CN112212523A - One-dimensional heat transfer mathematical model of heat pipe type vacuum tube light-gathering heat-collecting system and application thereof - Google Patents

One-dimensional heat transfer mathematical model of heat pipe type vacuum tube light-gathering heat-collecting system and application thereof Download PDF

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CN112212523A
CN112212523A CN201910612727.8A CN201910612727A CN112212523A CN 112212523 A CN112212523 A CN 112212523A CN 201910612727 A CN201910612727 A CN 201910612727A CN 112212523 A CN112212523 A CN 112212523A
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heat
heat transfer
wall surface
loss
efficiency
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CN112212523B (en
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张维蔚
高虹
聂晶
张伟杰
田瑞
巴旭阳
刘妍
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Inner Mongolia University of Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S10/00—Solar heat collectors using working fluids
    • F24S10/90—Solar heat collectors using working fluids using internal thermosiphonic circulation
    • F24S10/95—Solar heat collectors using working fluids using internal thermosiphonic circulation having evaporator sections and condenser sections, e.g. heat pipes
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S10/00—Solar heat collectors using working fluids
    • F24S10/40—Solar heat collectors using working fluids in absorbing elements surrounded by transparent enclosures, e.g. evacuated solar collectors
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S23/00—Arrangements for concentrating solar-rays for solar heat collectors
    • F24S23/70—Arrangements for concentrating solar-rays for solar heat collectors with reflectors
    • F24S23/74—Arrangements for concentrating solar-rays for solar heat collectors with reflectors with trough-shaped or cylindro-parabolic reflective surfaces
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S70/00—Details of absorbing elements
    • F24S70/10—Details of absorbing elements characterised by the absorbing material
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S70/00—Details of absorbing elements
    • F24S70/10—Details of absorbing elements characterised by the absorbing material
    • F24S70/12—Details of absorbing elements characterised by the absorbing material made of metallic material
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S70/00—Details of absorbing elements
    • F24S70/20—Details of absorbing elements characterised by absorbing coatings; characterised by surface treatment for increasing absorption
    • F24S70/225—Details of absorbing elements characterised by absorbing coatings; characterised by surface treatment for increasing absorption for spectrally selective absorption
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28—HEAT EXCHANGE IN GENERAL
    • F28D—HEAT-EXCHANGE APPARATUS, NOT PROVIDED FOR IN ANOTHER SUBCLASS, IN WHICH THE HEAT-EXCHANGE MEDIA DO NOT COME INTO DIRECT CONTACT
    • F28D15/00—Heat-exchange apparatus with the intermediate heat-transfer medium in closed tubes passing into or through the conduit walls ; Heat-exchange apparatus employing intermediate heat-transfer medium or bodies
    • F28D15/02—Heat-exchange apparatus with the intermediate heat-transfer medium in closed tubes passing into or through the conduit walls ; Heat-exchange apparatus employing intermediate heat-transfer medium or bodies in which the medium condenses and evaporates, e.g. heat pipes
    • F28D15/0266—Heat-exchange apparatus with the intermediate heat-transfer medium in closed tubes passing into or through the conduit walls ; Heat-exchange apparatus employing intermediate heat-transfer medium or bodies in which the medium condenses and evaporates, e.g. heat pipes with separate evaporating and condensing chambers connected by at least one conduit; Loop-type heat pipes; with multiple or common evaporating or condensing chambers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/40—Solar thermal energy, e.g. solar towers
    • Y02E10/44—Heat exchange systems

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Abstract

The invention discloses a heat pipe type vacuum tube light-gathering heat-collecting system one-dimensional heat transfer mathematical model and application thereof, wherein the establishment of the mathematical model comprises the following steps: (A-1) judging the heat transfer mechanism of the evaporation section; (A-2) establishing an energy balance equation; (A-3) establishing an optical model; (A-4) establishing an evaporation section heat transfer model; (A-5) establishing a condensation section heat transfer model; (A-6) establishment of thermal efficiency and
Figure DDA0002122830450000011
and (4) an efficiency model. The one-dimensional heat transfer mathematical model of the heat pipe type vacuum tube light-gathering heat collection system can be used for analyzing the heat efficiency and heat efficiency of the heat collection system caused by factors such as the inlet temperature, the inlet speed, the direct solar radiation intensity, the ambient temperature and the wind speed of the heat transfer fluid
Figure DDA0002122830450000012
The effect of efficiency; meanwhile, the temperature of the working medium in the heat pipe can be predicted so as to determine the reasonable value range of the inlet temperature and the flow rate of the heat transfer fluid when the system operates.

Description

One-dimensional heat transfer mathematical model of heat pipe type vacuum tube light-gathering heat-collecting system and application thereof
Technical Field
The invention relates to the technical field of solar energy utilization. In particular to a one-dimensional heat transfer mathematical model of a heat pipe type vacuum tube light-gathering heat-collecting system and application thereof.
Background
The effective utilization of solar energy is to deal with fossil energy exhaustion and CO2One of the effective solutions to the problems of greenhouse effect caused by excessive discharge and global energy demand increase. The solar heat utilization technology is an important way for utilizing solar energy, and solar heat power generation, industrial heating, space heating, cooling and the like belong to the solar heat utilization category. In commercial equipment for utilizing solar energy at medium and high temperature, a parabolic trough type heat collection technology is mature and is a hot spot researched by researchers in recent years.
At present, the receiver of the commercial parabolic trough heat collecting system is mostly a vacuum tube linear receiver with a single-layer glass sleeve, and problems exist in use. For example, due to reflection and convergence of the light rays by the condenser, the circumferential heat flow density distribution of the receiver is uneven, so that the wall temperature of the receiver and the temperature distribution of the heat transfer fluid are uneven, and the heat transfer performance of the heat collection system is directly affected. In addition, the vacuum tube linear receiver is relatively expensive to manufacture, and the vacuum level in the annular region is difficult to maintain for a long time. Therefore, many scholars have improved the receiver and studied the heat transfer performance of the improved receiver by using experimental and theoretical methods. At present, the improvement methods of the receiver can be roughly divided into two methods, firstly, the vacuum tube receiver is still used, but the local structure is improved so as to improve the heat transfer performance of the heat collection system; and secondly, a non-vacuum tube receiver is used for replacing a vacuum tube receiver in medium and low temperature utilization, so that the manufacturing cost is reduced.
The first method is more documented for local improvement of vacuum tube receivers. Some scholars have replaced linear receivers with non-linear receivers. Demagh et al used a sinusoidal-wave S-shaped metal tube instead of a straight tube, and at this time, although the heat flux density of the receiver in both axial and circumferential directions was not uniform, the maximum heat flux density was reduced, thus effectively improving the local high temperature of the wall surface. Wang et al have designed symmetrical evagination bellows receiver, and research shows that can improve receiver heat transfer performance, reduce the thermal stress. Bellos et al designed a converging-diverging absorber tube to increase the thermal efficiency of the receiver by 4.55%. Huang et al designed dimpled metal tubes to improve the heat transfer performance of the receiver.
Some researchers have placed inserts of different configurations in the metal tube of the receiver to increase the heat transfer performance of the receiver by increasing the turbulence of the fluid flow. However, this design comes at the expense of increased fluid flow resistance. Kumar et al added the porous disk plug-in components that have certain contained angle with the axis in the metal tube to the influence of porous disc, porous semicircle dish to the heat transfer effect under different mode of placement has been analyzed. Ghasemii et al added a porous annular insert and studied the effect of the distance between the rings and the inner diameter of the rings on heat transfer performance. Mwesigye et al added a porous disc insert with a diameter smaller than that of the metal tube and placed in the center of the tube, and studied the influence of the diameter, the distance and the included angle with the axis of the insert on the heat transfer performance. Reddy et al compared the thermal efficiency of the receiver and the temperature distribution within the tube when longitudinal fins and perforated fins were added to the metal tube. Reddy et al studied the heat transfer performance of square, round, trapezoidal and triangular porous ribbed receivers and showed that all were effective in improving thermal efficiency, with the trapezoidal being the most obvious. Mwesigye et al incorporate twisted sheet inserts that have some clearance from the wall of the metal tube. Song et al added an insert that rotated helically around a central thin cylinder. Cheng et al added a long swirl insert on the side of the inner wall surface of the metal tube facing the concentrator. Gong et al add a small cylindrical array insert to one side of the concentrator. Bellos et al incorporate longitudinal internal fins.
Because the vacuum tube receiver has the problems of high manufacturing cost, difficult long-term maintenance of the vacuum degree of an annular area and the like, some scholars propose to replace the vacuum tube receiver with a non-vacuum tube receiver in medium and low temperature heat utilization. However, although the non-vacuum tube receiver is low in cost, the heat exchange amount by convection between the glass sleeve and the metal tube is increased, and thus the heat loss of the receiver is also large. In response to the problem, some scholars have improved the structure of the non-vacuum pipe receiver. Chandra et al add thermal insulation to the upper half of the annular region of the non-vacuum tube receiver to reduce heat loss due to air convection.
In addition, there are many documents on the research on the operation performance of the parabolic trough heat collecting system. The literature generally employs energy analysis (first law of thermodynamics) and
Figure BDA0002122830430000021
the analytical (second law of thermodynamics) method studies the operating performance of the parabolic trough collector system as a heat exchanger or as the main equipment of a solar thermal power plant. By adopting the energy analysis method, the collected heat of the system can be effectively evaluated and compared. But adopt
Figure BDA0002122830430000022
The analytical method can obtain the maximum theoretical useful work obtained when the system and the environment reach an equilibrium state, and can quantify the irreversibility in the thermodynamic system. By using
Figure BDA0002122830430000031
Analytical methods have been optimizing thermodynamic devices and systems for over 50 years, and these methods are more effective, especially when evaluating new ideas or new equipment. However, in the prior art, the heat efficiency and heat efficiency of the heat collecting system of the heat transfer fluid due to factors such as inlet temperature, inlet speed, direct solar radiation intensity, ambient temperature and wind speed and the like are not analyzed
Figure BDA0002122830430000032
The mathematical model of the effect of efficiency also does not have a mathematical model that predicts the temperature of the working medium in the heat pipe in order to determine the reasonable value ranges of the inlet temperature and the flow rate of the heat transfer fluid when the system is in operation.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to provide a one-dimensional heat transfer mathematical model of a heat pipe type vacuum tube light-gathering heat collection system, which is used for analyzing factors such as the inlet temperature, the speed, the direct solar radiation intensity, the ambient temperature and the wind speed of a heat transfer fluid to the heat efficiency and the wind speed of the heat collection system
Figure BDA0002122830430000033
The effect of efficiency; meanwhile, the temperature of the working medium in the heat pipe can be predicted so as to determine the reasonable value range of the inlet temperature and the flow rate of the heat transfer fluid when the system operates.
In order to solve the technical problems, the invention provides the following technical scheme: one-dimensional heat transfer number of heat pipe type vacuum tube light-gathering heat-collecting systemThe model learning method comprises the following steps: (A-1) judging the heat transfer mechanism of the evaporation section; (A-2) establishing an energy balance equation; (A-3) establishing an optical model; (A-4) establishing an evaporation section heat transfer model; (A-5) establishing a condensation section heat transfer model; (A-6) establishment of thermal efficiency and
Figure BDA0002122830430000034
and (4) an efficiency model.
The technical scheme of the invention achieves the following beneficial technical effects:
the invention designs a set of novel heat pipe type vacuum pipe solar light and heat collecting system capable of providing hot water with the temperature of 200 ℃ at most, which comprises a parabolic trough type condenser, a heat pipe type vacuum pipe receiver and a steel material supporting structure. According to the heat transfer characteristics of the system, a one-dimensional mathematical model of the heat transfer process is established, and energy analysis are utilized
Figure BDA0002122830430000035
Analytical methods the heat transfer characteristics of the system were studied. In order to verify the accuracy of the established model, the calculation result is compared with the literature experiment result, and the coincidence is good. According to the calculation result, the heat efficiency and the heat efficiency of the heat collecting system caused by the factors such as the inlet temperature, the inlet speed, the direct solar radiation intensity, the ambient temperature and the wind speed of the heat transfer fluid are analyzed
Figure BDA0002122830430000036
The effect of efficiency. The research result shows that the heat efficiency of the system is obviously influenced by the inlet temperature of the heat transfer fluid and the direct solar radiation intensity, and the system
Figure BDA0002122830430000037
The efficiency is significantly affected by the heat transfer fluid inlet temperature and the ambient temperature. Wherein the heat transfer fluid inlet temperature is related to the system thermal efficiency
Figure BDA0002122830430000038
The trend of the effect of efficiency is the opposite. As the inlet temperature increases, the system thermal efficiency gradually decreases, and
Figure BDA0002122830430000039
the efficiency gradually increases. In addition, the system
Figure BDA0002122830430000041
In losses caused by irreversible heat transfer between the sun and the heat-collecting system
Figure BDA0002122830430000042
The loss is the largest. And finally, determining the reasonable value ranges of the inlet temperature and the flow rate of the heat transfer fluid when the system operates by predicting the temperature of the working medium in the heat pipe by using the established mathematical model.
The receiver of the parabolic trough type heat collecting system is improved, the heat pipe type vacuum pipe is used as the receiver, and a set of heat pipe type vacuum pipe parabolic trough type light-gathering heat collecting system is designed. The heat pipe is used as an efficient heat transfer element and has the advantages of high heat transfer efficiency, good isothermal performance, simple structure and the like. The heat pipe as a receiver has also been applied in the field of solar heat utilization, mainly plate heat collectors and vacuum tube heat collectors in the field of low-temperature heat utilization. In recent years, there have been some attempts to combine heat pipes with CPC concentrators that lower the light ratio. The literature on the combination of a heat pipe vacuum tube receiver and a parabolic trough concentrator is relatively few, and the detailed energy analysis and energy analysis of the system are not available in the literature at present
Figure BDA0002122830430000043
And (4) analyzing.
The heat pipe type vacuum tube solar light-gathering heat collecting system designed by the invention can be used as solar medium-temperature heat utilization equipment and is used for providing high-temperature hot water with the highest temperature of 200 ℃ because the light-gathering of the groove type light-gathering device is larger and the working temperature of a heat pipe can be improved. In addition, due to the good isothermal property of the heat pipe, the uneven wall surface temperature distribution caused by the uneven heat flow density of the receiver in the circumferential direction due to the light condensation of the condenser can be reduced as much as possible.
The mathematical model and the method can reveal the heat transfer characteristic and the influence factors of the heat pipe type vacuum tube light-gathering heat-collecting system; the design of a new heat collecting system and the determination of the optimal operation condition have certain use value.
Drawings
FIG. 1a is a view of a parabolic trough solar collector; FIG. 1b is a schematic view of the external structure of a heat pipe vacuum tube; FIG. 1c is a schematic view of the internal structure of the heat pipe type vacuum tube;
FIG. 2 is a working principle of a two-phase closed thermosiphon;
FIG. 3a is a one-dimensional energy balance; fig. 3b is a model of heat transfer and thermal resistance of the evaporation section and the condensation section of the heat pipe [ note: (1) working medium of the heat pipe; (2c) the inner wall surface of the metal pipe of the condensation section; (2e) the inner wall surface of the metal tube at the evaporation section; (3c) the outer wall surface of the metal pipe of the condensation section; (3e) the outer wall surface of the metal pipe at the evaporation section; (4) the inner wall surface of the glass sleeve; (5) the outer wall surface of the glass sleeve; (6) an environment; (7) the sky; (HTF) heat transfer fluid);
FIG. 4 is a flow chart of a model algorithm;
FIG. 5 is a graph comparing the results of calculation with those of the literature;
FIG. 6 thermal efficiency of the collector as a function of heat transfer fluid inlet temperature;
FIG. 7 Heat collecting System
Figure BDA0002122830430000051
Efficiency as a function of heat transfer fluid inlet temperature;
FIG. 8 illustrates the variation of the temperature of the heat collection system with the inlet temperature of the heat transfer fluid;
FIG. 9 System
Figure BDA0002122830430000052
Loss as a function of heat transfer fluid inlet temperature;
FIG. 10 variation of thermal efficiency of a heat collection system with flow rate of heat transfer fluid;
FIG. 11 Heat collector
Figure BDA0002122830430000053
Efficiency as a function of heat transfer fluid flow rate;
FIG. 12 System
Figure BDA0002122830430000054
Loss as a function of heat transfer fluid flow rate;
FIG. 13 thermal efficiency of collector as a function of direct solar radiation intensity;
FIG. 14 Heat collector
Figure BDA0002122830430000055
The efficiency varies with the intensity of direct solar radiation;
FIG. 15 illustrates the variation of thermal efficiency of the heat collecting system with the ambient temperature;
FIG. 16 Heat collecting System
Figure BDA0002122830430000056
The variation of efficiency with ambient temperature;
FIG. 17 is a graph of the temperature of the working fluid within the heat pipe as a function of the heat transfer fluid inlet temperature;
FIG. 18 is a graph showing the temperature of the working fluid in the heat pipe as a function of flow rate;
FIG. 19 is a graph of working fluid pressure in a heat pipe as a function of heat transfer fluid inlet temperature.
In the figure: 1-a parabolic trough concentrator; 2-heat pipe type vacuum pipe receiver; 3-an outlet; 4-an inlet; 5-a condensation section; 6-adiabatic section; 7-an evaporation section; 8-sealing plug; 9-a glass sleeve; 10-a metal tube; 11-a support structure; 12-an annular region; 13-Cooling jacket.
Detailed Description
First part brief introduction of Heat pipe vacuum tube concentrating System in this embodiment
Each basic unit of the heat pipe type vacuum tube light and heat collecting system comprises a parabolic trough type light condenser, a heat pipe type vacuum tube receiver and a steel material supporting structure. The heat pipe is of a water-stainless steel (coated with an anti-corrosion coating) type, namely the heat pipe is made of stainless steel, the anti-corrosion coating is coated in the heat pipe, and the working medium in the heat pipe is water. The heat transfer fluid for cooling the system is also water. The heat pipe type vacuum tube receiver comprises an evaporation section, a heat insulation section and a condensation section. The outer surface of the evaporation section metal tube is coated with a metal ceramic selective coating, and the metal ceramic selective coating has the characteristics of high heat absorption rate and low emissivity in a working temperature range, and can reduce the radiation heat loss transmitted to the outside. The metal tube is covered by a single-layer glass sleeve, and an annular area between the glass sleeve and the metal tube is vacuumized to increase the convective resistance and the thermal conductive resistance of the annular area. The condensation section of the heat pipe extends into the cooling jacket, a heat-insulating layer is arranged outside the cooling jacket to insulate heat with the outside, and heat of the condensation section is taken away by heat transfer fluid flowing through the jacket. The groove type condenser adopts a crank connecting rod single-axis tracking technology, and the included angle between the condenser and the ground is determined by the current sun inclination angle. FIG. 1(a) is a schematic diagram of a heat pipe type vacuum tube light-gathering and heat-collecting system, and FIG. 1(b) is a schematic diagram of a heat pipe type vacuum tube receiver. The structural parameters of the heat pipe type vacuum tube light and heat collecting system are shown in the table 1, and the optical performance parameters are shown in the table 2.
TABLE 1 parameters of heat pipe type evacuated-tube solar concentrator collector system
Figure BDA0002122830430000061
TABLE 2 optical Property parameters
Figure BDA0002122830430000062
Second part of establishment of one-dimensional heat transfer mathematical model of heat pipe type vacuum tube light-gathering and heat-collecting system in the embodiment
(A-1) judgment of Heat transfer mechanism in Evaporation segment
In this embodiment, the heat pipe used in the heat collecting system is a two-phase closed thermosiphon, and the working principle is shown in fig. 2. The working medium absorbs heat in the evaporation section and then is vaporized, flows upwards to the condensation section, and is condensed and heat-exchanged with the wall surface of the condensation section, and latent heat of vaporization is released and then is condensed. The condensed working medium flows downwards along the wall surface in a liquid film form under the action of gravity to enter the evaporation section. In the condensation section, the heat transfer mode is considered to be film-like condensation, since the liquid film thickness is much smaller than the inner diameter of the heat pipe. The heat transfer mode of the evaporation section of the heat pipe is complex. The evaporation section is divided into a liquid film part and a liquid pool part when working under the influence of the filling rate of the working medium. Therefore, the heat exchange mode of the inner wall surface of the evaporation section and the working medium is divided into liquid pool heat exchange and liquid film heat exchange. Moreover, the heating power of the wall surface is different, and the heat exchange mechanism of the liquid pool and the liquid film is also different.
The method for judging the heat transfer mechanism of the evaporation section in the mathematical model of the embodiment is as follows:
judgment of evaporation section liquid film heat transfer mechanism introduces dimensionless parameter Xlf:
Figure BDA0002122830430000071
Bubble size:
Figure BDA0002122830430000072
liquid film local Rex：
Figure BDA0002122830430000073
In the formula, subscript l represents that the working medium is in a liquid state, and subscript v represents that the working medium is in a gas state. q. q.seIs the heating power of the evaporation section, W/m2(ii) a p is the pressure in the heat pipe, Pa; rho is the working medium density, kg/m3；rlvIs the latent heat of vaporization of the working medium, J/kg; v is kinematic viscosity, m2S; μ is dynamic viscosity, Pa-s; sigmalvIs surface tension, N/m; g is the acceleration of gravity, m/s2；Le,lfIs the length of the liquid film at the evaporation section, m; x is the distance from the liquid film position to the entrance of the evaporation section, m; pr is the prandtl number.
When X is presentlf≤109When it is laminar film-like evaporation, when 109≤Xlf≤2.7×1010When it is a mixed convection, when Xlf≥2.7×1010Nucleate boiling is observed.
Judgment of evaporation section liquid pool heat transfer mechanism introduces dimensionless parameter Xlp:
Figure BDA0002122830430000081
Rayleigh number:
Figure BDA0002122830430000082
mixing coefficient:
Figure BDA0002122830430000083
wherein β is a thermal expansion coefficient, 1/K; λ is the thermal conductivity, W/(m-K); a is the thermal diffusivity, m2/s。
When X is presentlp≤106Natural convection when 106≤Xlp≤2×107When mixed convection, Xlp≥2×107Nucleate boiling is observed.
Since the heat transfer coefficient of the liquid film is much larger than that of the liquid pool, the length of the liquid film and the liquid pool has a great influence on the heat transfer effect of the evaporation section. Under the heating condition, bubbles are generated in the liquid pool, so the volume is expanded and the length is increased. The length of the expanded liquid pool can be calculated by adopting the following formula:
Figure BDA0002122830430000084
bubble drift velocity:
Figure BDA0002122830430000085
static length L of working medium stock in liquid poollp-sta-invAnd subtracting the liquid films and the steam of the evaporation section, the condensation section and the heat insulation section from the static height of the initial liquid filling amount of the heat pipe to convert into the static height of the liquid pool of the evaporation section. The radian of the liquid film is ignored in the calculation of the model of the embodiment because the thickness of the liquid film in the heat pipe is very small. Assuming that the thickness of the liquid film in the condensation section increases linearly and the thickness of the liquid film in the evaporation section decreases linearly along the direction of the liquid film flow,the thickness of the liquid film of the heat insulation section is not changed. Deducing the static height L of the working medium stock in the liquid poollp-sta-invThe calculation formula of (a) is as follows:
Llp,sta,inv＝Llp,sta,inf-Llp,e,con-Llp,ad,con-Llp,c,con (9)
in the formula, Llp,sta,infIs the initial static height, m, of the liquid pool at the evaporation section; l islp,e,con、Llp,ad,con、Llp,c,conThe static heights, m, converted from liquid film and vapor in the evaporation section, the heat insulation section and the condensation section, respectively.
Wherein:
Figure BDA0002122830430000091
Figure BDA0002122830430000092
Figure BDA0002122830430000093
in the formula, deltae、δadThe thickness m of the liquid film on the surface of the liquid pool of the evaporation section and the liquid film on the heat insulation section; l ise,lf、Lad、LcThe lengths of liquid films of the evaporation section, the heat insulation section and the condensation section are m respectively.
The liquid film thickness of the heat insulation section and the liquid film thickness of the surface of the liquid pool of the evaporation section are calculated by adopting a Nusselt theory, and the calculation formula is as follows:
Figure BDA0002122830430000094
Figure BDA0002122830430000095
in the formula, subscripts 1, 2c, 2e are described with reference to fig. 3. T is the temperature, K.
(A-2) establishing an energy balance equation;
the mathematical model established in the embodiment is based on the energy balance relationship between the heat transfer fluid in the heat collection system and the environment, and factors including the type of the condenser, the structure of the receiver, the optical performance, the environmental conditions and the like are considered in the model. Analyzing the heat transfer process of the system, and figure 3 shows an energy balance diagram and a thermal resistance network diagram of the cross section of the evaporation section and the condensation section of the heat pipe type vacuum pipe receiver. According to the first law of thermodynamics, the energy balance relationship can be listed for the working media of the inner wall surface and the outer wall surface of the evaporation section of the heat pipe, the inner wall surface and the outer wall surface of the glass sleeve and the evaporation section and the condensation section of the heat pipe respectively by neglecting the heat exchange between the receiver and the bracket and the heat transfer fluid and the environment.
Solar effective incident energy (Q)abs) Are respectively coated by selective absorption of the outer wall surface of the metal tube (Q)s,3e) And a glass sleeve (Q)s,5) And (4) absorbing. The heat absorbed by the selective absorption coating is divided into two parts, one of which is transferred to the inner wall surface (Q) by heat conduction3e,2e) (ii) a Another part by heat radiation (Q)3e,4rad) And convection heat transfer (Q)3e,4conv) Is transmitted to the inner wall surface of the glass sleeve. Then, this heat is transferred to the outer wall surface (Q) of the glass sleeve by heat conduction4,5cond) And solar radiation energy (Q) directly absorbed by the glass sleeves,5) That is, the heat dissipated from the glass sleeve to the environment, i.e., the heat loss (Q)loss) Including convective heat loss (Q)5,6conv) And radiation heat loss (Q)5,7rad). In addition, useful energy is transferred to the working medium (Q) of the heat pipe through the inner wall surface of the metal pipe2e,1) The working medium is evaporated and flows to the condensing section, and is transferred to the inner wall surface (Q) of the condensing section in a film-shaped condensation manner in the condensing section1,2c) By conduction to the outer wall surface (Q) of the condensation section2c,3c) And finally absorbed by the heat transfer fluid in a convective heat transfer manner (Q)3c,f) I.e. useful energy. From fig. 3, the following system energy balance equations can be listed:
Qabs＝Qs,3e+Qs,5 (15)
Qs,3e＝Q3e,2e+Q3e,4conv+Q3e,4rad (16)
Q3e,4conv+Q3e,4rad＝Q4,5cond (17)
Q4,5cond+Qs,5＝Q5,6conv+Q5,7rad (18)
Q3e,2e＝Q2e,1＝Q1,2c＝Q2c,3c＝Q3c,f (19)
to simplify the calculation process, the following assumptions are made: 1) the sun rays are parallel light, and the included angle of the sun is not considered; 2) the wall surface temperatures of the evaporation section and the condensation section of the heat pipe are the same along the axial direction, and the axial heat conduction of the wall surface is not considered; 3) the reflectivity and absorptivity of each surface and the transmissivity of the glass sleeve are constant; 4) the heat collecting system is in a stable operation state.
(A-3) establishing an optical model
The solar energy which can be utilized by the heat collecting system is the energy of the sun irradiating the lighting surface of the condenser and is equal to the opening area (A) of the condensera＝LaWa) Multiplying by the direct solar radiation intensity:
Qs＝IdirLaWa (20)
in the formula, LaIs the condenser length, m; waIs the concentrator width, m; i isdirIs the direct irradiation intensity of the sun, W/m2。
Due to optical losses of the concentrator, the energy reaching the receiver is less than the solar radiation energy received by the concentrator. The solar radiation energy (solar effective incident energy) reaching the receiver is:
Qabs＝Qsηopt (21)
in the formula etaoptIs the optical efficiency of the concentrator.
The optical performance of the condenser is affected by various factors, such as the reflectivity of the condenser, the system structure, the processing conditions, and the testing conditions. The calculation formula of the optical efficiency of the condenser is as follows:
ηopt＝ξ1ξ2ξ3ξ4ξ5ξ6ρclK (22)
in the formula, xi1For shading coefficient (supporting frame, protective cover, etc. shading sun rays), xi2To tracking error, xi3As geometric error (condenser arrangement), xi4Is the condenser fouling factor, ξ5Is the collector fouling factor, xi6Coefficient of unpredictable factor, pclK is the solar incident angle correction factor for concentrator reflectivity. The values of the coefficients are shown in table 2.
The solar incident angle correction coefficient (K) is a function of the solar incident angle (θ), and the following calculation formula can be used:
Figure BDA0002122830430000111
(A-4) establishing an evaporation section heat transfer model;
after being condensed by the condenser, the solar radiation heat energy reaching the surface of the receiver can be divided into two parts. Most of the water is absorbed by the selective absorption coating on the outer wall surface of the metal tube, and a small part of the water is absorbed by the glass sleeve.
The solar radiation heat energy absorbed by the selective absorbing coating on the outer wall surface of the metal pipe is as follows:
Qs,3e＝Qabsτcovαcoa (24)
the solar radiation heat energy absorbed by the glass sleeve is as follows:
Qs,5＝Qabsαenv (25)
the heat energy of solar radiation absorbed by the outer wall surface of the metal tube and transferred to the inner wall surface through heat conduction is as follows:
Figure BDA0002122830430000112
in the formula, the heat conductivity coefficient lambda of the metal tube material23,eIs the average temperature T of the inner and outer walls of the metal pipe23,e＝(T2e+T3e) Thermal conductivity at/2.
The heat transferred to the working medium by the inner wall surface of the metal pipe is as follows:
Q2e,1＝πD2(Le,lfh2e,1,lf+Le,lph2e,1,lp)(T2e-T1) (27)
in the formula, h2e,l,lf、h23,l,lpThe heat transfer coefficients of a liquid film and a liquid pool at an evaporation section are W/(m)2-K)；Le,lpIs the length of the liquid pool at the evaporation section, m.
According to the judgment of the formula (1), in the range of the direct solar radiation intensity of the embodiment, the liquid film heat transfer of the evaporation section belongs to the nucleate boiling heat transfer, and the heat transfer coefficient calculation formula is as follows:
Figure BDA0002122830430000121
viscosity coefficient:
Figure BDA0002122830430000122
according to equation (4), the liquid pool heat transfer in the evaporation section in the present embodiment is in the range of mixed convection heat transfer and nucleate boiling heat transfer. Wherein, the calculation formula of the mixed convection heat transfer coefficient is as follows:
Figure BDA0002122830430000123
when Bo is less than or equal to 10, n is 0.5; when Bo > 10, n is 1/6.
Number of Archimid:
Figure BDA0002122830430000124
froude number:
Figure BDA0002122830430000125
bond number:
Figure BDA0002122830430000126
the heat transfer coefficient of the nucleate boiling liquid pool can be calculated by the following formula:
Figure BDA0002122830430000127
in the formula, cpThe constant-pressure specific heat capacity of the working medium in the heat pipe is J/(kg-K); p is a radical ofaIs standard atmospheric pressure, Pa.
The heat transfer between the outer wall surface of the metal tube and the glass sleeve comprises radiation heat transfer and convection heat transfer. Because the annular region between the metal tube and the glass sleeve is vacuumized, the convective heat exchange is mainly free molecular convective heat exchange. This portion of the heat is very small and is therefore ignored in the calculation (Q)3e,4conv0) and only the radiative heat exchange between the metal tube and the glass sleeve is considered. The selective absorption coating on the outer wall surface of the metal tube transfers heat Q to the inner wall surface of the glass sleeve through infrared radiation3e,4radComprises the following steps:
Figure BDA0002122830430000131
in the formula, σSBIs the Stefan-Boltzmann constant, W/(m)2-K4)。
The inner wall of the glass sleeve transmits heat to the outer wall surface of the glass sleeve through heat conduction, and the calculation formula is as follows:
Figure BDA0002122830430000132
there are 2 types of heat exchange between the outer wall surface of the glass sleeve and the external environment, namely convection heat exchange with air and radiation heat exchange with sky. The convection heat exchange quantity between the outer wall surface of the glass sleeve and the environment is as follows:
Q5,6conv＝πD5Leh56(T5-T6) (37)
convective heat transfer coefficient h56Related to the ambient wind speed. When no wind exists, the heat exchange between the outer wall surface of the glass sleeve and the ambient air is natural convection heat exchange, and at the moment:
Figure BDA0002122830430000133
wherein the Rayleigh number Ra5The calculation formula of (2) is as follows:
Figure BDA0002122830430000134
in the formula, the subscript air represents ambient air.
When wind exists, the convection heat exchange of the glass sleeve and the surrounding air belongs to forced convection heat exchange, and at the moment:
Figure BDA0002122830430000135
wherein, Re51000-; pr (Pr) of6When the content is less than or equal to 10, n is 0.37.
Radiation heat exchange quantity Q of glass sleeve outer wall facing sky5,7radComprises the following steps:
Figure BDA0002122830430000136
in clear weather, the effective temperature T of sky7The calculation formula of (2) is as follows:
Figure BDA0002122830430000137
(A-5) establishing a condensation section heat transfer model;
the working medium is transferred to the heat Q of the inner wall of the condensation section in a film-shaped condensation mode1,2cComprises the following steps:
Q1,2c＝πD2Lch1,2c(T1-T2c) (43)
the calculation formula of the film-shaped condensation heat exchange coefficient is as follows:
Figure BDA0002122830430000141
the heat conducted to the outer wall surface by the inner wall surface of the metal pipe of the condensation section through heat conduction is as follows:
Figure BDA0002122830430000142
the heat Q transferred to the heat transfer fluid in the cooling jacket by the heat convection from the outer wall of the metal pipe of the condensing section3c,fComprises the following steps:
Q3c,f＝πD3Lch3c,f(T3c-Tf) (46)
in the formula, the subscript f represents a heat transfer fluid.
The flow of the heat transfer fluid in the cooling jacket is a turbulent flow in the inlet region of the annular sleeve, and the heat transfer coefficient can be determined by the Gnielinski formula:
Figure BDA0002122830430000143
(A-6) establishment of thermal efficiency and
Figure BDA00021228304300001410
and (4) an efficiency model.
The thermal efficiency of a heat collection system is defined as the ratio of the heat absorbed by the heat transfer fluid in the receiver (i.e., the useful energy) to the total direct solar radiation energy incident on the collector's daylighting area, i.e.:
Figure BDA0002122830430000144
Figure BDA0002122830430000145
in the formula (I), the compound is shown in the specification,
Figure BDA0002122830430000146
is the mass flow of the heat transfer fluid, kg/s; t isin、ToutThe heat transfer fluid inlet and outlet temperatures, K, respectively.
The embodiment will make the heat collecting system in detail
Figure BDA00021228304300001411
Analysis, including Total solar input
Figure BDA00021228304300001412
Figure BDA00021228304300001413
A flow output,
Figure BDA00021228304300001414
Loss and
Figure BDA00021228304300001415
and (4) loss. Heat collecting system
Figure BDA00021228304300001416
Efficiency is defined as heat transfer fluid heat in the receiver
Figure BDA00021228304300001417
Summation of incremental and solar input heat collection systems
Figure BDA00021228304300001418
The calculation formula is as follows:
Figure BDA0002122830430000147
the direct solar radiant energy received by the concentrator can be considered undiluted, and thus the total solar input
Figure BDA00021228304300001419
Petela model calculations can be used. In this model, the surface temperature (T) of the suns) Set to 5770K. Total input of sun
Figure BDA00021228304300001420
Comprises the following steps:
Figure BDA0002122830430000148
heat of heat transfer fluid in receiver
Figure BDA00021228304300001421
The incremental calculation formula is:
Figure BDA0002122830430000149
in the formula, T0Reference ambient temperature, K; Δ p is the inlet-outlet pressure difference of the heat transfer fluid, and the pressure difference is very small in the calculation of the embodiment. For making the heat collecting system complete
Figure BDA0002122830430000154
Analysis, this example pair
Figure BDA0002122830430000155
Loss and
Figure BDA0002122830430000156
losses were calculated. Heat collecting system
Figure BDA0002122830430000157
Losses associated with heat loss, including optics
Figure BDA0002122830430000158
Losses and heat loss from the receiver to the environment
Figure BDA0002122830430000159
And (4) loss.
Optical system
Figure BDA00021228304300001510
The formula for the loss is:
Eloss,opt＝(1-ηopt)Es (53)
heat generation
Figure BDA00021228304300001511
The formula for the loss is:
Figure BDA0002122830430000151
general description of the invention
Figure BDA00021228304300001512
The loss is:
Eloss＝Eloss,opt+Eloss,th (55)
Figure BDA00021228304300001513
losses are due to heat transfer from the high temperature object to the low temperature object, an irreversible process. In the heat collecting system of the present embodiment,
Figure BDA00021228304300001514
losses are included between the sun and the receiver, and between the receiver and the heat transfer fluid. Between the sun and the receiver
Figure BDA00021228304300001515
The loss calculation formula is:
Figure BDA0002122830430000152
between receptacle and fluid
Figure BDA00021228304300001516
The loss calculation formula is:
Figure BDA0002122830430000153
general description of the invention
Figure BDA00021228304300001517
The loss is:
Ed＝Ed,s-r+Ed,r-f (58)
method for calculating one-dimensional heat transfer mathematical model of heat pipe type vacuum tube light-gathering heat collection system in the third part of embodiment
The heat pipe type vacuum tube light-gathering heat collection system one-dimensional heat transfer mathematical model built in the embodiment operates in an EXCEL VBA environment, and researches the heat efficiency and heat efficiency of the heat collection system by using a plurality of factors such as the inlet temperature, flow speed, direct solar radiation intensity, environment temperature and wind speed of heat transfer fluid
Figure BDA00021228304300001518
The effect of efficiency. The algorithm flow of the calculation process is shown in fig. 4. The heat pipe type used by the receiver of the heat collection system of the embodiment is a water-stainless steel (coated with an anti-corrosion coating), namely the heat pipe is made of stainless steel, the anti-corrosion coating is coated in the heat pipe, and the working medium in the heat pipe is water. When the heat pipe is in operation, the working medium in the pipe is in a saturated state, and the physical parameters of water and steam in the saturated state are shown in the literature [53 ]]. The heat transfer fluid in the cooling jacket of the receiver is water, and the physical parameters of unsaturated water are shown in the literature [53 ]]. According to the design requirement, the temperature of the heat transfer fluid in the calculation is selected to be 40-200 ℃, and the mass flow rate is 1000-2800L/h. According to the local meteorological conditions, the direct solar radiation intensity is selected to be 300-1000W/m2The ambient temperature is 5-40 ℃, and the wind speed is 0-6 m/s. Calculating and analyzing heat of one parameter to the heat collecting system
Figure BDA0002122830430000162
When the influence of the performance is not specified, other parameters are set toA default value. The selection ranges and default values of the calculation parameters are shown in Table 3. To calculate the system thermal efficiency under different environmental temperature conditions
Figure BDA0002122830430000163
Efficiency, this example sets the reference ambient temperature to 5 ℃.
TABLE 3 calculation of parameter value ranges and Default values
Figure BDA0002122830430000161
Fourth part this embodiment heat pipe vacuum tube spotlight thermal-arrest system one-dimensional heat transfer mathematical model's accuracy is tested Certificate (certificate)
To verify the accuracy of the model constructed in this embodiment, the calculation result needs to be compared with the test result. At present, no relevant test documents of other heat pipe type vacuum tube light-gathering and heat-collecting systems exist, so that direct comparison cannot be carried out. The mathematical model for heat transfer of the metal tube and the glass sleeve of the evaporation section of the embodiment is also applied to other documents, and the accuracy is high after verification. Therefore, the test data of the common heat pipe in the document [ K.S.Ong, M.Haider-E-Alahi.Performance of a R-134 a-filtered Thermal Engineering [ J ]. Applied Thermal Engineering,2003,23, 2373 and 2381 ] is selected to verify the accuracy of the mathematical model of the heat pipe part constructed in the embodiment.
The heat pipe used in the document [ K.S.Ong, M.Haider-E-Alahi.Performance of A R-134a-filled Thermal Engineering [ J ]. Applied Thermal Engineering,2003,23, 2373-. The heat pipe evaporation section adopts a constant temperature water area for continuous heating, and the heating power of the evaporation section is changed by controlling the temperature of the constant temperature water area. The condensing section is externally provided with a cooling jacket, the cooling jacket is insulated from the outside by adopting a heat preservation measure, and the heat transfer fluid in the cooling jacket is water. The working medium in the heat pipe is R134a, which is a relatively common refrigerant, and the physical parameters of the refrigerant are shown in the document [ Y.Wu.Refrigeration priority and equality [ M ]. Xi' an Jianotong University Press,2010 ]. The literature test tests the wall temperature of the evaporation section and the condensation section of the heat pipe under the conditions of different heating powers, liquid filling rates and heat transfer fluid flow rates of the evaporation section.
In this embodiment, wall surface temperatures of an evaporation section and a condensation section of a heat pipe at four different heating powers of 30 ℃, 40 ℃, 50 ℃ and 60 ℃ are selected under the conditions that the liquid filling rate is 0.8 and the mass flow rate of a heat transfer fluid is 0.0121kg/s in a document [ K.S.Ong, M.Haider-E-Alahi.Performance of a R-134a-filled Thermal [ J ] Applied Thermal Engineering,2003,23, 2373-2381 ], and compared with a model calculation result, the comparison result is shown in FIG. 5. In fig. 5, the abscissa represents the axial length of the heat pipe, the point x equal to 0 represents the end of the evaporation section of the heat pipe, and the ordinate represents the wall temperature. As can be seen from fig. 5, the calculated results are well matched with the experimental results in the literature, and the average error is about 2.73%. Since the one-dimensional heat transfer model is built in the embodiment and the heat conduction in the length direction of the heat pipe material is not considered, the temperatures of the evaporation section and the condensation section in the length direction in the calculation result are the same, which is slightly different from the experimental test result. In addition, the influence of factors such as gas-liquid two-phase flow in the heat pipe on heat transfer resistance is not considered in the model, so that the wall surface temperature difference of the evaporation section and the condensation section in the calculation result is smaller than that of the test data.
Application of one-dimensional heat transfer mathematical model of heat pipe type vacuum tube light-gathering and heat-collecting system in the fifth embodiment
5.1, analyzing the heat efficiency of the heat collecting system and the heat transfer fluid inlet temperature
Figure BDA0002122830430000171
Effect of efficiency
FIG. 6 is a graph of thermal efficiency of a heat collection system as a function of heat transfer fluid inlet temperature. As the heat transfer fluid inlet temperature increases, the system thermal efficiency decreases progressively, with a more pronounced tendency to decrease. FIG. 7 is a heat collecting system
Figure BDA0002122830430000172
Efficiency versus heat transfer fluid inlet temperature. In this embodimentWithin the calculation range of the flow rate, the system
Figure BDA0002122830430000173
The efficiency increases gradually as the heat transfer fluid inlet temperature increases. As can be seen,
Figure BDA0002122830430000174
the efficiency is greatly affected by the inlet temperature. This is because the system
Figure BDA0002122830430000175
The losses are related to heat losses, and
Figure BDA0002122830430000176
losses are caused by irreversible processes in differential heat transfer, which are related to the heat transfer fluid inlet temperature.
As the heat transfer fluid inlet temperature increases, the receiver wall temperatures gradually increase. For ease of understanding, FIG. 8 shows the average temperature of the heat transfer fluid ((T)in+Tout) /2) outer wall temperature (T) of metal pipe3e) Outer wall temperature (T) of glass sleeve5) And ambient temperature (T)6) A profile with heat transfer fluid inlet temperature. It can be seen that as the heat transfer fluid inlet temperature increases, the temperature difference (T) between the outer wall surface of the glass sleeve and the environment increases5-T6) Gradually increases, and therefore the system heat loss QlossThe thermal efficiency is reduced. From the formula (54), QlossIncrease of system heat
Figure BDA0002122830430000177
Loss Eloss,thAnd also increases. But T3eThe higher, the heat collecting system
Figure BDA0002122830430000178
Loss Ed,s-r、Ed,r-HTFThe smaller (equation (56-57)).
FIG. 9 shows a system
Figure BDA0002122830430000179
Loss and
Figure BDA00021228304300001710
loss versus heat transfer fluid inlet temperature. In the calculation conditions of FIG. 9, the solar incident angle and the intensity of the direct solar radiation are not changed, so that the optical characteristics are obtained
Figure BDA00021228304300001711
The losses are constant. As can be seen, as the inlet temperature increases,
Figure BDA0002122830430000181
loss Ed,s-rAnd Ed,r-fThe magnitude of the reduction is significantly larger than Eloss,thThe magnitude of the increase. So the higher the inlet temperature, the higher the system
Figure BDA0002122830430000182
The greater the efficiency. As can also be seen in FIG. 9, the heat collection system is caused by irreversible heat transfer
Figure BDA0002122830430000183
Loss is system
Figure BDA0002122830430000184
The main cause of the loss. Among which, between the sun and the collector
Figure BDA0002122830430000185
Loss in total
Figure BDA0002122830430000186
The loss ratio is the largest, about 40.78-58.54%. Heat dissipated by the collector system to the environment
Figure BDA0002122830430000187
Total loss
Figure BDA0002122830430000188
The proportion of losses is minimal, about 0.49-1.95%.
Comparing FIG. 6 with FIG. 7, the system thermal efficiency is shown
Figure BDA0002122830430000189
The trend of efficiency with heat transfer fluid inlet temperature is opposite. The reason for this is the system
Figure BDA00021228304300001810
Losses are due to the transfer of heat by the temperature difference between the receiver and the heat transfer fluid, while losses are due to the transfer of heat by the temperature difference between the receiver and the environment. The higher the temperature of the heat transfer fluid, the higher the temperature of the receiver walls, and therefore the system
Figure BDA00021228304300001811
The smaller the loss, the greater the heat loss.
5.2, analyzing the heat efficiency of the heat collecting system by the flow velocity of the heat transfer fluid
Figure BDA00021228304300001812
Effect of efficiency
As can be seen from fig. 6, the thermal efficiency of the system gradually increases as the flow rate of the heat transfer fluid increases for the same inlet temperature. But the higher the temperature, the smaller the magnitude of the increase in thermal efficiency. FIG. 10 shows the flow rate as a function of the thermal efficiency of the system for the four different inlet temperatures (40 deg.C, 90 deg.C, 140 deg.C, 190 deg.C) under the conditions calculated in FIG. 6. It can be seen that the thermal efficiency of the system does not change substantially with the flow rate when the flow rate is greater than 2000L/h. This is because the heat transfer coefficient h of the heat transfer fluid to the wall surface is increased as the flow velocity increases3c,fThe heat absorption capacity of the heat transfer fluid increases and the thermal efficiency of the system increases (equation (47)). However, after the convective heat transfer is enhanced, the temperature of each wall surface of the receiver is reduced, and the heat loss between the receiver and the environment is reduced. Therefore, the thermal efficiency of the system increases more gradually as the flow rate of the heat transfer fluid increases.
As can be seen from FIG. 7, the heat transfer fluid flow rate changes versus system
Figure BDA00021228304300001813
The effect of efficiency is not significant. Because of the fact that
Figure BDA00021228304300001814
The relationship between the efficiency and the flow rate is mainly expressed in the resistance Δ p generated by the friction force when the fluid flows (equation (52)). In the heat collecting system, the heat transfer fluid is water (liquid), and the length of the cooling jacket is short, so that the resistance generated by the flow of the fluid is very small and can be ignored.
However, if the curves of FIG. 7 are enlarged partially, it can be seen that the system is operated at different inlet temperatures
Figure BDA00021228304300001815
The trend of efficiency with flow rate is different. FIG. 11 shows the system at four different inlet temperatures
Figure BDA00021228304300001816
Efficiency as a function of heat transfer fluid flow rate. When the inlet temperature is less than 40 ℃, the system
Figure BDA00021228304300001817
The efficiency gradually decreases with increasing flow rate; when the inlet temperature is more than 90 ℃, the system
Figure BDA00021228304300001818
The efficiency is gradually increased. As can be seen from equation (52), the system heat
Figure BDA00021228304300001819
Increment being the density ρ of the heat-transfer fluidf(m＝uAρf) And specific heat capacity at constant pressure (c)p,f) The influence of the magnetic field. As the temperature of the heat transfer fluid (water) increases, the trends of the density and the specific heat capacity at constant pressure are not the same. The density is gradually reduced when the temperature is increased, and the specific heat capacity at constant pressure is firstly reduced and then increased, and the increasing trend is gradually obvious. The constant pressure specific heat capacity of water changes with the temperature, so that the system can be operated at different inlet temperatures
Figure BDA00021228304300001820
The efficiency has a different trend with the flow rate.
FIG. 12 is a system
Figure BDA00021228304300001821
Loss versus heat transfer fluid flow rate. From FIG. 12, the heat transfer fluid flow velocity pair
Figure BDA00021228304300001822
The effect of the losses is relatively significant. Between sun and receiver as the heat transfer fluid flow rate increases
Figure BDA00021228304300001823
With increasing losses, between receiver and fluid
Figure BDA00021228304300001824
The losses gradually decrease. This is because the flow velocity has a negligible effect on the temperature difference of the heat transfer, although the resistance Δ p generated by the flow velocity is very small. As the flow rate of the heat transfer fluid increases, the average temperature of the heat transfer fluid inlet and outlet decreases, so that the temperature difference between the sun and the receiver increases and the temperature difference between the receiver and the environment decreases. However, this variation is for
Figure BDA00021228304300001825
In terms of loss, the proportion is very small, only about 3.5%.
5.3, analyzing the heat efficiency of the heat collecting system by the direct solar radiation intensity
Figure BDA0002122830430000191
Effect of efficiency
FIGS. 13 and 14 are respectively the system thermal efficiencies and
Figure BDA0002122830430000192
the efficiency is plotted against the intensity of direct solar radiation. As the intensity of the direct solar radiation increases, the heat input into the receiver increases, the wall temperature increases, the heat output of the system gradually increases, and the heat loss also increases. Therefore, as the intensity of direct solar radiation increases, the thermal efficiency of the system gradually increases, but the increasing tendency gradually flattens. Change of thermal efficiencyThe chemical trend is the same, and as the direct solar radiation intensity is increased, the system
Figure BDA0002122830430000193
The efficiency is also gradually increased. Solar irradiation intensity of 300-2Under the condition of TinAt 40 ℃, the thermal efficiency of the system is 75.37-75.53%,
Figure BDA0002122830430000194
the efficiency is 5.21-5.31%; t isinAt 190 ℃, the thermal efficiency of the system is 71.10-73.92%,
Figure BDA0002122830430000195
the efficiency is 28.02-29.17%.
5.4, analyzing the heat efficiency of the heat collecting system and the ambient temperature
Figure BDA0002122830430000196
Effect of efficiency
Figure BDA0002122830430000197
The calculation is based on reference environment conditions, when the system is balanced with the reference environment
Figure BDA0002122830430000198
Is zero. This example
Figure BDA0002122830430000199
In the analysis calculation, the reference ambient temperature was set to 5 ℃ and was constant. FIGS. 15 and 16 are respectively the system thermal efficiencies and
Figure BDA00021228304300001910
efficiency versus ambient temperature. As can be seen from the equations (37) and (41), the ambient temperature T6The higher the heat loss of the receiver to the environment by convective heat exchange and radiant heat exchange is, so that the heat efficiency of the system is increased. The amount of heat absorbed by the heat transfer fluid within the receiver increases, as defined by the thermal efficiency of the system. Strip with constant temperature at the inlet of the heat transfer fluidUnder conditions, the outlet temperature will rise. Therefore, under the condition that other conditions are not changed, the temperature of the system working medium is higher as the ambient temperature is increased. According to
Figure BDA00021228304300001911
The higher the temperature of the heat transfer fluid, the higher the quality of the heat, and therefore the system
Figure BDA00021228304300001912
The greater the efficiency. However, because the system receiver is a heat pipe type vacuum tube receiver and the annular area between the heat pipe and the glass sleeve is vacuumized, the wall temperature of the glass sleeve is lower, and the system thermal efficiency and the heat efficiency are lower
Figure BDA00021228304300001913
The rising tendency of the efficiency is small.
5.5, analyzing the heat efficiency of the heat collecting system and the sum of the wind speed
Figure BDA00021228304300001914
Effect of efficiency
The heat collecting system receiver of the present embodiment is a heat pipe type vacuum tube receiver, and the annular region between the metal tube and the glass sleeve is vacuumized, so that the wind speed is within the selected wind speed range of the present embodiment to the heat efficiency and heat efficiency of the heat collecting system
Figure BDA00021228304300001915
The effect of efficiency is very small. Under the calculation conditions of default values in Table 3, when the wind speed is 1m/s, the thermal efficiency of the system is 74.52 percent,
Figure BDA00021228304300001916
the efficiency is 23.29%; when the wind speed is 6m/s, the thermal efficiency of the system is 74.50 percent,
Figure BDA00021228304300001917
the efficiency was 23.28%. So wind speed is related to system thermal efficiency and
Figure BDA00021228304300001918
the impact of efficiency was not overestimated.
5.6, predicting the temperature of the working medium in the heat pipe so as to determine the reasonable value range of the inlet temperature and the flow rate of the heat transfer fluid when the system operates (analyzing the working state of the heat pipe receiver)
The mathematical model established in the embodiment can also be used for predicting the state of working media in the heat pipe when the heat collection system operates so as to determine the inlet temperature and the flow speed selection range of the heat transfer fluid when the system operates. The receiver of the heat collecting system of the embodiment adopts a water-stainless steel heat pipe, the working medium of the heat pipe is water, and the optimal working temperature of the heat pipe is 30-250 ℃.
FIGS. 17 and 18 show the temperature of the working fluid within the heat pipe as a function of the heat transfer fluid inlet temperature and flow rate, respectively. As the inlet temperature and the direct solar radiation intensity increase, the temperature of working media in the heat pipe increases in a linear trend. However, as the flow velocity increases, the temperature of the working medium in the heat pipe is gradually reduced, and the reduction trend gradually becomes slower. Under the calculation conditions of FIG. 17, the working temperature of the working medium in the heat pipe is 71.9-252.9 ℃. The highest working medium temperature exceeds the highest value of the optimal working temperature range of the water-stainless steel type heat pipe. Therefore, if the direct solar radiation intensity and the inlet temperature of the heat transfer fluid are high, the flow rate of the heat transfer fluid cannot be too low, otherwise the temperature of the working medium in the heat pipe is beyond the optimal temperature range. For example, when the intensity of direct solar radiation is 1000W/m2And when the inlet temperature of the heat transfer fluid is 200 ℃, the flow speed of the heat transfer fluid cannot be less than 1600L/h.
FIG. 19 is a graph of the pressure of the working fluid within the heat pipe versus the inlet temperature of the heat transfer fluid under the conditions of FIG. 17. And the system operates, and the working medium in the heat pipe is in a saturated state. As the temperature increases, the pressure of the working fluid will also increase. However, as can be seen from fig. 19, as the temperature of the heat transfer fluid increases, the pressure increases in a different manner from the temperature, and the increasing tendency becomes greater. For example, the temperature of the working medium in the heat pipe is increased from 71.9 ℃ to 105.4 ℃ (the temperature is increased by 33.5 ℃), and the corresponding pressure is increased from 0.034MPa to 0.124MPa (the pressure is increased by 0.09 MPa); the temperature of the working medium is increased from 222.3K to 252.9K (temperature rise is 30.6 ℃), and the corresponding pressure is increased from 2.43MPa to 4.18MPa (pressure rise is 1.75 MPa). Therefore, when the heat collecting system operates, the temperature of the working medium of the heat pipe is prevented from exceeding the design temperature, otherwise, the pressure bearing of the heat pipe is too large, and the service life of the heat pipe is reduced.
The present embodiment employs energy analysis and
Figure BDA0002122830430000201
the analysis method researches the heat transfer performance of the novel heat pipe type vacuum tube light-gathering heat collecting system. Each basic unit of the heat collection system comprises a trough concentrator, a heat pipe type vacuum tube receiver and a steel material support structure. A one-dimensional heat transfer mathematical model is established according to the heat transfer characteristics of the heat collection system, and the calculation result is compared with the literature test result in order to verify the effectiveness of the established model.
Using the calculation results, the present embodiment analyzes the heat efficiency and heat efficiency of the heat collecting system due to the heat transfer fluid inlet temperature, flow rate, direct solar radiation intensity, ambient temperature and wind speed
Figure BDA0002122830430000202
The effect of efficiency. Research results show that the thermal efficiency of the system is obviously influenced by the inlet temperature of the heat transfer fluid and the direct solar radiation intensity, and the influence of the flow velocity of the heat transfer fluid, the ambient temperature and the wind speed is basically negligible. And the system
Figure BDA0002122830430000203
The efficiency is obviously influenced by the inlet temperature of the heat transfer fluid and the ambient temperature, and the influence of the direct solar radiation intensity, the flow speed and the wind speed can be ignored. Wherein the heat transfer fluid inlet temperature is related to the heat efficiency of the heat collection system
Figure BDA0002122830430000204
The trend of the effect of efficiency is the opposite. The inlet temperature of the heat transfer fluid is increased, the thermal efficiency of the system is reduced,
Figure BDA0002122830430000205
The efficiency is increased.
In heat collecting systems, due to irreversible heat transfer processes
Figure BDA0002122830430000206
Loss is system
Figure BDA0002122830430000207
The main cause of the loss. Wherein: between the sun and the collector
Figure BDA0002122830430000208
Loss in total
Figure BDA0002122830430000209
The maximum proportion of losses, about 40.78-58.54%; heat dissipated by the collector system to the environment
Figure BDA00021228304300002010
The loss is a minimum, about 0.49-1.95%.
The working medium in the heat pipe is in a saturated state when the heat collecting system operates, and the pressure is correspondingly increased when the temperature of the working medium is increased. Research results show that the temperature of the working medium is increased along with the increase of the inlet temperature of the heat transfer fluid and the irradiation intensity of the direct solar radiation, and is reduced along with the increase of the flow velocity of the heat transfer fluid. Therefore, the temperature of the working medium in the heat pipe can be calculated by utilizing the model established by the embodiment, so that the reasonable value ranges of the inlet temperature and the flow speed of the heat transfer fluid are determined.

Claims (9)

1. The one-dimensional heat transfer mathematical model of the heat pipe type vacuum tube light-gathering heat-collecting system is characterized by comprising the following steps:
(A-1) judging the heat transfer mechanism of the evaporation section;
(A-2) establishing an energy balance equation;
(A-3) establishing an optical model;
(A-4) establishing an evaporation section heat transfer model;
(A-5) establishing a condensation section heat transfer model;
(A-6) establishment of thermal efficiency and
Figure FDA0002122830420000017
and (4) an efficiency model.
2. The one-dimensional heat transfer mathematical model of heat pipe type vacuum tube concentrating heat collection system according to claim 1, wherein in the step (A-1), the non-dimensional parameter X is introduced for judging the liquid film heat transfer mechanism of the evaporation sectionlf：
Figure FDA0002122830420000011
Bubble size:
Figure FDA0002122830420000012
liquid film local Rex：
Figure FDA0002122830420000013
When X is presentlf≤109When it is laminar film-like evaporation, when 109≤Xlf≤2.7×1010When it is a mixed convection, when Xlf≥2.7×1010Nucleate boiling is performed;
judgment of evaporation section liquid pool heat transfer mechanism introduces dimensionless parameter Xlp：
Figure FDA0002122830420000014
Rayleigh number:
Figure FDA0002122830420000015
mixing coefficient:
Figure FDA0002122830420000016
when X is presentlp≤106Natural convection when 106≤Xlp≤2×107When mixed convection, Xlp≥2×107Nucleate boiling is performed;
the length of the expanded liquid pool can be calculated by the following formula:
Figure FDA0002122830420000021
bubble drift velocity:
Figure FDA0002122830420000022
static length L of working medium stock in liquid poollp-sta-invThe calculation formula (9) is as follows:
Llp,sta,inv＝Llp,sta,inf-Llp,e,con-Llp,ad,con-Llp,c,con (9)；
the static height calculation formula of the liquid film and steam conversion at the evaporation section is as follows:
Figure FDA0002122830420000023
the calculation formula of the static height converted from the liquid film and the steam of the heat insulation section is as follows:
Figure FDA0002122830420000024
the static height calculation formula of the liquid film and steam conversion of the condensation section is as follows:
Figure FDA0002122830420000025
the liquid film thickness of the heat insulation section and the liquid film thickness of the surface of the liquid pool of the evaporation section are calculated by adopting a Nusselt theory, and the calculation formula is as follows:
Figure FDA0002122830420000026
Figure FDA0002122830420000027
3. the one-dimensional heat transfer mathematical model of heat pipe vacuum tube concentrating system according to claim 2, wherein in step (A-2), the system energy balance equation is as follows:
Qabs＝Qs,3e+Qs,5 (15)；
Qs,3e＝Q3e,2e+Q3e,4conv+Q3e,4rad (16)；
Q3e,4conv+Q3e,4rad＝Q4,5cond (17)；
Q4,5cond+Qs,5＝Q5,6conv+Q5,7rad (18)；
Q3e,2e＝Q2e,1＝Q1,2c＝Q2c,3c＝Q3c,f (19)；
Qabsfor effective incident energy of the sun, Qs,3eFor selectively absorbing the heat, Q, absorbed by the coating on the outer wall of the metal tubes,5Solar radiation energy directly absorbed by the glass sleeve; q3e,2eThe heat transferred to the inner wall surface by the outer wall surface of the metal tube in a heat conduction way, Q3e,4radThe heat transferred to the inner wall surface of the glass sleeve by the outer wall surface of the metal tube in a heat radiation mode, Q3e,4convThe heat transferred to the inner wall surface of the glass sleeve by the outer wall surface of the metal tube in a convection heat exchange mode; q4,5condHeat, Q, transferred to the outer wall surface in a heat-conducting manner for the inner wall surface of the glass sleeve5,6convFor the convection heat loss, Q, of the outer wall of the glass sleeve facing the surrounding environment5,7radFor radiation heat loss, Q, of the outer wall of the glass sleeve facing the surrounding environmentloss＝Q5,6conv+Q5,7rad，QlossFor receiver heat loss, Q2e,1For transferring heat to the working medium of the heat pipe from the inner wall surface of the metal pipe at the evaporation section, Q1,2cHeat quantity Q transferred to inner wall surface of metal pipe of condensing section for working medium of heat pipe2c,3cIs gold in the condensation sectionThe inner wall surface of the tube is used for transmitting heat, Q, to the outer wall surface in a heat conduction way3c,fHeat absorbed for the heat transfer fluid;
solar effective incident energy QabsRespectively coated by selective absorption of the outer wall surface of the metal tubes,3eAnd a glass sleeve Qs,5Absorption; the heat absorbed by the selective absorption coating is divided into two parts, one part is transferred to the inner wall surface Q through heat conduction3e,2e(ii) a Another part by heat radiation Q3e,4radAnd convection heat transfer Q3e,4convIs transmitted to the inner wall surface of the glass sleeve; then, this heat is transferred to the outer wall surface Q of the glass sleeve by heat conduction4,5condAnd solar radiation energy Q directly absorbed by the glass sleeves,5That is, the heat dissipated from the glass sleeve to the environment, i.e., the heat loss QlossHeat loss QlossIncluding convective heat dissipation loss Q5,6convAnd radiation heat loss Q5,7rad(ii) a Useful energy is transferred to working medium Q of heat pipe through inner wall surface of metal pipe2e,1The working medium is evaporated and flows to the condensing section, and is transferred to the inner wall surface Q of the condensing section in a film-shaped condensation manner in the condensing section1,2cBy conduction of heat to the outer wall surface Q of the condensation section2c,3cAnd finally absorbed by heat transfer fluid in a convection heat exchange mode Q3c,fI.e. useful energy.
4. The one-dimensional heat transfer mathematical model of heat pipe vacuum tube concentrating system according to claim 1, wherein in step (A-3):
solar energy Q that solar collecting system can utilizesThat is, the energy of the sun on the lighting surface of the condenser is equal to the opening area of the condenser multiplied by the direct solar radiation intensity, and the opening area A of the condensera＝LaWa：
Qs＝IdirLaWa (20)；
Due to the optical losses of the concentrator, the energy reaching the receiver is less than the solar radiation energy received by the concentrator, and the solar radiation energy reaching the receiver is:
Qabs＝Qsηopt (21)；
the optical performance of the condenser is affected by various factors, such as the reflectivity of the condenser, the system structure, the processing conditions, and the testing conditions. The calculation formula of the optical efficiency of the condenser is as follows:
ηopt＝ξ1ξ2ξ3ξ4ξ5ξ6ρclK (22)；
ξ1is a shadow coefficient, ξ2To tracking error, xi3Is a geometric error, xi4Is the condenser fouling factor, ξ5Is the collector fouling factor, xi6Coefficient of unpredictable factor, pclIs the condenser reflectivity;
the solar incident angle correction coefficient K is a function of the solar incident angle θ, and the following calculation formula can be used;
Figure FDA0002122830420000041
5. the heat pipe according to claim 1. The one-dimensional heat transfer mathematical model of the hollow tube light-gathering and heat-collecting system is characterized by comprising the following steps of (A-4):
the solar radiation heat energy absorbed by the selective absorbing coating on the outer wall surface of the metal pipe is as follows:
Qs,3e＝Qabsτcovαcoa (24)；
the solar radiation heat energy absorbed by the glass sleeve is as follows: qs,5＝Qabsαenv (25)；
The heat energy of solar radiation absorbed by the outer wall surface of the metal tube and transferred to the inner wall surface through heat conduction is as follows:
Figure FDA0002122830420000042
heat conductivity lambda of metal tube material23Is the average temperature of the inner and outer walls of the metal pipeT23＝(T2+T3) Thermal conductivity at/2;
the heat transferred to the working medium by the inner wall surface of the metal pipe is as follows:
Q2e,1＝πD2(Le,lfh2e,1,lf+Le,lph2e,1,lp)(T2e-T1) (27)；
judging according to the formula (1), in the range of the direct solar radiation intensity of the embodiment, the liquid film heat transfer of the evaporation section belongs to the nucleate boiling heat transfer, and the heat transfer coefficient calculation formula is as follows;
Figure FDA0002122830420000043
viscosity coefficient:
Figure FDA0002122830420000051
according to equation (4), the liquid pool heat transfer in the evaporation section in the present embodiment is in the range of mixed convection heat transfer and nucleate boiling heat transfer. Wherein, the calculation formula of the mixed convection heat transfer coefficient is as follows:
Figure FDA0002122830420000052
when Bo is less than or equal to 10, n is 0.5; when Bo > 10, n is 1/6;
number of Archimid:
Figure FDA0002122830420000053
froude number:
Figure FDA0002122830420000054
bond number:
Figure FDA0002122830420000055
the heat transfer coefficient of the nucleate boiling liquid pool can be calculated by the following formula:
Figure FDA0002122830420000056
the selective absorption coating on the outer wall surface of the metal tube transfers heat Q to the inner wall surface of the glass sleeve through infrared radiation3e,4radComprises the following steps:
Figure FDA0002122830420000057
the inner wall of the glass sleeve transmits heat to the outer wall surface of the glass sleeve through heat conduction, and the calculation formula is as follows:
Figure FDA0002122830420000058
the convection heat exchange quantity between the outer wall surface of the glass sleeve and the environment is as follows:
Q5,6conv＝πD5Leh56(T5-T6) (37)；
convective heat transfer coefficient h56Related to the ambient wind speed. When no wind exists, the heat exchange between the outer wall surface of the glass sleeve and the ambient air is natural convection heat exchange:
Figure FDA0002122830420000061
rayleigh number Ra5The calculation formula of (2) is as follows:
Figure FDA0002122830420000062
when wind exists, the convection heat exchange between the glass sleeve and the surrounding air belongs to forced convection heat exchange:
Figure FDA0002122830420000063
wherein, Re5When the value is 1000-200000, C is 0.26, and m is 0.6; pr (Pr) of6When the content is less than or equal to 10, n is 0.37.
Radiation heat exchange quantity Q of glass sleeve outer wall facing sky5,7radComprises the following steps:
Figure FDA0002122830420000064
in clear weather, the effective temperature T of sky7The calculation formula of (2) is as follows:
Figure FDA0002122830420000065
6. the one-dimensional heat transfer mathematical model of heat pipe vacuum tube concentrating system according to claim 5, wherein in step (A-5):
the working medium is transferred to the heat Q of the inner wall of the condensation section in a film-shaped condensation mode1,2cComprises the following steps:
Q1,2c＝πD2Lch1,2c(T1-T2c) (43)；
the calculation formula of the film-shaped condensation heat exchange coefficient is as follows:
Figure FDA0002122830420000066
the heat conducted to the outer wall surface by the inner wall surface of the metal pipe of the condensation section through heat conduction is as follows:
Figure FDA0002122830420000067
the outer wall of the metal pipe of the condensing section transfers heat to the heat transfer fluid in the cooling jacket through convection heat transferHeat quantity of Q3c,HTFComprises the following steps:
Q3c,f＝πD3Lch3c,f(T3c-Tf) (46)；
the flow of heat transfer fluid in the cooling jacket is attributed to turbulent flow in the inlet region of the annulus, where the heat transfer coefficient can be determined by the following gnilinski equation (47):
Figure FDA0002122830420000071
7. the one-dimensional heat transfer mathematical model of heat pipe vacuum tube concentrating system according to claim 1, wherein in step (A-6):
the thermal efficiency of a heat collection system is defined as the ratio of the heat absorbed by the heat transfer fluid in the receiver to the total direct solar radiation energy incident on the collector's daylighting area, i.e.:
Figure FDA0002122830420000072
Figure FDA0002122830420000073
heat collecting system
Figure FDA0002122830420000078
Efficiency is defined as heat transfer fluid heat in the receiver
Figure FDA0002122830420000079
Summation of incremental and solar input heat collection systems
Figure FDA00021228304200000710
The calculation formula is as follows:
Figure FDA0002122830420000074
total input of sun
Figure FDA00021228304200000711
Can be calculated by Petela model, in which the surface temperature Ts of the sun is set to 5770K and the total input of the sun is
Figure FDA00021228304200000712
Comprises the following steps:
Figure FDA0002122830420000075
heat of heat transfer fluid in receiver
Figure FDA00021228304200000713
The incremental calculation formula is:
Figure FDA0002122830420000076
in the formula, delta p is the pressure difference of the inlet and the outlet of the heat transfer fluid;
optical system
Figure FDA00021228304200000714
The formula for the loss is:
Eloss,opt＝(1-ηopt)Es (53)；
heat generation
Figure FDA00021228304200000715
The formula for the loss is:
Figure FDA0002122830420000077
general description of the invention
Figure FDA00021228304200000716
The loss is:
Eloss＝Eloss,opt+Eloss,th (55)；
between the sun and the receiver
Figure FDA0002122830420000083
The loss calculation formula is:
Figure FDA0002122830420000081
between receptacle and fluid
Figure FDA0002122830420000084
The loss calculation formula is:
Figure FDA0002122830420000082
general description of the invention
Figure FDA0002122830420000085
The loss is:
Ed＝Ed,s-r+Ed,r-f (58)。
8. the application of the one-dimensional heat transfer mathematical model of the heat pipe type vacuum tube light-gathering heat collection system is characterized in that the one-dimensional heat transfer mathematical model of the heat pipe type vacuum tube light-gathering heat collection system in any one of claims 1 to 7 is used for analyzing the heat efficiency and wind speed of the heat transfer fluid on the heat collection system by using the factors such as the inlet temperature, the speed, the direct solar radiation intensity, the ambient temperature and the wind speed of the heat transfer fluid
Figure FDA0002122830420000086
The effect of efficiency.
9. The application of the heat pipe type vacuum tube light-gathering heat collection system one-dimensional heat transfer mathematical model is characterized in that the temperature of a working medium in a heat pipe is predicted by using the heat pipe type vacuum tube light-gathering heat collection system one-dimensional heat transfer mathematical model according to any one of claims 1 to 7, and the reasonable value range of the inlet temperature and the flow speed of a heat transfer fluid during the operation of the system is determined.
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