conductivity of rock-soil layer is ksoil(i) (unit: W/m.K) and rock density is rhosoil(i) (unit: kg/m)3) Specific heat of rock and soil csoil(i) (unit: J/kg. degree. C.), thermal diffusivity of rock-soil α (i) (unit: m)2In s). If the calculated section is located in the aquifer, the flow rate of 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 exchangerin(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 medium3) And the specific heat c (unit: j/kg · c), the system run time t (unit: s), thermal conductivity k of the borehole backfill materialgrout(unit: W/m · K), and a small amount β (e.g., β -0.1) preset for the 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 isfluidThe flow rate of the working medium (unit: m/s); m is the mass flow (unit: kg/s) of the fluid working medium; dpipeFor 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 iscIs the heat conduction thermal resistance (unit: K/W) between the heat exchange pipeline and the surrounding rock soil; r isbIs the borehole radius (unit: m); k is a radical ofpipe、kgroutRespectively 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 (unit: m) of the current calculation segment.
S6: let i equal to 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. Tin(1)＝Tin。
S7: giving an initial value T to the outlet water temperature of the ith calculation sectionout(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, TmThe average temperature (unit: DEG C) of the working medium inlet and outlet of the current calculation section is calculated; t isout(i)、Tin(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:
q1＝mc[Tout(i)-Tin(i)]
wherein q is1The 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.
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＝-0.000023Tm 3+0.005073Tm 2-0.39525Tm+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 isfIs the heat resistance (unit: K/W) of the convection heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ]fluidThe 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 parametersb(i) In that respect For example, the following finite-length moving-line heat source formula is adopted for calculation:
wherein, TbThe temperature of the wall surface of the drilled hole (unit:. degree. C.), Tsoil(i)、ksoil(i) α (i) is the temperature (unit: DEG C), the heat conductivity (unit: W/m.K) and the heat diffusion coefficient (unit: m2/s) of the rock-soil layer where the first calculation section is located, u (i) is the flow velocity (unit: m/s) of water in the aquifer, x, y, 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 operation time (unit: s), and z' is an integral variable.
Wherein the content of the first and second substances,
erfc is the complementary error function.
In the above formula, the first and second carbon atoms are,
if not, based on the parameters, obtaining the temperature T of the outer wall surface of the heat exchanger at the current calculation section by using the existing formulas of limited long-line heat sources, column heat sources and the likeb(i) In that respect For example, the following formula is used for calculation:
where ρ issoil(i) Is the density of rock and soil (unit: kg/m)3)；csoil(i) The specific heat of rock 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 is2The heat exchange quantity (unit: W) between the section and the surrounding rock soil is calculated.
S12: judging | q1–q2If | is less than β, if so, q2Namely 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 formulaout(i) Namely, the accurate solution of the outlet temperature of the heat exchange working medium at the current calculation section is as follows:
wherein, Tout(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–q2|<β, 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 become i +1, make the heat transfer working medium inlet temperature of next calculation section equal to the heat transfer working medium outlet temperature of current calculation section, promptly: t isin(i+1)＝Tout(i) In that respect S7-S12 were repeated.
S14: and judging whether i is larger than or equal to n. If not, repeating S7-S13; if so, the calculation is finished, 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 underground 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 present invention, the following description will be given on an example of a butt heat exchange well which is 200 meters deep, has a center distance of a water supply and return pipe of 200 meters, and uses water as a heat exchange working medium, and runs for 1 day (t is 86400 s).
S1: and determining the structure and thermophysical parameters of the U-shaped buried heat exchanger. The depth H of the heat exchanger is 200m, and the outer diameter r of the heat exchanger pipelineo0.016m, heat exchanger tube wall thickness dpipe0.003m, bore wall radius rb0.065m, 0.06m center distance D of water supply and return pipe, and heat conductivity coefficient k of heat exchanger pipelinepipe＝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 iseq,oIs the equivalent radius (unit: m); r isoIs 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 req,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) of each calculation section is 50m, the temperature of the soil layer where the inlet is positioned is 15 ℃, the temperature of the innermost rock soil of the heat exchanger is 25 ℃, and the soil temperature T in each middle calculation sectionsoil(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 locatedsoil(i) 1.76W/m.K, rock density rhosoil(i)＝1949kg/m3Specific heat ofsoil(i) 1080J/kg DEG C, thermal diffusivity α (i) 8.39 × 10-7m2S; when i is>2, calculating the thermal conductivity k of the rock-soil layer where the section is locatedsoil(i) 2.20W/m.K, rock density ρsoil(i)＝1663kg/m3Specific heat ofsoil(i) 1361J/kg DEG C, thermal diffusivity α (i) ═ 9.72 × 10-7m2And s. The 2 nd calculation segment is located in the aquifer and the flow rate u (2) of water is 10-7m/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 exchangerinThe mass flow m of the heat exchange working medium is 2.78kg/s at 5 ℃, and the density rho of the water is 1000kg/m3The specific heat of water c is 4200J/kg DEG C, the system operation time t is 86400s, and the thermal conductivity k of the drill hole backfill materialgrout1.5W/m · K, and a small amount β for the determination error is 0.1.
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 isfluidThe flow rate of the working medium (unit: m/s); m is the mass flow (unit: kg/s) of the fluid working medium; dpipeIs the heat exchanger tube wall thickness (unit: m). Each parameter is substituted into the calculation to obtain ufluid＝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 iscIs the heat conduction thermal resistance (unit: K/W) between the heat exchange pipeline and the surrounding rock soil; r isbIs the borehole radius (unit: m); k is a radical ofpipe、kgroutRespectively 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 (unit: m) of the current calculation segment. Each parameter is substituted into a calculation to obtain Rc＝1.73×10-3K/W。
S6: let i equal to 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. Tin(1)＝Tin＝5℃。
S7: giving an initial value T to the outlet water temperature of the ith calculation sectionout(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, TmThe average temperature (unit: DEG C) of the working medium inlet and outlet of the current calculation section is calculated; t isout(i)、Tin(i) Respectively the working medium outlet temperature and inlet temperature (unit:. degree. C.) of the current calculation section. Calculated to obtain, Tm＝27.5℃。
Calculating the heat change of the fluid working medium after flowing through the current calculation section by using the following formula:
q1＝mc[Tout(i)-Tin(i)]
wherein q is1The 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 q1＝11760W。
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＝-0.000023Tm 3+0.005073Tm 2-0.39525Tm+13.344266
wherein Re is Reynolds number; pr is the prandtl number. Calculated, Re is 70599 and Pr is 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 isfIs the heat resistance (unit: K/W) of the convection heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ]fluidThe coefficient of heat conductivity (unit: W/m.K) of the heat exchange working medium is obtained by substituting each parameter into a calculation, 3.37 × 10-5K/W。
S10: the current calculation segment is the first calculation segment and is not located in the aquifer, so the borehole wall temperature is calculated by using the following formula:
wherein, TbThe temperature of the wall surface of the drilled hole (unit:. degree. C.), Tsoil(i)、ksoil(i) α (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: m2/s), 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 operation time (unit: s), all the parameters are substituted into the calculation, and T is the operation time (unit: s)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 is2The heat exchange quantity (unit: W) between the section and the surrounding rock soil is calculated. Calculated to obtain q2＝-325.44W。
S12: calculating the outlet temperature of the current working medium in the calculation section by adopting the following formula:
wherein, Tout(i) The working medium outlet temperature (unit:. degree. C.) of the current calculation section. Calculated to obtain, Tout(i)＝8.06℃。
At this time, | q1-q2|>β, therefore, repeating S8-S12. q calculated before convergence2The values of (a) are in order: 80.96W, 67.42W, 67.87W, 67.85W. When q is2When 67.85W, | q1-q2|<β, it can be obtained at this time that the outlet working medium temperature T of the current calculation sectionout(1) The heat exchange quantity q between the heat exchanger and the surrounding rock and soil is calculated at the current calculation section under the temperature of 10.40 DEG C2＝67.85W。
S13: the calculation of the next calculation segment is performed. Let i be 2, make the heat transfer working medium inlet temperature of second calculation section equal to the heat transfer working medium outlet temperature of current calculation section, promptly: t isin(2)＝Tout(1) 10.40 ℃. S7-S12 were repeated. At this time, the calculation section is located in the aquifer, and the temperature of the wall surface of the bore hole is calculated by adopting the following formula:
wherein, TbThe temperature of the wall surface of the drilled hole (unit:. degree. C.), Tsoil(i)、ksoil(i) α (i) is the temperature (unit: DEG C), the heat conductivity (unit: W/m.K) and the heat diffusion coefficient (unit: m2/s) of the rock-soil layer where the first calculation section is located, u (i) is the flow velocity (unit: m/s) of water in the aquifer, x, y, 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 operation time (unit: s), and z' is an integral variable.
Wherein the content of the first and second substances,
erfc is the complementary error function. The parameters are substituted into the calculation to obtain Tb＝18.75℃。
Repeating S8-S12 to obtain the accurate outlet working medium temperature T of the second calculation sectionout(2) The second calculates the heat exchange quantity q between the heat exchanger and the surrounding rock and soil at 10.52 DEG C2＝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 temperatureout＝Tout(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", and the like are used for descriptive purposes only and for distinguishing similar objects, and no precedence between the two is considered as indicating or implying relative importance. 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 appended claims, along with the full scope of equivalents to which such claims are entitled. The disclosures of all articles and references, including patent applications and publications, are hereby incorporated by reference for all purposes. The omission in the foregoing claims of any aspect of subject matter that is disclosed herein is not intended to forego such subject matter, nor should the 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 between the pipe wall in the equivalent circular pipe and the surrounding rock soil;
s6: let i equal to 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. Tin(1)＝Tin；
S7: giving an initial value T to the outlet water temperature of the ith calculation sectionout(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 Prandtl number Pr of the heat exchange working medium at 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 heat exchange of the current calculation section by utilizing the existing moving line heat source and column heat source formulas based on the parametersTemperature T of external wall surface of deviceb(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 sectionb(i)；
S11: calculating the heat exchange quantity of fluid heat exchange working media in the heat exchanger and surrounding rock and soil;
s12: judging | q1–q2Whether | is less than β:
if so, q2Namely 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 soilout(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–q2|<β, 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 become i +1, make the heat transfer working medium inlet temperature of next calculation section equal to the heat transfer working medium outlet temperature of current calculation section, promptly: t isin(i+1)＝Tout(i) (ii) a Repeating S7-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 method according to claim 1, wherein in step S2, the equivalent outer diameters of the two branch pipes of the U-shaped underground heat exchanger after being equivalent to a single round pipe are calculated by using the following formula:
wherein r iseq,oIs an equivalent radius; r isoIs 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 section is L (i), and the rock-soil layer temperature is Tsoil(i) Thermal conductivity of rock-soil layer is ksoil(i) Density of rock and soil is rhosoil(i) Specific heat of rock and soil csoil(i) Rock-soil thermal diffusivity α (i);
if the calculated segment is located in the aquifer, the flow rate of water is u (i).
4. The semi-analytic method for performance prediction of U-shaped underground heat exchanger of claim 1, wherein in S5
Wherein u isfluidThe flow rate of the working medium; m is the mass flow of the fluid working medium; dpipeThe 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 iscIs the heat conduction thermal resistance between the heat exchange pipeline and the surrounding rock soil; r isbIs the borehole radius; k is a radical ofpipe、kgroutThe 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:
q1＝mc[Tout(i)-Tin(i)]
wherein, TmThe average temperature of the working medium inlet and outlet of the current calculation section is calculated; t isout(i)、Tin(i) Respectively calculating the outlet temperature and the inlet temperature of the working medium of the current calculation section; q. q.s1The 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 respectively by using the following formulas:
Pr＝-0.000023Tm 3+0.005073Tm 2-0.39525Tm+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; rfIs thermal resistance for convective heat transfer between the heat exchange working medium and the pipeline; lambda [ alpha ]fluidIs the heat conductivity coefficient of the heat exchange working medium.
7. The method for semi-analyzing performance prediction of a U-type 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, TbFor wall surface temperature of drilled holeDegree, Tsoil(i)、ksoil(i) α (i) respectively represents the temperature, the heat conductivity coefficient and the heat diffusion coefficient of the rock-soil layer where the first calculation section is located, u (i) represents the flow velocity of water in the aquifer, x, y and z represent 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 represents the running time, and z' represents 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 issoil(i) The density of rock soil; c. Csoil(i) The 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 and soil is obtained by adopting the following formula:
wherein q is2To calculate the amount of heat exchange between the segment and the surrounding rock and soil.
9. The method according to claim 1, wherein T12 is calculated by the following equationout(i) Namely the outlet temperature of the heat exchange working medium at the current calculation section is accurateSolution:
wherein, Tout(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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