Method for analyzing stability of rotating disc boundary layer of turbine rotor-stator system disc cavity

Abstract

The invention provides a turbine rotor-stator system disc cavity turntable boundary layer stability analysis method, and relates to the technical field of aero-engines, and the method comprises the steps: simplifying a Navier-Stokes equation under a cylindrical coordinate system based on a local linearization theory, and solving a flow self-similarity solution in a turbine rotor-stator system disc cavity; extracting and converting the speed of the turntable side in the flowing self-similarity solution to obtain a self-similarity solution of a turntable boundary layer in the disc cavity; deriving a small disturbance equation set under a cylindrical coordinate system according to the self-similarity solution of the turntable boundary layer, expressing a small disturbance term as a regular mode, and substituting the small disturbance term in the regular mode into the small disturbance equation set to obtain a small disturbance equation in a spectrum form; and solving the small disturbance equation in the spectrum form through a Chebyshev polynomial method to obtain a dispersion relation of small disturbance terms, and obtaining the turntable boundary layer stability characteristics of the turbine rotor-stator disc cavity. The stability analysis method can effectively predict the stability of the turbine rotor-stator system disc cavity disc surface boundary layer.

Description

Technical Field

[0001] The invention relates to the technical field of aeroengines, and in particular to a method for analyzing the boundary layer stability of a rotating disk of a turbine rotor-static system cavity. Background Art

[0002] Local linear stability analysis is widely used in various basic flow models. Local stability analysis is based on solving the small perturbation Navier-Stokes equations. Through the assumption of the normal mode of the perturbation, the perturbation is written in the form of waves in the slowly varying spatial and temporal directions of the basic flow, thereby converting the solution of the small perturbation equation into the solution of the generalized eigenvalue problem. For the rotating disk cavity boundary layer of the turbine, the stator disk side boundary layer is extremely unstable, and the critical Reynolds number of the instability of the rotating disk side boundary layer is more than one order of magnitude higher than that of the stator disk side boundary layer. The basic flow equations and small perturbation equations based on the radial parallel flow and circumferential uniformity assumptions cannot directly obtain the stability characteristics of the rotating disk side boundary layer. Due to the limitations of the flow characteristics inside the rotating disk cavity, there is a rotating fluid core outside the rotating disk boundary layer, which makes the stability characteristics have changed compared with the traditional single rotating disk and is no longer applicable.

[0003] Since the rotating disk cavity of the turbine rotor-stator system is a key component of an aircraft engine, it is very important to predict the stability of the disk boundary layer through stability analysis methods, but there is a lack of relevant technology. Summary of the invention

[0004] In view of this, an embodiment of the present application provides a turbine rotor-stator system disk cavity rotating disk boundary layer stability analysis method, so as to predict the stability of the turbine rotor-stator system disk cavity disk surface boundary layer through a stability analysis method.

[0005] The embodiment of the present application provides the following technical solution: a method for analyzing the boundary layer stability of a rotating disk of a turbine rotor-static system cavity, comprising: Based on the local linearization theory, the Navier-Stokes equations in cylindrical coordinates are simplified to solve the self-similarity solution of the flow in the turbine rotor-stator disk cavity. Extracting and converting the velocity of the rotating disk side in the self-similarity solution of the flow in the turbine rotating-stationary system disk cavity, and obtaining the self-similarity solution of the rotating disk boundary layer in the turbine rotating-stationary system disk cavity; According to the self-similarity solution of the rotating disk boundary layer, a small perturbation equation group in a cylindrical coordinate system is derived, the small perturbation term is expressed in the form of a normal module, and the small perturbation term in the form of a normal module is substituted into the small perturbation equation group to obtain a small perturbation equation group in a spectral form; The spectral form of the small perturbation equations are solved by the Chebyshev polynomial method to obtain the dispersion relation of the small perturbation term and the stability characteristics of the rotating disk boundary layer of the turbine rotor-static system disk cavity. According to an embodiment of the present application, based on the local linearization theory, the Navier-Stokes equations in the cylindrical coordinate system are simplified, including: For turntable speed The Navier-Stokes equations in the rotating cylindrical coordinate system are expanded from a vector form to a scalar form, and the radial velocity U, circumferential velocity V, axial velocity W and pressure P in the expanded equations are respectively expressed in dimensionless forms to transform the Navier-Stokes equations into a set of ordinary differential equations about similarity solutions, thereby completing the simplification of the Navier-Stokes equations.

[0006] According to an embodiment of the present application, solving the self-similarity solution of the flow in the turbine rotor-stator system cavity includes: The boundary conditions of the turbine rotor-stator disc cavity are introduced into the simplified Navier-Stokes equations to obtain the self-similarity solution of the flow in the turbine rotor-stator disc cavity.

[0007] According to an embodiment of the present application, the velocity of the rotating disk side in the self-similarity solution of the flow in the turbine rotor-stator system disk cavity is extracted and converted to obtain the self-similarity solution of the rotating disk boundary layer in the turbine rotor-stator system disk cavity, including: Based on the Rossby number and viscosity scale of the self-similarity solution of the rotating disk boundary layer in the turbine rotor-stator disk cavity, the velocity on the rotating disk side is extracted and converted to obtain the self-similarity solution of the rotating disk boundary layer in the turbine rotor-stator disk cavity.

[0008] According to an embodiment of the present application, a small perturbation equation group in a cylindrical coordinate system is derived based on the self-similarity solution of the rotating disk boundary layer, including: The velocity term and the pressure term in the simplified Navier-Stokes equation are respectively expressed as the sum of the self-similar solution of the corresponding rotating disk boundary layer and the small disturbance velocity, so as to obtain the velocity term and the pressure term with small disturbance; Substitute the velocity term and pressure term with small disturbance into the simplified Navier-Stokes equation to obtain a group of small disturbance equations in a cylindrical coordinate system; wherein the velocity term and pressure term include radial velocity U, circumferential velocity V, axial velocity W and pressure P.

[0009] According to an embodiment of the present application, solving the spectral form of the small perturbation equations by the Chebyshev polynomial method includes: Construct a Chebyshev polynomial derivative matrix to transform the spectral form of the small perturbation equation group into an eigenvalue problem; wherein, for the evolution pattern of the disturbance in time, the spectral form of the small perturbation equation group is transformed into an eigenvalue problem, and for the evolution pattern of the disturbance in space, the spectral form of the small perturbation equation group is transformed into a nonlinear eigenvalue problem.

[0010] Compared with the prior art, the beneficial effects that can be achieved by at least one of the above-mentioned technical solutions adopted in the embodiments of this specification include at least the following: the embodiment of the present invention is a method based on the combination of Chebyshev polynomials and local linear theory, which is used to process the stability characteristics of the boundary layer on the rotating disk side of the turbine rotor-static disk cavity, and can be used for time mode and space mode analysis to obtain the convective instability neutral curve and the absolute instability neutral curve of the boundary layer on the rotating disk side of the turbine rotor-static disk cavity, thereby further obtaining the absolute instability linear global modal characteristics, and directly determining the flow state of its boundary layer by selecting characteristic parameters, thereby eliminating a lot of numerical simulation work. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0012] Figure 1 It is a schematic flow chart of a method for analyzing the boundary layer stability of a rotating disk of a turbine rotor-stator system cavity according to an embodiment of the present invention; Figure 2 is a schematic diagram of the distribution of self-similarity on the turntable side in an embodiment of the present invention; Figure 3 It is a schematic diagram of a neutral curve of convective instability and absolute instability of the boundary layer on the rotating disk side in the rotating-static system disk cavity in an embodiment of the present invention; Figure 4 Schematic diagram of local linear instability mode in the time mode in an embodiment of the present invention. DETAILED DESCRIPTION

[0013] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0014] The following describes the implementation methods of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.

[0015] like Figure 1 As shown, an embodiment of the present invention provides a method for analyzing the boundary layer stability of a rotating disk of a turbine rotor-stator system cavity, comprising: S101. Based on the local linearization theory, the Navier-Stokes equations in the cylindrical coordinate system are simplified to solve the self-similarity solution of the flow in the turbine rotor-stator disk cavity; S102. Extracting and converting the velocity of the rotating disk side in the self-similarity solution of the flow in the turbine rotating-stationary system disk cavity, and obtaining the self-similarity solution of the rotating disk boundary layer in the turbine rotating-stationary system disk cavity; S103. According to the self-similarity solution of the rotating disk boundary layer, a small perturbation equation group in a cylindrical coordinate system is derived, the small perturbation term is expressed in the form of a normal module, and the small perturbation term in the form of a normal module is substituted into the small perturbation equation group to obtain a small perturbation equation group in a spectral form; S104. Solve the spectral form of the small perturbation equation group by the Chebyshev polynomial method to obtain the dispersion relation of the small perturbation term and the stability characteristics of the rotating disk boundary layer of the turbine rotor-static system disk cavity. The embodiment of the present invention is a method for solving the stability of the rotating disk boundary layer of the turbine rotor-static system disk cavity, which is used to solve the stability characteristics of the rotating disk boundary layer in the turbine rotor-static system disk cavity of an aircraft engine, and give a neutral curve corresponding to its stability. By constructing a stability neutral curve, the flow state of its boundary layer can be directly determined by selecting characteristic parameters, thereby eliminating a large amount of numerical simulation work. Specifically, the embodiment of the present invention is based on local linear theory. First, it is necessary to simplify the Navier-Stokes equations in the cylindrical coordinate system, obtain the self-similarity solution in the rotor-static system disk cavity through the radial parallel flow and circumferential uniformity assumptions, further derive the small perturbation equation in the cylindrical coordinate system, and then, through the normal mode assumption of the small perturbation, write the perturbation in the form of a wave and bring it into the small perturbation equation, configure discrete points through Chebyshev polynomials, thereby solving the generalized eigenvalue problem and obtaining the stability characteristics of the rotor-static system disk cavity. In a specific implementation form of the embodiment of the present invention, in step S101, based on the local linearization theory, the Navier-Stokes equations in the cylindrical coordinate system are simplified, including: The Navier-Stokes equations in the rotating cylindrical coordinate system are expanded from a vector form to a scalar form, and the radial velocity U, circumferential velocity V, axial velocity W and pressure P in the expanded equations are respectively expressed in dimensionless forms to transform the Navier-Stokes equations into a set of ordinary differential equations about similarity solutions, thereby completing the simplification of the Navier-Stokes equations.

[0016] In a specific implementation form of an embodiment of the present invention, in step S101, solving the self-similarity solution of the flow in the turbine rotor-stator system disk cavity includes: bringing the boundary conditions of the turbine rotor-stator system disk cavity into the simplified Navier-Stokes equations, and solving to obtain the self-similarity solution of the flow in the turbine rotor-stator system disk cavity.

[0017] In a specific implementation form of an embodiment of the present invention, in step S102, the velocity on the turntable side in the self-similarity solution of the flow in the turbine rotor-stator disk cavity is extracted and converted to obtain a self-similarity solution of the turntable boundary layer in the turbine rotor-stator disk cavity, including: based on the Rossby number and viscosity scale of the self-similarity solution of the turntable boundary layer in the turbine rotor-stator disk cavity, the velocity on the turntable side is extracted and converted to obtain a self-similarity solution of the turntable boundary layer in the turbine rotor-stator disk cavity.

[0018] In specific implementation, step S101 and step S102 specifically include the following steps: Step 1, simplify the Navier-Stokes equations in the cylindrical coordinate system, and obtain the self-similar solution in the rotor-static disk cavity through the parallel flow assumption and the circumferential uniformity assumption.

[0019] Step 1.1, incompressible Navier-Stokes equations in cylindrical coordinates:

[0020]

[0021] in are the speeds in three directions. Since the equation is written in terms of the turntable speed In the rotated cylindrical coordinate system, are centrifugal force and Coriolis force respectively. In order to obtain the self-similar solution of steady state, it is assumed that the velocity does not change with time and the derivative of the velocity with respect to the circumferential direction is 0. The equation can be rewritten as:

[0022]

[0023]

[0024]

[0025] For an infinite rotating-static system cavity, the static disk and the rotating disk rotate around the same axis, and the angular velocity of the rotating disk is , the turntable is located at ,lie in In order to find the self-similar solution of such equations, the embodiment of the present invention introduces the following dimensionless form, U is radial velocity, V is circumferential velocity, w is axial velocity, and P is pressure:

[0026]

[0028] Step 1.2, bring the transformation into the simplified NS equations (Navier-Stokes equations), and you can get a set of ordinary differential equations about similarity solutions:

[0029]

[0030]

[0031]

[0032] in , Representatives Directional derivative, where the boundary conditions are:

[0033]

[0034] Step 1.3, the speed can be obtained by any ode solver and pressure The distribution characteristics of z, i.e. the similarity solution, can be used as the basic flow for stability analysis. In order to avoid the influence of the boundary layer on the stationary disk side, it is necessary to transform the similarity solution so that only the influence of the boundary layer on the rotating disk side is considered. For example, you need to The axes are transformed appropriately. For similarity solutions, For the linear stability analysis to be introduced, since the influence of the static disk side is ignored, the embodiment of the present invention will adopt the viscosity scale As a dimensionless length, where , ) / So the stability analysis . For the current self-similar solution, , , , so the Rossby number , of course, the velocity distribution also needs to be transformed accordingly, , , By this transformation, the distribution of the basic flow will no longer be related to the axial distance is related to and is applicable to all Reynolds numbers For the sake of simplicity, the present invention will remove the subscript 1 and directly describe it as .

[0035] Figure 2 The distribution of self-similarity on the turntable side is given.

[0036] In a specific implementation form of an embodiment of the present invention, in step S103, a group of small perturbation equations in a cylindrical coordinate system is derived according to the self-similarity solution of the turntable boundary layer, including: respectively expressing the velocity term and the pressure term in the simplified Navier-Stokes equation as the sum of the corresponding self-similarity solution of the turntable boundary layer and the small perturbation velocity, to obtain the velocity term and the pressure term with small perturbation; substituting the velocity term and the pressure term with small perturbation into the simplified Navier-Stokes equation to obtain a group of small perturbation equations in a cylindrical coordinate system; wherein the velocity term and the pressure term include radial velocity U, circumferential velocity V, axial velocity W and pressure P.

[0037] In a specific implementation form of an embodiment of the present invention, in step S104, the spectral form of the small perturbation equation group is solved by the Chebyshev polynomial method, including: constructing a Chebyshev polynomial derivative matrix to convert the spectral form of the small perturbation equation group into an eigenvalue problem; wherein, for the evolution pattern of the disturbance in time, the spectral form of the small perturbation equation group is converted into an eigenvalue problem, and for the evolution pattern of the disturbance in space, the spectral form of the small perturbation equation group is converted into a nonlinear eigenvalue problem.

[0038] In specific implementation, step S103 and step S104 specifically include the following steps: Step 1, derive the small perturbation equations, write the small perturbations in the form of canonical modules, solve the eigenvalue equations through Chebyshev polynomials, and obtain the local instability characteristics of the boundary layer on the turntable side.

[0039] Step 1.1, derive the small perturbation equations. The velocity term and pressure term in the NS equation can be divided into similarity solutions and small perturbation velocities, as follows:

[0040] in is a small disturbance term, which is substituted into the Navier-Stokes equation to obtain:

[0041] In order to make the linearized equation direction, it is necessary to ignore the variation of the Reynolds number with radius. This approximation is called the parallel flow assumption, that is, the applicable equation Substitute variables for the linearized system of equations , and ignore high-order small quantities such as , and write the perturbation in the form of a canonical module;

[0042] in yes The spectrum of is the radial wave number, is the circumferential wave number, is the disturbance at an angular velocity The frequency in the rotating coordinate system, through this equation, the small perturbation equation can be transformed into the following form:

[0043]

[0044] The perturbation on the disk surface and the boundary layer should be 0, that is, the boundary conditions are:

[0045]

[0046] Step 1.2, construct the Chebyshev polynomial derivative matrix and transform the small perturbation equation into an eigenvalue problem. The Chebyshev polynomial derivative matrix is ​​based on Recursively defined Chebyshev polynomial collocation points:

[0047]

[0048]

[0049] Assumption Function It can be expanded by Chebyshev , Since the small perturbation equation involves second-order derivatives, the first-order derivative and second-order derivative expressions of Chebyshev polynomials are needed:

[0050] in Superscript and Represent the first and second order derivatives of y respectively. Since the computational domain of the current problem is , the exponential mapping transformation will be used Transform to , and its transformation is:

[0051] Regarding the current problem, The transformation of coordinates also involves the change of the Chebyshev derivative matrix, namely:

[0052] In this way, the perturbation can be given by and at the configuration point The truncated series of the derivative at , as the sum of the contributions of all transformed Chebyshev polynomials;

[0053]

[0054] Step 1.3, construct the eigenvalue problem through the Chebyshev polynomial matrix. For the time mode, the small perturbation equation can be transformed into an eigenvalue problem:

[0055] in for For a specific problem, it is used to explore the time evolution of a disturbance of a given spatial form. Therefore, given the radial wave number (complex number) and the circumferential wave number (real number), solving the eigenvalue problem can obtain the time frequency (plural).

[0056] For spatial modes, the small perturbation equation can be formulated as a nonlinear eigenvalue problem:

[0057] in They are The matrix is ​​used to explore the development of a given disturbance along the flow direction for a specific problem, given its time-frequency characteristics and circumferential wave number characteristics.

[0058] The embodiment of the present invention gives the instability neutral curve of the boundary layer on the rotating disk side through a unified Reynolds number based on the viscosity scale. Using the method of the embodiment of the present invention, the convective instability neutral curve and the absolute instability neutral curve of the boundary layer on the rotating disk side in the turbine rotor-stator disk cavity can be obtained, and further, the absolute instability linear global modal characteristics can be obtained. Figure 3 and Figure 4 shown.

[0059] The spatial mode of the method in the embodiment of the present invention corresponds to a nonlinear eigenvalue problem, and there are three matrices. For the time mode, the matrix A can be constructed by a similar idea to solve the eigenvalue problem.

[0060] Next, a specific embodiment is used to further illustrate the present invention.

[0061] This embodiment provides a method suitable for solving the linear stability problem of the rotating disk boundary layer. By providing basic flow, constructing Chebyshev polynomial collocation points, and solving the eigenvalue problem, the linear stability problem of the rotating disk boundary layer can be solved. The specific implementation plan is as follows: Step 1, simplify the Navier-Stokes equations to obtain the self-similar solution in the rotor-static disk cavity. If there are direct numerical simulation results, the average flow of the direct numerical results can also be taken as the basic flow.

[0062] Step 1.1, simplify the Navier-Stokes equations according to the assumptions given in this method, and then use the dimensionless method:

[0063]

[0064] Step 1.2, bring the transformation into the simplified NS equation and solve the system of ordinary differential equations about similarity solutions:

[0065]

[0066]

[0067]

[0068] In specific implementation, the average flow at a certain radial position of the direct numerical simulation result can also be taken.

[0069] Step 1.3, the speed can be obtained by any ode solver and pressure The distribution characteristics of z, i.e. the similarity solution, can be used as the basic flow for stability analysis. And after the transformation given by this method, , , The basic flow is obtained, which can be used for local linear stability analysis.

[0070] Step 2, derive the small perturbation equation group, write the small perturbation in the form of canonical modules, solve the eigenvalue equation group through Chebyshev polynomials, and obtain the local instability characteristics of the boundary layer on the turntable side.

[0071] Step 2.1, derive the small perturbation equations. The velocity terms and pressure terms in the NS equations can be divided into similarity solutions and small perturbation velocities;

[0072]

[0073]

[0074]

[0075] The boundary conditions are:

[0076]

[0077] Step 2.2, construct the Chebyshev polynomial derivative matrix and transform the small perturbation equation into an eigenvalue problem.

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] And write the perturbation quantity of the disturbance in the form of Chebyshev polynomial series expansion:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] Step 2.3, solve the eigenvalue problem. For the time mode, the small perturbation equation can be transformed into a linear eigenvalue problem:

[0093] For spatial modes, the small perturbation equation can be formulated as a nonlinear eigenvalue problem:

[0094] The embodiment of the present invention provides a method suitable for solving the linear stability problem of the boundary layer of a rotating disk. By providing basic flow, constructing Chebyshev polynomial configuration points, and solving the eigenvalue problem, the linear stability problem of the boundary layer of a rotating disk can be solved.

[0095] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for analyzing the boundary layer stability of a turbine rotor-static system cavity rotating disk, characterized in that: include: Based on the local linearization theory, the Navier-Stokes equations in cylindrical coordinates are simplified to solve the self-similarity solution of the flow in the turbine rotor-stator disk cavity. Extracting and converting the velocity of the rotating disk side in the self-similarity solution of the flow in the turbine rotating-stationary system disk cavity, and obtaining the self-similarity solution of the rotating disk boundary layer in the turbine rotating-stationary system disk cavity; According to the self-similarity solution of the rotating disk boundary layer, a small perturbation equation group in a cylindrical coordinate system is derived, the small perturbation term is expressed in the form of a normal module, and the small perturbation term in the form of a normal module is substituted into the small perturbation equation group to obtain a small perturbation equation group in a spectral form; The spectral form of the small perturbation equations are solved by the Chebyshev polynomial method to obtain the dispersion relation of the small perturbation term and the stability characteristics of the rotating disk boundary layer of the turbine rotor-static system disk cavity.

2. The turbine rotor-stator system cavity rotating disk boundary layer stability analysis method according to claim 1 is characterized in that: Based on the local linearization theory, the Navier-Stokes equations in the cylindrical coordinate system are simplified, including: For turntable speed The Navier-Stokes equations in the rotating cylindrical coordinate system are expanded from a vector form to a scalar form, and the radial velocity U, circumferential velocity V, axial velocity W and pressure P in the expanded equations are respectively expressed in dimensionless forms to transform the Navier-Stokes equations into a set of ordinary differential equations about similarity solutions, thereby completing the simplification of the Navier-Stokes equations.

3. The turbine rotor-stator system cavity rotating disk boundary layer stability analysis method according to claim 1 is characterized in that: Solve the self-similarity solution of the flow in the turbine rotor-stationary system cavity, including: The boundary conditions of the turbine rotor-stator disc cavity are introduced into the simplified Navier-Stokes equations to obtain the self-similarity solution of the flow in the turbine rotor-stator disc cavity.

4. The method for analyzing the boundary layer stability of a turbine rotor-stator system cavity rotating disk according to claim 1 is characterized in that: Extracting and converting the velocity of the rotating disk side in the self-similarity solution of the flow in the turbine rotating-stationary system disk cavity to obtain the self-similarity solution of the rotating disk boundary layer in the turbine rotating-stationary system disk cavity, including: Based on the Rossby number and viscosity scale of the self-similarity solution of the rotating disk boundary layer in the turbine rotor-stator disk cavity, the velocity on the rotating disk side is extracted and converted to obtain the self-similarity solution of the rotating disk boundary layer in the turbine rotor-stator disk cavity.

5. The method for analyzing the boundary layer stability of a turbine rotor-stator system cavity rotating disk according to claim 1, characterized in that: According to the self-similarity solution of the rotating disk boundary layer, the small perturbation equations in the cylindrical coordinate system are derived, including: The velocity term and the pressure term in the simplified Navier-Stokes equation are respectively expressed as the sum of the self-similar solution of the corresponding rotating disk boundary layer and the small disturbance velocity, so as to obtain the velocity term and the pressure term with small disturbance; Substitute the velocity term and pressure term with small disturbance into the simplified Navier-Stokes equation to obtain a group of small disturbance equations in a cylindrical coordinate system; wherein the velocity term and pressure term include radial velocity U, circumferential velocity V, axial velocity W and pressure P.

6. The turbine rotor-stator system cavity rotating disk boundary layer stability analysis method according to claim 1 is characterized in that: The spectral form of the small perturbation equations is solved by the Chebyshev polynomial method, including: Construct a Chebyshev polynomial derivative matrix to transform the spectral form of the small perturbation equation group into an eigenvalue problem; wherein, for the evolution pattern of the disturbance in time, the spectral form of the small perturbation equation group is transformed into an eigenvalue problem, and for the evolution pattern of the disturbance in space, the spectral form of the small perturbation equation group is transformed into a nonlinear eigenvalue problem.

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