A method and apparatus for transient radial clearance prediction

Abstract

A transient radial clearance prediction method and device, the radial clearance refers to the radial distance between the engine rotor blade tip and the casing; the engine comprises a casing, a blade and a disc; characterized in that, the method comprises: obtaining the relevant input information of the transient radial clearance prediction, wherein the relevant input information comprises: geometric information, material information and boundary condition information; according to the relevant input information and the predetermined casing deformation model, blade deformation model and disc deformation model, the deformation values of the casing, blade and disc at the first time are determined; according to the predetermined transient radial clearance prediction model, and the radial change value of the casing, blade and disc, the radial clearance value at the first time is determined; wherein the dimensions of the predetermined casing deformation model, blade deformation model and disc deformation model are different.

Description

Technical Field

[0001] This article relates to the field of aero-engine impeller technology, and in particular to a transient radial clearance prediction method and device. Background Technology

[0002] Radial clearance in an aero-engine refers to the radial distance between the rotor blade tip and the casing. The presence of radial clearance leads to tip leakage flow, significantly impacting the efficiency of the compressor and turbine, and consequently affecting engine thrust and fuel consumption. When the radial clearance is too large, tip leakage flow increases and mixes with the mainstream flow, resulting in decreased compressor and turbine efficiency, thus reducing engine thrust and increasing fuel consumption. Conversely, when the radial clearance is too small, rotor blade tips may scrape against the casing, causing casing damage or even blade failure, potentially leading to engine seizure and compromising engine safety. Therefore, predicting the radial clearance of an aero-engine is crucial for engine performance evaluation and active clearance control.

[0003] The radial clearance variation of an aero-engine is caused by the deformation of the casing, blades, and rotor. Due to the differences in structural characteristics, thermal loads, and mechanical loads on each component, the variation law is complex, making accurate prediction of radial clearance extremely difficult. Especially during transient processes, the differences in thermal and mechanical inertia of each component lead to different transient variation laws, making it difficult to accurately predict transient radial clearance. This poses a significant challenge to the assessment of engine transient performance and the development of active clearance control strategies.

[0004] In some technologies, the prediction of transient radial clearance is mainly achieved through one-dimensional models and three-dimensional simulation methods, which has the following problems:

[0005] 1. When studying radial clearance using a one-dimensional model, only the one-dimensional radial characteristics of the component are considered. One-dimensional heat transfer and thermal deformation analysis, as well as one-dimensional centrifugal deformation analysis, can achieve rapid prediction of radial clearance. However, the axial heat transfer characteristics and axial thickness variation of the component are not considered, resulting in low prediction accuracy.

[0006] 2. The three-dimensional simulation method takes into account the three-dimensional features of the component, realizes the prediction of three-dimensional heat transfer and thermal deformation, as well as the prediction of three-dimensional centrifugal deformation, and improves the accuracy of radial clearance prediction. However, due to the huge time consumption, the calculation of a single point can take several weeks. It is only suitable for steady-state prediction and it is difficult to realize transient radial clearance prediction. Summary of the Invention

[0007] This application provides a transient radial clearance prediction method and apparatus. For different components, prediction models of different dimensions are established for analysis. The geometric and heat transfer characteristics of the components are fully considered, which solves the problems of low accuracy of one-dimensional prediction models and slow prediction of three-dimensional simulation methods. The method improves the prediction accuracy of transient radial clearance while making predictions faster.

[0008] This application provides a transient radial clearance prediction method, wherein the radial clearance refers to the radial distance between the engine rotor blade tip and the casing; the engine includes a casing, blades, and a rotor disk; the method includes:

[0009] Obtain relevant input information for transient radial clearance prediction, wherein the relevant input information includes: geometric information, material information, and boundary condition information;

[0010] Based on the relevant input information and the predetermined deformation models of the casing, blades, and wheel, the deformation values ​​of the casing, blades, and wheel at the first moment are determined.

[0011] Based on the predetermined transient radial clearance prediction model, and the radial variation values ​​of the casing, blades, and wheel, the radial clearance value at the first moment is determined;

[0012] The predetermined casing deformation model, blade deformation model, and wheel deformation model have different dimensions.

[0013] In one exemplary embodiment, the casing deformation model is as follows:

[0014] u shroud (t)=u shroud1 (t)+u shroud2 (t);

[0015] Among them, u shroud (t) represents the deformation value of the casing at the first moment, u shroud1 (t) represents the thermal deformation value of the casing at the first moment, u shroud2 (t) represents the mechanical deformation value of the casing at the first moment;

[0016] The blade deformation model is as follows:

[0017] u blade (t)=u blade1 (t)+u blade2 (t)

[0018] Among them, u blade (t) represents the deformation value of the blade at the first moment, u blade1 (t) represents the thermal deformation value of the blade at the first moment, u blade2 (t) represents the mechanical deformation value of the blade at the first moment;

[0019] The wheel deformation model is as follows:

[0020] u disk (t)=u disk1 (t)+u disk2 (t);

[0021] Among them, u disk (t) represents the deformation value of the wheel at the first moment, u disk1 (t) represents the thermal deformation value of the wheel at the first moment, u disk2 (t) represents the mechanical deformation value of the wheel at the first moment.

[0022] In one exemplary embodiment, the thermal deformation value of the casing at a first moment is determined based on the transient average temperature of the casing, wherein the transient average temperature of the casing is the average value of the transient temperatures of each node in the wear-resistant coating and the metal coating of the casing.

[0023] The mechanical deformation value of the casing at the first moment is determined based on the elastic modulus of the casing material, the inner diameter of the casing high-temperature alloy layer, the outer diameter of the casing high-temperature alloy layer, the Poisson's ratio of the casing material, the pressure on the inner wall of the casing, and the pressure on the outer wall of the casing.

[0024] In one exemplary embodiment, the thermal deformation value of the blade at the first moment is calculated using a one-dimensional thermal deformation model of the blade, based on the blade temperature, blade length, and the corresponding coefficient of thermal expansion of the blade material at that blade temperature; wherein, the one-dimensional thermal deformation model of the blade is:

[0025] u blade1 =α blade *L blade *T blade

[0026] Among them, u blade1 α is the thermal deformation value of the blade at the first moment. blade L is the coefficient of thermal expansion of the blade material. blade T is the blade length. blade This refers to the blade temperature.

[0027] In one exemplary embodiment, the blade variable cross-section slope characteristic parameter is determined based on the cross-sectional areas of the blade bottom and top;

[0028] The mechanical deformation value of the blade at the first moment is determined using a two-dimensional centrifugal deformation model of the blade based on the blade's variable cross-section slope, blade rotation speed, blade density, blade elastic modulus, and disk outer diameter.

[0029] The two-dimensional centrifugal deformation model of the blade is as follows:

[0030]

[0031] In the above model, 'a' represents the variable cross-section slope of the blade, 'N' represents the blade rotational speed, and 'ρ' represents the blade rotational speed. blade E represents the density of the leaf blade. blade The elastic modulus of the blade, r disk This indicates the outer diameter of the wheel.

[0032] In one exemplary embodiment, the thermal deformation value of the wheel at the first moment is determined by the thermal deformation formula of the wheel based on the thermal expansion coefficient of the wheel material, the outer diameter of the wheel, and the temperature of the wheel at the first moment.

[0033] The thermal deformation formula of the wheel is as follows:

[0034] u disk1 =α disk *r disk *T disk_ave ;

[0035] In the above formula, u disk1 α is the thermal deformation value of the disk at the first moment. disk r is the coefficient of thermal expansion of the disc material. disk T is the outer diameter of the wheel. disk_ave This represents the temperature of the roulette wheel at the first moment.

[0036] In one exemplary embodiment, the temperature of the wheel at a first moment is determined by the following steps:

[0037] Based on the heat transfer coefficient h a h b and heat exchange temperature T fa T fb Determine the temperatures of the left and right boundary nodes of the roulette wheel at the first moment;

[0038] The blade temperature T at the first moment blade As the temperature of all nodes along the axial direction of the upper boundary of the disk at time j=n+1, the shaft temperature T at the first moment is... shaft This represents the temperature of all nodes along the lower boundary axis of the disk at the first moment when j=0.

[0039] The temperature of each node of the wheel at the first moment is determined by the nodal heat transfer equation based on the temperatures of the left and right boundary nodes of the wheel at the first moment, the temperatures of all nodes along the upper boundary axis of the wheel at the first moment, and the temperatures of all nodes along the lower boundary axis of the wheel at the first moment.

[0040] The temperature of the roulette wheel at the first moment is obtained by averaging the temperatures of each node at the first moment.

[0041] In one exemplary embodiment, the node heat transfer equation is:

[0042]

[0043] In the above formula, T diski,j Let be the temperature of the wheel node, p be the time p, p+1 be the time p+1, and a be the temperature of the node. diski,j Let Δr be the thermal diffusivity of the disk, Δz be the radial element length of the node, and r be the axial element length of the node. j Where is the node radius.

[0044] In one exemplary embodiment, the mechanical deformation value of the wheel at the first moment is determined according to the following method:

[0045] The deformation values ​​at the inner diameter and outer diameter of each segment of the first, second, and third discs are determined respectively; wherein the first, second, and third discs are three discs of equal thickness obtained by dividing the disc; the discs are discs of variable thickness.

[0046] The mechanical deformation value of the wheel at the first moment is calculated based on the deformation values ​​at the inner diameter and outer diameter of each segment, the equal force on the contact surface, and the equal radial deformation of the contact surface.

[0047] This application also provides an apparatus for transient radial clearance prediction, the apparatus comprising: a memory and a processor; characterized in that the memory is used to store a program for performing transient radial clearance prediction, and the processor is used to read and execute the program for performing transient radial clearance prediction, and execute the method described in any one of the above embodiments.

[0048] Compared with related technologies, this application provides a transient radial clearance prediction method and apparatus, wherein the radial clearance refers to the radial distance between the rotor blade tip and the casing of an engine; the engine includes a casing, blades, and a rotor disk; the method is characterized by: acquiring relevant input information for transient radial clearance prediction, wherein the relevant input information includes: geometric information, material information, and boundary condition information; determining the deformation values ​​of the casing, blades, and rotor disk at a first moment based on the relevant input information and predetermined casing deformation models, blade deformation models, and rotor disk deformation models; determining the radial clearance value at the first moment based on the predetermined transient radial clearance prediction model and the radial change values ​​of the casing, blades, and rotor disk; wherein the predetermined casing deformation model, blade deformation model, and rotor disk deformation model have different dimensions. Through the technical solution of this invention, different dimensional prediction models are established for different components for analysis, fully considering the geometric and heat transfer characteristics of the components, solving the problems of low accuracy of one-dimensional prediction models and slow prediction speed of three-dimensional simulation methods, and improving the prediction accuracy of transient radial clearance while achieving rapid prediction.

[0049] Other features and advantages of this application will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the application. Other advantages of this application can be realized and obtained by means of the solutions described in the description and the accompanying drawings. Attached Figure Description

[0050] The accompanying drawings are used to provide an understanding of the technical solutions of this application and constitute a part of the specification. They are used together with the embodiments of this application to explain the technical solutions of this application and do not constitute a limitation on the technical solutions of this application.

[0051] Figure 1 This is a flowchart of the transient radial clearance prediction method according to an embodiment of this application;

[0052] Figure 2 This is a schematic diagram of the transient radial clearance prediction device according to an embodiment of this application;

[0053] Figure 3 This is a multi-dimensional transient radial clearance prediction process in some exemplary embodiments;

[0054] Figure 4 These are schematic diagrams of multi-dimensional transient radial clearance prediction models in some exemplary embodiments;

[0055] Figure 5 These are schematic diagrams of the casing heat exchange model in some exemplary embodiments;

[0056] Figure 6 These are schematic diagrams of blade variable thickness models in some exemplary embodiments;

[0057] Figure 7 These are schematic diagrams of a two-dimensional heat transfer model of a roulette wheel in some exemplary embodiments;

[0058] Figure 8 These are schematic diagrams of two-dimensional deformation models of a roulette wheel in some exemplary embodiments. Detailed Implementation

[0059] This application describes several embodiments, but these descriptions are exemplary and not restrictive, and it will be apparent to those skilled in the art that many more embodiments and implementations are possible within the scope of the embodiments described herein. Although many possible combinations of features are shown in the drawings and discussed in the detailed description, many other combinations of the disclosed features are also possible. Unless specifically limited, any feature or element of any embodiment may be used in combination with, or may replace, any feature or element of any other embodiment.

[0060] This application includes and contemplates combinations of features and elements known to those skilled in the art. The embodiments, features, and elements disclosed in this application may also be combined with any conventional features or elements to form a unique inventive scheme as defined by the claims. Any feature or element of any embodiment may also be combined with features or elements from other inventive schemes to form another unique inventive scheme as defined by the claims. Therefore, it should be understood that any feature shown and / or discussed in this application may be implemented individually or in any suitable combination. Therefore, the embodiments are not limited except by the limitations imposed by the appended claims and their equivalents. Furthermore, various modifications and changes may be made within the scope of the appended claims.

[0061] Furthermore, in describing representative embodiments, the specification may have presented methods and / or processes as a specific sequence of steps. However, the method or process should not be limited to the specific order of steps described herein, to the extent that it does not depend on such a specific order. As will be understood by those skilled in the art, other sequences of steps are also possible. Therefore, the specific order of steps set forth in the specification should not be construed as a limitation of the claims. Moreover, the claims concerning the method and / or process should not be limited to the steps performed in the written order, and those skilled in the art will readily understand that these orders can be varied and still remain within the spirit and scope of the embodiments of this application.

[0062] This disclosure provides a transient radial clearance prediction method, such as... Figure 1 As shown, the method includes steps S100-S120, as detailed below:

[0063] S100. Obtain relevant input information for transient radial clearance prediction;

[0064] S110. Based on the relevant input information and the predetermined casing deformation model, blade deformation model and wheel deformation model, determine the deformation values ​​of the casing, blade and wheel at the first moment;

[0065] S120. Determine the radial clearance value at the first moment based on the predetermined transient radial clearance prediction model and the radial variation values ​​of the casing, blades, and wheel.

[0066] In this embodiment, the relevant input information includes geometric information, material information, and boundary condition information. The predetermined deformation models of the casing, blades, and wheel are different in dimensionality.

[0067] The radial clearance value at the first moment represents the transient radial clearance change value, which can be calculated using the transient radial clearance change calculation formula (1). That is, the initial clearance value plus the radial change value of the casing, minus the radial change values ​​of the blade and the wheel, that is, based on the first moment radial change of the casing, the first moment radial change of the blade, and the first moment radial change of the wheel, the change of the radial clearance at the first moment can be predicted.

[0068] The formula for calculating the radial clearance change at the first moment is as follows:

[0069] TC(t)=TC initial (t0)+(u shroud (t)-u blade (t)-u disk (t)) (1)

[0070] In the above formula, TC(t) represents the radial clearance change at the first moment. initial (t0) is the initial radial clearance value, u shroud (t) represents the radial change value of the casing at the first moment, u blade (t) represents the radial change of the blade at the first moment, u disk (t) represents the radial change of the wheel at the first moment.

[0071] In one exemplary embodiment, the deformation values ​​of the casing, blade, and disk at the first moment are determined based on the relevant input information and predetermined casing deformation models, blade deformation models, and disk deformation models, respectively.

[0072] First, it is necessary to determine the deformation models of the casing, blades, and wheel. These three models can each adopt different dimensions. Specifically, the casing deformation adopts one-dimensional thermal deformation and one-dimensional mechanical deformation, the blade deformation adopts one-dimensional thermal deformation and quasi-two-dimensional mechanical deformation, and the wheel deformation adopts two-dimensional thermal deformation and quasi-two-dimensional mechanical deformation.

[0073] Secondly, the deformation values ​​of each model in the computer box deformation model, blade deformation model, and wheel disk deformation model at the first moment are calculated.

[0074] In one exemplary embodiment, a casing model is established, and the radial variation value of the blades is calculated using equation (2):

[0075] u shroud (t)=u shroud1 (t)+u shroud2 (t) (2)

[0076] Among them, u shroud (t) represents the deformation value of the casing at the first moment, u shroud1 (t) represents the thermal deformation value of the casing at the first moment, u shroud2(t) represents the mechanical deformation value of the casing at the first moment.

[0077] In one exemplary embodiment, the deformation value of the casing at the first moment includes the thermal deformation value and the mechanical deformation value of the casing at the first moment. The thermal deformation value of the casing at the first moment can be determined based on the transient average temperature of the casing, wherein the transient average temperature of the casing is the average of the transient temperatures of each node in the wear-resistant coating and the metal coating of the casing. The mechanical deformation value of the casing at the first moment can be determined based on the elastic modulus of the casing material, the inner diameter of the high-temperature alloy layer of the casing, the outer diameter of the high-temperature alloy layer of the casing, the Poisson's ratio of the casing material, the inner wall pressure of the casing, and the outer wall pressure of the casing.

[0078] In one exemplary embodiment, the computer case undergoes thermal deformation u at the first moment. shroud1 (t) can be calculated using a one-dimensional model to determine the thermal deformation of the housing at the first moment. The calculation process is as follows:

[0079] Step 1. Temperature of each node in the computer case;

[0080] like Figure 5 The heat transfer model of the casing shown includes a wear-resistant coating and a metallic coating. Based on relevant heat transfer principles, the heat transfer formula for the casing can be established as follows:

[0081]

[0082] Among them, T shroud For the casing temperature (which is calculated using the difference equation described later), a shroud x is the thermal diffusivity of the casing (which can be obtained from the material property table). shroud The radial unit length of the casing (the radial unit length is customizable; for example, if the casing thickness is 1mm, and it is divided into 10 parts, the unit length is 0.1mm).

[0083] The one-dimensional heat transfer of the casing is analyzed by establishing a difference equation based on equation (3). The heat transfer equations for the wear-resistant coating and the metal layer are shown in equations (4) and (5). The temperature T of the i-th node of the wear-resistant coating of the casing can be obtained using equation (4). shroudAi The temperature T of the i-th node of the metal layer of the casing can be calculated using formula (5). shroundBi ;

[0084]

[0085]

[0086] Among them, T shroundAi T represents the temperature at each node of the wear-resistant coating on the casing. shroundBiLet a be the temperature of each node in the metal layer of the casing, p be the time p, p+1 be the time p+1, and a be the temperature of each node in the metal layer of the casing. shroundAi a is the thermal diffusivity of the wear-resistant coating on the casing. shroundBi The thermal diffusivity of the casing metal layer is . Let be the thermal diffusivity of the wear-resistant coating of the casing at time p, which can be obtained from the material property table. Let Δx be the thermal diffusivity of the casing metal layer at time p of node i (which can be obtained from the material property table). a Δx represents the length of the wear-resistant coating node element. b Δt represents the length of the metal layer node elements. The lengths of these two node elements can be customized based on the thickness of the wear-resistant coating and the metal layer. For example, the wear-resistant coating thickness could be 0.5, and the metal layer thickness 1.5. To ensure that the node lengths on both sides are the same, the wear-resistant coating element length could be set to 0.1, and the metal layer element length to 0.3. Δt represents the time difference between time p+1 and time p. The temperature of the wear-resistant coating of the casing at the i-th node at time p is either the temperature of the metal layer of the casing at the i-th node at time p.

[0087] Among them, such as Figure 5 As shown in the heat exchange model of the middle casing, T0 and T n+m+1 This is the temperature at the casing boundary nodes, obtained through experiments or other simulation analyses. It can be determined using the heat transfer coefficient h at the casing boundary. a h b and heat exchange temperature T fa T fb (These four parameters can be obtained through experimental measurement or steady-state three-dimensional simulation) and calculated.

[0088] Step 2. Based on the transient temperature T of each node shroudi The transient average temperature T of the casing is obtained by averaging. shroud_ave ;

[0089] Step 3. Based on the calculated transient average temperature T of the casing shroud_ave Using the one-dimensional thermal deformation formula (6) for the casing, the one-dimensional thermal deformation of the casing at the first moment is obtained:

[0090] u shroud1 =α shroud *r shroud1 *T shroud_ave (6)

[0091] Where u shroud1 α represents the thermal deformation of the casing. shroud r is the coefficient of thermal expansion of the casing material. shroud1 T is the inner diameter of the high-temperature alloy layer of the casing. shroud_aveThe average temperature of the casing is given; the material properties can be determined based on the casing temperature T. shroud_ave Select. Material properties include elastic modulus, coefficient of thermal expansion, thermal diffusivity, Poisson's ratio, thermal conductivity, and specific heat capacity; these can be obtained from material property tables and are functions of temperature.

[0092] In one exemplary embodiment, the mechanical deformation of the computer case at a first moment u shroud2 ;

[0093] The mechanical deformation of the casing can be calculated using equation (7) based on the knowledge of elasticity mechanics.

[0094]

[0095] Among them, u shroud2 E represents the mechanical deformation of the casing at the first moment caused by the pressure load. shroud Let r be the elastic modulus of the casing material (obtainable from a material property table, and is a function of temperature). shroud1 r is the inner diameter of the high-temperature alloy layer of the casing. shroud2 The outer diameter of the high-temperature alloy layer of the casing (obtained by direct measurement), ν shroud P represents the Poisson's ratio of the casing material (obtainable from a material property table, and is a function of temperature). i P is the pressure inside the casing wall. o The pressure on the outer wall of the casing (the pressure can be obtained through experimental measurement or steady-state three-dimensional simulation), and the material properties can be determined based on the casing temperature T. shroud_ave Select.

[0096] In one exemplary embodiment, a blade model is established, and the radial variation value of the blade is calculated using equation (8):

[0097] u blade (t)=u blade1 (t)+u blade2 (t) (8)

[0098] Among them, u blade (t) represents the deformation of the blade at the first moment, u blade1 (t) represents the thermal deformation of the blade at the first moment, u blade2 (t) represents the mechanical deformation of the blade at the first moment. The thermal deformation model and mechanical deformation model of the blade are established below to determine the amount of thermal deformation and mechanical deformation of the blade.

[0099] In one exemplary embodiment, the thermal deformation value of the blade at the first moment is calculated using a one-dimensional thermal deformation model of the blade, based on the blade temperature, blade length, and the corresponding coefficient of thermal expansion of the blade material at that blade temperature; wherein, the one-dimensional thermal deformation model of the blade is:

[0100] u blade1 =α blade *L blade *T blade

[0101] Among them, u blade1 α is the thermal deformation value of the blade at the first moment. blade L is the coefficient of thermal expansion of the blade material. blade T is the blade length. blade This refers to the blade temperature.

[0102] The blade temperature was calculated using equation (9) based on relevant knowledge of heat transfer.

[0103]

[0104] Where p is the time p, p+1 is the time p+1, τ is the time constant determined by the heat transfer characteristics of the blade, and T blade For the blade temperature, T ref The heat exchange reference temperature can be determined based on the mainstream temperature of the compressor blades or the equivalent heat exchange temperature of the turbine, as shown in Equation (10).

[0105]

[0106] Among them, T ref T is the heat exchange reference temperature. mf The gas temperature in the turbine's main flow region (which can be obtained through experimental measurement or three-dimensional steady-state simulation), T cool η is the cooling gas temperature at the turbine film cooling hole (which can be obtained through experimental measurement or three-dimensional steady-state simulation), and η is the cooling efficiency (the efficiency is the design value, and different blade designs have different efficiencies).

[0107] Using equation (11), the one-dimensional thermal deformation of the blade is obtained.

[0108] u blade1 =α blade *L blade *T blade (11)

[0109] Among them, u blade1 α represents the thermal deformation of the blade. blade L is the coefficient of thermal expansion of the blade material (which can be obtained from a material property table and is a function of temperature). blade T represents the blade length (obtained by measurement). blade This is the blade temperature (i.e., the temperature obtained according to Formula 9).

[0110] In one exemplary embodiment, the mechanical deformation of the blade at a first moment is calculated, wherein the centrifugal deformation thickness characteristics of the blade are as follows: Figure 6 As shown:

[0111] 1. According to the characteristic relationship of blade cross section (12), the characteristic parameter a of blade cross section can be obtained by measuring the cross-sectional area of ​​the bottom and top.

[0112]

[0113] Where A(x) represents the change in the cross-sectional area of ​​the leaf blade at different distances x from the leaf root. When x = 0, A(x) = A0, which is the cross-sectional area of ​​the leaf root, and x = L. blade A(x) = A0(1-a) 2 This refers to the blade tip cross-sectional area. A(x) is the variable cross-sectional area of ​​the blade, and a is the characteristic parameter of the variable cross-section of the blade, representing the slope of the variable cross-section of the blade, which is measured according to the designed blade.

[0114] II. Based on the analysis of elasticity theory, the centrifugal deformation of the blade is considered using equation (13) to account for the quasi-two-dimensional centrifugal deformation of the blade.

[0115]

[0116] Where 'a' represents the blade's variable cross-section slope, 'ρ' represents the thickness change (calculated in the above steps), 'N' represents the blade's rotational speed (obtained through direct measurement), and 'ρ' represents the blade's rotational speed. blade E represents the density of the leaves (obtained through direct measurement). blade This represents the elastic modulus of the blade (which can be obtained from a material property table and is a function of temperature). s r id This indicates the outer diameter of the wheel (obtained through direct measurement).

[0117] In one exemplary embodiment, the thermal deformation value of the wheel at the first moment is determined by the thermal deformation formula of the wheel based on the thermal expansion coefficient of the wheel material, the outer diameter of the wheel, and the temperature of the wheel at the first moment.

[0118] The thermal deformation formula of the wheel is as follows:

[0119] u disk1 =α disk *r disk *T disk_ave ;

[0120] In the above formula, u disk1 α is the thermal deformation value of the disk at the first moment. disk r is the coefficient of thermal expansion of the disc material. disk T is the outer diameter of the wheel. disk_ave This represents the temperature of the roulette wheel at the first moment.

[0121] In one exemplary embodiment, the temperature of the wheel at a first moment is determined by the following steps:

[0122] Based on the heat transfer coefficient h a h b and heat exchange temperature T fa T fb Determine the temperatures of the left and right boundary nodes of the roulette wheel at the first moment;

[0123] The blade temperature T at the first moment blade As the temperature of all nodes along the axial direction of the upper boundary of the disk at time j=n+1, the shaft temperature T at the first moment is... shaft This represents the temperature of all nodes along the lower boundary axis of the disk at the first moment when j=0.

[0124] The temperature of each node of the wheel at the first moment is determined by the nodal heat transfer equation based on the temperatures of the left and right boundary nodes of the wheel at the first moment, the temperatures of all nodes along the upper boundary axis of the wheel at the first moment, and the temperatures of all nodes along the lower boundary axis of the wheel at the first moment.

[0125] The temperature of the roulette wheel at the first moment is obtained by averaging the temperatures of each node at the first moment.

[0126] In one exemplary embodiment, the node heat transfer equation is:

[0127]

[0128] In the above formula, T diski,j Let be the temperature of the wheel node, p be the time p, p+1 be the time p+1, and a be the temperature of the node. diski,j Let Δr be the thermal diffusivity of the disk, Δz be the radial element length of the node, and r be the axial element length of the node. j Where is the node radius.

[0129] In one exemplary embodiment, the mechanical deformation value of the wheel at the first moment is determined according to the following method:

[0130] The deformation values ​​at the inner diameter and outer diameter of each segment of the first, second, and third discs are determined respectively; wherein the first, second, and third discs are three discs of equal thickness obtained by dividing the disc; the discs are discs of variable thickness.

[0131] The mechanical deformation value of the wheel at the first moment is calculated based on the deformation values ​​at the inner diameter and outer diameter of each segment, the equal force on the contact surface, and the equal radial deformation of the contact surface.

[0132] The following example illustrates the process of calculating the thermal deformation of the wheel at the first moment:

[0133] S1. Establish a roulette wheel model and calculate the roulette wheel change value using equation (14).

[0134] u disk (t)=u disk1 (t)+u disk2 (t) (14)

[0135] Among them, u disk (t) represents the deformation of the wheel at the first moment, u disk1 (t) represents the thermal deformation of the wheel at the first moment, u disk2 (t) represents the mechanical deformation of the wheel at the first moment. The thermal deformation model and the mechanical deformation model of the wheel are established below.

[0136] S2. Considering the symmetrical deformation of the disk in the circumferential direction, the two-dimensional heat transfer model of the disk is analyzed by relevant knowledge of heat transfer, as shown in Equation (15).

[0137]

[0138] Among them, T disk Let r be the wheel temperature, r be the radial position of the wheel, z be the axial position of the wheel, and a be the axial position of the wheel. disk dr and dz are the radial and axial element lengths of the disk, respectively. The element lengths are customized according to the disk geometry. For example, if the radial length of the disk is 10 and the axial length is 2, then if the radial length is divided into 10 elements, then dr is 1, and if the axial length is divided into 10 elements, then dz is 0.2.

[0139] S3. Determine T diski,j The temperature of the disk node;

[0140] Based on Equation 15, a two-dimensional heat transfer difference equation is further established to study the axial and radial heat conduction of the disk, with the configuration as follows: Figure 7 As shown, the nodal heat transfer equation (16) is established, and T is obtained. diski,j Temperature of the disk node:

[0141]

[0142] Among them, T diski,j Let be the temperature of the wheel node, p be the time p, p+1 be the time p+1, and a be the temperature of the node. diski,j Let be the thermal diffusivity of the disk (obtainable from a material property table, a function of temperature), Δr be the radial element length of the node, and Δz be the axial element length of the node. j The node radius (also set) is used. The temperatures of the left and right boundary nodes of the disk can be determined based on the heat transfer coefficient h. a h b and heat exchange temperature T fa Tfb (This can be calculated based on experiments or other simulation analyses.) Flange temperature T blade The blade temperature is equivalent to temperature j = n + 1, and the wheel center temperature is T. shaft The axial temperature is equivalent to the temperature at j=0, which is the temperature of all nodes along the axial direction of the upper and lower boundaries. It can also be obtained through experiments or simulation analysis.

[0143] S4. Calculate the transient temperature T of the wheel. disk_ave ;

[0144] The transient temperature T of the wheel is obtained by averaging the temperatures at each node of the wheel according to Formula 16. disk_ave ,

[0145] S5. Calculate the radial thermal deformation of the wheel;

[0146] The radial thermal deformation of the wheel is analyzed using equation (17):

[0147] u disk1 =α disk *r disk *T disk_ave (17)

[0148] Among them, u disk1 α represents the thermal deformation of the wheel. disk Let r be the coefficient of thermal expansion of the disk material (which can be obtained from a material property table and is a function of temperature). disk T is the outer diameter of the wheel (obtained by direct measurement). disk_ave The temperature is the wheel temperature; material properties are determined based on the wheel temperature T. disk_ave get.

[0149] S6. Mechanical deformation of the wheel: (The outer diameter affects the clearance, but the deformation of the outer diameter needs to be obtained by solving the equations for the deformation of the inner and outer diameters.)

[0150] When calculating mechanical deformation, the variable thickness disc can be simplified as follows: Figure 8 The three equal-thickness disks A, B, and C shown are solved. According to the relevant theories of elasticity, equations (18), (19), and (20) can be used to analyze the deformation of disks A, B, and C at the inner diameter.

[0151] u r,Ai =g(σ r,Ai ,σ r,Ae ,N)

[0152]

[0153]

[0154]

[0155] Where, ρ disk The density of disks A, B, and C, E disk Let υ be the elastic modulus of disks A, B, and C. disk Let N be the Poisson's ratio of disks A, B, and C, and r be the rotational speed. Ai r Bi r Ci The inner diameters r of disks A, B, and C are respectively. Ae r Be r Ce These are the outer diameters of disks A, B, and C, respectively, u r,Ai u r,Bi u r,Ci The deformations at the inner diameters of A, B, and C are respectively, σ r,Ai σ r,Bi σ r,Ci The stresses at the inner diameters of disks A, B, and C are respectively, σ r,Ae σ r,Be σ r,Ce These represent the stresses at the outer diameters of disks A, B, and C, respectively. Deformation and stress are unknowns and need to be solved.

[0156] According to the relevant theories of elasticity, equations (21), (22), and (23) can be used to analyze the deformation of disks A, B, and C at their outer diameter.

[0157]

[0158]

[0159]

[0160] u r,Ae u r,Be u r,Ce The deformations at the outer diameters of points A, B, and C are respectively, and these need to be solved.

[0161] To solve for stress and deformation, we need to utilize the deformation compatibility relationship of the variable thickness disk, which satisfies the following equation:

[0162] 1) The forces at the contact surfaces of the three equal-thickness discs are equal, i.e., equations (24) and (25).

[0163] σ r,Ci h C =σ r,Be h B (twenty four)

[0164] σ r,Bi h B =σ r,Ae h A (25)

[0165] 2) The radial deformation of the three contact surfaces is equal, i.e., equations (26) and (27).

[0166] u r,Be =u r,Ci (26)

[0167] u r,Bi =u r,Ae (27)

[0168] 3) Stress at the inner and outer diameters of the wheel:

[0169] σ r,Ai =0 (28)

[0170] σ r,Ce =0 (29)

[0171] The simultaneous equations can be used to solve for the quasi-two-dimensional centrifugal deformation u of the wheel. disk2 , that is u r,Ce .

[0172] To address the issues of low accuracy in one-dimensional prediction models and slow prediction in three-dimensional simulation methods, this invention proposes a rapid prediction method for transient radial clearance based on a multi-dimensional coupled model. Different dimensional prediction models are established and analyzed for different components, fully considering the geometric and heat transfer characteristics of the components. This method improves the prediction accuracy of transient radial clearance while achieving rapid prediction.

[0173] 1. Compared to one-dimensional prediction models, the computational accuracy is improved. This method considers the geometric and heat transfer characteristics of components, including the variable cross-section characteristics of blades and the axial and convective heat transfer characteristics of the disk, which greatly improves the accuracy of component heat transfer and deformation prediction, and improves the accuracy of transient clearance prediction.

[0174] 2. Compared to three-dimensional prediction methods, computation time is reduced. Three-dimensional methods are suitable for predicting steady-state gaps, while predicting transient gaps requires weeks or longer. This method combines the characteristics of low-dimensional models, coupling models of different dimensions to achieve rapid prediction, greatly reducing computation time.

[0175] This disclosure also provides an apparatus for predicting transient radial clearance, such as... Figure 2 As shown, the device includes a memory 210 and a processor 220; the memory is used to store a program for performing transient radial clearance prediction, and the processor is used to read and execute the program for performing transient radial clearance prediction, and to perform the method described in any of the above embodiments.

[0176] Example 1

[0177] This example illustrates a fast prediction method for transient radial clearance of aero-engines based on a multi-dimensional coupling model, such as... Figure 3 As shown, the implementation process is as follows:

[0178] 1. Establish a transient radial clearance prediction model;

[0179] A transient radial clearance prediction model is established. The transient radial clearance value is the initial clearance value plus the radial variation value of the casing, minus the radial variation values ​​of the blades and the impeller. The transient radial clearance prediction model is as follows:

[0180] TC(t)=TC initial (t0)+(u shroud (t)-u blade (t)-u disk (t));

[0181] Where TC(t) represents the radial gap change at the first moment, TC initial (t0) is the initial radial clearance value, u shroud (t) represents the radial change value of the casing at the first moment, u blade (t) represents the radial change of the blade at the first moment, u disk (t) represents the radial change of the wheel at the first moment;

[0182] 2. Establish prediction models of different dimensions for the casing, blades, and wheel;

[0183] In this step, a one-dimensional model can be created for the casing, one-dimensional and quasi-two-dimensional models can be created for the blades, and two-dimensional and quasi-two-dimensional models can be created for the wheel.

[0184] In this embodiment, the different dimensional models are only examples, including but not limited to establishing a one-dimensional thermal deformation and mechanical deformation model for the casing, a one-dimensional thermal deformation and quasi-two-dimensional mechanical deformation model for the blades, and a two-dimensional thermal deformation and quasi-two-dimensional mechanical deformation model for the wheel. The purpose is to establish different dimensional models based on the characteristics of different components to predict the radial clearance.

[0185] 3. Based on the established model, input the boundary conditions and calculate the deformation of the casing, blades, and disk respectively;

[0186] The radial deformation of the computer casing is calculated based on the casing deformation model:

[0187] The casing deformation model is as follows:

[0188] u shroud (t)=u shroud1 (t)+u shroud2 (t);

[0189] Among them, u shroud (t) represents the deformation value of the casing at the first moment, u shroud1(t) represents the thermal deformation value of the casing at the first moment, u shroud2 (t) represents the mechanical deformation value of the casing at the first moment;

[0190] The radial deformation of the blade is calculated based on the blade deformation model:

[0191] The blade deformation model is as follows:

[0192] u blade (t)=u blade1 (t)+u blade2 (t)

[0193] Among them, u blade (t) represents the deformation value of the blade at the first moment, u blade1 (t) represents the thermal deformation value of the blade at the first moment, u blade2 (t) represents the mechanical deformation value of the blade at the first moment;

[0194] Calculate the radial deformation of the wheel based on the wheel deformation model:

[0195] The wheel deformation model is as follows:

[0196] u disk (t)=u disk1 (t)+u disk2 (t);

[0197] Among them, u disk (t) represents the deformation value of the wheel at the first moment, u disk1 (t) represents the thermal deformation value of the wheel at the first moment, u disk2 (t) represents the mechanical deformation value of the wheel at the first moment.

[0198] 4. Based on the predetermined transient radial clearance prediction model and the radial variation values ​​of the casing, blades, and wheel calculated in step 3, determine the radial clearance value at the first moment.

[0199] Example 2

[0200] The flowchart of a transient radial clearance prediction method is as follows:

[0201] S1. Establish a transient radial clearance prediction model

[0202] Establish such as Figure 4 The transient radial clearance prediction model shown uses Equation (1) to predict the change of the transient radial clearance. The initial clearance value is added to the radial change value of the casing, and the radial change values ​​of the blade and the wheel are subtracted. That is, the change of the radial clearance at the first moment is predicted based on the first moment radial change of the casing, the first moment radial change of the blade, and the first moment radial change of the wheel.

[0203] The formula for calculating the radial clearance change at the first moment is as follows:

[0204] TC(t)=TC initial (t0)+(u shroud (t)-u blade (t)-u disk (t)) (1)

[0205] In the above formula, TC(t) represents the radial clearance change at the first moment. initial (t0) is the initial radial clearance value, u shroud (t) represents the radial change value of the casing at the first moment, u blade (t) represents the radial change of the blade at the first moment, u disk (t) represents the radial change of the wheel at the first moment.

[0206] S2. Establish models of the casing, blades, and disk respectively to calculate the radial change values ​​of the casing, blades, and disk at the first moment.

[0207] S21. Establish the casing model and use formula (2) to calculate the radial change value of the casing at the first moment.

[0208] u shroud (t)=u shroud1 (t)+u shroud2 (t) (2)

[0209] Among them, u shroud (t) represents the deformation of the casing at the first moment, u shroud1 (t) represents the thermal deformation of the casing at the first instant, u shroud2 (t) represents the mechanical deformation of the casing at the first moment.

[0210] The first-moment thermal deformation of the computer casing and the first-moment mechanical deformation of the casing are distinguished:

[0211] S211. Determine the first-moment thermal deformation of the casing. shroud1 (t);

[0212] In the first-moment thermal deformation of the computer case, a one-dimensional model of the computer case's first-moment thermal deformation can be used:

[0213] Step 1. Temperature of each node in the computer case;

[0214] like Figure 5 The heat transfer model of the casing shown includes a wear-resistant coating and a metallic coating. Based on relevant heat transfer principles, the heat transfer formula for the casing can be established as follows:

[0215]

[0216] Among them, T shroud For the casing temperature (which is calculated using the difference equation described later), a shroud x is the thermal diffusivity of the casing (which can be obtained from the material property table). shroud The radial unit length of the casing (the radial unit length is customizable; for example, if the casing thickness is 1mm, and it is divided into 10 parts, the unit length is 0.1mm).

[0217] The one-dimensional heat transfer of the casing is analyzed by establishing a difference equation based on equation (3). The heat transfer equations for the wear-resistant coating and the metal layer are shown in equations (4) and (5). T is obtained from equation (4). shroudAi T is the temperature of the i-th node of the wear-resistant coating on the casing, obtained by equation (5). shroundBi The temperature of the i-th node of the casing metal layer:

[0218]

[0219]

[0220] Among them, T shroundAi T represents the temperature at each node of the wear-resistant coating on the casing. shroundBi Let a be the temperature of each node in the metal layer of the casing, p be the time p, p+1 be the time p+1, and a be the temperature of each node in the metal layer of the casing. shroundAi a is the thermal diffusivity of the wear-resistant coating on the casing. shroundBi The thermal diffusivity of the casing metal layer is . Let be the thermal diffusivity of the wear-resistant coating of the casing at time p, which can be obtained from the material property table. Let Δx be the thermal diffusivity of the casing metal layer at time p of node i (which can be obtained from the material property table). a Δx represents the length of the wear-resistant coating node element. b Δt represents the length of the metal layer node elements. The lengths of these two node elements can be customized based on the thickness of the wear-resistant coating and the metal layer. For example, the wear-resistant coating thickness could be 0.5, and the metal layer thickness 1.5. To ensure that the node lengths on both sides are the same, the wear-resistant coating element length could be set to 0.1, and the metal layer element length to 0.3. Δt represents the time difference between time p+1 and time p. The temperature of the wear-resistant coating of the casing at the i-th node at time p is either the temperature of the metal layer of the casing at the i-th node at time p.

[0221] Among them, such as Figure 5 As shown in the heat exchange model of the middle casing, T0 and T n+m+1 This is the temperature at the casing boundary nodes, obtained through experiments or other simulation analyses. It can be determined using the heat transfer coefficient h at the casing boundary. a h b and heat exchange temperature T fa Tfb (These four parameters can be obtained through experimental measurement or through steady-state three-dimensional simulation)

[0222] Step 2. Based on the transient temperature T of each node shroudi The transient average temperature T of the casing is obtained by averaging. shroud_ave ;

[0223] Step 3. Based on the calculated transient average temperature T of the casing shroud_ave Using the one-dimensional thermal deformation formula (6) for the casing, the one-dimensional thermal deformation of the casing at the first moment is obtained:

[0224] u shroud1 =α shroud *r shroud1 *T shroud_ave (6)

[0225] Where u shroud1 α represents the thermal deformation of the casing. shroud r is the coefficient of thermal expansion of the casing material. shroud1 T is the inner diameter of the high-temperature alloy layer of the casing. shroud_ave The average temperature of the casing is given; the material properties can be determined based on the casing temperature T. shroud_ave Select. Material properties include elastic modulus, coefficient of thermal expansion, thermal diffusivity, Poisson's ratio, thermal conductivity, and specific heat capacity; these can be obtained from material property tables and are functions of temperature.

[0226] S212. Determine the first-moment mechanical deformation of the casing. shroud2 ;

[0227] The mechanical deformation of the casing is calculated using formula (7) based on the knowledge of elasticity mechanics.

[0228]

[0229] Among them, u shroud2 E represents the mechanical deformation of the casing at the first moment caused by the pressure load. shroud Let r be the elastic modulus of the casing material (obtainable from a material property table, and is a function of temperature). shroud1 r is the inner diameter of the high-temperature alloy layer of the casing. shroud2 The outer diameter of the high-temperature alloy layer of the casing (obtained by direct measurement), ν shroud P represents the Poisson's ratio of the casing material (obtainable from a material property table, and is a function of temperature). i P is the pressure inside the casing wall. o The pressure on the outer wall of the casing (the pressure can be obtained through experimental measurement or steady-state three-dimensional simulation), and the material properties can be determined based on the casing temperature T. shroud_ave Select.

[0230] S22. Establish a blade model and use equation (8) to calculate the radial variation value of the blade.

[0231] u blade (t)=u blade1 (t)+u blade2 (t) (8)

[0232] Among them, u blade (t) represents the deformation of the blade at the first moment, u blade1 (t) represents the thermal deformation of the blade at the first moment, u blade2 (t) represents the mechanical deformation of the blade at the first moment. The thermal deformation model and mechanical deformation model of the blade are established below to determine the amount of thermal deformation and mechanical deformation of the blade.

[0233] S221. Calculate the thermal deformation of the blade.

[0234] The blade heat transfer model is analyzed using the lumped parameter method. Based on the relevant knowledge of heat transfer, the blade temperature is calculated using equation (9).

[0235]

[0236] Where p is the time p, p+1 is the time p+1, τ is the time constant determined by the heat transfer characteristics of the blade, and T blade For the blade temperature, T ref The heat exchange reference temperature can be determined based on the mainstream temperature of the compressor blades or the equivalent heat exchange temperature of the turbine, as shown in Equation (10).

[0237] T ref =η(T) cool -T mf )+T mf (10)

[0238] Among them, T ref T is the heat exchange reference temperature. mf The gas temperature in the turbine's main flow region (which can be obtained through experimental measurement or three-dimensional steady-state simulation), T cool η is the cooling gas temperature at the turbine film cooling hole (which can be obtained through experimental measurement or three-dimensional steady-state simulation), and η is the cooling efficiency (the efficiency is the design value, and different blade designs have different efficiencies).

[0239] Using equation (11), the one-dimensional thermal deformation of the blade is obtained.

[0240] u blade1 =α blade *L blade *T blade (11)

[0241] Among them, u blade1α represents the thermal deformation of the blade. blade L is the coefficient of thermal expansion of the blade material (which can be obtained from a material property table and is a function of temperature). blade T represents the blade length (obtained by measurement). blade This is the blade temperature (i.e., the temperature obtained according to Formula 9).

[0242] S222. Calculate the mechanical deformation of the blade.

[0243] The characteristics of blade centrifugal deformation and thickness variation are as follows Figure 6 As shown.

[0244] I. According to the characteristic relationship of blade cross section (12), a can be obtained by measuring the cross-sectional areas of the bottom and top.

[0245]

[0246] Where A(x) represents the change in the cross-sectional area of ​​the leaf blade at different distances x from the leaf root. When x = 0, A(x) = A0, which is the cross-sectional area of ​​the leaf root, and x = L. blade A(x) = A0(1-a) 2 This refers to the blade tip cross-sectional area. A(x) is the variable cross-sectional area of ​​the blade, and a is the characteristic parameter of the variable cross-section of the blade, representing the slope of the variable cross-section of the blade, which is measured according to the designed blade.

[0247] II. Based on the analysis of elasticity theory, the centrifugal deformation of the blade is considered using equation (13) to account for the quasi-two-dimensional centrifugal deformation of the blade.

[0248]

[0249] Where 'a' represents the slope of the variable cross-section, 'ρ' represents the change in thickness (calculated in the above steps), 'N' represents the rotational speed (obtained through direct measurement), and 'ρ' represents the rotational speed. blade E represents density (obtained through direct measurement). blade This represents the elastic modulus (which can be obtained from a material property table and is a function of temperature). This indicates the outer diameter of the wheel (obtained through direct measurement).

[0250] S23. Establish a roulette wheel model and use equation (14) to calculate the roulette wheel change value.

[0251] u disk (t)=u disk1 (t)+u disk2 (t) (14)

[0252] Among them, u disk (t) represents the deformation of the wheel at the first moment, u disk1 (t) represents the thermal deformation of the wheel at the first moment, u disk2(t) represents the mechanical deformation of the wheel at the first moment. The thermal deformation model and the mechanical deformation model of the wheel are established below.

[0253] S231. Considering the symmetrical deformation of the wheel in the circumferential direction, the two-dimensional heat transfer model of the wheel is analyzed by relevant knowledge of heat transfer, as shown in Equation (15).

[0254]

[0255] Among them, T disk Let r be the wheel temperature, r be the radial position of the wheel, z be the axial position of the wheel, and a be the axial position of the wheel. disk dr and dz are the radial and axial element lengths of the disk, respectively. The element lengths are customized according to the disk geometry. For example, if the radial length of the disk is 10 and the axial length is 2, then if the radial length is divided into 10 elements, then dr is 1, and if the axial length is divided into 10 elements, then dz is 0.2.

[0256] Based on Equation 15, a two-dimensional heat transfer difference equation is further established to study the axial and radial heat conduction of the disk, with the configuration as follows: Figure 5 As shown, the nodal heat transfer equation (16) is established:

[0257]

[0258] Where T diski,j Let be the temperature of the wheel node, p be the time p, p+1 be the time p+1, and a be the temperature of the node. diski,j Let be the thermal diffusivity of the disk (obtainable from a material property table, a function of temperature), Δr be the radial element length of the node, and Δz be the axial element length of the node. j The node radius (which is also set).

[0259] The temperatures at the left and right boundary nodes of the disk can be determined based on the heat transfer coefficient h. a h b and heat exchange temperature T fa T fb (It can be calculated based on experiments or other simulation analyses.)

[0260] Flange temperature T blade The blade temperature is equivalent to temperature j = n + 1, and the wheel center temperature is T. shaft The axial temperature is equivalent to the temperature at j=0, which is the temperature of all nodes along the axial direction of the upper and lower boundaries. It can also be obtained through experiments or simulation analysis.

[0261] The transient temperature T of the wheel is obtained by averaging the temperatures at each node of the wheel according to Formula 16. disk_ave The radial thermal deformation of the wheel is analyzed using equation (17).

[0262] udisk1 =α disk *r disk *T disk_ave (17)

[0263] Where u disk1 α represents the thermal deformation of the wheel. disk Let r be the coefficient of thermal expansion of the disk material (which can be obtained from a material property table and is a function of temperature). disk T is the outer diameter of the wheel (obtained by direct measurement). disk_ave The temperature is the wheel temperature; material properties are determined based on the wheel temperature T. disk_ave get.

[0264] Mechanical deformation of the wheel: (The outer diameter affects the clearance, but the deformation of the outer diameter needs to be obtained by solving equations for the deformation of the inner and outer diameters.)

[0265] When calculating mechanical deformation, the variable thickness disc can be simplified as follows: Figure 8 The three equal-thickness disks A, B, and C shown are solved. According to the relevant theories of elasticity, equations (18), (19), and (20) can be used to analyze the deformation of disks A, B, and C at the inner diameter.

[0266]

[0267]

[0268]

[0269] Where, ρ disk The density of disks A, B, and C, E disk Let υ be the elastic modulus of disks A, B, and C. disk Let N be the Poisson's ratio of disks A, B, and C, and r be the rotational speed. Ai r Bi r Ci The inner diameters r of disks A, B, and C are respectively. Ae r Be r Ce These are the outer diameters of disks A, B, and C, respectively, u r,Ai u r,Bi u r,Ci The deformations at the inner diameters of A, B, and C are respectively, σ r,Ai σ r,Bi σ r,Ci The stresses at the inner diameters of disks A, B, and C are respectively, σ r,Ae σ r,Be σ r,Ce These represent the stresses at the outer diameters of disks A, B, and C, respectively. Deformation and stress are unknowns and need to be solved.

[0270] According to the relevant theories of elasticity, equations (21), (22), and (23) can be used to analyze the deformation of disks A, B, and C at their outer diameter.

[0271]

[0272]

[0273]

[0274] u r,Ae u r,Be u r,Ce The deformations at the outer diameters of points A, B, and C are respectively, and these need to be solved.

[0275] To solve for stress and deformation, we need to utilize the deformation compatibility relationship of the variable thickness disk, which satisfies the following equation:

[0276] 1) The forces at the contact surfaces of the three equal-thickness discs are equal, i.e., equations (24) and (25).

[0277] σ r,Ci h C =σ r,Be h B (twenty four)

[0278] σ r,Bi h B =σ r,Ae h A (25)

[0279] 2) The radial deformation of the three contact surfaces is equal, i.e., equations (26) and (27).

[0280] u r,Be =u r,Ci (26)

[0281] u r,Bi =u r,Ae (27)

[0282] 3) Stress at the inner and outer diameters of the wheel:

[0283] σ r,Ai =0 (28)

[0284] σ r,Ce =0 (ignoring blade influence) (29)

[0285] The simultaneous equations can be used to solve for the quasi-two-dimensional centrifugal deformation u of the wheel. disk2 , that is u r,Ce .

[0286] This embodiment proposes a rapid prediction method for transient radial clearance based on a multi-dimensional coupling model. Different prediction models with different dimensions are established for analysis for different components, which fully considers the geometric and heat transfer characteristics of the components, thereby improving the prediction accuracy of transient radial clearance while achieving rapid prediction.

[0287] It will be understood by those skilled in the art that all or some of the steps, systems, or apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all components may be implemented as software executed by a processor, such as a digital signal processor or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software may be distributed on a computer-readable medium, which may include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

Claims

1. A transient radial clearance prediction method, wherein the radial clearance refers to the radial distance between the engine rotor blade tip and the casing; the engine includes a casing, blades, and a rotor disk; characterized in that, The method includes: Obtain relevant input information for transient radial clearance prediction, wherein the relevant input information includes: geometric information, material information, and boundary condition information; Based on the relevant input information and the predetermined deformation models of the casing, blades, and wheel, the deformation values ​​of the casing, blades, and wheel at the first moment are determined. Based on the predetermined transient radial clearance prediction model, and the radial variation values ​​of the casing, blades, and wheel, the radial clearance value at the first moment is determined; Among them, the predetermined casing deformation model, blade deformation model and wheel deformation model have different dimensions; The blade deformation model is as follows: ； in, This represents the deformation value of the blade at the first moment. This represents the thermal deformation value of the blade at the first moment. This represents the mechanical deformation value of the blade at the first moment. The thermal deformation value of the blade at the first moment is calculated using a one-dimensional thermal deformation model of the blade based on the blade temperature, blade length, and the corresponding coefficient of thermal expansion of the blade material at that blade temperature. The mechanical deformation value of the blade at the first moment is determined using a two-dimensional centrifugal deformation model of the blade based on the variable cross-sectional slope of the blade, the blade rotation speed, the blade density, the blade elastic modulus, and the outer diameter of the wheel. The variable cross-sectional slope of the blade is determined based on the cross-sectional areas at the bottom and top of the blade. The two-dimensional centrifugal deformation model of the blade is as follows: ； In the above model, This indicates the blade's variable cross-section slope, and N represents the blade's rotational speed. Indicates the density of the leaves. For the blade length, This represents the elastic modulus of the blade. This indicates the outer diameter of the wheel.

2. The transient radial clearance prediction method according to claim 1, characterized in that, The casing deformation model is as follows: ； in, This represents the deformation value of the casing at the first moment. This represents the thermal deformation value of the casing at the first moment. This represents the mechanical deformation value of the casing at the first moment. The wheel deformation model is as follows: ； in, This represents the deformation value of the roulette wheel at the first moment. This represents the thermal deformation value of the wheel at the first moment. This represents the mechanical deformation value of the wheel at the first moment.

3. The transient radial clearance prediction method according to claim 2, characterized in that, The thermal deformation value of the casing at the first moment is determined based on the transient average temperature of the casing, wherein the transient average temperature of the casing is the average value of the transient temperatures of each node in the wear-resistant coating and the metal coating of the casing. The mechanical deformation value of the casing at the first moment is determined based on the elastic modulus of the casing material, the inner diameter of the casing high-temperature alloy layer, the outer diameter of the casing high-temperature alloy layer, the Poisson's ratio of the casing material, the pressure on the inner wall of the casing, and the pressure on the outer wall of the casing.

4. The transient radial clearance prediction method according to claim 2, characterized in that, The one-dimensional thermal deformation model of the blade is as follows: in, This represents the thermal deformation value of the blade at the first moment. The coefficient of thermal expansion of the blade material. This refers to the blade temperature.

5. The transient radial clearance prediction method according to claim 2, characterized in that, The thermal deformation value of the wheel at the first moment is determined by the thermal deformation formula of the wheel based on the thermal expansion coefficient of the wheel material, the outer diameter of the wheel, and the temperature of the wheel at the first moment. The thermal deformation formula of the wheel is as follows: ； In the above formula, This represents the thermal deformation value of the wheel at the first moment. The coefficient of thermal expansion of the disc material is _____. The outer diameter of the wheel, This represents the temperature of the roulette wheel at the first moment.

6. The transient radial clearance prediction method according to claim 5, characterized in that, The temperature of the wheel at the first moment is determined by the following steps: Based on heat transfer coefficient , and heat exchange temperature , Determine the temperatures of the left and right boundary nodes of the roulette wheel at the first moment; The blade temperature at the first moment As the temperature of all nodes along the axial direction of the upper boundary of the disk at the first moment when j=n+1, the shaft temperature at the first moment. This represents the temperature of all nodes along the lower boundary axis of the disk at the first moment when j=0. The temperature of each node of the wheel at the first moment is determined by the nodal heat transfer equation based on the temperatures of the left and right boundary nodes of the wheel at the first moment, the temperatures of all nodes along the upper boundary axis of the wheel at the first moment, and the temperatures of all nodes along the lower boundary axis of the wheel at the first moment. The temperature of the roulette wheel at the first moment is obtained by averaging the temperatures of each node at the first moment.

7. The transient radial clearance prediction method according to claim 6, characterized in that, The heat transfer equation at the node is: ； In the above formula, The temperature of the disk node, For the first time, For the first time, Let be the thermal diffusivity of the wheel. The length of the radial element at the node. , where is the axial element length of the node. Where is the node radius.

8. The transient radial clearance prediction method according to claim 7, characterized in that, The mechanical deformation value of the wheel at the first moment is determined as follows: The deformation values ​​at the inner diameter and outer diameter of each segment of the first, second, and third discs are determined respectively; wherein the first, second, and third discs are three discs of equal thickness obtained by dividing the disc; the discs are discs of variable thickness. The mechanical deformation value of the wheel at the first moment is calculated based on the deformation values ​​at the inner diameter and outer diameter of each segment, the equal force on the contact surface, and the equal radial deformation of the contact surface.

9. An apparatus for predicting transient radial clearance, the apparatus comprising: A memory and a processor; characterized in that the memory is used to store a program for performing transient radial clearance prediction, and the processor is used to read and execute the program for performing transient radial clearance prediction, performing the method according to any one of claims 1-8.

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