CN102855414A - Efficient calculating method for parametrization design of vertical ground heat exchanger - Google Patents

Efficient calculating method for parametrization design of vertical ground heat exchanger Download PDF

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CN102855414A
CN102855414A CN2012103571778A CN201210357177A CN102855414A CN 102855414 A CN102855414 A CN 102855414A CN 2012103571778 A CN2012103571778 A CN 2012103571778A CN 201210357177 A CN201210357177 A CN 201210357177A CN 102855414 A CN102855414 A CN 102855414A
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temperature
function
heat exchanger
fluid
drilling well
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陈友明
张训水
杜次元
魏鹏飞
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Hunan University
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Abstract

The invention discloses an efficient calculating method for parametrization design of a vertical ground heat exchanger. According to the efficient calculating method provided by the invention, the method comprises the steps of expressing the hourly heat absorbing and radiating heat flow of the vertical ground heat exchanger of a heat pump system as a rectangular pulse heat flow sequence; introducing a concept of underground rock dimensionless transient temperature response g function under the effect of unit rectangular pulse heat flow, so as to obtain the function with the integrating interval of [0, deltaF0]; and taking drill parameters into design calculation, so that the calculating result is accurate and reliable, the calculation time is greatly shortened, and the efficient calculation method is provided for achieving the parametrization design of the vertical ground heat exchanger.

Description

A kind of efficient calculation method of vertical ground heat exchanger Parametric designing
Technical field
The present invention relates to the earth source heat pump field, particularly a kind of efficient calculation method of vertical ground heat exchanger Parametric designing.
Background technology
In earth source heat pump, vertical buried pipe type water loop heat pump system more and more is widely used because underground ground temperature field is stable, energy efficiency is high.It mainly is used in the heating air conditioning and hot water supply system of all kinds of buildings.Vertical ground heat exchanger construction cost is high, and design of heat exchanger is crossed conference and caused initial cost waste, operating cost high; Design of heat exchanger is less than normal then can not to guarantee heat pump stable operation, can not satisfy the demand of system's suction heat, reduces running efficiency of system.When design water loop heat pump system, the designing and calculating of vertical ground heat exchanger is very crucial.
The heat pump runtime is generally 10-30.In order to design the vertical ground heat exchanger of appropriate size, need to according to heat pump in the runtime by the time suction calorimeter calculate in the vertical ground heat exchanger pipe by the time fluid temperature (F.T.), underground ground by the time transient temperature, whether can satisfy the suction heat demand of heat pump within the runtime with the size of assessment heat interchanger.
The designing and calculating parameter of vertical ground heat exchanger is many, must just can design by Parametric designing the ground heat exchanger of suitable size.Present mostly employing g functional based method calculates fluid temperature (F.T.) when pursuing in the pipe of ground heat exchanger within the runtime, transient temperature when underground ground pursues.So-called g function is exactly single vertical drilling ground heat exchanger pipe surface temperature and response of underground ground dimensionless transient temperature under the effect of unit hot-fluid.Had g functional value and heat pump within the runtime by the time suction heat, by drilling well superposition and convolution or frequency domain Fast Fourier Transform (FFT) (FFT) just can try to achieve the drilling well group within the runtime Tube Sheet of Heat Exchanger wall temperature and underground ground transient temperature pursue duration.The g function can be the data form that goes out with numerical calculations; Also can be the analytic solution of single drilling well being regarded as Tube Sheet of Heat Exchanger wall temperature and the underground ground transient temperature response under unit hot-fluid effect of limited line heat source, infinite line thermal source and cylinder thermal source.Regardless of being with numerical method or using analytic method, calculate the g function and need to consume the plenty of time by duration.Generally be first with the g function calculation of different drilling parameters out, when designing and calculating by tabling look-up and interpolation method obtains g functional value under the drilling well calculating parameter.It also is very consuming time that convolution calculates.So there is the expert to propose the methods such as " load aggregation method " (Load aggregation method) based on the g function and Fourier transform Spline Method (FFT-s) to reduce computing time.With limited line source model analytic expression g function designing and calculating ground heat exchanger, for example calculate one group of parameter of 30 year runtime of 40 drilling wells, with the time of time domain convolutional calculation needs more than 1 day, also need more than 2 hour (containing the time of calculating the g function) with FFT calculating.The drilling well group has many groups of parameter configuration to calculate, and storing the g functional value with the data form form needs a very large database, and the database that precomputes is difficult to comprise the four corner of the related whole parameters of designing and calculating.On the other hand, no matter be to table look-up to obtain the g functional value with interpolation, the methods such as still " load aggregation method " (Load aggregation method) and Fourier transform Spline Method (FFT-s) all can be brought than the computation error.Therefore, be difficult to realize the Parametric designing of vertical ground heat exchanger with g function and derivative computing method thereof.
Summary of the invention
Technical matters to be solved by this invention is, and is not enough for prior art, and a kind of efficient calculation method of vertical ground heat exchanger Parametric designing is provided, and guarantees result of calculation accurately and reliably, greatly reduces computing time.
For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of efficient calculation method of vertical ground heat exchanger Parametric designing, and the method may further comprise the steps:
1) can use floor area according to vertical ground heat exchanger drilling well group, tentatively choose one group of drilling parameter configuration: the wells spacing parameter D, offset distance x, and the drilling well number N, boring radius r b , drilling depth H, the ground coefficient of heat conductivity k s , the ground thermal diffusion coefficient
Figure 2012103571778100002DEST_PATH_IMAGE001
, need design-calculated heat pump operation year number n
2) with in the earth-source hot-pump system need to by ground heat exchanger from underground extraction or enter each hour underground 1 year heat constantly divided by ( H N) after, the square pulse of conductive heat flow when the unit's of being expressed as vertical shaft length is pursued [( Q (t 1 ), q ( t 2 ), q ( t 3 ) ..., q ( t 8760)];
3) underground any degree of depth of utilizing the limited line source model of single drilling well under the effect of unit step hot-fluid, to derive z(or h) and radius distance ( r) response of dimensionless transient temperature gThe analytical form of function:
Figure 552223DEST_PATH_IMAGE002
(1)
In the formula,
Figure 2012103571778100002DEST_PATH_IMAGE003
Figure 537496DEST_PATH_IMAGE004
Figure 2012103571778100002DEST_PATH_IMAGE005
Figure 2012103571778100002DEST_PATH_IMAGE007
Figure 855662DEST_PATH_IMAGE008
, be called Fourier's time;
Figure 2012103571778100002DEST_PATH_IMAGE009
Be the time; Erfc (z)Be complementary error function,
Figure 846752DEST_PATH_IMAGE010
Ask formula (1) gFunction is to Fourier's time variable FoPartial derivative, have
Figure 2012103571778100002DEST_PATH_IMAGE011
Figure 686532DEST_PATH_IMAGE012
(2)
Obtain underground any degree of depth and radius distance gAnother analytical form of function:
Figure 2012103571778100002DEST_PATH_IMAGE013
Figure 104875DEST_PATH_IMAGE014
(3)
4), opposite direction identical with two sizes, time phase difference
Figure DEST_PATH_IMAGE015
Step hot-fluid stack obtain the rect.p. hot-fluid, definition Function is single drilling well underground any degree of depth and response of radius distance dimensionless transient temperature under unit rect.p. hot-fluid effect, so,
Figure 690632DEST_PATH_IMAGE016
The function analytical form is:
Figure DEST_PATH_IMAGE017
Figure 384918DEST_PATH_IMAGE018
(4)
In the formula,
Figure DEST_PATH_IMAGE019
Be Fourier's time step,
Figure 974163DEST_PATH_IMAGE020
Be time step, in designing and calculating, be taken as 1 hour, so, drilling well wall neutral temperature
Figure 414688DEST_PATH_IMAGE016
Function is:
(5)
Drilling well wall medial temperature
Figure 989206DEST_PATH_IMAGE016
Function is:
Figure DEST_PATH_IMAGE023
Figure 193923DEST_PATH_IMAGE024
(6)
In the formula,
Figure DEST_PATH_IMAGE025
5) neutral temperature of arbitrary borehole wall and medial temperature in the selected drilling well in the step 1)
Figure 392823DEST_PATH_IMAGE016
Function is respectively:
Figure 796122DEST_PATH_IMAGE026
(7)
(8)
Underground ground initial temperature is
Figure 491284DEST_PATH_IMAGE028
, rect.p. hot-fluid sequence [( q( t 1 ), q( t 2 ), q( t 3 ) ... ] effect under, the relative transient temperature of the underground any degree of depth of single drilling well and radius distance is:
Figure DEST_PATH_IMAGE029
(9)
When The time, being the borehole wall surface temperature, the boring relative transient state neutral temperature of wall and medial temperature are:
Figure DEST_PATH_IMAGE031
(10)
Figure 920308DEST_PATH_IMAGE032
(11)
6) obtain each temperature or each temperature constantly of boring wall constantly of underground ground by relative transient temperature, calculate the boring internal thermal resistance of single U-shaped and double u-tube with fluid medial temperature method R b , each tube fluid temperature constantly of ground heat exchanger so Be calculated as follows:
Figure 381376DEST_PATH_IMAGE034
? (12)
Or
Figure DEST_PATH_IMAGE035
(13)
By the Performance Ratio of fluid temperature (F.T.) and heat pump, calculate the energy consumption of heat pump;
7) for different drilling parameter combinations, repeat above-mentioned calculation procedure, calculate drilling well total length, borehole wall surface temperature and the tube fluid temperature of respectively organizing parameter; By drilling well total length, borehole wall surface temperature and tube fluid temperature, subsurface temperature variation range, cost, heat pump energy consumption and the reciprocation cycle under the parameter respectively organized in assessment, selects the vertical ground heat exchanger parameter, is the vertical ground heat exchanger of design.
Compared with prior art, the beneficial effect that has of the present invention is: the present invention by introduce underground ground dimensionless transient temperature response under the unit rect.p. hot-fluid effect- The concept of function, obtain its integrating range for [0,
Figure 724950DEST_PATH_IMAGE019
]
Figure 265653DEST_PATH_IMAGE016
Function can be brought drilling parameter into designing and calculating, guarantees result of calculation accurately and reliably, has greatly reduced computing time again, for the vertical ground heat exchanger Parametric designing provides a kind of efficient computing method.
Description of drawings
Fig. 1 be one embodiment of the invention creep into group and creep between apart from schematic diagram;
Fig. 2 is that one embodiment of the invention unit length ground heat exchanger hot-fluid is by the rect.p. presentation graphs of duration;
Fig. 3 is that one embodiment of the invention obtains rect.p. hot-fluid schematic diagram with two step hot-fluid stacks;
Fig. 4 is the single drilling well wall of one embodiment of the invention medial temperature
Figure 909124DEST_PATH_IMAGE036
Function curve diagram;
Fig. 5 is the suction heat schematic diagram of every meter heat interchanger of one embodiment of the invention heat pump;
Fig. 6 is the wall medial temperature curve map of the 1st drilling well of one embodiment of the invention;
Fig. 7 is the fluid temperature (F.T.) curve map of one embodiment of the invention ground heat exchanger outlet.
Embodiment
One embodiment of the invention method step is as follows:
1. as shown in Figure 1, can use floor area according to vertical ground heat exchanger drilling well group, tentatively choose one group of drilling parameter configuration: the wells spacing parameter D, offset distance x, and the drilling well number N( N= m n, mWith nBe columns anyhow), boring radius r b , drilling depth H, the ground coefficient of heat conductivity k s , the ground thermal diffusion coefficient
Figure 244290DEST_PATH_IMAGE001
, need design-calculated heat pump operation year number n
With in the earth-source hot-pump system need to by ground heat exchanger from underground extraction or enter underground 1 year each constantly heat divided by ( H N) after, the square pulse of conductive heat flow when the unit's of being expressed as vertical shaft length is pursued [( Q (t 1 ), q ( t 2 ), q ( t 3 ) ..., q ( t 8760)], as shown in Figure 2.With the rect.p. hot-fluid sequence in 1 year repeat to extend rect.p. hot-fluid sequence for n 8760.
3. underground any degree of depth of utilizing the limited line source model of single drilling well under the effect of unit step hot-fluid, to derive z(or h) and radius distance rThe response of dimensionless transient temperature gThe analytical form of function:
Figure 409430DEST_PATH_IMAGE002
(1)
In the formula,
Figure 488244DEST_PATH_IMAGE003
Figure 492289DEST_PATH_IMAGE005
Figure 646190DEST_PATH_IMAGE006
Figure 528696DEST_PATH_IMAGE007
Figure 881180DEST_PATH_IMAGE008
, be called Fourier's time;
Figure 823728DEST_PATH_IMAGE009
Be the time; Erfc (z)Be complementary error function,
Figure 199345DEST_PATH_IMAGE010
Ask formula (1) gFunction is to Fourier's time variable FoPartial derivative, have
Figure 619962DEST_PATH_IMAGE011
Figure 92532DEST_PATH_IMAGE012
(2)
Obtain underground any degree of depth and radius distance gAnother analytical form of function.
Figure 940402DEST_PATH_IMAGE013
Figure 803316DEST_PATH_IMAGE014
(3)
4. as shown in Figure 3, any time
Figure DEST_PATH_IMAGE037
The rect.p. hot-fluid can be identical by 2 sizes, opposite direction, time phase difference
Figure 27624DEST_PATH_IMAGE015
Step heat transfer capacity stack obtain.Definition
Figure 354700DEST_PATH_IMAGE016
Function is single drilling well underground any degree of depth and response of radius distance dimensionless transient temperature under unit rect.p. hot-fluid effect.So, The function analytical form is:
Figure 487796DEST_PATH_IMAGE038
Figure 125582DEST_PATH_IMAGE018
(4)
In the formula, Be Fourier's time step,
Figure 762417DEST_PATH_IMAGE020
Figure 662240DEST_PATH_IMAGE015
Be time step, in designing and calculating, be taken as 1 hour.So, drilling well wall neutral temperature
Figure 166033DEST_PATH_IMAGE016
Function is:
Figure 202122DEST_PATH_IMAGE021
Figure 828276DEST_PATH_IMAGE022
(5)
Drilling well wall medial temperature
Figure 215395DEST_PATH_IMAGE016
Function is:
Figure DEST_PATH_IMAGE039
Figure 755835DEST_PATH_IMAGE024
(6)
In the formula,
Figure 912010DEST_PATH_IMAGE025
.
The single drilling well wall medial temperature of typical case
Figure 709065DEST_PATH_IMAGE016
Function as shown in Figure 4.The integrating range of formula (4), (5) and (6) be [0,
Figure 255584DEST_PATH_IMAGE019
], be about 1 10/1000000ths of formula (1) integrating range [0,1] -6Doubly).Thereby,
Figure 429076DEST_PATH_IMAGE016
Ratio computing time of function gThe computing time of function is little a lot, thereby has greatly accelerated computing velocity.
5. for the drilling well group of Fig. 1, drilling well eThe mid point of hole wall and medial temperature
Figure 439758DEST_PATH_IMAGE016
Function is respectively:
Figure 407714DEST_PATH_IMAGE026
(7)
Figure 441529DEST_PATH_IMAGE027
(8)
Underground ground initial temperature is
Figure 887553DEST_PATH_IMAGE028
, rect.p. hot-fluid sequence [( q( t 1 ), q( t 2 ), q( t 3 ) ... ] effect under, the relative transient temperature of the underground any degree of depth of single drilling well and radius distance is:
Figure 18321DEST_PATH_IMAGE029
(9)
When
Figure 94861DEST_PATH_IMAGE030
The time, be the borehole wall surface temperature.Boring among the boring group eThe relative transient state neutral temperature of wall and medial temperature are:
Figure 678289DEST_PATH_IMAGE031
(10)
Figure 928005DEST_PATH_IMAGE032
(11)
In the formula,
Figure 913278DEST_PATH_IMAGE028
Initial temperature for underground ground.Formula (9), (10) and (11) are the calculating formulas of convolution, adopt FFT to calculate convolution and can further improve computing velocity.
6. can get each temperature or each temperature constantly of boring wall constantly of underground ground by relative transient temperature, calculate the boring internal thermal resistance of single U-shaped and double u-tube with fluid medial temperature method or additive method R b , each tube fluid temperature constantly of ground heat exchanger so
Figure 659255DEST_PATH_IMAGE033
Be calculated as follows:
Figure 729979DEST_PATH_IMAGE034
? (12)
Or
Figure 783386DEST_PATH_IMAGE035
(13)
Can by the Performance Ratio of fluid temperature (F.T.) and heat pump, calculate the energy consumption of heat pump.
7. for different drilling parameter combination (parameters Dx, Dy, x, H, r b , m, n, k s ,
Figure 560849DEST_PATH_IMAGE001
, list or double u-tube etc.), repeat above-mentioned calculation procedure, calculate drilling well total length, borehole wall surface temperature and the tube fluid temperature etc. of respectively organizing parameter.By data such as drilling well total length, borehole wall surface temperature and tube fluid temperature, subsurface temperature variation range, cost, heat pump energy consumption and the reciprocation cycle etc. under the parameter are respectively organized in assessment, to select the rational vertical ground heat exchanger parameter of economy, be the vertical ground heat exchanger of design.
Demonstrate computing method of the present invention below by the computation process to one 58 (m=5, n=8) drilling well group's vertical ground heat exchanger.If wells spacing is Dx=Dy=5m, deviation distance x=0m, drilling depth H=60m, the drilling well radius r b =0.055m,
Figure 41509DEST_PATH_IMAGE040
=18.5 ℃, k s =2.3W/ (m ℃), A=1.25 10 -6(m 2/ s), time step
Figure 333950DEST_PATH_IMAGE015
Be 1 hour (3600s).Load when pursuing in 1 year with the synthetic heat pump of formula (14) Q(W/m), and be expressed as the suction hot-fluid of unit length heat interchanger, as shown in Figure 5.
Figure DEST_PATH_IMAGE041
(14)
In the formula A=-4.25 W/m, B=25 W/m, C=12.5 W/m, D=6.25 W/m.
The variation in 30 years of the flat temperature of wall of the 1st drilling well of drilling well group that calculates, as shown in Figure 6.Get the thermal resistance in the drilling well R b =0.087m 2℃/W, the variation in 30 years of the ground heat exchanger that calculates outlet fluid temperature (F.T.), shown in Figure 7.

Claims (1)

1. the efficient calculation method of a vertical ground heat exchanger Parametric designing is characterized in that, the method may further comprise the steps:
1) can use floor area according to vertical ground heat exchanger drilling well group, tentatively choose one group of drilling parameter configuration: the wells spacing parameter D, offset distance x, and the drilling well number N, boring radius r b , drilling depth H, the ground coefficient of heat conductivity k s , the ground thermal diffusion coefficient
Figure 2012103571778100001DEST_PATH_IMAGE002
, need design-calculated heat pump operation year number n
2) with in the earth-source hot-pump system need to by ground heat exchanger from underground extraction or enter each hour underground 1 year heat constantly divided by ( H N) after, the square pulse of conductive heat flow when the unit's of being expressed as vertical shaft length is pursued [( Q (t 1 ), q ( t 2 ), q ( t 3 ) ..., q ( t 8760)];
3) underground any degree of depth of utilizing the limited line source model of single drilling well under the effect of unit step hot-fluid, to derive zOr hAnd radius distance rThe response of dimensionless transient temperature gThe analytical form of function:
Figure 2012103571778100001DEST_PATH_IMAGE004
(1)
In the formula,
Figure 2012103571778100001DEST_PATH_IMAGE006
Figure 2012103571778100001DEST_PATH_IMAGE008
Figure 2012103571778100001DEST_PATH_IMAGE010
Figure 2012103571778100001DEST_PATH_IMAGE012
Figure 2012103571778100001DEST_PATH_IMAGE014
Figure 2012103571778100001DEST_PATH_IMAGE016
, be called Fourier's time;
Figure 2012103571778100001DEST_PATH_IMAGE018
Be the time; Erfc (z)Be complementary error function,
Figure 2012103571778100001DEST_PATH_IMAGE020
Ask formula (1) gFunction is to Fourier's time variable FoPartial derivative, have
Figure 2012103571778100001DEST_PATH_IMAGE022
Figure 2012103571778100001DEST_PATH_IMAGE024
(2)
Obtain underground any degree of depth and radius distance gAnother analytical form of function:
Figure DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE028
(3)
4), opposite direction identical with two sizes, time phase difference
Figure DEST_PATH_IMAGE030
Step hot-fluid stack obtain the rect.p. hot-fluid, definition
Figure DEST_PATH_IMAGE032
Function is single drilling well underground any degree of depth and response of radius distance dimensionless transient temperature under unit rect.p. hot-fluid effect, so,
Figure 805874DEST_PATH_IMAGE032
The function analytical form is:
Figure DEST_PATH_IMAGE034
(4)
In the formula, Be Fourier's time step,
Figure DEST_PATH_IMAGE040
Figure 785331DEST_PATH_IMAGE030
Be time step, in designing and calculating, be taken as 1 hour, so, drilling well wall neutral temperature
Figure 378118DEST_PATH_IMAGE032
Function is:
Figure DEST_PATH_IMAGE042
Figure DEST_PATH_IMAGE044
(5)
Drilling well wall medial temperature
Figure 773327DEST_PATH_IMAGE032
Function is:
Figure DEST_PATH_IMAGE048
(6)
In the formula,
Figure DEST_PATH_IMAGE050
5) neutral temperature of arbitrary borehole wall and medial temperature in the selected drilling well in the step 1)
Figure 961601DEST_PATH_IMAGE032
Function is respectively:
(7)
Figure DEST_PATH_IMAGE054
(8)
Underground ground initial temperature is
Figure DEST_PATH_IMAGE056
, rect.p. hot-fluid sequence [( q( t 1 ), q( t 2 ), q( t 3 ) ... ] effect under, the relative transient temperature of the underground any degree of depth of single drilling well and radius distance is:
Figure DEST_PATH_IMAGE058
(9)
When
Figure DEST_PATH_IMAGE060
The time, being the borehole wall surface temperature, the boring relative transient state neutral temperature of wall and medial temperature are:
(10)
Figure DEST_PATH_IMAGE064
(11)
6) obtain each temperature or each temperature constantly of boring wall constantly of underground ground by relative transient temperature, calculate the boring internal thermal resistance of single U-shaped and double u-tube with fluid medial temperature method R b , each tube fluid temperature constantly of ground heat exchanger so
Figure DEST_PATH_IMAGE066
Be calculated as follows:
Figure DEST_PATH_IMAGE068
? (12)
Or
Figure DEST_PATH_IMAGE070
(13)
By the Performance Ratio of fluid temperature (F.T.) and heat pump, calculate the energy consumption of heat pump;
7) for different drilling parameter combinations, repeat above-mentioned calculation procedure, calculate drilling well total length, borehole wall surface temperature and the tube fluid temperature of respectively organizing parameter.
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CN106354984A (en) * 2016-10-21 2017-01-25 山东中瑞新能源科技有限公司 Temperature response calculation method of pile foundation spiral buried pipe under condition of underground water seepage
CN107145705A (en) * 2017-03-29 2017-09-08 中国海洋石油总公司 A kind of method and device for obtaining circulating temperature
CN107391807A (en) * 2017-06-28 2017-11-24 西安交通大学 Plate-fin heat exchanger heat transfer flow performance value analogy method based on transient technology
CN109948182A (en) * 2019-01-30 2019-06-28 西安交通大学 A kind of calculation method for mid-deep strata geothermal well well spacing
CN111539130A (en) * 2020-05-29 2020-08-14 山东建筑大学 Design and calculation method for drilling depth of geothermal heat exchanger of middle-deep buried pipe
CN112487527A (en) * 2020-11-25 2021-03-12 浙江工业大学 Design method of solar ground source heat pump heat supply and air conditioning system
CN113343444A (en) * 2021-05-24 2021-09-03 河南中烟工业有限责任公司 Structural design method of double-U-shaped cold and hot dual-purpose ground heat exchanger

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Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103235860A (en) * 2013-05-07 2013-08-07 北京工业大学 Hole wall representation temperature based simulation design method for drill hole space
CN103235860B (en) * 2013-05-07 2016-01-20 北京工业大学 The emulation design method of spacing between a kind of boring based on hole wall representation temperature
CN106354984A (en) * 2016-10-21 2017-01-25 山东中瑞新能源科技有限公司 Temperature response calculation method of pile foundation spiral buried pipe under condition of underground water seepage
CN106354984B (en) * 2016-10-21 2020-05-19 山东中瑞新能源科技有限公司 Temperature response calculation method of pile foundation spiral buried pipe under underground water seepage condition
CN107145705A (en) * 2017-03-29 2017-09-08 中国海洋石油总公司 A kind of method and device for obtaining circulating temperature
CN107391807B (en) * 2017-06-28 2019-10-29 西安交通大学 Plate-fin heat exchanger heat transfer flow performance value analogy method based on transient technology
CN107391807A (en) * 2017-06-28 2017-11-24 西安交通大学 Plate-fin heat exchanger heat transfer flow performance value analogy method based on transient technology
CN109948182A (en) * 2019-01-30 2019-06-28 西安交通大学 A kind of calculation method for mid-deep strata geothermal well well spacing
CN109948182B (en) * 2019-01-30 2020-10-27 西安交通大学 Calculation method for well spacing of middle-deep geothermal well
CN111539130A (en) * 2020-05-29 2020-08-14 山东建筑大学 Design and calculation method for drilling depth of geothermal heat exchanger of middle-deep buried pipe
CN111539130B (en) * 2020-05-29 2023-04-18 山东建筑大学 Design and calculation method for drilling depth of geothermal heat exchanger of middle-deep buried pipe
CN112487527A (en) * 2020-11-25 2021-03-12 浙江工业大学 Design method of solar ground source heat pump heat supply and air conditioning system
CN113343444A (en) * 2021-05-24 2021-09-03 河南中烟工业有限责任公司 Structural design method of double-U-shaped cold and hot dual-purpose ground heat exchanger

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Application publication date: 20130102