A method for correcting the comprehensive cooling efficiency modeling theory of curved surface hot end components

Abstract

The application discloses a method for correcting a comprehensive cooling efficiency modeling theory of a curved surface hot end component, and belongs to the field of turbine heat analysis of an aero-engine and a gas turbine engine; firstly, in combination with the existing comprehensive cooling efficiency modeling theory of the hot end component, reasons for unreasonable application of the theory and a calculation formula in a high-curvature area are pointed out; secondly, a one-dimensional heat conduction model is combined with a cylindrical coordinate system and a theoretical model to be deduced; finally, according to a dimensionless theory and definition of a characteristic criterion number, a corrected comprehensive cooling efficiency calculation expression is obtained, and a correction method suitable for the high-curvature area is provided for the comprehensive cooling efficiency modeling theory of the hot end component. The application takes the one-dimensional heat conduction model in the cylindrical coordinate system as a starting point, obtains a comprehensive cooling efficiency calculation formula under a condition that a one-dimensional semi-infinite model is not applicable through a dimensionless heat analysis method, and realizes rationality and accuracy of the comprehensive cooling efficiency modeling analysis in the area with a larger curvature.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of turbine heat analysis of aero-engine and gas turbine engine, and particularly relates to a method for correcting a comprehensive cooling efficiency modeling theory of a curved surface hot end component. BACKGROUND

[0002] Impingement cooling and film cooling are widely used in aero-engine and gas turbine as common and efficient turbine blade cooling methods. However, due to the extreme service environment of the hot end component of the aero-engine, it is basically not feasible to conduct a comprehensive cooling efficiency experiment under the same working condition in the laboratory. Through the comprehensive cooling efficiency modeling theory of the hot end component, a reliable result close to the actual engine working condition can be obtained under the laboratory working condition.

[0003] The dimensionless theory is a very important method in the field of heat transfer heat analysis, and is widely concerned and applied in the turbine of aero-engine and gas turbine. In the research of turbine comprehensive cooling, the early stage mainly matched the Bi number on the mainstream side, but other influencing factors were not considered, and the results were not verified by matching the actual engine. Kyle et al. measured the comprehensive cooling efficiency of the whole blade (film cooling + complex internal cooling structure) under the condition of matching the Bi number on the mainstream side, and the author also verified the effectiveness of the one-dimensional comprehensive cooling efficiency prediction formula. S G Ramachandran et al. numerically studied the matching principle of comprehensive cooling of ribbed channels under actual engine conditions and experimental conditions. The results show that it is very important to match the Bi numbers on the inside and outside. William et al. studied the principle of matching the Bi number on the mainstream side and provided some suggestions for selecting appropriate solid materials. The research results show that matching the temperature ratio of the mainstream and secondary flow can obtain a better result. However, the comprehensive cooling efficiency modeling theory is based on one-dimensional semi-infinite heat conduction, and when in the areas with large curvature and change such as blade leading edge and trailing edge, the one-dimensional semi-infinite theory model is not established, and the comprehensive cooling efficiency prediction formula in these areas is not accurate. SUMMARY

[0004] The technical problem to be solved is:

[0005] In order to avoid the shortcomings of the prior art, the present application provides a method for correcting the comprehensive cooling efficiency modeling theory of the curved surface hot end component, which is an experimental method for comprehensive cooling efficiency under laboratory conditions, analyzes and corrects the comprehensive cooling efficiency modeling theory of the hot end component, so as to have more accurate and reliable prediction results in these areas, which is of great significance to guide the comprehensive cooling efficiency related experiment and engineering practice.

[0006] The technical scheme of the present application is: a method for correcting the comprehensive cooling efficiency modeling theory of the curved surface hot end component, characterized in that the specific steps are as follows:

[0007] Step one: combined with the existing hot end component comprehensive cooling efficiency modeling theory, deduce the comprehensive cooling efficiency expression;

[0008] Step two: the calculation formula obtained in step one is redefined and deduced by using cylindrical coordinates;

[0009] Step three: the boundary conditions of the gas film cooling wall impacted by the cooling gas are set;

[0010] Step four: integral solution of control equation;

[0011] Step five: derivation of the comprehensive cooling efficiency correction relationship.

[0012] Further technical solutions of the application are: in step one, the comprehensive cooling efficiency expression is as follows:

[0013]

[0014] In the formula, is the adiabatic cooling efficiency; is the mainstream side Biot number, temperature rise coefficient

[0015] Further technical solutions of the application are: in step two, the area with large blade curvature is selected for analysis, including the blade leading edge and trailing edge.

[0016] Further technical solutions of the application are: in step two, the control equation in cylindrical coordinates is first determined, when the axial and axial heat conduction is not considered, the heat conduction is assumed to be one-dimensional along the radial direction, and the heat conduction differential equation is:

[0017]

[0018] According to the one-dimensional steady-state heat conduction assumption, the temperature changes only along the radial direction, so formula (1) can be changed to:

[0019]

[0020] Further technical solutions of the application are: in step three, the inner wall surface is in contact with the cooling gas, which is recorded as boundary 1: the outer wall surface is in contact with the combustion gas, which is recorded as boundary 2; the heat flux density on the boundary is transferred along the radial direction, which meets the third type of boundary condition of convective heat transfer, that is:

[0021]

[0022]

[0023] And the above two equations are dimensionless, first dimensionless of thickness and temperature: The comprehensive cooling efficiency of the outer surface is expressed as:

[0024]

[0025] The formula (2), (3) and (4) can be processed in a dimensionless form as follows:

[0026]

[0027]

[0028]

[0029] The further technical scheme of the present application is that in the step four, the relationship between θ and R obtained by the integral of formula (5) is and θ=C1LnR+C2, and the undetermined coefficients C1 and C2 are obtained by combining the definite conditions (R1, θ1) and (R2, θ2), and the expression of θ is as follows:

[0030]

[0031] The further technical scheme of the present application is that in the step five, the formula (6), (7) and (8) are solved simultaneously, and θ1 is eliminated to obtain the following formula:

[0032]

[0033] Since θ2=φ, the modified expression of the comprehensive cooling efficiency φ is obtained by solving:

[0034]

[0035] Thus, the modified calculation formula of the comprehensive cooling efficiency modeling theory of the hot end component in the high curvature area is obtained, compared with the original calculation formula of Φ, and which is modified as a correction factor to the original comprehensive cooling efficiency calculation formula. The further technical scheme of the present application is that the modified expression of the comprehensive cooling efficiency φ is written as:

[0036]

[0037] Advantageous effects

[0038] The beneficial effects of this invention are as follows: This invention proposes a method for correcting the comprehensive cooling efficiency modeling theory of hot-end components in high-curvature regions. By re-deriving the comprehensive cooling efficiency modeling formula of hot-end components in cylindrical coordinates, a set of correction factors is obtained, which then guides experimental and numerical simulation analysis. This experiment starts with a one-dimensional heat conduction model in cylindrical coordinates. Through dimensionless thermal analysis, a comprehensive cooling efficiency calculation formula is obtained under the condition that a one-dimensional semi-infinite model is not applicable. This realizes the rationality and accuracy of comprehensive cooling efficiency modeling analysis in regions with high curvature, improves the accuracy and reliability of comprehensive cooling efficiency prediction in high-curvature regions of engine turbine blades, and expands the applicability of the modeling theory. Attached Figure Description

[0039] Figure 1 Schematic diagram of heat transfer coupling in impingement film cooling;

[0040] Figure 2 Blade model and curvature diagram;

[0041] Figure 3 Schematic diagram of a coupled heat transfer model for impact film cooling in high curvature regions;

[0042] Figure label explanation: T g —Mainstream temperature, T c,e —Air conditioning outlet temperature, T W —Cooling wall temperature, h g —Mainstream heat transfer coefficient, k s — Thermal conductivity in the thickness direction, δ— Wall thickness, h c —Coefficient of heat transfer of cold air, r1—radius of curvature of inner wall surface, r2—radius of curvature of outer wall surface, T2—temperature of outer wall surface, T1—temperature of inner wall surface. Detailed Implementation

[0043] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0044] This embodiment provides a method for modifying the comprehensive cooling efficiency modeling theory of curved surface hot-end components, wherein T... g Representing the mainstream temperature, T c,e T represents the outlet temperature of the cold air. W h represents the temperature of the cooling wall surface. g Representing the mainstream heat transfer coefficient, under the condition that the wall thickness is known and the heat transfer coefficients of the mainstream and cooling fluid are determined. The mainstream side of the Bishop number; φ represents the temperature rise coefficient in this study. φ represents the overall cooling efficiency, which is a comprehensive measure of internal and external cooling.

[0045] The application is further described below in combination with specific derivation process and the drawings:

[0046] Step one: in combination with the existing hot end component comprehensive cooling efficiency modeling theory, the prediction formula is derived, and the physical model is analyzed.

[0047] In combination with the attached Figure 1 , the expression of the comprehensive cooling efficiency modeling theory model is derived. First, the model is assumed to be a one-dimensional semi-infinite heat conduction model, that is, the heat conduction process is only along the thickness δ direction, the x direction is the flow direction, the y direction is the span direction, and the z direction is the thickness direction. The heat conduction differential equation is as follows:

[0048]

[0049] The temperature and thickness are dimensionless, and let Then formula (1) can be converted into the following form:

[0050]

[0051] The heat flux density on the boundary is transferred along the thickness direction, satisfying the third type of boundary condition of convective heat transfer:

[0052]

[0053]

[0054] In the formula, h r is the equivalent convective heat transfer coefficient of radiation heat transfer. The boundary condition is dimensionless, and the following two formulas are obtained:

[0055]

[0056]

[0057] The formula (3) (5) (6) is solved, and θ| Z＝0 is eliminated, and the following formula is obtained:

[0058]

[0059] That is

[0060] Formula (7) is the calculation formula of the comprehensive cooling efficiency obtained by the comprehensive cooling efficiency modeling method, that is, the comprehensive cooling efficiency can be expressed and calculated by the adiabatic cooling efficiency, the main flow side Biot number, the ratio of the main flow side cold gas flow heat transfer coefficient, and the temperature rise coefficient. However, the premise of this method is the establishment of the one-dimensional semi-infinite heat conduction model assumption, as shown in the attached Figure 2The chordal suction surface pressure of the shown blade is relatively large and changes little, so the one-dimensional semi-infinite model has a high matching degree, and the non-dimensional calculation formula of the comprehensive cooling efficiency is established. However, in the high-curvature regions such as the leading edge and the trailing edge, the assumption condition of the one-dimensional semi-infinite flat plate is not established, and there are unreasonable and inaccurate problems in using this calculation formula in these regions.

[0061] Step two: to solve the problem raised in step one, in the region with large curvature, the embodiment proposes to redefine and deduce the above calculation formula by using cylindrical coordinates, combined with the attached Figure 3 The schematic diagram shown, first, the control equation under the cylindrical coordinates is determined, when the axial and axial heat conduction conditions are not considered, the heat conduction differential equation is assumed to be one-dimensional radial heat conduction, and the heat conduction differential equation is:

[0062]

[0063] According to the one-dimensional steady-state heat conduction assumption, the temperature changes only along the radial direction, so formula (8) can be changed to:

[0064]

[0065] Step three: the boundary condition setting of the gas film cooling wall surface impacted by the cold gas, combined with the attached Figure Three As shown, the inner wall of the outer wall surface is in contact with the cooling gas, which is recorded as boundary 1: the outer wall surface is in contact with the combustion gas, which is recorded as boundary 2. The heat flux density on the boundary of the two wall surfaces is transmitted along the radial direction, which meets the third type of boundary condition of convective heat transfer, that is:

[0066]

[0067]

[0068] And the above two equations are non-dimensionalized, first, the thickness and temperature are non-dimensionalized: Then the comprehensive cooling efficiency of the outer surface can be expressed as:

[0069]

[0070] Then formula (9) (10) (11) can be non-dimensionalized as follows:

[0071]

[0072]

[0073]

[0074] Step four: integral solution of control equation. The relationship between θ and R obtained by integral from (12) and θ = C1LnR + C2, and combined with the definite solution conditions (R1, θ1), (R2, θ2) to obtain the undetermined coefficients C1C2, the expression of θ is as follows:

[0075]

[0076] Step five: derivation of the comprehensive cooling efficiency correction relationship. Simultaneous equations (13) (14) (15) and eliminate θ1, to obtain the following formula:

[0077]

[0078] And because θ2= φ, the solution is obtained to obtain the corrected expression of the comprehensive cooling efficiency φ:

[0079]

[0080] That is:

[0081]

[0082] Thus, the modified calculation formula (17) of the thermal end component comprehensive cooling efficiency modeling theory in the high curvature area can be obtained, compared with the original Φ calculation formula, and As a correction factor to modify the original comprehensive cooling efficiency calculation formula.

[0083] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and modifications to the above embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. A method for revising the theoretical modeling of the cooling effectiveness of a curved hot end component, comprising: The specific steps are as follows: ​ Step one: based on the existing hot end component comprehensive cooling efficiency modeling theory, deduce the comprehensive cooling efficiency expression; the comprehensive cooling efficiency expression is as follows: In the formula, is the adiabatic cooling efficiency; is the primary flow side Biot number, temperature rise coefficient ; Step two: use the cylindrical coordinate to redefine and deduce the calculation formula obtained in step one; select the area with large blade curvature for analysis, including the blade leading edge and trailing edge; The specific process is as follows: Firstly, the control equation under the cylindrical coordinate is determined, when the axial and axial heat conduction is not considered, it is assumed that the heat conduction is along the one-dimensional radial direction, at this time the heat conduction differential equation is: （1） According to the one-dimensional steady-state heat conduction assumption, the temperature changes only along the radial direction, then formula (1) can be changed to: （2） Step three: set the boundary conditions for the film cooling wall surface impacted by the cold gas; wherein the inner wall surface is in contact with the cooling gas, which is recorded as boundary 1: the outer wall is in contact with the combustion gas, which is recorded as boundary 2; the heat flux density on the boundary is transferred along the radial direction, which meets the third type of boundary condition of convective heat transfer, that is: （3） （4） And the dimensionless treatment is carried out on the above two equations, firstly, the thickness and temperature are dimensionless: ; The overall cooling efficiency of the outer surface is expressed as: Then formula (2)(3)(4) can be dimensionless as follows: （5） （6） （7） Step four: the control equation is integrated to solve; the relationship of (5) integral and R and , and the undetermined coefficient C1C2is obtained by combining the definite condition (R1, ), (R2, ), and the expression of is as follows:​ （8） Step five: derivation of the comprehensive cooling efficiency correction relationship; simultaneously with (6) (7) (8) formula, and eliminate , get the following formula: （9） Again, because = , the modified expression of the comprehensive cooling efficiency is obtained. （10） Thus, the modified calculation formula of the comprehensive cooling efficiency modeling theory of the hot end component in the high curvature area is obtained, compared with the original calculation formula Φ , and The original comprehensive cooling efficiency calculation formula is modified as a correction factor. or the overall cooling efficiency The modified expression for the overall cooling efficiency is written as: （11）。

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