CN104036122A - Characterization method for fluid flow pattern behavior and heat transfer synergic relation based on calculation of homology groups - Google Patents
Characterization method for fluid flow pattern behavior and heat transfer synergic relation based on calculation of homology groups Download PDFInfo
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Abstract
The invention relates to a characterization method for a fluid flow pattern behavior and heat transfer synergic relation based on the calculation of homology groups and belongs to the technical field of direct contact type heat exchanger performance index evaluation. The manner for photographing mixed images through a high-speed camera is adopted so as to collect images of fluid flow pattern behaviors of homology groups in different working conditions; a digital image processing technology is conducted on all the collected images of the fluid flow pattern behaviors of the homology groups in different working conditions to calculate the perimeters of the edges of bubble groups; curve charts corresponding to the working conditions are fitted out through the perimeters of the edges of the bubble groups according to time sequence points, the stable state time of the working conditions is obtained, the average perimeter of the edges of the bubble groups in each working condition is obtained, and then the stable state time is divided by the average perimeter of the edges of the bubble groups to obtain the unit time perimeter; characterization of the heat transfer conditions in the heat transfer process is achieved by adopting the synergic relation between the unit time perimeter and the average value of volume heat transfer coefficients of the fluid flow pattern behaviors of the homology groups. The characterization method has the high application value and is easy to conduct.
Description
Technical field
The present invention relates to a kind ofly based on calculating the liquid flow pattern behavior of homology group and the characterizing method of heat transfer conspiracy relation, belong to direct-contact heat exchanger performance index assessment technique field.
Background technology
In recent years, the drastic change of international energy situation, crude oil price constantly rise violently, and energy problem highlights day by day.One of main social problems that energy crisis faces as world, increasingly serious along with the development of human social economy especially.Since reform and opening-up, with the high flow rate of resource, the extensive economy pattern that the havoc of environment is cost can not guarantee the sustainable and healthy development of China's economic, and the energy has formed serious restriction to sound economic growth.The world today, human use's the energy is mainly the fossil fuels such as oil, coal, rock gas.Yet along with the development of human society suitability for industrialized production and the raising of people's living standard, the mankind are also growed in intensity to the contradiction between the demand of the energy and its limited reserves.Therefore, rationally utilize the existing energy and tap a new source of energy the research topic that becomes international.
In exploitation with rationally utilize under the trend of new forms of energy, heat interchanger is as reasonable utilization and save the energy, develop the key equipment of new forms of energy, in industrial and agricultural production, is widely used.Direct contact heat transfer is a kind of new and effective heat exchange mode, have advantages of that heat transfer coefficient is high, be difficult for that burn into can operate at low temperatures and traditional heat exchange mode such as less scaling incomparable, and due to the moving disturbance of stream-liquid two-phase flow, large 20～100 times of the comparable single-phase flow of its heat transfer coefficient, thereby all have a wide range of applications in the numerous areas such as petrochemical complex, power, the energy, power-saving technology.Volumetric heat transfer coefficient is important performance index of direct-contact heat exchanger, and it is the key of weighing direct contact heat transfer efficiency, and its influence factor is numerous, comprises external phase volume, temperature difference distribution situation, heat exchange amount etc. in generator.Direct-contact heat exchanger internal heat transfer is very complicated, the calculate and measurement of volumetric heat transfer coefficient difficulty very, and its influence factor value itself is also time to time change, actual measurement is difficult to carry out or accurately measures, and causes measurement result can not correctly reflect actual heat transfer situation.Therefore, invent a kind of heat transfer process characterizing method simple to operation and effective heterogeneous contact heat transfer and there is certain realistic meaning and higher using value.
Summary of the invention
The problem and the deficiency that for above-mentioned prior art, exist, the invention provides a kind of based on calculating the liquid flow pattern behavior of homology group and the characterizing method of heat transfer conspiracy relation.This method has higher using value, and simple, and the heat that can characterize sensitive, quick, reliably, in real time in heat transfer process is transmitted situation, and the present invention is achieved through the following technical solutions.
Based on calculating the liquid flow pattern behavior of homology group and a characterizing method for heat transfer conspiracy relation, its concrete steps are as follows:
(1) mode that first adopts high-speed camera to take vision-mix is collected the image of liquid flow pattern behavior of the homology group of different operating modes, and from heat exchange mixes the zero hour, 6000 width vision-mix of this operating mode are collected in continuous shooting for 8 minutes;
(2), under matlab environment, the image of liquid flow pattern behavior of step (1) being collected to the homology group of each Zhang Butong operating mode adopts digital image processing techniques to calculate bubble population rim circumference, is specially:
1. first adopt matlab function imread to read in matlab all images in each operating mode;
2. each image in selecting step each operating mode in 1. successively, then adopts matlab function im2bw to make binary conversion treatment;
3. the image after binary conversion treatment is adopted matlab function imerode to do corrosion treatment to it;
4. the image after corrosion treatment is adopted matlab function imdilate to do expansion process to it;
5. finally the image of expansion process is used function regionprops (L{i}, ' Perimeter') calculate the rim circumference of each bubble in each width expansion plans picture and add up, obtain the bubble population rim circumference of every piece image;
6. 4. 1. the image of rest working conditions extremely processed according to step, obtained the bubble population rim circumference of each image of all images that gather;
(3) all bubble population rim circumference of each operating mode are simulated to the curve map of corresponding this operating mode according to time series point according to matlab function plot, by this curve map steady state (SS), obtain the steady state (SS) time of this operating mode
, its unit is: s obtains average bubble group's rim circumference of each operating mode simultaneously by the data analysis of matlab
, then by average bubble group rim circumference, divided by the steady state (SS) time, obtain unit interval girth, unit interval girth=
;
(4) mean value of the volumetric heat transfer coefficient of the bubble population edge unit interval girth in employing step (3) and the behavior of homology group liquid flow pattern
the heat that characterizes in heat transfer process of conspiracy relation transmit situation, by step (3), obtain the unit interval girth in different work areas, after the size of the unit interval perimeter value in more different work areas, the heat transfer boundary condition in unit interval perimeter value maximal value work area is applied in production run.
The mean value of described volumetric heat transfer coefficient
be the mean value of 8 minutes internal volume coefficients of heat transfer.
In certain factory's production run, have 9 operating modes to need solution-air heat exchange, for simple to operation the heat of understanding in heat transfer process is transmitted situation, this factory verifies and the conspiracy relation of conducting heat by calculating the liquid flow pattern behavior of homology group, specifically:
(1) mode that first adopts high-speed camera to take vision-mix is collected the image of liquid flow pattern behavior of the homology group of 9 operating modes, i.e. continuous shooting 8 minutes from heat exchange mixes the zero hour, collects each operating mode enough for 6000 width vision-mix of statistical study bubble population performance;
(2), under matlab environment, the image of liquid flow pattern behavior of step (1) being collected to the homology group of each Zhang Butong operating mode adopts digital image processing techniques to calculate bubble population rim circumference, is specially:
1. first adopt matlab function imread to read in matlab all images in each operating mode;
2. each image in selecting step each operating mode in 1. successively, then adopts matlab function im2bw to make binary conversion treatment;
3. the image after binary conversion treatment is adopted matlab function imerode to do corrosion treatment to it, with noise tiny on removal of images;
4. image after corrosion treatment is adopted matlab function imdilate to do expansion process to it, its objective is and connect the breakpoint at bubble edge and make bubble edge-smoothing, be convenient to calculate bubble rim circumference, 1. to original image treatment scheme 4. as shown in Figure 1;
5. finally the image of expansion process is used to function regionprops (L{i}, ' Perimeter') calculate the rim circumference of each bubble in each width expansion plans picture and add up, obtain the bubble population rim circumference of every piece image, corresponding 6000 the bubble population rim circumference of each operating mode;
6. 4. 1. the image of rest working conditions extremely processed according to step, obtained the bubble population rim circumference of each image of all images that gather, treatment step as shown in Figure 1;
(3) all bubble population rim circumference of each operating mode are simulated to the curve map of corresponding this operating mode according to time series point according to matlab function plot, with perimeter change in this curve map, characterize the homology group liquid flow pattern behavior in this operating mode heat transfer process, by this curve map steady state (SS), obtain the steady state (SS) time of this operating mode
, its unit is: s, wherein curve map steady state (SS) refers to: the state that curve fluctuation tends to be steady, steady state (SS) time
refer to: the zero hour that curve fluctuation tends to be steady; By the data analysis of matlab, obtain average bubble group's rim circumference of each operating mode simultaneously
, then by average bubble group rim circumference, divided by the steady state (SS) time, obtain unit interval girth, unit interval girth=
, Fig. 2 is operating mode 5 bubble population rim circumference fitted figure, in Fig. 2, curve first fluctuates greatlyr, starts to tend to be steady, i.e. the steady state (SS) time of this operating mode after time 142.6s
=142.6s, as can be seen from Figure 2, average bubble group's rim circumference of this operating mode
=32393.6, its be unit interval girth=
=227.2;
(4) volumetric heat transfer coefficient of each operating mode is calculated in 8 minutes to the volumetric heat transfer coefficient of every whole minute by coefficient of heat transfer formula, each operating mode volumetric heat transfer coefficient temporal evolution as shown in Figure 3, then calculates 8 minutes volumetric heat transfer coefficient mean value of each operating mode
, each operating mode is the 1st minute, and the 2nd minute, the 3rd minute ..., the mean value of the 8th minute volumetric heat transfer coefficient
, its unit is:
;
(5) in order to make unit interval girth and volumetric heat transfer coefficient conspiracy relation more directly perceived, the unit interval girth of each operating mode that step (3) is obtained dwindles 150 times,
, take each operating mode as horizontal ordinate, 8 minutes volumetric heat transfer coefficient mean value of this operating mode
dwindle 150 times with the unit interval girth of each operating mode
for ordinate obtains different points, rest working conditions also obtains about 8 minutes volumetric heat transfer coefficient mean values corresponding to this operating mode
dwindle 150 times with unit interval girth
difference, by 8 minutes volumetric heat transfer coefficient mean values of different operating modes
point connects into curve, also the unit interval girth of different operating modes is dwindled to 150 times simultaneously
point connects into curve, intuitively observes 8 minutes volumetric heat transfer coefficient mean value
dwindle 150 times with unit interval girth
correlativity and variation tendency, as shown in Figure 4, unit interval girth as shown in Figure 4
with volumetric heat transfer coefficient mean value
variation tendency basically identical, both conspiracy relations are better.
(6) by the unit interval girth of each operating mode
for horizontal ordinate, 8 minutes volumetric heat transfer coefficient mean value of this operating mode
for ordinate obtains a point, by all the other each operating modes, according to unit interval girth, be horizontal ordinate, 8 minutes volumetric heat transfer coefficient mean value of this operating mode
for ordinate draws all the other points, all points that obtain are carried out to fitting a straight line, obtain related coefficient, as shown in Figure 5, its related coefficient is 0.94.By above simple operating process, prove available units time girth
with volumetric heat transfer coefficient mean value
the heat that characterizes in heat transfer process of conspiracy relation transmit situation, characterizing method of the present invention is simple, sensitive, quick, characterized the heat in heat transfer process reliably, in real time and transmit situation, the data result of calculation of above-mentioned each operating mode is as shown in table 1.
Each floor data result of calculation of table 1 (t unit: s,
unit:
)
Above-mentioned parameter Ruo Wu unit is all matlab default value.
The invention has the beneficial effects as follows: (1) Gu characterizing method of the present invention be adapted to solution-air, gas-liquid-solid, liquid-liquid, solid-liquid, solid-, the heterogeneous mixed system such as gas-solid, as long as the different material density of mixing there are differences (if density is the same, can add the tracer grain that distinguishes over other materials); (2) characterizing method of the present invention is interesting and effective, overcome the deficiency of volumetric heat transfer coefficient sign diabatic process difficulty, simple easily enforcement, from practical application, the method for this sign diabatic process has larger application prospect in chemical industry and metallurgical process; (3) characterizing method of the present invention is simple, and the heat that can characterize sensitive, quick, reliably, in real time in heat transfer process is transmitted situation.
Accompanying drawing explanation
Fig. 1 is original image process flow diagram of the present invention;
Fig. 2 is operating mode 5 bubble population rim circumference evolution diagrams of the present invention;
Fig. 3 is each operating mode volumetric heat transfer coefficient temporal evolution of the present invention figure;
Fig. 4 is the average volume coefficient of heat transfer of the present invention and unit interval girth conspiracy relation;
Fig. 5 is the average volume coefficient of heat transfer of the present invention and unit interval girth matched curve related coefficient.
Embodiment
Below in conjunction with the drawings and specific embodiments, the invention will be further described, but use of the present invention is not limited in this.
Embodiment 1
Should be based on calculating the liquid flow pattern behavior of homology group and the characterizing method of heat transfer conspiracy relation, its concrete steps are as follows:
(1) mode that first adopts high-speed camera to take vision-mix is collected the image of liquid flow pattern behavior of the homology group of 9 operating modes, i.e. continuous shooting 8 minutes from heat exchange mixes the zero hour, collects each operating mode enough for 6000 width vision-mix of statistical study bubble population performance;
(2), under matlab environment, the image of liquid flow pattern behavior of step (1) being collected to the homology group of each Zhang Butong operating mode adopts digital image processing techniques to calculate bubble population rim circumference, is specially:
1. first adopt matlab function imread to read in matlab all images in each operating mode;
2. each image in selecting step each operating mode in 1. successively, then adopts matlab function im2bw to make binary conversion treatment;
3. the image after binary conversion treatment is adopted matlab function imerode to do corrosion treatment to it, with noise tiny on removal of images;
4. image after corrosion treatment is adopted matlab function imdilate to do expansion process to it, its objective is and connect the breakpoint at bubble edge and make bubble edge-smoothing, be convenient to calculate bubble rim circumference, 1. to original image treatment scheme 4. as shown in Figure 1;
5. finally the image of expansion process is used to function regionprops (L{i}, ' Perimeter') calculate the rim circumference of each bubble in each width expansion plans picture and add up, obtain the bubble population rim circumference of every piece image, corresponding 6000 the bubble population rim circumference of each operating mode;
6. 4. 1. the image of rest working conditions extremely processed according to step, obtained the bubble population rim circumference of each image of all images that gather, treatment step as shown in Figure 1;
(3) all bubble population rim circumference of each operating mode are simulated to the curve map of corresponding this operating mode according to time series point according to matlab function plot, with perimeter change in this curve map, characterize the homology group liquid flow pattern behavior in this operating mode heat transfer process, by this curve map steady state (SS), obtain the steady state (SS) time of this operating mode
, its unit is: s, wherein curve map steady state (SS) refers to: the state that curve fluctuation tends to be steady, steady state (SS) time
refer to: the zero hour that curve fluctuation tends to be steady; By the data analysis of matlab, obtain average bubble group's rim circumference of each operating mode simultaneously
, then by average bubble group rim circumference, divided by the steady state (SS) time, obtain unit interval girth, unit interval girth=
, Fig. 2 is operating mode 5 bubble population rim circumference fitted figure, in Fig. 2, curve first fluctuates greatlyr, starts to tend to be steady, i.e. the steady state (SS) time of this operating mode after time 142.6s
=142.6s, as can be seen from Figure 2, average bubble group's rim circumference of this operating mode
=32393.6, its be unit interval girth=
=227.2;
(4) volumetric heat transfer coefficient of each operating mode is calculated in 8 minutes to the volumetric heat transfer coefficient of every whole minute by coefficient of heat transfer formula, each operating mode volumetric heat transfer coefficient temporal evolution as shown in Figure 3, then calculates 8 minutes volumetric heat transfer coefficient mean value of each operating mode
, each operating mode is the 1st minute, and the 2nd minute, the 3rd minute ..., the mean value of the 8th minute volumetric heat transfer coefficient
, its unit is:
;
(5) in order to make unit interval girth and volumetric heat transfer coefficient conspiracy relation more directly perceived, the unit interval girth of each operating mode that step (3) is obtained dwindles 150 times,
, take each operating mode as horizontal ordinate, 8 minutes volumetric heat transfer coefficient mean value of this operating mode
dwindle 150 times with the unit interval girth of each operating mode
for ordinate obtains different points, rest working conditions also obtains about 8 minutes volumetric heat transfer coefficient mean values corresponding to this operating mode
dwindle 150 times with unit interval girth
difference, by 8 minutes volumetric heat transfer coefficient mean values of different operating modes
point connects into curve, also the unit interval girth of different operating modes is dwindled to 150 times simultaneously
point connects into curve, intuitively observes 8 minutes volumetric heat transfer coefficient mean value
dwindle 150 times with unit interval girth
correlativity and variation tendency, as shown in Figure 4, unit interval girth as shown in Figure 4
with volumetric heat transfer coefficient mean value
variation tendency basically identical, both conspiracy relations are better.
(6) by the unit interval girth of each operating mode
for horizontal ordinate, 8 minutes volumetric heat transfer coefficient mean value of this operating mode
for ordinate obtains a point, by all the other each operating modes, according to unit interval girth, be horizontal ordinate, 8 minutes volumetric heat transfer coefficient mean value of this operating mode
for ordinate draws all the other points, all points that obtain are carried out to fitting a straight line, obtain related coefficient, as shown in Figure 5, its related coefficient is 0.94.By above simple operating process, prove available units time girth
with volumetric heat transfer coefficient mean value
the heat that characterizes in heat transfer process of conspiracy relation transmit situation, characterizing method of the present invention is simple, sensitive, quick, characterized the heat in heat transfer process reliably, in real time and transmit situation, the data result of calculation of above-mentioned each operating mode is as shown in table 1.
As can be seen from Figure 4, by step (3), obtain the unit interval girth in different work areas, after the size of the unit interval perimeter value in more different work areas, work area six (L
6) unit interval perimeter value maximum, therefore should be by the work area six (L of value
6) heat transfer boundary condition be applied in production run.
Embodiment 2
Should be based on calculating the liquid flow pattern behavior of homology group and the characterizing method of heat transfer conspiracy relation, its concrete steps are as follows:
(1) mode that first adopts high-speed camera to take vision-mix is collected the image of liquid flow pattern behavior of the homology group of 10 operating modes, and from heat exchange mixes the zero hour, 6000 width vision-mix of this operating mode are collected in continuous shooting for 8 minutes;
(2), under matlab environment, the image of liquid flow pattern behavior of step (1) being collected to the homology group of each Zhang Butong operating mode adopts digital image processing techniques to calculate bubble population rim circumference, is specially:
1. first adopt matlab function imread to read in matlab all images in each operating mode;
2. each image in selecting step each operating mode in 1. successively, then adopts matlab function im2bw to make binary conversion treatment;
3. the image after binary conversion treatment is adopted matlab function imerode to do corrosion treatment to it;
4. the image after corrosion treatment is adopted matlab function imdilate to do expansion process to it;
5. finally the image of expansion process is used function regionprops (L{i}, ' Perimeter') calculate the rim circumference of each bubble in each width expansion plans picture and add up, obtain the bubble population rim circumference of every piece image;
6. 4. 1. the image of rest working conditions extremely processed according to step, obtained the bubble population rim circumference of each image of all images that gather;
(3) all bubble population rim circumference of each operating mode are simulated to the curve map of corresponding this operating mode according to time series point according to matlab function plot, by this curve map steady state (SS), obtain the steady state (SS) time of this operating mode
, its unit is: s obtains average bubble group's rim circumference of each operating mode simultaneously by the data analysis of matlab
, then by average bubble group rim circumference, divided by the steady state (SS) time, obtain unit interval girth, unit interval girth=
;
(4) mean value of the volumetric heat transfer coefficient of the bubble population edge unit interval girth in employing step (3) and the behavior of homology group liquid flow pattern
the heat that characterizes in heat transfer process of conspiracy relation transmit situation, by step (3), obtain the unit interval girth in different work areas, after the size of the unit interval perimeter value in more different work areas, the heat transfer boundary condition in unit interval perimeter value maximal value work area is applied in production run.
The mean value of volumetric heat transfer coefficient wherein
be the mean value of 8 minutes internal volume coefficients of heat transfer.
Embodiment 3
Should be based on calculating the liquid flow pattern behavior of homology group and the characterizing method of heat transfer conspiracy relation, its concrete steps are as follows:
(1) mode that first adopts high-speed camera to take vision-mix is collected the image of liquid flow pattern behavior of the homology group of 20 operating modes, and from heat exchange mixes the zero hour, 6000 width vision-mix of this operating mode are collected in continuous shooting for 8 minutes;
(2), under matlab environment, the image of liquid flow pattern behavior of step (1) being collected to the homology group of each Zhang Butong operating mode adopts digital image processing techniques to calculate bubble population rim circumference, is specially:
1. first adopt matlab function imread to read in matlab all images in each operating mode;
2. each image in selecting step each operating mode in 1. successively, then adopts matlab function im2bw to make binary conversion treatment;
3. the image after binary conversion treatment is adopted matlab function imerode to do corrosion treatment to it;
4. the image after corrosion treatment is adopted matlab function imdilate to do expansion process to it;
5. finally the image of expansion process is used function regionprops (L{i}, ' Perimeter') calculate the rim circumference of each bubble in each width expansion plans picture and add up, obtain the bubble population rim circumference of every piece image;
6. 4. 1. the image of rest working conditions extremely processed according to step, obtained the bubble population rim circumference of each image of all images that gather;
(3) all bubble population rim circumference of each operating mode are simulated to the curve map of corresponding this operating mode according to time series point according to matlab function plot, by this curve map steady state (SS), obtain the steady state (SS) time of this operating mode
, its unit is: s obtains average bubble group's rim circumference of each operating mode simultaneously by the data analysis of matlab
, then by average bubble group rim circumference, divided by the steady state (SS) time, obtain unit interval girth, unit interval girth=
;
(4) mean value of the volumetric heat transfer coefficient of the bubble population edge unit interval girth in employing step (3) and the behavior of homology group liquid flow pattern
the heat that characterizes in heat transfer process of conspiracy relation transmit situation, by step (3), obtain the unit interval girth in different work areas, after the size of the unit interval perimeter value in more different work areas, the heat transfer boundary condition in unit interval perimeter value maximal value work area is applied in production run.
The mean value of volumetric heat transfer coefficient wherein
be the mean value of 8 minutes internal volume coefficients of heat transfer.
Claims (2)
1. based on calculating the liquid flow pattern behavior of homology group and a characterizing method for heat transfer conspiracy relation, it is characterized in that concrete steps are as follows:
(1) mode that first adopts high-speed camera to take vision-mix is collected the image of liquid flow pattern behavior of the homology group of different operating modes, and from heat exchange mixes the zero hour, 6000 width vision-mix of this operating mode are collected in continuous shooting for 8 minutes;
(2), under matlab environment, the image of liquid flow pattern behavior of step (1) being collected to the homology group of each Zhang Butong operating mode adopts digital image processing techniques to calculate bubble population rim circumference, is specially:
1. first adopt matlab function imread to read in matlab all images in each operating mode;
2. each image in selecting step each operating mode in 1. successively, then adopts matlab function im2bw to make binary conversion treatment;
3. the image after binary conversion treatment is adopted matlab function imerode to do corrosion treatment to it;
4. the image after corrosion treatment is adopted matlab function imdilate to do expansion process to it;
5. finally the image of expansion process is used function regionprops (L{i}, ' Perimeter') calculate the rim circumference of each bubble in each width expansion plans picture and add up, obtain the bubble population rim circumference of every piece image;
6. 4. 1. the image of rest working conditions extremely processed according to step, obtained the bubble population rim circumference of each image of all images that gather;
(3) all bubble population rim circumference of each operating mode are simulated to the curve map of corresponding this operating mode according to time series point according to matlab function plot, by this curve map steady state (SS), obtain the steady state (SS) time of this operating mode
, its unit is: s obtains average bubble group's rim circumference of each operating mode simultaneously by the data analysis of matlab
, then by average bubble group rim circumference, divided by the steady state (SS) time, obtain unit interval girth, unit interval girth=
;
(4) mean value of the volumetric heat transfer coefficient of the bubble population edge unit interval girth in employing step (3) and the behavior of homology group liquid flow pattern
the heat that characterizes in heat transfer process of conspiracy relation transmit situation, by step (3), obtain the unit interval girth in different work areas, after the size of the unit interval perimeter value in more different work areas, the heat transfer boundary condition in unit interval perimeter value maximal value work area is applied in production run.
2. as claimed in claim 1 based on calculating the liquid flow pattern behavior of homology group and the characterizing method of heat transfer conspiracy relation, it is characterized in that: the mean value of described volumetric heat transfer coefficient
be the mean value of 8 minutes internal volume coefficients of heat transfer.
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| CN104239724A (en) * | 2014-09-19 | 2014-12-24 | 国家电网公司 | Online monitoring and assessment method for heat exchange efficiency of water-cooling system of converter valve |
| CN109903243A (en) * | 2019-02-20 | 2019-06-18 | 云南农业大学 | A method of multiphase stirring and mixing effect is characterized based on Logistics model |
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