A method for calculating heat exchange of a casing based on mainstream pressure gradient

Abstract

The application belongs to the inside cavity structure of the thin-wall casing of an aero-engine, and particularly relates to a casing heat exchange calculation method based on a main flow pressure gradient, which comprises the following steps: obtaining a relationship between an inside cavity heat exchange coefficient and a main flow inlet-outlet pressure difference, wherein the relationship contains an unknown coefficient; obtaining multiple main flow inlet-outlet pressure differences and corresponding inside cavity heat exchange coefficients through experiments, and solving the unknown coefficient to obtain the relationship without the unknown coefficient; and calculating the inside cavity temperature based on the relationship. The application fully considers the gas flow condition of the inside cavity of the casing, and reflects different influences of different pressure gradients on flow and heat exchange. The main flow inlet-outlet pressure difference of the inside cavity and the heat exchange coefficient of the inside cavity are calculated, and different heat exchange coefficients of the inside cavity can be calculated according to different main flow inlet-outlet pressure differences.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of the inner cavity structure of the thin-walled casing of an aero-engine, and particularly relates to a casing heat exchange calculation method based on the pressure gradient of a main flow. BACKGROUND

[0002] The casing of an aero-engine is usually a large-diameter thin-walled part, which has poor rigidity and is high in temperature. The thermal deformation of the casing assembly has an important influence on the clearance between the casing and the rotor and vibration. In order to accurately evaluate the temperature distribution of the casing assembly and improve the reliability of the casing, the casing temperature simulation calculation method needs to be further improved.

[0003] In the existing casing temperature calculation method, the position of a small cavity inside the casing, where the flow is weak, is treated as adiabatic.

[0004] In the casing temperature calculation, the position of the inner cavity where the flow is weak is treated as adiabatic, which lacks a theoretical basis and has a certain deviation from the test data. SUMMARY

[0005] In order to solve the above problems, the application provides a casing heat exchange calculation method based on the pressure gradient of a main flow. The casing and the outer ring bottom plate of the rotor form an inner cavity. There is a main flow through the outer ring bottom plate, and there is a secondary flow through the inner cavity. The method comprises the following steps:

[0006] A relationship between the heat exchange coefficient of the inner cavity and the pressure difference between the inlet and outlet of the main flow is obtained. The relationship contains unknown coefficients.

[0007] A plurality of pressure differences between the inlet and outlet of the main flow and the corresponding heat exchange coefficients of the inner cavity are obtained through experiments, and the unknown coefficients are solved to obtain the relationship without unknown numbers.

[0008] Based on the relationship, the temperature of the inner cavity is calculated.

[0009] Preferably, the relationship is:

[0010] h=a0+a1*DeltaP;

[0011] a0 is an unknown coefficient, a1 is an unknown coefficient, DeltaP is the pressure difference between the inlet and outlet of the main flow, and h is the heat exchange coefficient.

[0012] Preferably, the method for obtaining the relationship is:

[0013] According to the Bernoulli equation of gas, a first relationship between the pressure difference between the inlet and outlet of the inner cavity and the inlet and outlet velocity of the inner cavity is obtained.

[0014] Based on the first relationship, a second relationship between the average velocity of the fluid in the inner cavity and the heat exchange coefficient is obtained.

[0015] A third relationship between the heat exchange coefficient and the pressure difference between the inlet and outlet of the inner cavity is obtained based on the second relationship;

[0016] The pressure difference between the inlet and outlet of the inner cavity in the third relationship is replaced by the pressure difference between the inlet and outlet of the main flow through the flow resistance characteristic relationship to obtain a fourth relationship between the pressure difference between the inlet and outlet of the main flow and the heat exchange coefficient;

[0017] The fourth relationship is Taylor expanded and fitted to obtain the relationship.

[0018] Preferably, when the distance between the inlet and outlet of the inner cavity is less than a preset length, the difference between the velocities of the inlet and outlet of the inner cavity is a constant; and the terms of the Taylor expansion of the fourth relationship with a power greater than a preset power are all 0.

[0019] Preferably, the heat exchange coefficient calculation method under different states is:

[0020] The pressure difference between the inlet and outlet of the main flow under the to-be-calculated state is converted from the pressure difference between the inlet and outlet of the main flow under a known state.

[0021] The heat exchange coefficient under the to-be-calculated state is calculated by substituting the pressure difference between the inlet and outlet of the main flow under the to-be-calculated state into the relationship.

[0022] Preferably, the pressure difference between the inlet and outlet of the main flow under the to-be-calculated state is converted from the speed ratio between the known state and the to-be-calculated state.

[0023] Preferably, the preset power term is a second-order power term.

[0024] The advantages of the present application include:

[0025] 1) The gas flow in the inner cavity of the casing is fully considered, and the different effects of different pressure gradients on flow and heat exchange are also reflected.

[0026] 2) The pressure difference between the inlet and outlet of the main flow in the inner cavity and the heat exchange coefficient of the inner cavity are calculated, and different heat exchange coefficients of the inner cavity can be calculated according to different pressure differences between the inlet and outlet of the main flow. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is a preferred embodiment of the present application, which is a flow chart of a casing heat exchange calculation method based on the pressure gradient of the main flow.

[0028] Figure 2 is a schematic diagram of a turbine casing structure according to an embodiment of the present application. DETAILED DESCRIPTION

[0029] For the purpose, technical solutions and advantages of the embodiments of the present application to be clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar notations represent the same or similar elements or elements with the same or similar functions throughout. The described embodiments are part of the embodiments of the present application, rather than all the embodiments. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application. The embodiments of the present application will be described in detail below with reference to the drawings.

[0030] To solve the above problems, the present application provides a casing heat exchange calculation method based on mainstream pressure gradient. The casing forms an inner cavity between the casing and the rotor outer ring bottom plate. The mainstream passes outside the rotor outer ring bottom plate, and the secondary flow passes through the inner cavity. As shown in Figure 1 The calculation method comprises:

[0031] Obtaining a relationship between the heat exchange coefficient of the inner cavity and the pressure difference between the inlet and outlet of the mainstream, which contains unknown coefficients;

[0032] Obtaining a plurality of pressure differences between the inlet and outlet of the mainstream and the corresponding heat exchange coefficients of the inner cavity through experiments, and solving the unknown coefficients to obtain the relationship without unknowns;

[0033] Based on the relationship, the temperature of the inner cavity is calculated.

[0034] In some optional embodiments, the relationship is:

[0035] h=a0+a1×ΔP;

[0036] a0 is an unknown coefficient, a1 is an unknown coefficient, ΔP is the pressure difference between the inlet and outlet of the mainstream, and h is the heat exchange coefficient.

[0037] In some optional embodiments, the method for obtaining the relationship is:

[0038] According to Bernoulli's equation of gas, a first relationship between the pressure difference between the inlet and outlet of the inner cavity and the inlet and outlet velocity of the inner cavity is obtained;

[0039] Based on the first relationship, a second relationship between the average velocity of the fluid in the inner cavity and the heat exchange coefficient is obtained;

[0040] Based on the second relationship, a third relationship between the heat exchange coefficient and the pressure difference between the inlet and outlet of the inner cavity is obtained;

[0041] The third relationship is replaced by the main flow pressure difference through the flow resistance characteristic relationship to obtain a fourth relationship between the main flow pressure difference and the heat exchange coefficient.

[0042] The fourth relationship is Taylor expanded to obtain the relationship.

[0043] In some optional embodiments, when the distance between the inlet and the outlet of the inner cavity is less than a preset length, the difference between the velocities of the inlet and the outlet of the inner cavity is a constant; the terms of the Taylor expansion of the fourth relationship with a power greater than a preset order are all 0.

[0044] In some optional embodiments, the heat exchange coefficient calculation method in different states is:

[0045] The main flow inlet and outlet pressure difference in the known state is used to convert the main flow inlet and outlet pressure difference in the state to be calculated.

[0046] The main flow inlet and outlet pressure difference in the state to be calculated is substituted into the relationship to calculate the heat exchange coefficient in the state to be calculated.

[0047] In some optional embodiments, the main flow inlet and outlet pressure difference in the state to be calculated is converted through the speed ratio of the known state and the state to be calculated.

[0048] In some optional embodiments, the preset order term is a second order term.

[0049] The relationship is obtained by combining the accompanying drawings Figure 2 The relationship is obtained by combining the accompanying drawings

[0050] The low-pressure turbine casing inner cavity heat exchange calculation is taken as an example for description, and the application is applicable to all similar thin-walled casing inner cavity structures.

[0051] The area between the outer ring bottom plate of the rotor and the stator and the low-pressure turbine casing is filled with heat insulation cotton, and in the previous heat exchange calculation, the heat insulation treatment is adopted, and it is considered that the high-temperature gas in the main channel cannot enter the area. The CFD simulation calculation on the area between the casing and the rotor and the stator shows that there is a certain flow, and the test test data show that the temperature of the casing at the area is relatively high, and there is a large deviation between the casing temperature obtained by the previous heat exchange calculation and the heat insulation treatment.

[0052] According to the principle of fluid mechanics, the heat exchange coefficient in the heat exchange calculation and the fluid pressure difference can be related.

[0053] The positions of the parameters are shown in the accompanying drawings. Figure 2

[0054] ​Firstly, the gas flow in the thin-walled casing inner cavity is approximately considered as steady, incompressible and inviscid. According to Bernoulli equation of the gas, a first relationship between the pressure difference and the velocity at the inlet and outlet of the inner cavity can be obtained, which is as follows:

[0055]

[0056] Vcavity is the average flow velocity; v1 is the inlet flow velocity in the cavity, v2 is the outlet flow velocity in the cavity, P q2 is the outlet pressure in the cavity, P q1 is the inlet pressure in the cavity; ΔP q is the pressure difference at the inlet and outlet of the cavity; ρ is the fluid density.

[0057] According to the following relationship, a second relationship between the average flow velocity v in the cavity and the heat transfer coefficient h can be obtained, that is:

[0058]

[0059] Where Re is the Reynolds number, n, a, b are constants; k is the thermal conductivity; μ is the dynamic viscosity coefficient; Pr is the Prandtl number, L is the length of the inner cavity, and d is the diameter of the inner cavity.

[0060] The average flow velocity v in the cavity in formula (1) is brought into formula (2), and a third relationship between the heat transfer coefficient h and the pressure difference ΔP q at the inlet and outlet of the cavity can be obtained.

[0061]

[0062] According to the CFD simulation results, the velocity difference v2-v1 at the inlet and outlet of the inner cavity of the thin-walled casing developed by the patent is approximately constant, so that Formula (3) can be expressed as:

[0063] h=f(ΔP q )=AB a (ΔP q ) a (4)

[0064] According to the flow resistance characteristic relationship between the pressure of the inner cavity and the pressure of the main flow, the pressure difference ΔP q at the inlet and outlet of the inner cavity can be converted into the pressure difference ΔP of the main flow, which is as follows:

[0065]

[0066] Where ε1 is the flow resistance of the z11 region; ε is the flow resistance of the z1 region; and ε2 is the flow resistance of the z12 region.

[0067] Substitute equation (5) into equation (4) to obtain a fourth relationship, and perform Taylor series expansion at ΔP = ΔP0 to obtain a Taylor expansion:

[0068]

[0069] wherein, is a constant.

[0070] Therefore, it can be concluded that there is a certain relationship between the main flow pressure difference and the heat exchange coefficient;

[0071] The pressure difference at the inlet and outlet of the thin-walled casing inner cavity corresponds to the main flow pressure difference at the inlet and outlet, and the test data also shows that the value of ΔP-ΔP0 is very small, and the 2nd power to the n-th power term in equation (6) can be ignored;

[0072] Replace the constant part in the expansion with a0 and a1 to obtain the relationship:

[0073] h = a0 + a1 x ΔP

[0074] a0 is an unknown coefficient, a1 is an unknown coefficient, and a1 unit: W / (m 2 ·K·kPa).

[0075] Based on the above calculation, taking the first rotor as an example, as shown in Figure 1 , the multi-stage rotor and stator method is the same. According to the test state S2 parameter, the blade inlet and outlet static pressure difference ΔP 试验 (ΔP 试验 = inlet static pressure P1 试验 - outlet static pressure P2 试验 , unit: kPa), the heat exchange temperature is taken as the main channel recovery temperature T; the heat exchange coefficient h 试验 of multiple regions is calculated; based on the heat exchange coefficient h 试验 and the blade inlet and outlet static pressure difference ΔP 试验 , the relationship is substituted to obtain the a0 of the thin-walled casing inner cavity of this experiment, which is 0, and the a1 is 1; that is, the relationship is:

[0076] h = ΔP;

[0077] Based on the above relationship and the test state calculation method, the corresponding speed conversion is performed in other states, the test state speed N1, and the other state speed Nn, then the heat exchange coefficient h 目标 of other states is taken as ΔP*Nn / N1, and the heat exchange temperature is taken as the recovery temperature T;

[0078] Nn is the engine speed of the target state.

[0079] Wherein the partition Z1 partition can be according to the actual situation, if the heat insulation cotton full area, can be done heat insulation treatment.

[0080] In summary, the heat transfer coefficient in the temperature calculation of the thin-walled casing inner cavity is given according to the corresponding rotor and stator pressure difference (pressure unit: kPa). The inlet and outlet pressure difference of different states can be converted according to the speed.

[0081] The heat transfer calculation method based on the main flow pressure gradient is used for the thin-walled casing inner cavity, which fully considers the gas flow condition at this place and reflects the different effects of different pressure gradients on flow and heat transfer.

[0082] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for calculating heat exchange of a casing based on a main flow pressure gradient, wherein the casing and a rotor outer ring bottom plate form an inner side cavity, the rotor outer ring bottom plate has a main flow passing outside, and the inner side cavity has a secondary flow passing inside, and the method is characterized in that, The method comprises the following steps: obtaining a relationship between the heat exchange coefficient of the inner cavity and the pressure difference between the inlet and outlet of the main flow, wherein the relationship contains unknown coefficients; obtaining a plurality of pressure differences between the inlet and outlet of the main flow and corresponding heat exchange coefficients of the inner cavity through experiments, and solving the unknown coefficients to obtain the relationship without unknowns; calculating the temperature of the inner cavity based on the relationship; the relationship is: h=a0+a1*ΔP; a0 is an unknown coefficient, a1 is an unknown coefficient, ΔP is the pressure difference between the inlet and outlet of the main flow, and h is the heat exchange coefficient; the method for obtaining the relationship is: obtaining a first relationship between the pressure difference between the inlet and outlet of the inner cavity and the inlet and outlet velocities of the inner cavity according to the Bernoulli equation of the gas; obtaining a second relationship between the average velocity of the fluid in the inner cavity and the heat exchange coefficient based on the first relationship; obtaining a third relationship between the heat exchange coefficient and the pressure difference between the inlet and outlet of the inner cavity based on the second relationship; replacing the pressure difference between the inlet and outlet of the inner cavity in the third relationship with the pressure difference of the main flow through the flow resistance characteristic relationship to obtain a fourth relationship between the pressure difference of the main flow and the heat exchange coefficient; Taylor expanding the fourth relationship to obtain the relationship.

2. The mainstream pressure gradient-based calculation method of heat transfer in a turbine casing according to claim 1, characterized in that, When the distance between the inlet and outlet of the inner cavity is less than a preset length, the difference between the velocities of the inlet and outlet of the inner cavity is a constant; the terms with powers greater than a preset power in the Taylor expansion of the fourth relationship are all 0.

3. The mainstream pressure gradient-based calculation method of heat transfer in a combustor according to claim 1, wherein, The heat exchange coefficient calculation method under different states is: calculating the pressure difference between the inlet and outlet of the main flow under the state to be calculated through the pressure difference between the inlet and outlet of the main flow under the known state; substituting the pressure difference between the inlet and outlet of the main flow under the state to be calculated into the relationship to calculate the heat exchange coefficient under the state to be calculated.

4. The mainstream pressure gradient-based calculation method of heat transfer in a combustor according to claim 3, wherein, The pressure difference between the inlet and outlet of the main flow under the state to be calculated is obtained through the speed ratio between the known state and the state to be calculated.

5. The mainstream pressure gradient-based calculation method of heat transfer in a combustor according to claim 2, wherein, The preset power term is the second-order power term.

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