CN116702572A - Method and device for determining heat exchange area in heat and humidity exchange process and method for improving heat exchange efficiency - Google Patents
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Abstract
A method and a device for determining heat exchange area and a method for improving heat exchange efficiency in a heat-moisture exchange process relate to the technical field of ventilation and spray wet dust removal. The method comprises the following steps: constructing a fractal model of the particle size distribution of the spray liquid drop group; taking the spray liquid drop group as an object, and determining the scale relation between the accumulated number of the spray liquid drop group and the liquid drop size; integrating all single droplet areas in an atomization field, and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship; calculating to obtain the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension; and obtaining the sum of the surface areas of all the liquid drops with different sizes in the atomization field, namely the heat exchange area between the air and the liquid drop group in the heat-moisture exchange process. The application can more accurately determine the heat exchange area between the air and the liquid drop group in the heat and humidity exchange process.
Description
Technical Field
The application relates to the technical field of ventilation and spray wet dust removal, in particular to a method and a device for determining heat exchange area and a method for improving heat exchange efficiency in a heat-moisture exchange process.
Background
At present, the spraying is widely applied to the field of exhaust waste heat recovery and wet dust removal. The solid liquid sprayed out by the nozzle is subjected to the action of disturbance waves, cannot bear deformation to be crushed and atomized, a spray liquid drop group is formed, the liquid drop group takes away heat and dust in the process of being mutually coupled with exhaust air flow, and the liquid drop after absorbing the heat falls and flows back into the heat pump unit to extract heat, so that hot water in a mining area and a shaft are supplied for freezing prevention, and the purpose of recovering waste heat is achieved.
In the process of carrying out direct contact type heat exchange with air by taking an atomized liquid drop group as a heat exchange carrier, when the air state and the water spray amount are fixed, the particle size distribution of the liquid drop group in a limited space directly influences the air-water contact area, further influences the heat exchange efficiency, and the larger the contact area of two media is, the larger the total heat exchange amount is, and the heat exchange area is the sum of the surface areas of all liquid drops with different sizes in an atomization field. Because the heat and humidity exchange condition between air and the liquid drop group is very complex, the average diameter is adopted to estimate the surface area of the liquid drop group at present, irregular liquid drops with different sizes are simplified into the liquid drop group with uniform size, and then the liquid drop group is converted according to the volume ratio. The method assumes that all liquid drops in an atomization field are particle groups with the same particle size, ignores randomness and disorder of the particle size distribution of the liquid drop groups, and cannot accurately reflect the actual situation of the liquid drop group distribution.
Disclosure of Invention
The application aims to solve the technical problem of providing a method for determining the heat exchange area in the heat-moisture exchange process based on the fractal dimension, which can more accurately determine the heat exchange area between air and a liquid drop group.
In order to achieve the above purpose, the present application adopts the following technical scheme: the method for determining the heat exchange area in the heat and humidity exchange process comprises the following steps:
(1) Constructing a fractal model of the particle size distribution of the spray droplet group according to a fractal theory;
(2) Taking the spray liquid drop group as an object, and determining the scale relation between the accumulated number of the spray liquid drop group and the liquid drop size;
(3) Integrating all single droplet areas in the atomization field, and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship:
wherein A is d A surface area for a population of droplets; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless;D min m is the minimum droplet size in the atomizing field;
(4) Calculating to obtain the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension;
(5) And obtaining the sum of the surface areas of all the liquid drops with different sizes in the atomization field, namely the heat exchange area between the air and the liquid drop group in the heat-moisture exchange process.
Preferably, in the step (1), in the constructed fractal model of the particle size distribution of the spray droplet group, the fractal scale relationship of the particle size distribution of the spray droplet group is:
wherein D is the droplet size, m; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless.
Preferably, in the step (1), in the constructed fractal model of the particle size distribution of the spray droplet group, the droplet group consisting of droplets ejected from the nozzles has a self-similar hierarchical structure in the particle size distribution; the liquid drops are spherical liquid drops with irregular shapes and equivalent diameters D, and are not overlapped with each other; the droplet size distribution of the droplet group in the unrestricted space is random and disordered.
Preferably, in the step (2), the cumulative number of spray droplet groups is the ratio Y n (D) The scale relationship with droplet size D is as follows:
wherein Y is n (D) The ratio of the number of the liquid drops with the diameter smaller than D to the total number of the liquid drops in the atomization field is dimensionless; n is the total number of the spray liquid drops; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless; d is the droplet size, m.
Preferably, in the step (3), the method for determining the droplet population surface area calculation formula based on the fractal dimension is as follows:
the surface area of all droplets in the droplet group is obtained by summing the integral from the smallest droplet to the largest droplet, then the droplet group surface area A d The method comprises the following steps:
the number dN of droplets having diameters between D and (D+dD) is:
dN＝NdY n (D) (5)
combined formula (3), formula (4) and formula (5), yields:
solving equations, settingThe method comprises the following steps:
the formula (8) is a liquid drop group surface area calculation formula based on fractal dimension;
wherein D is max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless; d is the droplet size, m; d (D) min M is the minimum droplet size in the atomizing field.
Preferably, in step (4), the fractal dimension of the droplet population particle size distribution is in the range of 1 to 3, and the droplet population surface area increases as the fractal dimension of the droplet population particle size distribution increases.
Preferably, the droplet population particle size distribution fractal dimension ranges from 2.3 to 3.
Preferably, in the step (4), the larger the fractal dimension of the particle size distribution of the droplet group is, the larger the ratio of fine droplets in the droplet group is, and the more uniform the particle size distribution of the droplet group is.
Another object of the present application is to provide a device for determining a heat exchange area in a heat-moisture exchange process, which includes:
the model construction unit is used for constructing a fractal model of the particle size distribution of the spray droplet group according to a fractal theory;
a scale relation determining unit for determining a scale relation between the accumulated number of spray droplet groups and the droplet size, with the spray droplet groups as targets;
the formula determining unit is used for integrating all single droplet areas in the atomization field and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship;
the surface area determining unit is used for calculating the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension;
and the heat exchange area determining unit is used for calculating the sum of the surface areas of all the liquid drops with different sizes in the atomization field so as to determine the heat exchange area between the air and the liquid drop group in the heat and humidity exchange process.
Another object of the present application is to provide a method for improving heat exchange efficiency in a heat and humidity exchange process, comprising: the heat exchange area of the air and the liquid drop group is determined by adopting the method for determining the heat exchange area in the heat-moisture exchange process, and then the fractal dimension of the liquid drop group is increased, so that the heat exchange area is increased, the heat exchange area is in direct proportion to the heat exchange quantity, and then the heat exchange quantity is increased, so that the heat exchange efficiency is improved.
The application emphasizes the difference of the single droplet size in the droplet group, can more accurately approximate the actual situation of droplet group distribution, can accurately quantify the influence of different particle size distribution on the actual surface area of the droplet group, and more accurately determine the heat exchange area between air and the droplet group in the heat-moisture exchange process.
Drawings
FIG. 1 is a schematic diagram of a fractal model of spray droplet population particle size distribution;
FIG. 2 is a schematic diagram of a change rule of the surface area of a droplet group based on fractal dimension;
FIG. 3 is a schematic representation of a comparison analysis of the results of a droplet population surface area calculation.
Detailed Description
In order to facilitate a better understanding of the improvements of the present application with respect to the prior art, a further description of the application is provided below in connection with the accompanying drawings and examples.
The embodiment provides a method for determining a heat exchange area in a heat and humidity exchange process based on fractal dimension, which comprises the following steps:
(1) Constructing a fractal model of the particle size distribution of the spray droplet group according to a fractal theory;
(2) Taking the spray liquid drop group as an object, and determining the scale relation between the accumulated number of the spray liquid drop group and the liquid drop size;
(3) Integrating all single droplet areas in the atomization field, and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship:
wherein A is d A surface area for a population of droplets; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless;D min m is the minimum droplet size in the atomizing field;
(4) Calculating to obtain the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension;
(5) And obtaining the sum of the surface areas of all the liquid drops with different sizes in the atomization field, namely the heat exchange area between the air and the liquid drop group in the heat-moisture exchange process.
The method emphasizes the difference of the sizes of single liquid drops in the liquid drop group, can more accurately approximate the actual situation of the distribution of the liquid drop group, can accurately quantify the influence of different particle size distributions on the actual surface area of the liquid drop group, and more accurately determine the heat exchange area between air and the liquid drop group.
This example is further described below.
1) And constructing a fractal model of the particle size distribution of the spray liquid drop group according to a fractal theory. Under a certain pressure working condition, the particle size distribution of the liquid drop group formed by liquid drops sprayed out of the nozzle has a self-similar hierarchical structure; the liquid drops are spherical liquid drops with irregular shapes and equivalent diameters D, and are not overlapped with each other; the droplet size distribution of the droplet group in the unrestricted space is random and disordered. Thus, a fractal model of the spray droplet population particle size distribution as shown in fig. 1 was established.
According to the fractal theory, the particle size distribution of the atomized liquid drop group with the self-similar characteristic accords with the fractal scale relation, so the fractal scale relation of the particle size distribution of the atomized liquid drop group can be written as:
2) The spray liquid drop group is taken as a research object, and the accumulated number of the spray liquid drop group is determined to be the ratio Y n (D) The scaling relationship with droplet size D is as follows:
let the total number of droplets of the spray droplet group be N, the ratio of the number of droplets having a diameter smaller than D to the total number of droplets can be expressed as:
wherein Y is n (D) The ratio of the number of the liquid drops with the diameter smaller than D to the total number of the liquid drops in the atomization field is dimensionless; n is the total number of the spray liquid drops; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless.
3) Integrating all single droplet areas in an atomization field, and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship, wherein the specific operation is as follows:
the surface area of all droplets in a droplet population can be obtained by summing the integral from the smallest droplet to the largest droplet, and the droplet population surface area can be expressed as:
the number dN of droplets having a diameter between D and (D+dD) can be expressed as:
dN＝NdY n (D) (5)
the combination formula (3), the formula (4) and the formula (5) can be obtained:
solving equations, settingThe method can obtain:
the formula (8) is a liquid drop group surface area calculation formula based on fractal characterization.
According to the fractal theory, the droplet group consists of innumerable fine droplets, the surface area is infinite, and the occupied 3-dimensional space is limited, and the fractal dimension is between 1 and 3. The change rule of the surface area of the liquid drop group based on the fractal dimension is shown in figure 2 within the particle size range of 10-1000 mu m.
As can be seen from fig. 2, as the fractal dimension of the droplet population particle size distribution increases, the droplet population surface area increases. The surface area of the liquid drop group increases gradually when the fractal dimension is 1 to 2, and the surface area of the liquid drop group increases obviously with the increase of the fractal dimension when the fractal dimension is more than 2. When the fractal dimension was 1, the droplet population surface area was 0.31X10 -5 m 2 At a fractal dimension equal to 3, the droplet population surface area was 9.33X10 -4 m 2 The fractal dimension varies from 1 to 3, increasing the droplet population surface area 300-fold. Under the same particle size range, the larger the fractal dimension is, the larger the proportion of fine liquid drops in the liquid drop group is, and the particle size distribution of the liquid drop group is more uniform. In the process of wind-water direct contact heat-humidity exchange, the surface area of a liquid drop group in an atomization field is increased, the heat-humidity transfer area is increased, and the total heat exchange amount is increased. According to the result, the heat exchange area and the heat exchange amount in the direct contact heat exchange process are positiveCompared with the liquid drop group fractal dimension is increased from 1 to 3, the heat exchange quantity is also increased in multiple, and the heat exchange efficiency of the heat recovery device can be greatly optimized.
4) Comparing and analyzing a liquid drop group surface area calculation formula based on fractal characterization with the existing liquid drop group surface area calculation formula based on average diameter, and determining the superiority of the liquid drop group surface area calculation formula based on fractal characterization. The surface area of the liquid drop group based on the average diameter is calculated as follows:
wherein epsilon is the disperse phase fraction of the liquid drop group, which means the volume ratio of the liquid drop volume to the total space, and represents the density of the liquid drops in the space; v is spray field volume, m 3 ；D 32 The average Sauter diameter (average Sauter diameter) and m.
Sauter mean diameter D of different types of nozzles at each sampling segment was measured by an unrestricted space atomization test 32 And a dispersed phase fraction epsilon, the surface area of the population of droplets estimated based on the Sauter mean diameter can be calculated from equation (9). Meanwhile, according to the fractal dimension and the particle size range, the surface area of the droplet group based on the fractal dimension can be obtained by calculating from the formula (8), as shown in fig. 3.
In fig. 3, comparing the two algorithm results can be seen: the atomized field droplet population is regarded as an equal-particle-diameter population in the formula (9), and the difference of the particle diameters of the droplets is ignored, so that the method is based on D 32 The calculated liquid drop group has small fluctuation of surface area; based on D f The calculated surface area of the liquid drop group increases along with the increase of the fractal dimension, and the main reason is that the content of fine liquid drops in an atomization field increases, and the specific surface area of the liquid drop group increases; when the fractal dimension of the particle size distribution of the liquid drop group is smaller than 2.3, the method is based on D 32 Calculated droplet population surface area is greater than D-based f Calculated, when the fractal dimension is greater than 2.3, based on D f The calculated droplet population surface area is larger and follows D f The larger the difference between them, the more the fractal dimension of the droplet population was measured at 55cm to be 2.72, D 32 =99.64 μm based on D 32 The calculated surface area of the droplet group was 9.46×10 -5 m 2 Based on D f The calculated surface area of the droplet group was 3.15X10 -4 m 2 About 3 times different; the fractal dimension of the droplet population decreases with increasing distance, focusing more on between 1.9 and 2.5, indicating that the fine droplet duty cycle decreases with increasing distance of migration. To sum up, based on D f The calculated liquid drop group surface area algorithm can obtain more accurate liquid drop group surface area on the basis of comprehensively representing the particle size distribution difference. D can also be used when the fractal dimension of the droplet group particle size distribution is about 2.3 32 To characterize the droplet population surface area.
In addition, this embodiment also provides a device for determining a heat exchange area in a heat-moisture exchange process, which includes:
the model construction unit is used for constructing a fractal model of the particle size distribution of the spray droplet group according to a fractal theory;
a scale relation determining unit for determining a scale relation between the accumulated number of spray droplet groups and the droplet size, with the spray droplet groups as targets;
the formula determining unit is used for integrating all single droplet areas in the atomization field and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship;
the surface area determining unit is used for calculating the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension;
and the heat exchange area determining unit is used for calculating the sum of the surface areas of all the liquid drops with different sizes in the atomization field so as to determine the heat exchange area between the air and the liquid drop group in the heat and humidity exchange process.
In addition, the embodiment also provides a method for improving heat exchange efficiency in the heat-moisture exchange process, which comprises the following steps: the heat exchange area of the air and the liquid drop group is determined by adopting the method for determining the heat exchange area in the heat-moisture exchange process, and then the fractal dimension of the liquid drop group is increased, so that the heat exchange area is increased, the heat exchange area is in direct proportion to the heat exchange quantity, and then the heat exchange quantity is increased, so that the heat exchange efficiency is improved.
The foregoing embodiments are preferred embodiments of the present application, and in addition, the present application may be implemented in other ways, and any obvious substitution is within the scope of the present application without departing from the concept of the present application.
Finally, it should be emphasized that some descriptions of the present application have been simplified and some other elements have been omitted for clarity in order to make it easier for a person of ordinary skill in the art to understand the improvements of the present application over the prior art, and those omitted elements may also constitute the content of the present application.
Claims (9)
1. The method for determining the heat exchange area in the heat and humidity exchange process is characterized by comprising the following steps of:
(1) Constructing a fractal model of the particle size distribution of the spray liquid drop group;
(2) Taking the spray liquid drop group as an object, and determining the scale relation between the accumulated number of the spray liquid drop group and the liquid drop size;
(3) Integrating all single droplet areas in the atomization field, and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship:
wherein A is d A surface area for a population of droplets; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless;D min m is the minimum droplet size in the atomizing field;
(4) Calculating to obtain the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension;
(5) And obtaining the sum of the surface areas of all the liquid drops with different sizes in the atomization field, namely the heat exchange area between the air and the liquid drop group in the heat-moisture exchange process.
2. The method for determining heat exchange area in heat and humidity exchange process according to claim 1, wherein in the step (1), in the constructed fractal model of particle size distribution of spray droplet groups, the fractal scale relationship of the particle size distribution of spray droplet groups is:
wherein D is the droplet size, m; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless.
3. The method for determining heat exchange area in heat and humidity exchange process according to claim 1, wherein in the step (1), in the constructed fractal model for particle size distribution of spray droplet groups, the droplet groups consisting of droplets ejected from nozzles have self-similar hierarchical structure; the liquid drops are spherical liquid drops with irregular shapes and equivalent diameters D, and are not overlapped with each other; the droplet size distribution of the droplet group in the unrestricted space is random and disordered.
4. The method for determining heat exchange area in a heat and humidity exchange process according to claim 1 wherein in the step (2), the cumulative number of spray droplet groups is the ratio Y n (D) The scale relationship with droplet size D is as follows:
wherein Y is n (D) In mist for a number of droplets of diameter less than DThe ratio of the total liquid drop number of the chemical field is dimensionless; n is the total number of the spray liquid drops; d (D) max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless; d is the droplet size, m.
5. The method for determining heat exchange area in heat and humidity exchange process according to claim 4 wherein in the step (3), the method for determining the droplet group surface area calculation formula based on the fractal dimension is as follows:
the surface area of all droplets in the droplet group is obtained by summing the integral from the smallest droplet to the largest droplet, then the droplet group surface area A d The method comprises the following steps:
the number dN of droplets having diameters between D and (D+dD) is:
dN＝NdY n (D) (5)
combined formula (3), formula (4) and formula (5), yields:
solving equations, settingThe method comprises the following steps:
the formula (8) is a liquid drop group surface area calculation formula based on fractal dimension;
wherein the method comprises the steps of，D max M is the maximum droplet size in the atomizing field; d (D) f Is fractal dimension, dimensionless; d is the droplet size, m; d (D) min M is the minimum droplet size in the atomizing field.
6. The method according to claim 1, wherein in the step (4), the fractal dimension of the droplet group particle size distribution is in the range of 1 to 3, and the surface area of the droplet group increases as the fractal dimension of the droplet group particle size distribution increases.
7. The method according to claim 1, wherein in the step (4), the larger the fractal dimension of the particle size distribution of the droplet group is, the larger the ratio of fine droplets in the droplet group is, and the more uniform the particle size distribution of the droplet group is in the same particle size range.
8. The device for determining the heat exchange area in the heat and humidity exchange process is characterized by comprising the following components:
the model construction unit is used for constructing a fractal model of the particle size distribution of the spray liquid drop group;
a scale relation determining unit for determining a scale relation between the accumulated number of spray droplet groups and the droplet size, with the spray droplet groups as targets;
the formula determining unit is used for integrating all single droplet areas in the atomization field and obtaining a droplet group surface area calculation formula based on fractal dimension by utilizing a fractal scale relationship;
the surface area determining unit is used for calculating the surface area of the liquid drop group based on the fractal dimension according to a liquid drop group surface area calculation formula based on the fractal dimension;
and the heat exchange area determining unit is used for calculating the sum of the surface areas of all the liquid drops with different sizes in the atomization field so as to determine the heat exchange area between the air and the liquid drop group in the heat and humidity exchange process.
9. The method for improving the heat exchange efficiency in the heat-moisture exchange process is characterized by comprising the following steps of: the method for determining the heat exchange area in the heat-moisture exchange process according to any one of claims 1-7 is adopted to determine the heat exchange area of air and the liquid drop group, then the fractal dimension of the liquid drop group is increased, so that the heat exchange area is increased, the heat exchange area is in direct proportion to the heat exchange amount, and then the heat exchange amount is increased, so that the heat exchange efficiency is improved.
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