CN117408053A - Method for establishing low-temperature flat plate drying mode frosting characteristic curve under strong convection condition - Google Patents
Method for establishing low-temperature flat plate drying mode frosting characteristic curve under strong convection condition Download PDFInfo
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Abstract
The invention discloses a method for establishing a low-temperature flat plate dry mode frosting characteristic curve under a strong convection condition, which relates to the field of low-temperature flat plate dry mode frosting prediction and comprises the following steps: simulating low-temperature flat plate dry mode frosting, and constructing a mass conservation equation corresponding to the frosting layer; obtaining a characteristic value related to low-temperature flat plate dry mode frosting, and processing a mass conservation equation based on the characteristic value to obtain a dimensionless mass conservation equation; if the density and the heat conductivity of the frost layer are unchanged in the frosting process, in a narrower temperature interval, the convection heat is far greater than the latent heat release of frosting phase change, and when the incoming flow temperature is far greater than the difference between the dew point temperature and the cold surface temperature, a second expression between the thickness of the frost layer and the frosting time is obtained; the invention can establish the low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition based on the second expression.
Description
Technical Field
The invention relates to the field of low-temperature flat plate dry mode frosting prediction, in particular to a method for establishing a low-temperature flat plate dry mode frosting characteristic curve under a strong convection condition.
Background
The novel low-temperature heat exchanger can rapidly cool high-temperature gas flowing at high speed to deep low temperature. When the gas is cooled to a sub-zero temperature, the saturation humidity of the air will be greatly reduced, whereby the water vapour in the air will be caused to sublimate into frost at the low temperature surface of the heat exchange unit. The low-temperature surface frosting action of high-speed airflow flowing through the heat exchange unit belongs to the low-temperature surface frosting problem under the strong convection condition, and is the gas-solid phase transition action of water vapor desublimation. The gas-solid phase transition behavior of the vapor directly sublimating into frost is called dry mode frosting, and liquid water cannot appear in the dry mode frosting process. Because the dry mode frosting on the low-temperature surface can cause blockage of a heat exchanger channel, the control of the dry mode frosting thickness growth condition under frosting conditions such as different incoming flow speeds, incoming flow temperatures, low-temperature surface temperatures, low-temperature element sizes and the like is important to design the heat exchange unit size and the distance of the heat exchanger and determine the cooling strategy of the heat exchanger. For this reason, it is necessary to predict the dry mode frosting behavior of low temperature surfaces under different frosting conditions.
Under the dry mode frosting condition of certain inflow temperature, inflow speed, low-temperature flat plate temperature and low-temperature flat plate length, a numerical calculation prediction method for the change of the frost layer thickness on the low-temperature flat plate with time exists at present. According to the method, an energy equation and a quality equation are constructed according to dimensionalized incoming flow temperature, incoming flow speed, low-temperature flat plate temperature, low-temperature flat plate length and other parameters, and time iterative solution is carried out. However, this numerical calculation prediction method requires iterative solution, which is inconvenient in practical use. In addition, independent calculation is required to be carried out on frosting condition combinations such as different inflow temperatures, inflow speeds, low-temperature flat plate temperatures, low-temperature flat plate lengths and the like, the frosting layer thickness growth curves obtained under different conditions are different, and a low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition cannot be established.
In summary, the technical scheme of establishing the low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition is not found in the prior art, and the low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition is ignored in the prior art.
Disclosure of Invention
The invention aims to establish a low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition.
In order to achieve the above purpose, the invention provides a method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under a strong convection condition, which comprises the following steps:
simulating low-temperature flat plate dry mode frosting, and constructing a mass conservation equation corresponding to the frosting according to the relationship between the mass change rate of the frosting and the phase change rate of the water vapor;
obtaining a characteristic value related to low temperature flat plate dry mode frosting, comprising: dimensionless temperature, dimensionless frost layer thickness, dimensionless frost time, dimensionless humidity, and dimensionless frost layer density;
processing the mass conservation equation based on the dimensionless temperature, the dimensionless frost layer thickness, the dimensionless frost formation time, the dimensionless humidity and the dimensionless frost layer density to obtain a dimensionless mass conservation equation;
if the density and the heat conductivity of the frost layer are unchanged in the frosting process, simplifying a dimensionless mass conservation equation to obtain a first dimensionless mass conservation equation;
when the ratio of the heat exchange amount of convection to the latent heat release amount of frosting phase change is larger than a first threshold value and the ratio of the incoming flow temperature to the first temperature difference is larger than a second threshold value in a preset temperature interval, simplifying the first dimensionless mass conservation equation to obtain a first expression between the dimensionless frost layer thickness and the dimensionless frosting time, wherein the preset temperature interval is that the temperature difference between the maximum temperature value and the minimum temperature value of the temperature interval is smaller than the preset temperature value, and the first temperature difference is the difference between the dew point temperature and the cold surface temperature;
reducing the first expression to obtain a second expression between the frost layer thickness and the frosting time;
and drawing a low-temperature flat plate drying mode frosting characteristic curve under the strong convection condition based on the second expression.
Firstly simulating low-temperature flat plate dry mode frosting, constructing a mass conservation equation corresponding to a frost layer according to the relation between the mass change rate of the frost layer and the phase change rate of water vapor, then obtaining characteristic values related to the low-temperature flat plate dry mode frosting, and processing the mass conservation equation based on the characteristic values to obtain a dimensionless mass conservation equation; the applicant finds that if the density and the thermal conductivity of the frost layer are unchanged in the frosting process, the dimensionless mass conservation equation can be simplified to obtain a first dimensionless mass conservation equation; the applicant has found that when the convection heat transfer is far greater than the latent heat release of frosting phase change in a narrow temperature interval (i.e. in a preset temperature interval), and when the incoming flow temperature is far greater than the difference between the dew point temperature and the cold face temperature, the first expression between the thickness of the non-dimensional frost layer and the non-dimensional frosting time can be further obtained by simplifying the first non-dimensional mass conservation equation; then carrying out reduction treatment on the first expression to obtain a second expression between the frost layer thickness and the frosting time; and in the second expression, the dimensionless frosting time and the dimensionless frosting layer thickness are in one-to-one correspondence, so that a low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition can be drawn based on the second expression.
The low-temperature flat plate dry mode frosting characteristic curve drawn by the method can be used for predicting low-temperature flat plate dry mode frosting under the strong convection condition, for example, the low-temperature flat plate dry mode frosting characteristic curve drawn by the method is stored, when the low-temperature flat plate dry mode frosting prediction under the strong convection condition is carried out, the corresponding frosting thickness can be obtained by inputting corresponding time, iterative calculation is not needed, the calculated amount is small, and the quick prediction can be realized.
In some embodiments, the first expression is obtained by:
when the air saturation humidity is linearly simplified in a preset temperature interval, a first linear function of the simplified air saturation humidity with respect to temperature is obtained;
bringing the expression of the dimensionless frost surface saturated humidity into the first linear function to obtain a second function;
when the convection heat exchange quantity is far larger than the latent heat release quantity of frosting phase change, the second function is arranged to obtain a first relational expression of the non-dimensional frosting surface saturated humidity with respect to the thickness of the non-dimensional frosting layer;
when the incoming flow temperature is far greater than the difference between the dew point temperature and the cold surface temperature, the first relation is arranged to obtain a second relation which is equal to the thickness of the dimensionless frost layer on the dimensionless frost surface saturated humidity value;
substituting the second relation into the first dimensionless mass conservation equation to obtain a first expression of the thickness of the dimensionless frost layer with respect to the dimensionless frost formation time.
In some embodiments, the first linear function is:
ρ sa (T)＝ρ sa (T w )+α(T-T w )
wherein T is the temperature ρ sa (T) the saturation humidity of air at the temperature T ρ sa (T w ) At a temperature T w Air saturation humidity at the time T w Alpha is the slope coefficient of the first linear function for the low temperature plate temperature;
the second function is:
wherein omega sa (θ s ) Is non-dimensional saturated humidity corresponding to non-dimensional temperature of the surface of the frost layer, theta s Is the dimensionless temperature of the frost surface, ρ sa (θ w ) Is the temperature theta w Air saturation humidity at the time T d For incoming flow dew point temperature, T s For the frost surface temperature ρ v For incoming air humidity ρ s The air saturation humidity corresponding to the surface temperature of the frost layer;
the first relation is:
wherein delta is the thickness of the dimensionless frost layer, T a Is the incoming flow temperature;
the second relation is:
ω sa (θ s )＝δ
the first expression is:
δ＝1-e -τ
wherein τ is the dimensionless frosting time.
In some embodiments, the second expression is:
wherein X is f For the thickness of the frost layer, delta b For the equilibrium thickness of the frost layer, η is the characteristic time of frosting and t is the time of frosting.
In some embodiments, the first dimensionless mass conservation equation is:
wherein delta is the thickness of the dimensionless frost layer, tau is the dimensionless frost forming time, theta s Is the dimensionless temperature of the surface of the frost layerDegree, omega sa (θ s ) And the non-dimensional saturated humidity corresponding to the non-dimensional temperature of the surface of the frost layer is represented.
In some embodiments, the mass conservation equation is obtained in the following manner:
obtaining a heat transfer control equation in the frost layer based on the fact that the interior of the frost layer meets quasi-steady-state heat conduction in each moment in the frosting process;
based on a heat transfer control equation in the frost layer, constructing a mass conservation equation corresponding to the frost layer according to the relationship between the mass change rate of the frost layer and the phase change rate of the water vapor.
In some embodiments, the heat transfer control equation is:
wherein x is the height of the interior of the frost layer, k f The thermal conductivity of the frost layer at x, T is the temperature at x of the frost layer;
the energy conservation equation is:
wherein,to conduct heat inside the frost layer, h (T a -T s ) To heat exchange by convection, h m (ρ v -ρ sa (T s ) Gamma is the latent heat released when the vapor condenses into frost, X f X is the thickness of the frost layer f The thickness of the frost layer is h is the convection heat transfer coefficient, T a For incoming flow temperature, T s The temperature of the frosting surface is h m Is the convection mass transfer coefficient of water vapor, ρ v For incoming water vapor density, gamma is the latent heat of desublimation of water vapor, ρ sa (T s ) The saturated humidity corresponding to the frost temperature;
the mass conservation equation is:
wherein,h is the mass change rate of the frost layer m (ρ v -ρ sa (T s ) Is the phase change rate of the water vapor, t is the frosting time, ρ f The density of the frost layer at the frost surface at time t.
In some embodiments, the dimensionless temperature is calculated using the following formula:
wherein θ is the dimensionless temperature, T is the temperature at the frost layer x, T w Is the low temperature plate temperature, T d For the incoming flow dew point temperature.
The thickness of the dimensionless frost layer is calculated by the following formula:
wherein delta b Is the thickness of the non-dimensional frost layer,balance heat conductivity for frost layer, h is convection heat exchange coefficient, θ a Dimensionless temperature for incoming air;
the dimensionless frosting time is calculated by the following formula:
wherein eta is dimensionless frosting time and delta b For the equilibrium thickness of the frost layer, ζ is the characteristic growth rate of the frost layer;
the dimensionless humidity is calculated by the following formula:
wherein ω is dimensionless humidity, ρ is water vapor density, ρ sa (θ w ) Saturated steam density ρ corresponding to dimensionless cold surface temperature v To the incoming water vapor density;
the dimensionless frost layer density is calculated using the following formula:
wherein,is the non-dimensional frost layer density ρ f For the frost density at x ρ f0 Is the frost layer density at the initial moment of frosting.
In some embodiments, the low temperature flat plate dry mode frost characteristic curve has an abscissa of dimensionless frost time and an ordinate of dimensionless frost layer thickness.
In some embodiments, the method further comprises: and storing or outputting or displaying the low-temperature flat plate dry mode frosting characteristic curve in a display unit.
The low-temperature flat plate dry mode frosting characteristic curve is stored after being obtained so as to be convenient for subsequent frosting prediction, and can be displayed in a display unit or sent to other terminals for prediction or display so as to be convenient for visual observation.
The one or more technical schemes provided by the invention have at least the following technical effects or advantages:
the invention can establish the frosting characteristic curve of the low-temperature flat plate drying mode under the strong convection condition, and overcomes the technical blank in the field.
The invention can be used for predicting the frosting behavior of the low-temperature flat plate under the strong convection condition very conveniently and rapidly through the established frosting characteristic curve by the established frosting characteristic curve under the strong convection condition.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1 is a flow chart of a method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under a strong convection condition;
FIG. 2 is a graph showing the frosting characteristic curves of the low-temperature flat plate drying mode under the strong convection condition.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description. In addition, the embodiments of the present invention and the features in the embodiments may be combined with each other without collision.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than within the scope of the description, and the scope of the invention is therefore not limited to the specific embodiments disclosed below.
Example 1
Referring to fig. 1, fig. 1 is a flow chart of a method for establishing a frosting characteristic curve of a low-temperature flat plate under a strong convection condition, and the method provided by the invention comprises the following steps:
simulating low-temperature flat plate dry mode frosting, and constructing a mass conservation equation corresponding to the frosting according to the relationship between the mass change rate of the frosting and the phase change rate of the water vapor;
obtaining a characteristic value related to low temperature flat plate dry mode frosting, comprising: dimensionless temperature, dimensionless frost layer thickness, dimensionless frost time, dimensionless humidity, and dimensionless frost layer density;
processing the mass conservation equation based on the dimensionless temperature, the dimensionless frost layer thickness, the dimensionless frost formation time, the dimensionless humidity and the dimensionless frost layer density to obtain a dimensionless mass conservation equation;
if the density and the heat conductivity of the frost layer are unchanged in the frosting process, simplifying a dimensionless mass conservation equation to obtain a first dimensionless mass conservation equation;
when the ratio of the heat exchange amount of convection to the latent heat release amount of frosting phase change is larger than a first threshold value and the ratio of the incoming flow temperature to the first temperature difference is larger than a second threshold value in a preset temperature interval, simplifying the first dimensionless mass conservation equation to obtain a first expression between the dimensionless frost layer thickness and the dimensionless frosting time, wherein the preset temperature interval is that the temperature difference between the maximum temperature value and the minimum temperature value of the temperature interval is smaller than the preset temperature value, and the first temperature difference is the difference between the dew point temperature and the cold surface temperature;
reducing the first expression to obtain a second expression between the frost layer thickness and the frosting time;
and drawing a low-temperature flat plate drying mode frosting characteristic curve under the strong convection condition based on the second expression, as shown in figure 2.
The embodiment performs linear approximation of temperature on air saturation humidity in a narrower temperature range based on a dimensionless mass conservation equation of plate dry mode frosting under strong convection condition under normal physical property condition, and ignores phase change latent heat of frosting with respect to small amount, thereby obtaining a dimensionless frost layer thickness relational expression only related to dimensionless frost time, namely a dimensionless frost characteristic curve of low-temperature plate dry mode frosting under strong convection condition.
The preset temperature interval is a narrower temperature interval, for example, in a temperature interval in which the difference between the highest temperature and the lowest temperature is less than 10K, the first threshold is usually 10, for example, the convection heat exchange amount is more than one order of magnitude of latent heat release of frosting phase change, the second threshold is usually 10, for example, the incoming flow temperature is more than one order of magnitude of difference between the dew point temperature and the cold surface temperature, and the incoming flow temperature is more than one order of magnitude of 10 (for example, the incoming flow temperature is 300K, and the difference between the dew point temperature and the cold surface temperature is 30K).
The strong convection condition is that the incoming flow speed is larger than 10m/s, and the frosting phenomenon is obviously different from the natural convection and low-speed (generally smaller than 6 m/s) convection incoming flow condition, and the flow above 10m/s is called the strong convection condition for distinguishing the natural convection and the low-speed convection.
The idea of the invention is as follows: one-dimensional simulation method for plate dry mode frosting based on strong convection condition (engineering thermophysics report-2022-01-01 year, 43 volumes, 001 phase-rapid incoming flow condition low-temperature plate normal-physical frosting layer one-dimensional dry mode frosting simulation research), selecting equilibrium thickness delta of frosting layer b And normalizing parameters such as the initial frost layer growth rate xi, the frost formation characteristic time eta and the like to obtain a dimensionless frost layer thickness and dimensionless frost formation time, and carrying out dimensionless treatment on an energy conservation equation and a mass conservation equation.
The invention discloses a method for obtaining similar factors of low-temperature plate dry mode frosting under the strong convection condition, which is obtained based on a one-dimensional simulation method of plate dry mode frosting under the strong convection condition, and comprises the following steps:
one-dimensional simulation of plate dry mode frosting is based on two-point assumptions and simplifications: 1) The formed frost layer is compact, mass transfer inside the frost layer can be ignored, and once the frost layer is formed, the density and the heat conductivity of the frost layer are not changed any more; 2) Because the thickness of the frost layer changes slowly, the interior of the frost layer can be considered to meet the quasi-steady state heat conduction at each moment. Based on quasi-steady state heat conduction assumption, the heat transfer control equation in the frost layer is as follows
Wherein x is the height of the interior of the frost layer, k f For the frost thermal conductivity at x, T is the temperature at x of the frost.
The energy conservation equation is constructed according to the heat transfer equilibrium relationship at the frost surface as follows:
the left side of the equation of the formula 2 is the heat conduction quantity in the frost layer, the first term on the right side of the equation is the convection heat conduction quantity, and the second term on the right side of the equation is the latent heat released when the water vapor condenses to form frost. Wherein X is f Is the thickness of the frost layer, h is the convection heat transfer coefficient, T a To the incoming flow temperature T s Is the frost temperature, h m Is the convection mass transfer coefficient ρ of water vapor v For incoming water vapor density (i.e., incoming humidity), γ is the latent heat of sublimation of water vapor ρ sa Is saturated humidity (ρ) sa (T s ) Saturated humidity corresponding to frost temperature).
Constructing a mass conservation equation according to the relation between the mass change rate of the frost layer and the phase change rate of the water vapor:
wherein the left side of equation 3 is the mass change rate of the frost layer, the right side of equation is the phase change rate of the water vapor, wherein t is the frosting time, ρ f The density of the newly generated frost layer at the frost surface at the moment t.
By giving the incoming flow temperature T at time t=0 a Temperature T of frosting face s (time t=0 equals the low temperature plate temperature T w ) Incoming water vapor density ρ v And (3) solving the formula (2) and the formula (3) by numerical iteration to obtain the thickness change condition of the frosted layer of the low-temperature flat plate drying mode frosting related to frosting time.
Selecting a characteristic value for dimensionless treatment, carrying out dimensionless treatment on an energy conservation equation and a mass conservation equation to obtain the dimensionless energy conservation equation and the dimensionless mass conservation equation, wherein the method comprises the following steps of:
using the outflow dew point temperature T d (incoming water vapor density ρ) v Corresponding dew point temperature) and a low temperature plate temperature T w The dimensionless temperature is defined as:
incoming flow dew point temperature T d Surface temperature T of frost layer s And low temperature plate temperature T w The corresponding dimensionless temperature values (ranges) are:
θ d ＝1，0≤θ s ≤1，θ w ＝0 (5)
wherein θ d For incoming flow dew point temperature T d Non-dimensional temperature value, θ s Is the frost layer surface temperature T s Corresponding dimensionless temperature value, theta w At a low temperature plate temperature T w Corresponding dimensionless temperature values;
when the frosting reaches equilibrium, the thickness of the frosting layer is not changed any more, and in the energy conservation equation (2), the thickness of the frosting layer is equal to the equilibrium thickness, and the temperature T of the frosting surface s Equal to the incoming flow dew point temperature T d And the water vapor phase change release latent heat term (second right term) is 0, then the energy conservation equation (2) can be written as:
wherein,the average heat conductivity when the frost layer reaches the equilibrium thickness is called as the equilibrium heat conductivity of the frost layer for short.
Substituting dimensionless temperature into the formula (6) and finishing, and writing into the equilibrium thickness delta of the frost layer b The expression of (2) is as follows:
balancing the frost layer to a thickness delta b As a characteristic thickness of frosting for frosting thickness dimensionless, the normalized dimensionless frosting thickness can be written as:
the initial frost growth rate at time 0 was defined as the characteristic frost growth rate, denoted ζ:
wherein ρ is f0 For the frost layer density at the initial moment of frosting, the frost layer density is simply called initial frost layer density, and the frost layer density is obtained by the temperature T of a low-temperature flat plate w And (5) determining.
Balancing the frost layer to a thickness delta b The characteristic growth rate ζ of the frost layer is divided by the characteristic time of frost formation, denoted as η:
the humidity was treated as follows to obtain dimensionless humidity:
the frost density was treated as follows to obtain a dimensionless frost density:
the thermal conductivity of the frost layer is processed in the following way to obtain the non-dimensional thermal conductivity of the frost layer:
wherein k is f0 The thermal conductivity of the frost layer at the initial moment of frosting is simply called initial frost layer thermal conductivity.
The non-dimensional mass conservation equation can be obtained by substituting the non-dimensional temperature in the formula (4), the non-dimensional frost layer thickness in the formula (8), the non-dimensional frost formation time in the formula (10), the non-dimensional humidity in the formula (11) and the non-dimensional frost layer density in the formula (12) into the mass conservation equation in the formula (3):
substituting the dimensionless temperature in the formula (4), the dimensionless frost layer thickness in the formula (8), the dimensionless humidity in the formula (11) and the dimensionless frost layer thermal conductivity in the formula (13) into an energy conservation equation (2) to obtain a dimensionless energy conservation equation:
gamma is the latent heat of sublimation of water vapor, ρ v Substituting the equilibrium thickness of the frost layer of formula (7) into formula (15) for the incoming water vapor density, omitting the Le number equal to 1, and arranging the energy conservation equation into the dimensionless frost surface temperature theta s The expression form of (a) is as follows:
when the incoming flow dew point temperature T d And low temperature plate temperature T w The physical properties (the density and the heat conductivity of the frost layer) of the frost layer in the frosting process are not greatly different, and the frost layer can be similar to the normal physical properties at the moment, namely, the density and the heat conductivity of the frost layer are not changed in the whole frosting process. The thermal conductivity of the frost layer is constant, the thermal conductivity of the dimensionless frost layer is 1, and the frost layer has equilibrium thickness delta for the thermal conductivity of the frost layer under given frosting conditions b Also a determined value, and can be found by the following equation:
substituting equation (18) into equation (16), the dimensionless energy conservation equation can be further simplified to the form:
the dimensionless mass conservation equation and the dimensionless energy conservation equation can be obtained through the mode.
The method specifically comprises the following steps:
step 1: the invention discloses a method for establishing a low-temperature flat plate dry mode frosting characteristic curve under a strong convection condition, which is developed based on a flat plate dry mode frosting dimensionless mass conservation equation under a strong convection condition under a normal physical frost layer approximation condition. The non-dimensional mass conservation equation of the plate dry mode frosting under the strong convection condition of the normal frost layer is as follows:
wherein delta is the thickness of the dimensionless frost layer, tau is the dimensionless frost time, omega is the dimensionless humidity of the incoming air, and theta s Is the dimensionless temperature of the frost surface, omega sa (θ s ) And the non-dimensional saturated humidity corresponding to the non-dimensional temperature of the surface of the frost layer is represented.
In the non-dimensional mass conservation equation of the formula (1), the left side of the equation is the growth rate of the non-dimensional frost layer, the equation is the non-dimensional humidity difference (non-dimensional excess humidity), and the physical meaning is that the driving force of the growth rate of the non-dimensional frost layer is the non-dimensional humidity difference.
Step 2: in the case of a true physical meaning, a three-term approximate simplification is performed.
Step 2.1: the air saturation humidity is a polynomial nonlinear relation with respect to temperature, and no more beneficial information can be obtained by equation (1). But within a narrower temperature interval (i.e., when within a preset temperature interval), the change in air saturation humidity with respect to temperature may be approximately linear. Thus, the air saturation humidity is linearly simplified, and the linear function of the simplified air saturation humidity with respect to temperature is as follows:
ρ sa (T)＝ρ sa (T w )+α(T-T w ) (2)
wherein T is temperature, ρ sa (T) the saturation humidity of air at the temperature T, T w Is the slope coefficient of the linear function of the temperature of the low-temperature flat plate and alpha.
Step 2.2: according to the definition of the non-dimensional frost surface saturation humidity, and substituting the definition into the linear relation of the formula (2), the non-dimensional frost surface saturation humidity can be written as the ratio of two temperature differences, and the formula is as follows:
wherein T is d For incoming flow dew point temperature, T s Is the surface temperature ρ of the frost layer v For incoming air humidity ρ s The air saturation humidity corresponding to the surface temperature of the frost layer.
Step 2.3: for the temperature difference value on the right term denominator in the formula (3), it can be obtained by the energy conservation equation at the time of frost balance as shown in the following formula:
wherein k is f Is the thermal conductivity of the frost layer, h is the convective heat transfer coefficient and T a For incoming flow temperature, delta b The thickness was balanced for the frost layer.
Step 2.4: when the amount of convective heat transfer is much greater than the latent heat release from the frosting phase change, then the latent heat portion of the heat transfer can be ignored. Therefore, for the temperature difference value on the right term molecule of formula (3), it can be obtained by the energy conservation equation during frosting, which ignores latent heat:
wherein X is f Is the thickness of the frost layer.
Step 2.5: after finishing the formula (4) and the formula (5), substituting the formula (3), and obtaining a relational expression of the non-dimensional frost surface saturation humidity relative to the thickness of the non-dimensional frost layer:
step 2.6: since the frost temperature is between the cold temperature and the dew point temperature (T w ≤T s ≤T d ) When the incoming flow temperature is far greater than the difference between the dew point temperature and the cold face temperature, namely:
T a ＞＞(T d -T w ) (7)
when the temperature difference ratio of formula (6) may be approximately equal to 1, namely:
(T a -T s )/(T a -T d )＝1 (8)
step 2.8: substituting the formula (8) into the formula (6) to obtain a relational expression that the saturated humidity value of the dimensionless frost surface is equal to the thickness of the dimensionless frost layer:
ω sa (θ s )＝δ (9)
step 3: substituting formula (9) into the dimensionless mass conservation equation of formula (1), namely replacing the dimensionless frost surface saturation humidity in the dimensionless mass conservation equation with the dimensionless frost layer thickness, the following relationship can be obtained:
step 4: after the integral solution is carried out on the formula (10), an analytical expression of the thickness of the non-dimensional frost layer relative to the non-dimensional frost forming time is obtained:
δ＝1-e -τ (11)
therefore, the non-dimensional frost layer thickness can be directly resolved by the resolution formula (11) without iteratively solving given initial conditions.
In the formula (11), only two variable parameters of the dependent variable non-dimensional frosting time tau and the dependent variable non-dimensional frost layer thickness delta are provided, and the relation between the non-dimensional frosting time and the non-dimensional frost layer thickness is fixed. The curve of the non-dimensional frosting time with respect to the thickness of the non-dimensional frosting layer is unique, and therefore, the curve is called a non-dimensional frosting characteristic curve, which is abbreviated as frosting characteristic curve.
Step 5: expanding the thickness of the dimensionless frost layer and the dimensionless frost formation time in the formula (11), and reducing to an expression of the thickness of the frost layer relative to the frost formation time:
wherein delta b The frost characteristic time is calculated by the equilibrium thickness delta of the frost layer b Divided by the initial frost growth rate ζ.
Under the frosting condition meeting the physical meaning represented by approximate simplification, the frost layer thickness X at the time t can be directly calculated by the formula (12) f Without the need for iterative computations. The frosting characteristic time is endowed with the meaning of a time constant, and the frosting characteristic time characterizes the frosting speed. The characteristic time and the characteristic thickness respectively represent the frosting speed and the maximum thickness of the frosting layer, and are the most important and most visual two quantities in dynamic frosting.
The invention elaborates a method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition, and compared with the prior art, the frosting characteristic curve established by the method has the following beneficial effects:
(1) By the approximate simplification with physical significance provided in the method, an analytical expression of the dimensionless frosting time and the dimensionless frosting layer thickness is established. The curve corresponding to the analytical expression has uniqueness and is called a frosting characteristic curve.
(2) Under the frosting condition meeting the physical meaning represented by approximate simplification, the frosting thickness (or dimensionless frosting thickness) corresponding to a certain frosting time (or dimensionless frosting time) can be directly calculated through the frosting characteristic curve, iterative calculation is not needed, and a theoretical basis is provided for rapidly and conveniently predicting the frosting thickness.
Example two
The second embodiment of the invention also provides a method for predicting the frosting thickness of the low-temperature flat plate under the strong convection condition, which specifically comprises the following steps:
firstly, establishing a low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition by the method in the first embodiment;
then storing the frosting characteristic curve of the low-temperature flat plate drying mode under the strong convection condition;
obtaining dimensionless frosting time corresponding to the thickness to be predicted of the low-temperature flat plate dry mode frosting, and inputting the dimensionless frosting time into a low-temperature flat plate dry mode frosting characteristic curve to obtain the corresponding dimensionless frosting layer thickness;
outputting the predicted thickness of the low-temperature flat plate dry mode frosting.
The prediction method does not need iterative computation, and has high prediction efficiency and small calculated amount.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the present invention without departing from the spirit or scope of the invention. Thus, it is intended that the present invention also include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
Claims (10)
1. The method for establishing the frosting characteristic curve of the low-temperature flat plate drying mode under the strong convection condition is characterized by comprising the following steps:
simulating low-temperature flat plate dry mode frosting, and constructing a mass conservation equation corresponding to the frosting according to the relationship between the mass change rate of the frosting and the phase change rate of the water vapor;
obtaining a characteristic value related to low temperature flat plate dry mode frosting, comprising: dimensionless temperature, dimensionless frost layer thickness, dimensionless frost time, dimensionless humidity, and dimensionless frost layer density;
processing the mass conservation equation based on the dimensionless temperature, the dimensionless frost layer thickness, the dimensionless frost formation time, the dimensionless humidity and the dimensionless frost layer density to obtain a dimensionless mass conservation equation;
if the density and the heat conductivity of the frost layer are unchanged in the frosting process, simplifying a dimensionless mass conservation equation to obtain a first dimensionless mass conservation equation;
when the ratio of the heat exchange amount of convection to the latent heat release amount of frosting phase change is larger than a first threshold value and the ratio of the incoming flow temperature to the first temperature difference is larger than a second threshold value in a preset temperature interval, simplifying the first dimensionless mass conservation equation to obtain a first expression between the dimensionless frost layer thickness and the dimensionless frosting time, wherein the preset temperature interval is that the temperature difference between the maximum temperature value and the minimum temperature value of the temperature interval is smaller than the preset temperature value, and the first temperature difference is the difference between the dew point temperature and the cold surface temperature;
reducing the first expression to obtain a second expression between the frost layer thickness and the frosting time;
and drawing a low-temperature flat plate drying mode frosting characteristic curve under the strong convection condition based on the second expression.
2. The method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition according to claim 1, wherein the first expression is obtained in the following manner:
when the air saturation humidity is linearly simplified in a preset temperature interval, a first linear function of the simplified air saturation humidity with respect to temperature is obtained;
bringing the expression of the dimensionless frost surface saturated humidity into the first linear function to obtain a second function;
when the ratio of the convection heat exchange amount to the latent heat release amount of frosting phase change is larger than a first threshold value, the second function is arranged to obtain a first relational expression of the non-dimensional frosting surface saturation humidity with respect to the thickness of the non-dimensional frosting layer;
when the ratio of the incoming flow temperature to the first temperature difference is larger than a second threshold value, the first relation is sorted, and a second relation with the non-dimensional frost layer thickness equal to the non-dimensional frost layer saturation humidity in value is obtained;
substituting the second relation into the first dimensionless mass conservation equation to obtain a first expression of the thickness of the dimensionless frost layer with respect to the dimensionless frost formation time.
3. The method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition according to claim 1, wherein the first linear function is as follows:
ρ sa (T)＝ρ sa (T w )+α(T-T w )
wherein T is the temperature ρ sa (T) the saturation humidity of air at the temperature T ρ sa (T w ) At a temperature T w Air saturation humidity at the time T w Alpha is the slope coefficient of the first linear function for the low temperature plate temperature;
the second function is:
wherein omega sa (θ s ) Is non-dimensional saturated humidity corresponding to non-dimensional temperature of the surface of the frost layer, theta s Is the dimensionless temperature of the frost surface, ρ sa (θ w ) Is the temperature theta w Air saturation humidity at the time T d For incoming flow dew point temperature, T s For the frost surface temperature ρ v For incoming air humidity ρ s The air saturation humidity corresponding to the surface temperature of the frost layer;
the first relation is:
wherein delta is the thickness of the dimensionless frost layer, T a Is the incoming flow temperature;
the second relation is:
ω sa (θ s )＝δ
the first expression is:
δ＝1-e -τ
wherein τ is the dimensionless frosting time.
4. The method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition according to claim 1, wherein the second expression is:
wherein X is f For the thickness of the frost layer, delta b For the equilibrium thickness of the frost layer, η is the characteristic time of frosting and t is the time of frosting.
5. The method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition according to claim 1, wherein the first dimensionless mass conservation equation is as follows:
wherein delta is the thickness of the dimensionless frost layer, tau is the dimensionless frost forming time, theta s Is the dimensionless temperature of the frost surface, omega sa (θ s ) And the non-dimensional saturated humidity corresponding to the non-dimensional temperature of the surface of the frost layer is represented.
6. The method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition according to claim 1, wherein a mass conservation equation is obtained by adopting the following modes:
obtaining a heat transfer control equation in the frost layer based on the fact that the interior of the frost layer meets quasi-steady-state heat conduction in each moment in the frosting process;
based on a heat transfer control equation in the frost layer, constructing a mass conservation equation corresponding to the frost layer according to the relationship between the mass change rate of the frost layer and the phase change rate of the water vapor.
7. The method for establishing the frosting characteristic curve of the low-temperature flat plate drying mode under the strong convection condition of claim 6, which is characterized in that:
the heat transfer control equation is:
wherein x is the height of the interior of the frost layer, k f The thermal conductivity of the frost layer at x, T is the temperature at x of the frost layer;
the energy conservation equation is:
wherein,to conduct heat inside the frost layer, h (T a -T s ) To heat exchange by convection, h m (ρ v -ρ sa (T s ) Gamma is the latent heat released when the vapor condenses into frost, X f X is the thickness of the frost layer f The thickness of the frost layer is h is the convection heat transfer coefficient, T a For incoming flow temperature, T s The temperature of the frosting surface is h m Is the convection mass transfer coefficient of water vapor, ρ v For incoming water vapor density, gamma is the latent heat of desublimation of water vapor, ρ sa (T s ) The saturated humidity corresponding to the frost temperature;
the mass conservation equation is:
wherein,h is the mass change rate of the frost layer m (ρ v -ρ sa (T s ) Is the phase change rate of the water vapor, t is the frosting time, ρ f The density of the frost layer at the frost surface at time t.
8. The method for establishing a frosting characteristic curve of a low-temperature flat plate under the strong convection condition according to claim 1, wherein the dimensionless temperature is calculated by adopting the following formula:
wherein θ is the dimensionless temperature, T is the temperature at the frost layer x, T w Is the low temperature plate temperature, T d For the incoming flow dew point temperature.
The thickness of the dimensionless frost layer is calculated by the following formula:
wherein delta b Is the thickness of the non-dimensional frost layer,balance heat conductivity for frost layer, h is convection heat exchange coefficient, θ a Dimensionless temperature for incoming air;
the dimensionless frosting time is calculated by the following formula:
wherein eta is dimensionless frosting time and delta b For the equilibrium thickness of the frost layer, ζ is the characteristic growth rate of the frost layer;
the dimensionless humidity is calculated by the following formula:
wherein ω is dimensionless humidity, ρ is water vapor density, ρ sa (θ w ) Saturated steam density ρ corresponding to dimensionless cold surface temperature v To the incoming water vapor density;
the dimensionless frost layer density is calculated using the following formula:
wherein,is the non-dimensional frost layer density ρ f For the frost density at x ρ f0 Is the frost layer density at the initial moment of frosting.
9. The method for establishing the low-temperature flat plate dry mode frosting characteristic curve under the strong convection condition according to claim 1, wherein the low-temperature flat plate dry mode frosting characteristic curve is characterized in that the abscissa of the low-temperature flat plate dry mode frosting characteristic curve is non-dimensional frosting time, and the ordinate of the low-temperature flat plate dry mode frosting characteristic curve is non-dimensional frosting layer thickness.
10. The method for establishing a frosting characteristic curve of a low-temperature flat plate drying mode under the strong convection condition according to claim 1, wherein the method further comprises: and storing or outputting or displaying the low-temperature flat plate dry mode frosting characteristic curve in a display unit.
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109209790A (en) * | 2018-10-09 | 2019-01-15 | 浙江运达风电股份有限公司 | A kind of wind electricity blade icing estimation method based on data modeling |
| CN112800700A (en) * | 2021-04-13 | 2021-05-14 | 中国空气动力研究与发展中心计算空气动力研究所 | Low-temperature surface dry mode frosting simulation method and device, electronic equipment and medium |
| CN113255239A (en) * | 2021-07-12 | 2021-08-13 | 南京信息工程大学 | Deep learning method for predicting icing thickness of ultrahigh voltage transmission line tower |
| US20210332796A1 (en) * | 2017-12-14 | 2021-10-28 | Beijing Goldwind Science & Creation Windpower Equipment Co., Ltd. | Method and apparatus for icing prediction, method and apparatus for generatng icing prediction model |
| CN113779904A (en) * | 2021-06-09 | 2021-12-10 | 中国空气动力研究与发展中心低速空气动力研究所 | Icing phase change calculation method based on coupling of continuous liquid film and discrete liquid film |
| CN114180072A (en) * | 2022-02-16 | 2022-03-15 | 中国空气动力研究与发展中心低速空气动力研究所 | Icing thickness detection method |
| CN114896906A (en) * | 2022-05-12 | 2022-08-12 | 中国空气动力研究与发展中心低速空气动力研究所 | Ice accretion simulation method considering heat conduction in ice layer and solid wall surface |
| CN115099048A (en) * | 2022-07-06 | 2022-09-23 | 四川大学 | Messinger model-based icing numerical simulation method, system, equipment and medium |
-
2023
- 2023-10-18 CN CN202311358570.3A patent/CN117408053A/en active Pending
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20210332796A1 (en) * | 2017-12-14 | 2021-10-28 | Beijing Goldwind Science & Creation Windpower Equipment Co., Ltd. | Method and apparatus for icing prediction, method and apparatus for generatng icing prediction model |
| CN109209790A (en) * | 2018-10-09 | 2019-01-15 | 浙江运达风电股份有限公司 | A kind of wind electricity blade icing estimation method based on data modeling |
| CN112800700A (en) * | 2021-04-13 | 2021-05-14 | 中国空气动力研究与发展中心计算空气动力研究所 | Low-temperature surface dry mode frosting simulation method and device, electronic equipment and medium |
| CN113779904A (en) * | 2021-06-09 | 2021-12-10 | 中国空气动力研究与发展中心低速空气动力研究所 | Icing phase change calculation method based on coupling of continuous liquid film and discrete liquid film |
| CN113255239A (en) * | 2021-07-12 | 2021-08-13 | 南京信息工程大学 | Deep learning method for predicting icing thickness of ultrahigh voltage transmission line tower |
| CN114180072A (en) * | 2022-02-16 | 2022-03-15 | 中国空气动力研究与发展中心低速空气动力研究所 | Icing thickness detection method |
| CN114896906A (en) * | 2022-05-12 | 2022-08-12 | 中国空气动力研究与发展中心低速空气动力研究所 | Ice accretion simulation method considering heat conduction in ice layer and solid wall surface |
| CN115099048A (en) * | 2022-07-06 | 2022-09-23 | 四川大学 | Messinger model-based icing numerical simulation method, system, equipment and medium |
Non-Patent Citations (3)
| Title |
|---|
| ZHIYUAN WANG; ZHIWEN TONG: "The performance test of heat exchanger under low-temperature frosting conditions", PROCEEDINGS OF THE 2013 INTERNATIONAL CONFERENCE ON ADVANCED MECHATRONIC SYSTEMS, 19 December 2013 (2013-12-19) * |
| 夏斌;梁新刚;徐向华;: "快速来流条件下低温平板结霜行为实验研究", 工程热物理学报, no. 08, 15 August 2020 (2020-08-15) * |
| 王丽红;王骥;温永刚;陈光奇;董亮;孙冬花;: "低温罩表面结霜过程数值模拟", 真空与低温, no. 04, 15 December 2010 (2010-12-15) * |
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