CN109631439B - Air source heat pump effective frost inhibition method based on temperature and humidity two-dimensional relation - Google Patents

Air source heat pump effective frost inhibition method based on temperature and humidity two-dimensional relation Download PDF

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CN109631439B
CN109631439B CN201811603263.6A CN201811603263A CN109631439B CN 109631439 B CN109631439 B CN 109631439B CN 201811603263 A CN201811603263 A CN 201811603263A CN 109631439 B CN109631439 B CN 109631439B
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temperature
moisture content
air
humidity
relative humidity
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CN109631439A (en
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王智伟
魏鹏
赵健
孙婷婷
刘艳峰
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Xian University of Architecture and Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B47/00—Arrangements for preventing or removing deposits or corrosion, not provided for in another subclass
    • F25B47/006—Arrangements for preventing or removing deposits or corrosion, not provided for in another subclass for preventing frost
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B49/00—Arrangement or mounting of control or safety devices
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F25—REFRIGERATION OR COOLING; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS; MANUFACTURE OR STORAGE OF ICE; LIQUEFACTION SOLIDIFICATION OF GASES
    • F25B—REFRIGERATION MACHINES, PLANTS OR SYSTEMS; COMBINED HEATING AND REFRIGERATION SYSTEMS; HEAT PUMP SYSTEMS
    • F25B2700/00—Sensing or detecting of parameters; Sensors therefor
    • F25B2700/02—Humidity

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Abstract

The invention discloses an effective frost inhibition method of an air source heat pump based on a temperature and humidity two-dimensional relation, which analyzes the driving force of mass transfer: moisture content difference, the determination of which is solely related to the outdoor air temperature, the relative humidity and the evaporation temperature. On the basis, the aim of frost inhibition is to provide a coupling function of the evaporation temperature of the unit and the outdoor air temperature and relative humidity. And solving to obtain a two-dimensional relational expression of the evaporation temperature, the air dry bulb temperature and the relative humidity according to the constructed objective function, the constraint condition and the boundary condition. When the air temperature and the relative humidity are known, the evaporation temperature value required to be set during the operation of the unit is calculated according to the obtained coupling relation between the evaporation temperature and the air temperature and humidity, and the evaporation temperature of the unit is adjusted, so that the effective frost inhibition is realized.

Description

Air source heat pump effective frost inhibition method based on temperature and humidity two-dimensional relation
Technical Field
The invention belongs to the technical field of effective frost inhibition of air source heat pumps, and particularly relates to an effective frost inhibition method based on a temperature and humidity two-dimensional relation.
Background
The air source heat pump has the advantages of flexible installation, low operation cost, energy conservation, environmental protection and the like, and is more and more widely applied and wide in prospect. However, the air source heat pump has a well-known disadvantage that the surface of the outdoor coil fin is easily frosted during heating in winter, and the heating capacity is reduced.
The frost formation on the surface of the evaporator fin is most directly related to the temperature of air, relative humidity and surface temperature of the fin, and the current research on frost inhibition mainly focuses on the factors. The frost inhibition method mainly comprises the following steps: systematic studies to reduce the moisture content of mainstream air; the research of external uniform electric field and magnetic field interference frost formation; research on the reduction of the water drop attachment rate by surface modification. These methods all have different disadvantages in the practical application process: 1) as time increases, the moisture absorption capacity of the desiccant is continuously weakened, and the frost inhibition effect is gradually lost; 2) the design and operation processes of the system are complicated, so that the system of the whole unit is too complex and cannot be widely applied in the actual operation process of the unit; 3) in general outdoor environment, the surface modified paint can keep no frosting for a long time, but the effect is not obvious when the condition is severe, and in addition, the surface after modification is soft and does not resist impact under the severe environment.
Therefore, a defrosting mode which is more universal and has stronger feasibility in the actual operation process of the unit needs to be found, and the research of defrosting from the setting mechanism of the evaporation temperature of the unit is a feasible method. The evaporation temperature of the existing air source heat pump unit is set only by depending on the single-value relation between the evaporation temperature and the air dry bulb temperature, and under the relation, the evaporation temperature of the unit does not change along with the change of the relative humidity of outdoor atmosphere. Under the same temperature, when the relative humidity of outdoor atmosphere rises, the moisture content of the atmosphere also rises, but the evaporation temperature of the unit is not changed, the corresponding saturated vapor pressure and the moisture content do not change, and the difference between the saturated vapor pressure and the moisture content is caused to increase along with the rise of the relative humidity of the air, so that the frosting phenomenon is also serious. Therefore, such univalent relationship setting is disadvantageous from the viewpoint of frost suppression. Aiming at the defects of the setting mechanism, starting from the driving force of mass transfer, namely the moisture content difference, a coupling function of the evaporation temperature of the unit and the outdoor atmospheric temperature and relative humidity is constructed, and the frost inhibition is of great significance on the basis.
Disclosure of Invention
In order to solve the defects in the prior art, the invention aims to provide an air source heat pump frost suppression method based on a temperature and humidity two-dimensional relation, and the method can be used for solving the problem of the existing frost suppression technology of an air source heat pump unit. The method makes up the defect of a setting mechanism of the univalent relationship of the evaporation temperature of the existing unit, and changes the evaporation temperature of the unit along with the change of the air temperature and the relative humidity by considering two factors of the air dry bulb temperature and the relative humidity during the setting of the evaporation temperature, thereby changing the moisture content difference. The mass transfer driving force, namely the moisture content difference, is reduced along with the increase of the temperature and the relative humidity, and the aim of inhibiting frost is fulfilled.
The invention is realized by the following technical scheme.
An effective frost inhibition method of an air source heat pump based on a temperature and humidity two-dimensional relation comprises the following steps:
step 1: according to the frosting mechanism, the difference of moisture content of frosting is analyzed to obtain the difference of moisture content and the temperature t of the air dry bulbaRelative humidity of
Figure BDA0001923026530000021
And evaporation temperature teThe relationship of (1);
step 2: targeting frost suppression, establishing an evaporation temperature teAnd air dry bulb temperature taRelative humidity of
Figure BDA0001923026530000022
Coupling a target function of the relation and setting constraint conditions;
and step 3: providing a frosting starting point and boundary conditions for solving an objective function when the relative humidity is 100%;
and 4, step 4: solving to obtain a two-dimensional relational expression of the evaporation temperature, the air dry bulb temperature and the relative humidity according to the objective function, the constraint condition and the boundary condition;
and 5: and calculating an evaporation temperature value required to be set during the operation of the unit at the moment according to the obtained coupling relation between the evaporation temperature and the air temperature and humidity and the known air temperature and relative humidity according to the relation, and adjusting the evaporation temperature of the unit to realize frost inhibition.
Further, in the step 1, the moisture content difference and the air dry bulb temperature t are obtainedaRelative humidity of air
Figure BDA0001923026530000031
And evaporation temperature teThe steps are as follows:
1a) the moisture content difference is the difference between the moisture content of the wet air and the moisture content of the surface of the frost layer, and the moisture content in the wet air is as follows:
Figure BDA0001923026530000032
in the formula, PsaIs the saturated vapor pressure in the air, Pa; b is atmospheric pressure, Pa;
for the frost surface, it is assumed that the air of the frost surface is saturated air, and thus the moisture content of the frost surface is:
Figure BDA0001923026530000033
thus, the magnitude of the moisture content difference is:
Figure BDA0001923026530000034
1b) the relationship between the saturated vapor pressure and the temperature is:
Ps＝exp(6.42+7.2×10-2Ta-2.71×10-4Ta 2+7.23×10-7Ta 3)，
that is, the saturated vapor pressure of the vapor is only related to the vapor temperature, and the influence factor of the moisture content difference is mainly the air dry bulb temperature taRelative humidity of air
Figure BDA0001923026530000035
And evaporation temperature te。
Further, in the step 2, the specific steps are as follows:
2a) targeting frost suppression, establishing an evaporation temperature teAnd air dry bulb temperature taRelative humidity of air
Figure BDA0001923026530000036
Objective function of coupling relation:
Figure BDA0001923026530000041
2b) setting a constraint condition one: v is measured byexRepresenting a new frosting rate,. DELTA.dexRepresenting a new moisture content difference, the mathematical expression for the frost formation rate change curve is:
Figure BDA0001923026530000042
and
Figure BDA0001923026530000043
the mathematical expression of the variation trend of the moisture content difference is as follows:
Figure BDA0001923026530000044
2c) setting a second constraint condition: in order to suppress the increase of the moisture content difference under the same relative humidity, the moisture content of the surface of the fin should also have the following increasing trend:
Figure BDA0001923026530000045
in the formula (d)exThe moisture content of saturated air on the surface of the fin is g/kg. dry;
2d) setting a constraint condition three: the principle that the frost inhibition proportion is larger in areas with more severe frosting is adopted, so that the attenuation of the moisture content difference of the unit is more severe under the weather condition with more severe frosting, and the mathematical expression is as follows:
Figure BDA0001923026530000046
in the formula: Δ d is the moisture content difference in a univocal relationship, g/kg. dry.
Further, in the step 3, the specific steps are as follows:
3a) at a relative humidity
Figure BDA0001923026530000047
55% as the starting point for the calculation, let:
Figure BDA0001923026530000048
Figure BDA0001923026530000049
in the formula: Δ dexG/kg. dry for new moisture content difference in coupling relation; delta d is the moisture content difference in a univalent relationship, g/kg. is dry;
3b) calculating a boundary condition when
Figure BDA0001923026530000051
In time, order:
Figure BDA0001923026530000052
wherein K is the minimum allowable heat exchange temperature difference and is DEG C.
Further, in the step 4, the relationship between the moisture content difference and the air dry bulb temperature and the relative humidity is as follows:
Figure BDA0001923026530000053
in the formula,. DELTA.dexG/kg. dry for new moisture content difference in coupling relation; A. b, C is a constant.
Further, in the step 4, the obtained relation is integrated to obtain a coupling relation between the humidity content difference and the air temperature and humidity:
Figure BDA0001923026530000054
wherein, deltad is the moisture content difference, g/kg. is dry; A. b, C, D, E is a constant.
Further, in the step 4, when the corresponding relationship between the variables is calculated, the step size is calculated from-16 ℃ to 6 ℃ with 0.5 ℃ as the temperature, and the step size is calculated from 55% to 100% with 5% as the humidity.
Further, in the step 4, fitting is performed on data of the calculation result to obtain an evaporation temperature expression of the coupled air temperature and humidity, and the specific form of the function is as follows:
Figure BDA0001923026530000055
in the formula: a. b, c and d are constants.
Due to the adoption of the technical scheme, the invention has the following beneficial effects:
1) compared with the existing setting of the evaporation temperature, the method adds the parameter of the relative humidity of the air in the setting of the evaporation temperature of the air source heat pump unit, and sets the evaporation temperature through the two-dimensional coupling relation of the air temperature, the relative humidity and the evaporation temperature. Under the same air temperature, the higher the relative humidity is, the higher the evaporation temperature set value is, the heat exchange temperature difference is reduced, and the frost inhibition purpose is realized.
2) The invention provides a two-dimensional relational expression of coupling of the evaporation temperature, the air temperature and the relative humidity, and when the unit operates, the reasonable evaporation temperature value can be simply, conveniently and quickly calculated according to the environment of the unit, so that the unit is adjusted, and the operation of dynamic frost inhibition is realized.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention:
FIG. 1 is a technical route diagram of a frost suppression method based on a temperature and humidity two-dimensional relationship according to the present invention;
FIG. 2 is a graph of the change in the desired frosting rate;
FIG. 3 is a graph of expected moisture content difference variation;
FIG. 4 is a starting point
Figure BDA0001923026530000061
Setting a schematic diagram of the time boundary condition;
FIG. 5 is a drawing showing
Figure BDA0001923026530000062
Setting a schematic diagram of the time boundary condition;
FIGS. 6(a) - (d) are comparative analyses of moisture content differences before and after a change in heat exchange temperature difference;
wherein: FIG. 6(a) is a comparison of moisture content difference at an air temperature of-16 ℃; FIG. 6(b) is a comparison of moisture content difference at an air temperature of-13 ℃; FIG. 6(c) is a comparison of moisture content difference at an air temperature of-10 ℃; FIG. 6(d) is a comparison of moisture content difference at an air temperature of-7 ℃;
FIGS. 7(a) - (d) comparative analysis of frosting rate before and after heat exchange temperature differential change.
Wherein: FIG. 7(a) is a comparison of the frosting rate at an air temperature of-16 ℃; FIG. 7(b) is a comparison of the frosting rate at an air temperature of-13 deg.C; FIG. 7(c) is a comparison of the frosting rate at an air temperature of-10 ℃; FIG. 7(d) is a comparison of the frosting rate at an air temperature of-7 ℃.
Detailed Description
The present invention will now be described in detail with reference to the drawings and specific embodiments, wherein the exemplary embodiments and descriptions of the present invention are provided to explain the present invention without limiting the invention thereto.
As shown in fig. 1, the effective frost inhibiting method of the air source heat pump based on the temperature and humidity two-dimensional relationship comprises the following steps:
step 1: according to the frosting mechanism, the difference of moisture content of frosting is analyzed to obtain the difference of moisture content and the temperature t of the air dry bulbaRelative humidity of
Figure BDA0001923026530000071
And evaporation temperature teThe relationship of (1);
(1) the moisture content difference is the difference between the moisture content of the wet air and the moisture content of the surface of the frost layer, and the moisture content in the wet air is as follows:
Figure BDA0001923026530000072
in the formula, PsaIs the saturated vapor pressure in the air, Pa; b is atmospheric pressure, Pa;
for the frost surface, it is assumed that the air of the frost surface is saturated air, and thus the moisture content of the frost surface is:
Figure BDA0001923026530000073
thus, the magnitude of the moisture content difference is:
Figure BDA0001923026530000074
(2) as can be seen from the moisture content difference formula, the moisture content difference is only related to the relative humidity of air, the saturated vapor pressure of wet air and the saturated vapor pressure of the frost surface at a certain atmospheric pressure. The relationship between the saturated vapor pressure and the temperature is:
Ps＝exp(6.42+7.2×10-2×Ta-2.71×10-4×Ta 2+7.23×10-7×Ta 3) That is, the saturated vapor pressure of the vapor is only related to the vapor temperature, and the influence factor of the moisture content difference is mainly analyzed to be the temperature t of the air dry bulbaRelative humidity of air
Figure BDA0001923026530000075
And evaporation temperature te。
(3) The moisture content difference is positively correlated with the air temperature and the relative humidity, and negatively correlated with the evaporation temperature.
Step 2: aiming at frost inhibition, the evaporation temperature and the air dry bulb temperature t are establishedaRelative humidity of air
Figure BDA0001923026530000076
Coupling the objective function of the relation and setting the constraint condition.
(1) Aiming at frost inhibition, the evaporation temperature and the air dry bulb temperature t are establishedaRelative humidity of air
Figure BDA0001923026530000087
An objective function of the coupling relation, the objective function to be solved being:
Figure BDA0001923026530000081
(2) setting a constraint condition one: when solving the new correlation, the expected frosting rate change curve is given, see fig. 2. V is measured byexRepresenting a new frosting rate,. DELTA.dexRepresenting a new moisture content differential. Change of frosting rate in figure 2The curve can be in mathematical form
Figure BDA0001923026530000082
And
Figure BDA0001923026530000083
to describe. The variation trend of moisture content difference is the same as the frosting rate, see figure 3.
The mathematical expression of the variation trend of the moisture content difference is as follows:
Figure BDA0001923026530000084
(3) setting a second constraint condition: under the same relative humidity, the moisture content of the humid air increases with the increase of the air temperature, so in order to restrain the increase of the moisture content difference, the moisture content of the surface of the fin should also have the following increasing trend:
Figure BDA0001923026530000085
in the formula (d)exIs the moisture content of saturated air on the surface of the fin, is univalent to the surface temperature of the fin, and is g/kg. dry.
(4) Setting a constraint condition three: in frosted areas, the higher the temperature and relative humidity, the more severe the frosting. The frost inhibiting method adopts the principle that the frost inhibiting proportion of areas with more severe frosting is larger, even if the attenuation of the moisture content difference of the unit is more severe under the climatic condition with more severe frosting, the mathematical expression form is
Figure BDA0001923026530000086
In the formula: Δ d is the moisture content difference in a univocal relationship, g/kg. dry.
And step 3: the frost onset and boundary conditions for the objective function solution at 100% relative humidity are given.
(1) When the equal dew point line is determined, the corresponding relative humidity is different under different air dry bulb temperatures, and strictly speaking, the frosting critical humidity is different under different dry bulb temperatures. To simplify the calculation, the method uses the relative humidity of 55% as the starting point of the calculation. The setting of the starting point calculation conditions is shown in FIG. 4 when
Figure BDA0001923026530000098
In time, order:
Figure BDA0001923026530000091
Figure BDA0001923026530000092
in the formula: Δ dexG/kg. dry for new moisture content difference in coupling relation; delta d is the moisture content difference in a univalent relationship, g/kg. is dry; t is taAir dry bulb temperature, deg.C;
Figure BDA0001923026530000093
air relative humidity,%.
(2) The heat exchange temperature difference can be reduced to 2-4 ℃ generally, and the heat exchange temperature difference is within the range of
Figure BDA0001923026530000094
The minimum achievable is 4 ℃. The setting of the calculation boundary conditions is shown in FIG. 5 when
Figure BDA0001923026530000095
In time, order:
Figure BDA0001923026530000096
and 4, step 4: and solving to obtain a two-dimensional relational expression of the evaporation temperature, the air dry-bulb temperature and the relative humidity.
(1) Under the condition of satisfying the constraint conditions, the following assumptions are made for the function form of the moisture content difference change rate as a general solution of the solving equation, and the mathematical expression is as follows:
Figure BDA0001923026530000097
in the formula,. DELTA.dexG/kg. dry for new moisture content difference in coupling relation; A. b, C is a constant.
The above formula combines with the boundary conditions to obtain various constant values in the general solution:
A＝58.9；B＝0.164；C＝5。
(2) and integrating the obtained general solution to obtain a coupling relation between the moisture content difference and the air temperature and the air humidity:
Figure BDA0001923026530000101
(3) the method can not directly calculate the functional relation between the evaporation temperature and the relative humidity, and obtains the one-to-one corresponding relation between the evaporation temperature and the air temperature and the relative humidity by the calculation formula of the moisture content difference delta d and the coupling relation formula of the moisture content difference and the air temperature and the relative humidity, thereby obtaining a specific functional expression by fitting.
(4) When calculating the corresponding relationship between the variables, the calculation step size was calculated from-16 ℃ to 6 ℃ with 0.5 ℃ as the temperature, and from 55% to 100% with 5% as the humidity, and the data of 460 state points were calculated, and the partial results of the calculation are shown in table 1.
TABLE 1 Evaporation temperature values (unit:. degree. C.) for different temperatures and humidities
Figure BDA0001923026530000102
(5) Fitting the data of the calculation result to obtain an evaporation temperature expression of the coupled air temperature and humidity, wherein the specific form of the function is as follows:
Figure BDA0001923026530000103
the correlation coefficient is R2＝0.9986。
And 5: and calculating an evaporation temperature value required to be set during the operation of the unit at the moment according to the obtained coupling relation between the evaporation temperature and the air temperature and humidity and the known air temperature and relative humidity according to the relation, and adjusting the evaporation temperature of the unit to realize frost inhibition.
Taking Hongyuan county in Sichuan Tibet district as an example, the unit sets the evaporation temperature value of the unit operation according to the evaporation temperature relational expression of coupled air temperature and humidity. And comparing the change conditions of the evaporation temperature value, the moisture content difference and the frosting rate before and after coupling.
(1) Change of evaporation temperature
The total heating season of Hongyuan county is 5448 hours, and the gradual evaporation temperature before the coupling of the relative humidity is
tei＝0.83×tai-10.26
In the formula: t is taiThe hourly air temperature in the Hongyuan county in the heating season is 5448 hours, and the temperature is DEG C; t is teiThe unit evaporation temperature, deg.C, corresponding to the dry bulb temperature; when i is 1, the first hour at the beginning of the heating season is represented, and so on;
the hourly evaporation temperature after coupling was:
Figure BDA0001923026530000111
the average rate of change of the evaporation temperature after coupling is calculated by the following formula:
Figure BDA0001923026530000112
the evaporation temperature of Hongyuan county in 5448 hours is calculated respectively, and comparison of the evaporation temperature before and after coupling shows that after the evaporation temperature is coupled with the relative humidity of air, the evaporation temperature of the unit in the whole heating season averagely rises by 21.5%.
(2) Moisture content difference variation
After the heat exchange temperature difference is correlated with the relative humidity, the most direct and obvious effect is that the influence on the moisture content difference is achieved, in order to more obviously analyze the change condition of the moisture content difference at different temperatures, partial working conditions are selected to analyze and compare the moisture content difference before and after the change, as shown in the attached figures 6(a) - (d), all working condition points in Hongyuan county are calculated, and after the evaporation temperature is coupled with the relative humidity of air, the average moisture content difference is reduced by 27.3%.
(3) Change in frosting rate
The final purpose of performing the heat exchange temperature difference correlation is to reduce the frosting rate, and further reduce the overall frosting frequency of the unit so as to improve the overall performance of the unit in winter. Therefore, the value of the decrease in the frosting rate is the most direct indicator for evaluating the applicability of the method. The frosting rate under part of working conditions is selected for calculation, and comparative analysis before and after the frosting rate changes under different working conditions is shown in attached figures 7(a) - (d).
As can be seen from fig. 7(a) - (d), the increase trend of the frosting rate becomes more gradual with the increase of the relative humidity under different dry bulb temperatures after the evaporation temperature of the unit is correlated with the relative humidity of the air. The rate of increase of the frosting rate also becomes progressively smaller with increasing relative humidity. When the relative humidity is 100%, the rate of increase in the frosting rate is almost 0. And calculating the frosting rate before and after the coupling of the 5448 working condition point evaporation temperature and the air relative humidity in the heating season of Hongyuan county, wherein the frosting rate after the coupling is averagely reduced by 32.4 percent before the relative coupling.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.

Claims (5)

1. An effective frost inhibition method of an air source heat pump based on a temperature and humidity two-dimensional relation is characterized by comprising the following steps:
step 1: according to the frosting mechanism, the difference of moisture content of frosting is analyzed to obtain the difference of moisture content and the temperature t of the air dry bulbaRelative humidity of
Figure FDA0002557668430000011
And evaporation temperature teThe relationship of (1);
step 2: targeting frost suppression, establishing an evaporation temperature teAnd air dry bulb temperature taRelative humidity of
Figure FDA0002557668430000012
Coupling a target function of the relation and setting constraint conditions;
in the step 2, the concrete steps are as follows:
2a) targeting frost suppression, establishing an evaporation temperature teAnd air dry bulb temperature taRelative humidity of air
Figure FDA0002557668430000013
Objective function of coupling relation:
Figure FDA0002557668430000014
2b) setting a constraint condition one: v is measured byexRepresenting a new frosting rate,. DELTA.dexRepresenting a new moisture content difference, the mathematical expression for the frost formation rate change curve is:
Figure FDA0002557668430000015
and
Figure FDA0002557668430000016
the mathematical expression of the variation trend of the moisture content difference is as follows:
Figure FDA0002557668430000017
2c) setting a second constraint condition: in order to suppress the increase of the moisture content difference under the same relative humidity, the moisture content of the surface of the fin should also have the following increasing trend:
Figure FDA0002557668430000018
in the formula (d)exThe moisture content of saturated air on the surface of the fin is g/kg dry;
2d) setting a constraint condition three: the principle that the frost inhibition proportion is larger in areas with more severe frosting is adopted, so that the attenuation of the moisture content difference of the unit is more severe under the weather condition with more severe frosting, and the mathematical expression is as follows:
Figure FDA0002557668430000021
in the formula: delta d is the moisture content difference in a univalent relationship, g/kg dry;
and step 3: providing a frosting starting point and boundary conditions for solving an objective function when the relative humidity is 100%;
in the step 3, the specific steps are as follows:
3a) at a relative humidity
Figure FDA0002557668430000022
55% as the starting point for the calculation, let:
Figure FDA0002557668430000023
Figure FDA0002557668430000024
in the formula: Δ dexThe new moisture content difference is g/kg dry under the coupling relation; delta d is the moisture content difference in a univalent relationship, g/kg dry;
3b) calculating a boundary condition when
Figure FDA0002557668430000025
In time, order:
Figure FDA0002557668430000026
in the formula, K is the minimum allowable heat exchange temperature difference of DEG C;
and 4, step 4: solving to obtain a two-dimensional relational expression of the evaporation temperature, the air dry bulb temperature and the relative humidity according to the objective function, the constraint condition and the boundary condition;
in the step 4, fitting is performed on the data of the calculation result to obtain an evaporation temperature expression of the coupled air temperature and humidity, wherein the specific form of the function is as follows:
Figure FDA0002557668430000027
in the formula: a. b, c and d are constants;
and 5: and calculating an evaporation temperature value required to be set during the operation of the unit at the moment according to the obtained two-dimensional relational expression of the evaporation temperature and the air temperature and humidity and the relational expression when the air temperature and the relative humidity are known, and adjusting the evaporation temperature of the unit to realize frost inhibition.
2. The effective frost inhibiting method of the air source heat pump based on the temperature and humidity two-dimensional relation according to claim 1, wherein in the step 1, the moisture content difference and the air dry bulb temperature t are obtainedaRelative humidity of air
Figure FDA0002557668430000031
And evaporation temperature teThe steps are as follows:
1a) the moisture content difference is the difference between the moisture content of the wet air and the moisture content of the surface of the frost layer, and the moisture content in the wet air is as follows:
Figure FDA0002557668430000032
in the formula, PsaIs the saturated vapor pressure in the air, Pa; b is atmospheric pressure, Pa;
for the frost surface, it is assumed that the air of the frost surface is saturated air, and thus the moisture content of the frost surface is:
Figure FDA0002557668430000033
thus, the magnitude of the moisture content difference is:
Figure FDA0002557668430000034
1b) the relationship between the saturated vapor pressure and the temperature is:
Ps＝exp(6.42+7.2×10-2Ta-2.71×10-4Ta 2+7.23×10-7Ta 3)，
that is, the saturated vapor pressure of the vapor is only related to the vapor temperature, and the influence factor of the moisture content difference is mainly the air dry bulb temperature taRelative humidity of air
Figure FDA0002557668430000035
And evaporation temperature te。
3. The effective frost inhibiting method of the air source heat pump based on the temperature and humidity two-dimensional relationship according to claim 1, wherein in the step 4, the relationship between the moisture content difference and the air dry bulb temperature and the relative humidity is as follows:
Figure FDA0002557668430000041
in the formula,. DELTA.dexThe new moisture content difference is g/kg dry under the coupling relation; A. b, C is a constant.
4. The effective frost inhibiting method of the air source heat pump based on the temperature and humidity two-dimensional relationship according to claim 1, wherein in the step 4, the coupling relation between the humidity content difference and the air temperature and humidity is obtained by integrating the obtained relation:
Figure FDA0002557668430000042
wherein, deltad is the moisture content difference, g/kg dry; A. b, C, D, E is a constant.
5. The effective frost suppressing method of an air source heat pump based on a temperature-humidity two-dimensional relationship according to claim 1, wherein in the step 4, when the corresponding relationship between the variables is calculated, the step length is calculated from-16 ℃ to 6 ℃ with 0.5 ℃ as the temperature, and the step length is calculated from 55% to 100% with 5% as the humidity.
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