CN117493744B - Determination method for ice crystal particle convection heat exchange experiment association type - Google Patents
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- PYWVYCXTNDRMGF-UHFFFAOYSA-N rhodamine B Chemical compound [Cl-].C=12C=CC(=[N+](CC)CC)C=C2OC2=CC(N(CC)CC)=CC=C2C=1C1=CC=CC=C1C(O)=O PYWVYCXTNDRMGF-UHFFFAOYSA-N 0.000 claims description 12
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Abstract
The invention belongs to the technical field of ice crystal particle melting, and particularly discloses a method for determining association of ice crystal particle convection heat exchange experiments, which comprises the following steps: and determining a heat and mass transfer equation of the ice crystal particles in a melting stage, determining a semi-empirical formula of Nu number of convective heat transfer of the spherical particles, simplifying the relationship between the resistance coefficient C d and the Nu number according to a comparison theory, and determining the general association of the convective heat transfer of the ice crystal particles based on the simplified relationship between the resistance coefficient C d and the Nu number and the semi-empirical formula of the Nu number. Aiming at the problem of ice crystal convection heat transfer melting, experimental research and theoretical analysis are developed, and finally an experimental correlation formula aiming at the ice crystal convection heat transfer under the air is obtained, and the ice crystal melting time determined based on the correlation formula has higher accuracy.
Description
Technical Field
The invention relates to the technical field of ice crystal particle melting, in particular to a method for determining association of an ice crystal particle convection heat exchange experiment.
Background
When the ice crystal at high altitude enters the engine, the ice crystal moves in a warm environment to melt, and further part of melted ice crystal particles impact the internal parts of the engine to form ice accumulation in the engine, and engine faults can be caused when the ice crystal particles are serious. The ice crystal melting rate has a great influence on the ice crystal ice accumulation, and the accuracy of the ice crystal movement melting phase change is greatly dependent on a convective heat transfer coefficient model between the ice crystal and the air. The technology develops a melting phase change experiment of ice crystals under convective heat transfer, and obtains experimental correlation type ice crystal convective heat transfer coefficients by analyzing experimental data and combining theoretical analysis.
Disclosure of Invention
The invention aims to provide a method for determining association of ice crystal particle convection heat exchange experiments, which aims to solve the problems in the background technology.
In order to achieve the above purpose, the invention provides a method for determining the association type of ice crystal particle convection heat exchange experiments, which adopts the following technical scheme:
a method of determining a correlation of ice crystal particle convective heat transfer experiments, the method comprising:
the equation for heat and mass transfer to determine ice crystal particles during the melting phase is shown below:
in the above formula, d p is the particle diameter; t p is the particle temperature; t a is the air temperature; k a is the air heat conductivity coefficient; and/> The evaporation rate and the melting rate of ice crystals respectively; l v and L f are latent heat of evaporation and latent heat of melting, respectively; m p,i and d p,i are mass and diameter of ice nuclei during thawing,/>, respectivelySh is Serpentis number; ρ a is the ice crystal particle density; d v,a is the vapor diffusivity in air, y v,s and y v,a represent the mass fraction of vapor in the particle surface and free surface, respectively; phi is the sphericity of the particles; nu is the number of Knoossels and is a dimensionless number that characterizes convective heat transfer intensity.
The semi-empirical formula for determining the Nu number of spherical particles for convective heat transfer is expressed as:
Wherein Re is the Reynolds number, which is the dimensionless number for representing the flow condition of the fluid, pr is the Plandt number, which is the dimensionless number for representing the relation between the temperature boundary layer and the flow boundary layer;
According to a theory of comparison, the relationship between the drag coefficient C d and the Nu number is expressed as:
the formula (5) is simplified to obtain:
the simultaneous expression (4) and the expression (6) are obtained:
obtaining the general association of ice crystal particle convection heat transfer according to the formula (7):
wherein a is a coefficient to be determined.
Further, the magnitude of the value of the undetermined coefficient a is determined by the following method:
Setting an initial value of a coefficient a to be determined under the determined experimental parameters, and simulating a melting process by using a phase-change melting model based on ice crystals to obtain simulated melting time, wherein the phase-change melting model based on the ice crystals is determined by a heat and mass transfer equation of the ice crystal particles in a melting stage through the universal association of ice crystal particle convection heat exchange;
comparing the simulated melting time with the experimental melting time, and determining a relative error;
and adjusting the value of the coefficient a to be determined according to the relative error, and determining the value of the coefficient a to be determined.
Further, the adjusting the value of the coefficient to be determined a according to the relative error, to determine the value of the coefficient to be determined a specifically includes:
And setting the initial value of the undetermined coefficient a to be 0.375, and increasing the value of the undetermined coefficient a if the current relative error is reduced relative to the previous relative error according to different values of the undetermined coefficient a set twice until the relative error is not reduced any more, and taking the value of the undetermined coefficient a corresponding to the minimum relative error as the value of the undetermined coefficient a.
Further, determining the value of the undetermined coefficient a to be 0.45 to obtain an experimental correlation formula of ice crystals under convective heat transfer under air:
The experimental parameters included ambient humidity, pressure, gas flow rate, temperature, and ice crystal particle diameter.
Further, utilize ice crystal to melt measuring device and acquire experiment melting time, ice crystal melts measuring device includes control terminal, CCD camera, laser emitter, ultrasonic wave isolator, air current pipeline, high-pressure nitrogen gas jar, heat exchanger and room temperature air pipeline, the signal output part of CCD camera is connected control terminal's signal input part, laser emitter set up in one side of ultrasonic wave isolator for send laser to ultrasonic wave isolator, the CCD camera set up in one side of ultrasonic wave isolator for acquire ice crystal melting image and feed to control terminal, the one end of air current pipeline is connected ultrasonic wave isolator, its other end is connected the heat exchanger, the high-pressure nitrogen gas jar passes through the nitrogen gas pipeline and connects the heat exchanger, be provided with the relief pressure valve on the nitrogen gas pipeline, set up gas flowmeter on the air current pipeline, room temperature air pipeline is connected air current pipeline, set up the ball valve on the room temperature air pipeline.
Further, the nitrogen pipeline is connected with the air flow pipeline through a temperature control pipeline, and a needle valve is arranged on the temperature control pipeline.
Further, obtaining the experimental melting time using the ice crystal melting measurement device includes:
A pipette is used for transferring a set volume of rhodamine B solution to a standing point position generated by the ultrasonic suspension;
Opening a valve of a pressure reducing valve, cooling normal-temperature nitrogen into low-temperature nitrogen through a heat exchanger, and enabling the low-temperature nitrogen of an outlet pipeline to exchange heat with liquid drops, wherein the liquid drops are gradually frozen;
After the liquid drops are frozen to reach a stable state, a laser emitter is started, room temperature air is introduced, particles are melted uniformly, and the melting rate is calculated through experimental pictures shot by a CCD camera, so that the melting time of ice crystal particles in an experiment is obtained.
The beneficial effects of the invention are as follows:
Aiming at the problem of ice crystal convection heat transfer melting, experimental research and theoretical analysis are developed, and finally an experimental correlation formula aiming at the ice crystal convection heat transfer under the air is obtained, and the ice crystal melting time determined based on the correlation formula has higher accuracy.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. Like elements or portions are generally identified by like reference numerals throughout the several figures. In the drawings, elements or portions thereof are not necessarily drawn to scale.
Fig. 1 shows a flow chart of ice crystal melting according to an embodiment of the invention.
Fig. 2 shows a schematic diagram of melting rate measurement according to an embodiment of the present invention.
Fig. 3 shows a block diagram of an ice crystal melting measurement apparatus according to an embodiment of the present invention.
Fig. 4 shows a schematic diagram of a laboratory bench built based on an ice crystal melting measurement apparatus according to an embodiment of the invention.
Fig. 5 shows a fitting correlation flow chart according to an embodiment of the invention.
Fig. 6 shows an analysis chart of experimental results according to an embodiment of the present invention.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict.
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples.
The embodiment of the invention provides a method for determining association of ice crystal particle convective heat transfer experiments. The determination is based on the development of a model of ice crystals during the thawing phase.
According to the Mason three-stage melting model, the phase change process of ice crystal particles is divided into three stages, and the melting temperature of the particles is T m.
(1) Solid state phase: the temperature T of the particles is less than T m, the particles are pure solid ice crystals, the ice crystal particles and the external environment perform convective heat exchange, the ice crystals sublimate and the temperature rises until the temperature reaches the melting temperature T m.
(2) Melting stage: the particle temperature t=t m, under the further heat exchange action, the ice crystals begin to melt from the outside, the water film surrounds the inner ice nuclei, and at this stage the heat absorbed by the partially melted ice crystal particles is used entirely to supply both latent heat of melting and latent heat of evaporation, the temperature being maintained.
(3) Liquid phase: the particle temperature T is more than T m, the ice crystal particles are completely melted to be in a liquid drop state, heat is continuously absorbed from the external environment, liquid water drops are evaporated, and the temperature is continuously increased.
The determination method is specifically realized by the following steps:
step 1, determining a heat and mass transfer equation of ice crystal particles in a melting stage as follows:
In the above formula, d p is the particle diameter; t p is the particle temperature, the initial temperature is 273.15K; t a is the air temperature; k a is the air heat conductivity coefficient; and/> The evaporation rate and the melting rate of ice crystals respectively; l v and L f are latent heat of evaporation and latent heat of fusion, respectively. m p,i and d p,i are mass and diameter of ice nuclei during thawing,/>, respectivelySh is Serpentis number; ρ a is the ice crystal particle density; d v,a is the vapor diffusivity in air. y v,s and y v,a represent the mass fraction of the vapor in the particle surface and free surface, respectively; phi is the sphericity of the particles.
In the equations (1) - (3), nu expression is unknown, ranz and Marshall et al obtain a semi-empirical formula of Nu number of convective heat transfer of spherical particles according to theoretical analysis and experiments.
In combination with the test result, the following theoretical analysis is performed, and firstly, according to a comparison theory, the resistance coefficient C d and the Nu number can be compared and linked by using Chilton-Colburn to obtain the following relationship:
For a moderately Reynolds number of non-spherical particle sweep, the flow is based on And Sommerfled et al, can be obtained as a simplified version of the drag coefficient formula:
Substituting into the above formula, one can obtain:
Considering that the above equation should be compatible with the correlation of Ranz, then the general correlation of convective heat transfer for the resulting ice crystal particles is as follows:
In the above equation, the coefficient a is pending. Considering that in the process of melting ice crystal particles, melted ice forms a water film covering the surfaces of the particles, and compared with solid ice crystals, the liquid water film is easier to evaporate, and the evaporated water vapor can change the temperature and the composition of surrounding gas, thereby indirectly influencing the heat transfer rate. This effect can hinder the heat transfer process of phase-change melting, and therefore, the coefficient a is determined in combination with experimental data and theoretical analysis.
According to the experimental result, the constants in the correlation formula are fitted, and a fitting flow chart is shown in fig. 5. First, experimental parameters of each set of experiments, such as ambient humidity, pressure, air flow velocity, temperature, ice crystal particle diameter, etc., are inputted into the program, and specific settings of the experimental parameters are shown in table 1. Simulating a melting process by using a simulation program written by a phase-change melting model based on ice crystals to obtain simulated melting time; comparing the melting time of the simulation analysis with the experimental melting time, and calculating an average relative error; according to the differential equation of melting, nu number and melting time are monotonous, so the constant a in the correlation is further adjusted to gradually reduce the relative error, iterative calculation is performed until the relative error between simulation and experimental melting time is minimum, and the constant a=0.45 is obtained.
Table 1 experimental parameters
Thus, we obtain the experimental correlation of ice crystals under convective heat transfer in air:
Comparing the experimental correlation (9) obtained in this example with the Ranz empirical correlation (4) based on spherical particles, it was found that the average relative error in melting time was reduced from 13.4% to 8.6%, as shown in fig. 6. The experimental correlation formula determined by the embodiment has higher accuracy.
In this embodiment, the ice crystal-based phase-change melting model may be determined according to formulas (1) to (3) and formula (8). As shown in fig. 3, this embodiment provides a measuring device is melted to ice crystal, measuring device is melted to ice crystal includes control terminal 1, CCD camera 2, laser emitter 3, ultrasonic suspension 4, air current pipeline 5, high-pressure nitrogen jar 6, heat exchanger 7 and room temperature air pipeline 8, the signal output part of CCD camera 2 is connected the signal input part of control terminal 1, laser emitter 3 set up in one side of ultrasonic suspension 4 for send laser to ultrasonic suspension 4, CCD camera 2 set up in one side of ultrasonic suspension 4 for acquire ice crystal melting image and feed to control terminal 1, the one end of air current pipeline is connected ultrasonic suspension 4, and its other end is connected heat exchanger 7, high-pressure nitrogen jar 6 passes through nitrogen gas pipeline 9 and connects heat exchanger 7, be provided with relief valve 10 on nitrogen gas pipeline 9, set up gas flowmeter 11 on air current pipeline 5, room temperature air pipeline 8 is connected air current pipeline 5 is last to be provided with ball valve 12, nitrogen gas pipeline 9 is connected through nitrogen gas temperature control pipeline 13, be provided with temperature control needle valve 13 on the nitrogen gas pipeline 13.
Fig. 4 is a schematic diagram of an experiment table constructed based on the apparatus shown in fig. 3, and an experiment is performed by using the ice crystal melting measurement apparatus to obtain an experimental melting time, wherein the experimental steps are as follows:
1) A pipette is used to remove a designated volume of rhodamine B solution and place the droplet at the dwell point location created by the ultrasonic suspension.
2) And opening a valve of the pressure reducing valve, cooling the normal-temperature nitrogen into low-temperature nitrogen through a heat exchanger, and enabling the low-temperature nitrogen of the outlet pipeline to exchange heat with the liquid drops, wherein the liquid drops are gradually frozen.
3) After the liquid drops are frozen to reach a stable state for a period of time, air at room temperature is introduced, particles are melted uniformly, and the melting rate is calculated through an experimental picture gray level conversion program, so that the melting time of the ice crystal particles in an experiment is obtained.
Based on the ice crystal melting measuring device, the control terminal can calculate parameters such as particle size, equivalent diameter, volume, surface area and the like according to the photographed image. And then using a thermal measuring instrument to measure experimental parameters such as air flow pressure, temperature, speed, humidity and the like, and obtaining theoretical calculation working conditions of experimental correlation of convection heat transfer coefficients.
It should be noted that the control terminal is a device capable of implementing data processing, for example, may be implemented as a computer device, such as a notebook computer, a desktop computer, or other related products that are currently available in the market.
As shown in fig. 1 and 2, the principle of measuring ice crystal melting time by using the ice crystal melting measuring device is as follows:
according to the characteristics of rhodamine B aqueous solution, the dynamic measurement of the ice crystal particle melting rate is realized by utilizing a fluorescence induction technology and combining a self-programming program.
Rhodamine B is easy to dissolve in water, the aqueous solution is blue-red, and the rhodamine B is scarlet after dilution, has strong fluorescence, and has the characteristics of good stability, insensitivity to PH and the like. The maximum absorption wavelength, emission wavelength and concentration of rhodamine B are related, and furthermore, the fluorescence intensity generated by the rhodamine B aqueous solution is also affected by the concentration and temperature. With the increase of the concentration, the fluorescence intensity is increased and then reduced, and at normal temperature, the influence of temperature change on the fluorescence intensity is obvious, and the higher the temperature is, the lower the fluorescence intensity is.
At a certain temperature and concentration, the fluorescence intensity of rhodamine B aqueous solution depends only on the number of rhodamine B molecules dissolved in water. FIG. 2 is a schematic diagram of melting rate measurement, wherein 532nm laser is required to be strong enough, the emitted laser can penetrate through the whole particle, rhodamine B molecules in the liquid can be excited to generate orange fluorescence of about 580nm, and rhodamine B molecules in frozen ice cores cannot be excited to generate fluorescence. Therefore, the melting rate of ice crystals can be quantitatively measured from the intensity of fluorescence generated.
Calculating the number of Pichia pastoris of suspended particles in experimental rangeWhere h is the particle heat transfer coefficient, d is the particle diameter, λ is the particle heat transfer coefficient, and it can be considered that the temperature inside the particles is uniform.
Based on the above characteristics, it can be inferred that the droplet gradually freezes under a low-temperature air flow, and the fluorescence intensity eventually decreases to 0. After the air flow with the temperature higher than the melting temperature is introduced, the temperature of the particles gradually rises to the melting temperature, then the particles start to melt, the fluorescence intensity gradually increases, the temperature of the particles in the phase of melting phase is equal to the melting temperature, after the particles are completely melted, the temperature of the liquid particles further rises, and the fluorescence intensity can be slowly reduced. Therefore, at the time of complete melting, the fluorescence intensity of the particles has a maximum value. Thus, the data points at the start of melting and the complete melting can be quantitatively obtained from these characteristics.
The melting rate measuring method comprises the following steps:
the camera is used for collecting image information, the image is converted into gray values, and a gray calculation formula is as follows:
Igray＝R×0.229+G×0.587+B×0.114 (10)
Wherein I gray is an image gray value, and R, G, B is a numerical value of each channel in the image. The maximum gray value I max before melting and the camera reference gray value I min are recorded using a program, the gray value I in a certain melting state. According to the measurement principle, the ice crystal melting rate m r at the current moment can be obtained by using the linear difference value, and the formula is as follows:
As shown in FIG. 1, the melting rate measurement experiment chart shows that the melting rate gradually decreases in the freezing stage to 0% and reaches the completely frozen state, the melting rate gradually increases in the melting stage to be finally close to 100% and becomes the completely melted state, then the temperature of the liquid drops gradually increases in the temperature increasing stage, the fluorescence intensity decreases, and the calculated melting rate decreases.
The above embodiments are only for illustrating the present invention, not for limiting the present invention, and various changes and modifications may be made by one of ordinary skill in the relevant art without departing from the spirit and scope of the present invention, and therefore, all equivalent technical solutions are also within the scope of the present invention, and the scope of the present invention is defined by the claims.
Claims (6)
1. A method for determining a correlation of ice crystal particle convective heat transfer experiments, the method comprising:
the equation for heat and mass transfer to determine ice crystal particles during the melting phase is shown below:
in the above formula, d p is the particle diameter; t p is the particle temperature; t a is the air temperature; k a is the air heat conductivity coefficient; and/> The evaporation rate and the melting rate of ice crystals respectively; l v and L f are latent heat of evaporation and latent heat of melting, respectively; m p,i and d p,i are the mass and diameter of the ice core during melting, respectively, sh is the Serpentis number; ρ a is the ice crystal particle density; d v,a is the vapor diffusivity in air, y v,s and y v,a represent the mass fraction of vapor in the particle surface and free surface, respectively; phi is the sphericity of the particles; nu is the Nussel number and is a dimensionless number for representing the intensity of convective heat transfer;
the semi-empirical formula for determining the Nu number of spherical particles for convective heat transfer is expressed as:
Wherein Re is the Reynolds number, which is a dimensionless number for representing the flow condition of the fluid; pr is the Plandter number, and is a dimensionless number for representing the relationship between a temperature boundary layer and a flow boundary layer;
According to a theory of comparison, the relationship between the drag coefficient C d and the Nu number is expressed as:
the formula (5) is simplified to obtain:
the simultaneous expression (4) and the expression (6) are obtained:
obtaining the general association of ice crystal particle convection heat transfer according to the formula (7):
Wherein a is a coefficient to be determined;
the magnitude of the value of the undetermined coefficient a is determined by the following method:
Setting an initial value of a coefficient a to be determined under the determined experimental parameters, and simulating a melting process by using a phase-change melting model based on ice crystals to obtain simulated melting time, wherein the phase-change melting model based on the ice crystals is determined by a heat and mass transfer equation of the ice crystal particles in a melting stage through the universal association of ice crystal particle convection heat exchange;
comparing the simulated melting time with the experimental melting time, and determining a relative error;
and adjusting the value of the coefficient a to be determined according to the relative error, and determining the value of the coefficient a to be determined.
2. The method for determining the association of ice crystal particle convective heat transfer experiments according to claim 1, wherein the adjusting the value of the coefficient to be determined a according to the relative error, determining the value of the coefficient to be determined a, specifically comprises:
And setting the initial value of the undetermined coefficient a to be 0.375, and increasing the value of the undetermined coefficient a if the current relative error is reduced relative to the previous relative error according to different values of the undetermined coefficient a set twice until the relative error is not reduced any more, and taking the value of the undetermined coefficient a corresponding to the minimum relative error as the value of the undetermined coefficient a.
3. The method for determining experimental correlation of convective heat transfer of ice crystal particles according to claim 1, wherein the value of the undetermined coefficient a is determined to be 0.45, and the experimental correlation of ice crystal under convective heat transfer under air is obtained:
The experimental parameters included ambient humidity, pressure, gas flow rate, temperature, and ice crystal particle diameter.
4. The method for determining the experimental correlation of ice crystal particle convective heat transfer according to claim 1, wherein the experimental melting time is obtained by using an ice crystal melting measurement device, the ice crystal melting measurement device comprises a control terminal, a CCD camera, a laser emitter, an ultrasonic wave suspension, an air flow pipeline, a high-pressure nitrogen tank, a heat exchanger and a room temperature air pipeline, a signal output end of the CCD camera is connected with a signal input end of the control terminal, the laser emitter is arranged on one side of the ultrasonic wave suspension and is used for emitting laser to the ultrasonic wave suspension, the CCD camera is arranged on one side of the ultrasonic wave suspension and is used for obtaining ice crystal melting images and feeding the ice crystal melting images to the control terminal, one end of the air flow pipeline is connected with the ultrasonic wave suspension, the other end of the air flow pipeline is connected with the heat exchanger, the high-pressure nitrogen tank is connected with the heat exchanger through a nitrogen pipeline, a pressure reducing valve is arranged on the nitrogen pipeline, a gas flowmeter is arranged on the air flow pipeline, the room temperature air pipeline is connected with the air flow pipeline, and a ball valve is arranged on the room temperature air pipeline.
5. The method for determining the association of ice crystal particle convective heat transfer experiments according to claim 4, wherein the nitrogen pipeline is connected with the gas flow pipeline through a temperature control pipeline, and a needle valve is arranged on the temperature control pipeline.
6. The method of claim 5, wherein obtaining the experimental melting time by using the ice crystal melting measurement device comprises:
A pipette is used for transferring a set volume of rhodamine B solution to a standing point position generated by the ultrasonic suspension;
Opening a valve of a pressure reducing valve, cooling normal-temperature nitrogen into low-temperature nitrogen through a heat exchanger, and enabling the low-temperature nitrogen of an outlet pipeline to exchange heat with liquid drops, wherein the liquid drops are gradually frozen;
After the liquid drops are frozen to reach a stable state, a laser emitter is started, room temperature air is introduced, particles are melted uniformly, and the melting rate is calculated through experimental pictures shot by a CCD camera, so that the melting time of ice crystal particles in an experiment is obtained.
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