CN115034042A - Method for correcting convection heat transfer coefficient of variable-property transformer oil - Google Patents
Method for correcting convection heat transfer coefficient of variable-property transformer oil Download PDFInfo
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Abstract
The invention provides a method for correcting the convective heat transfer coefficient of variable-property transformer oil, which corrects the existing convective heat transfer coefficient calculation formula by considering the characteristic that the dynamic viscosity of the transformer oil is changed along with the temperature violently. The specific implementation steps comprise: establishing a physical model of the variable-property transformer oil sweeping the solid surface in FLUENT; setting different temperature boundary conditions by adopting a parametric simulation method; calculating the temperature field distribution in the boundary layer by combining a finite element method and a finite volume method; calculating to obtain the convective heat transfer coefficient of the transformer oil with variable physical properties under different temperature working conditions by extracting the heat flow distribution on the solid surface along the way; and introducing the temperature variable into a calculation formula of the convective heat transfer coefficient by using a least square method to correct the temperature variable. The method has the advantages that the physical characteristics of the transformer oil are comprehensively considered, the calculation formula of the convection heat transfer coefficient is corrected by the influence factor of the coupling-in temperature, and the calculation accuracy of the temperature field of the oil-immersed transformer can be improved.
Description
Technical Field
The invention belongs to the technical field of calculation of a fluid temperature field of an oil-immersed transformer, and particularly relates to a method for correcting the convection heat transfer coefficient of variable-property transformer oil.
Background
The oil-immersed transformer is a key device of a power system, and the load capacity of the oil-immersed transformer is an important safety index and performance index. When the load capacity is limited or the overload is damaged, large-area electricity limitation or power failure of a power grid can be caused, and great economic loss is caused. The hottest point temperature of the transformer winding insulation system is the main determinant of the load capacity. When the hot spot temperature exceeds the long term average operating temperature of the insulation there will result insulation breakdown or loss of life. Therefore, the accurate acquisition of the temperature field distribution in the oil-immersed transformer has important significance for improving the safe operation level of the transformer and the power grid.
At present, the establishment of a thermal circuit model of an oil-immersed transformer is a rapid calculation method for solving the temperature field distribution, and the convective heat transfer coefficient between transformer oil and each solid component is an important parameter in the model. The traditional calculation formula of the convective heat transfer coefficient ignores the characteristic that the thermophysical parameters of the fluid change along with the temperature in the derivation process. However, the dynamic viscosity of transformer oil exhibits a strong dependence on temperature. On the other hand, when the heat exchange is carried out with the solid surface in a convection way, the temperature of the transformer oil in the boundary layer is limited by the temperature of the inlet oil and the temperature of the solid surface oil. The convection heat transfer coefficient of the transformer oil is calculated by directly applying a traditional formula, so that the heat transfer characteristic inside the oil-immersed transformer cannot be comprehensively described, and a large error is brought when the temperature field distribution is solved. Therefore, the convective heat transfer coefficient of the variable property transformer oil needs to be accurately obtained, so that the convective heat transfer coefficient is suitable for calculating the temperature field distribution inside the oil-immersed transformer under various operation conditions, and the online monitoring and the real-time analysis of the operation state of the transformer are realized.
Disclosure of Invention
Aiming at the defects or improvement requirements of the existing calculation method, the invention provides a method for correcting the convective heat transfer coefficient of the variable-property transformer oil, aiming at correcting the traditional convective heat transfer calculation formula by considering the severe influence of temperature on the thermal property parameters of the transformer oil and improving the accuracy of solving the internal temperature field distribution of the oil-immersed transformer.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for correcting convection heat transfer coefficient of variable-property transformer oil comprises the following steps:
step S1, establishing a two-dimensional physical model containing transformer oil and a solid surface, determining corresponding size parameters, setting material properties of each part, and subdividing the two-dimensional physical model by adopting a mesh with a triangle and a quadrangle matched with each other: dividing a main body area by adopting a quadrilateral mesh, and performing encryption division by adopting a triangular mesh in a boundary layer area, wherein the boundary layer area refers to a coupling interface of the transformer oil and the solid;
step S2, setting different temperature boundary conditions including the inlet temperature T of transformer oil by using a parametric simulation method 1 And temperature T of the solid surface 2 ，T 1 And T 2 Different values are combined to form various simulation analysis models;
step S3, based on the two-dimensional physical model of the transformer oil sweeping the solid surface, the finite element method and the finite volume method are combined to solve and calculate the temperature field distribution in the boundary layer area, and the speed and the temperature distribution characteristic of the transformer oil in the boundary layer are controlled by a mass conservation equation, a momentum conservation equation and an energy conservation equation:
where ρ is the density of the transformer oil, w is the velocity vector of the transformer oil, F is the external volumetric force, P is the pressure, u is the dynamic viscosity of the transformer oil, c is the specific heat capacity of the transformer oil, k is the thermal conductivity of the transformer oil, S h Is the calorific value per unit volume of the solid component;
step S4, after solving and calculating, obtaining the temperature field distribution of the transformer oil in the boundary layer and the heat flow distribution output by the solid surface along the moving direction of the transformer oil in the post-processing;
and step S5, introducing the temperature variable into a traditional convective heat transfer coefficient calculation formula by using a least square method to correct the temperature variable, and searching the optimal function matching between the convective heat transfer coefficient and the temperature variable by minimizing the error sum of squares.
Further, in step S1, for the transformer oil, the material properties at different temperatures are introduced by using a piecewise linear method.
Further, in the step S1, the material properties of each component include density, thermal conductivity, specific heat capacity and dynamic viscosity of the solid and the transformer oil.
Further, in step S3, when the temperature field distribution of the transformer oil in the boundary layer is solved, the radiation heat exchange process is omitted, and the convection heat exchange quantity output by the solid surface is separated.
Further, in step S4, the local convective heat transfer coefficient along the way is calculated according to the newton cooling formula:
q x ＝h x (T 2 -T 1 )
in the formula, q x Is a solid watchDistribution of heat flow output by the surface in the direction of movement of the transformer oil, h x Is the local convective heat transfer coefficient along the way.
Further, in step S5, the temperature variable includes an inlet temperature T of the transformer oil 1 And the temperature difference Δ T between the transformer oil and the solid surface ═ T 2 -T 1 The conventional convective heat transfer coefficient calculation formula is as follows:
where x is the displacement in the direction of the transformer oil movement and u ∞ Is the inlet velocity of the transformer oil, upsilon is the kinematic viscosity of the transformer oil, and a is the thermal conductivity of the transformer oil.
Further, in step S5, the convective heat transfer coefficient correction formula after introducing the temperature variable is as follows:
υ(T)＝(120-8.1T+0.28T 2 -0.006T 3 )×10 -6
wherein h is x ' is the corrected convective heat transfer coefficient.
Generally, compared with the prior art, the technical scheme of the invention can achieve the following beneficial effects:
(1) according to the method for correcting the convection coefficient of the variable-physical-property transformer oil, the hypothesis that the fluid thermal physical property parameters are unchanged in the convection heat exchange process is eliminated, the temperature variable is introduced into the traditional calculation formula of the convection heat exchange coefficient, the accuracy of solving the internal temperature field of the oil-immersed transformer can be improved, and the method is suitable for different structures and operation conditions;
(2) the parametric simulation analysis method is adopted, the speed of generating and modifying the model is greatly improved, theoretical formula derivation and numerical calculation results are combined through the least square method, and the parametric simulation analysis method has the advantages of high efficiency and high precision.
Drawings
FIG. 1 is a schematic flow chart of one embodiment of the method for correcting the convective heat transfer coefficient of the transformer oil with variable properties of the invention;
FIG. 2 is a two-dimensional physical model of convective heat transfer between transformer oil and a solid surface as embodied in embodiments of the present invention;
FIG. 3 is a graph of kinematic viscosity of transformer oil as a function of temperature, according to an embodiment of the present invention;
FIG. 4 is a graph of on-way convective heat transfer coefficient of transformer oil under different temperature boundary conditions according to an embodiment of the present invention;
FIG. 5 is a diagram of a model of a forced oil circulation transformer provided by an embodiment of the present invention;
fig. 6 is a temperature profile of a winding in an axial direction according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, an embodiment of the present invention provides a specific correction process for a convective heat transfer coefficient of variable-property transformer oil, which is used for coupling a temperature variable into a conventional convective heat transfer coefficient calculation formula, and includes the following specific implementation steps:
step S1, as shown in fig. 2, a two-dimensional physical model containing transformer oil and solid surface is established in FLUENT, corresponding dimensional parameters are determined, and material properties of each component are set.
Specifically, the dimension parameters comprise the length and width of the solid domain and the fluid domain, and are derived from the transformer design drawing; the material properties of each component include density, thermal conductivity, specific heat capacity and kinematic viscosity of the solids and transformer oil. For the transformer oil, the material properties at different temperatures are introduced by a piecewise linear method, and fig. 3 shows a curve of the dynamic viscosity of the transformer oil changing with the temperature.
Preferably, the two-dimensional physical model can be subdivided by adopting a mesh with the mutual matching of a triangle and a quadrangle, so that the calculation accuracy is ensured, and the overall calculation efficiency can be improved. Specifically, quadrilateral meshes are adopted for subdivision in the main body areas of the transformer oil and the solid, and triangular meshes are adopted for encryption subdivision in the coupling interface of the transformer oil and the solid.
Step S2, setting different temperature boundary conditions including the inlet temperature T of transformer oil by using a parametric simulation method 1 And temperature T of the solid surface 2 。
T 1 And T 2 Different value combinations among the simulation analysis models directly form various simulation analysis models, manual parameter adjustment is not needed, and the speed of generating and modifying the models is greatly improved.
And step S3, based on the two-dimensional physical model of the transformer oil swept on the solid surface, solving and calculating the temperature field distribution in the boundary layer region by combining a finite element method and a finite volume method.
Specifically, the speed and temperature distribution characteristics of the transformer oil in the boundary layer are controlled by a mass conservation equation, a momentum conservation equation and an energy conservation equation:
where ρ is the density of the transformer oil, w is the velocity vector of the transformer oil, F is the external volume force, P is the pressure, and u is the momentum of the transformer oilThe dynamic viscosity, c is the specific heat capacity of the transformer oil, k is the heat conductivity coefficient of the transformer oil, S h Is the heat generation per unit volume of the solid component.
Particularly, when the temperature field distribution of the transformer oil in the boundary layer is solved, the radiation heat exchange process is ignored, and the convection heat exchange quantity output by the solid surface is separated.
Step S4, after the solution calculation is finished, obtaining the temperature field distribution of the transformer oil in the boundary layer and the heat flow distribution output by the solid surface along the moving direction of the transformer oil in the post-treatment, and calculating according to a Newton cooling formula to obtain the local convective heat transfer coefficient along the way:
q x ＝h x (T 2 -T 1 )
in the formula, q x Is the heat flow distribution output from the solid surface along the moving direction of the transformer oil, h x Is the local convective heat transfer coefficient along the way.
Step S5, knowing the convective heat transfer coefficient of the variable property transformer oil under different temperature working conditions, and introducing the temperature variable into a traditional convective heat transfer coefficient calculation formula by using a least square method to correct the temperature variable.
Specifically, the best functional match between convective heat transfer coefficient and temperature variation is found by minimizing the sum of squared errors.
In particular, the temperature variable comprises the inlet temperature T of the transformer oil 1 And the temperature difference between the transformer oil and the solid surface, Δ T ═ T 2 -T 1 The traditional convective heat transfer coefficient calculation formula is as follows:
where x is the displacement in the direction of the transformer oil movement and u ∞ Is the inlet velocity of the transformer oil, upsilon is the kinematic viscosity of the transformer oil, and a is the thermal conductivity of the transformer oil.
Further, the convective heat transfer coefficient correction formula after introducing the temperature variable is as follows:
υ(T)＝(120-8.1T+0.28T 2 -0.006T 3 )×10 -6
wherein h is x ' is the corrected convective heat transfer coefficient.
FIG. 4 shows the on-way convective heat transfer coefficient curves of the transformer oil with varying properties under different temperature boundary conditions. The result shows that when the delta T is larger than 0, the corrected value of the convective heat transfer coefficient is increased, namely, the transformer oil grabs the surface of a high-temperature solid to improve the actual convective heat transfer strength; conversely, when Δ T <0, the corrected value of the convective heat transfer coefficient decreases.
Fig. 5 is a model diagram of a forced oil circulation transformer. During operation of the transformer, the internal heat source includes load losses of the windings and no-load losses of the core. The transformer oil with the given temperature flows in from the inlet and takes away part of heat and flows out from the outlet. Because the axial convective heat transfer coefficient of the winding is inconsistent with that of the transformer oil, the axial temperature of the winding can change along the way, and a model for calculating the axial temperature of the winding through the convective heat transfer coefficient is as follows:
in the formula, T winding Is the winding temperature, Q is the heat productivity of the winding, A is the area of convective heat transfer, T oil Is the inlet oil temperature.
For the transformer model shown in fig. 5, the corrected convective heat transfer coefficient is used to calculate the axial temperature of the winding, and as a result, as shown in fig. 6, the maximum temperature error on the winding is reduced from 4% to 1%.
According to the method for correcting the convection coefficient of the variable-property transformer oil, the hypothesis that the fluid thermal property parameters are unchanged in the convection heat exchange process is eliminated, the accuracy of solving the internal temperature field of the oil-immersed transformer can be improved by introducing the temperature variable into the traditional calculation formula of the convection heat exchange coefficient, and the method is suitable for different structures and operation conditions; in addition, a parameterized simulation analysis method is adopted, so that the speed of generating and modifying the model is greatly increased; theoretical formula derivation and numerical calculation results are combined through a least square method, and the advantages of high efficiency and high precision are achieved.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A method for correcting convection heat transfer coefficient of variable-property transformer oil is characterized by comprising the following steps:
step S1, establishing a two-dimensional physical model containing transformer oil and a solid surface, determining corresponding size parameters, setting material attributes of each part, and subdividing the two-dimensional physical model by adopting a mesh with a triangle and a quadrangle matched with each other: dividing a main body area by adopting a quadrilateral mesh, and performing encryption division by adopting a triangular mesh in a boundary layer area, wherein the boundary layer area refers to a coupling interface of the transformer oil and the solid;
step S2, setting different temperature boundary conditions including the inlet temperature T of transformer oil by using a parametric simulation method 1 And temperature T of the solid surface 2 ，T 1 And T 2 Different value combinations between the two modules form various simulation analysis models;
step S3, based on the two-dimensional physical model of the transformer oil sweeping the solid surface, the finite element method and the finite volume method are combined to solve and calculate the temperature field distribution in the boundary layer area, and the speed and the temperature distribution characteristic of the transformer oil in the boundary layer are controlled by a mass conservation equation, a momentum conservation equation and an energy conservation equation:
where ρ is the density of the transformer oil, w is the velocity vector of the transformer oil, F is the external volumetric force, P is the pressure, u is the dynamic viscosity of the transformer oil, c is the specific heat capacity of the transformer oil, k is the thermal conductivity of the transformer oil, S h Is the calorific value per unit volume of the solid component;
step S4, after solving and calculating, obtaining the temperature field distribution of the transformer oil in the boundary layer and the heat flow distribution output by the solid surface along the moving direction of the transformer oil in the post-treatment, and calculating the convection heat transfer coefficient;
and step S5, introducing the temperature variable into a traditional convective heat transfer coefficient calculation formula by using a least square method to correct the temperature variable, and searching the optimal function matching between the convective heat transfer coefficient and the temperature variable by minimizing the error sum of squares.
2. The method for modifying the convection heat transfer coefficient of a transformer oil according to claim 1, wherein in step S1, the transformer oil is subjected to the material properties at different temperatures by a piecewise linear method.
3. The method for modifying the convection heat transfer coefficient of the transformer oil with variable physical properties of claim 1 or 2, wherein in the step S1, the material properties of each component comprise the density, the thermal conductivity, the specific heat capacity and the dynamic viscosity of the solid and the transformer oil.
4. The method for modifying the convection heat transfer coefficient of the transformer oil with the variable properties according to claim 1, wherein in step S3, when the temperature field distribution of the transformer oil in the boundary layer is solved, the convection heat transfer amount output from the solid surface is separated by omitting the radiation heat transfer process.
5. The method for correcting the convection heat transfer coefficient of the variable property transformer oil as claimed in claim 1, wherein in step S4, the local convection heat transfer coefficient along the way is calculated according to the newton' S cooling formula:
q x ＝h x (T 2 -T 1 )
in the formula, q x Is the heat flow distribution output from the solid surface along the moving direction of the transformer oil, h x Is the local convective heat transfer coefficient along the way.
6. The method for modifying the convective heat transfer coefficient of a variable property transformer oil as claimed in claim 1, wherein in step S5, the temperature variable comprises the inlet temperature T of the transformer oil 1 And the temperature difference Δ T between the transformer oil and the solid surface ═ T 2 -T 1 The conventional convective heat transfer coefficient calculation formula is as follows:
where x is the displacement in the direction of the transformer oil movement and u ∞ Is the inlet velocity of the transformer oil, upsilon is the kinematic viscosity of the transformer oil, and a is the thermal conductivity of the transformer oil.
7. The method for correcting the convection heat transfer coefficient of the variable property transformer oil as claimed in claim 6, wherein in step S5, the convection heat transfer coefficient correction formula after introducing the temperature variable is as follows:
υ(T)＝(120-8.1T+0.28T 2 -0.006T 3 )×10 -6
wherein h is x ' is the corrected convective heat transfer coefficient.
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